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https://diego.assencio.com/?index=6890b8c50169ef45b74db135063c227c
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Generating random numbers in C++
Posted by Diego Assencio on 2015.11.19 under Programming (C/C++)
Before C++11 was released, the easiest way to generate random numbers in C++ was through the std::rand() function. However, C++11 now offers easy-to-use and vastly superior mechanisms for generating random numbers and provides developers with the ability to sample from many commonly used distributions using only machinery available in the STL. In this post, we will show the new C++11 methods for generating random integers from a uniform distribution over a closed interval; sampling from other distributions will be a trivial task after one understands the concepts illustrated below.
Let's solve the following problem: sample ten integer values from the closed interval $[1,6]$ (i.e., the set $\{1,2,3,4,5,6\}$) assuming a uniform distribution. This is equivalent to simulating ten rolls of a dice with six faces. The code below shows how this can be done:
#include <random>
#include <iostream>
int main()
{
std::random_device device;
std::mt19937 generator(device());
std::uniform_int_distribution<int> distribution(1,6);
/* generate ten random numbers in [1,6] */
for (size_t i = 0; i < 10; ++i)
{
std::cout << distribution(generator) << ' ';
}
std::cout << std::endl;
return 0;
}
Try compiling and running the code above. One possible output is:
1 2 4 5 4 4 2 1 4 6
Let's now discuss what the code above does. The first thing we do is to create an instance of :
std::random_device device;
This is a special class which produces uniformly-distributed unsigned integers with 32 bits of length. It can produce random numbers either by accessing the operational system's entropy pool via system calls or by using hardware random number generators such as Intel's RdRand when available (but not all implementations of std::random_device allow this). Developers must be warned, however, that even though 32-bit unsigned integers are generated, the entropy of this random number generator may be lower than 32 bits.
Unfortunately, it is not advisable to use std::random_device repeatedly as this may quickly deplete the entropy pool and therefore reduce the level of randomness available to the other processes running in the system. Additionally, its reliance on system calls makes it a very slow random number generator. To be precise, the following code also generates random integers in the closed interval $[1,6]$ but is not a good way to do it:
#include <random>
#include <iostream>
int main()
{
/*
* this is a BAD WAY to generate random numbers; never use
* std::random_device to repeatedly generate random numbers!
*/
std::random_device device;
std::uniform_int_distribution<int> distribution(1,6);
/* generate ten random numbers in [1,6] */
for (size_t i = 0; i < 10; ++i)
{
std::cout << distribution(device) << ' ';
}
std::cout << std::endl;
return 0;
}
If we cannot use std::random_device repeatedly, then what should we do to generate multiple random numbers? The answer is simple: use std::random_device to generate a single random number which is then used as a seed for a pseudorandom number generator (PRNG) and then use the PRNG itself to generate as many pseudorandom numbers as we wish. For those who do not know what a PRNG is, think of it as an algorithm that takes an initial seed (a random number) and applies it on an internal mechanism to produce numbers which while not truly random, are still "sufficiently close to random".
The procedure we just described is exactly what we did on our original piece of code: we used std::random_device to generate a seed for a very commonly used PRNG called Mersenne Twister which is implemented by the std::mt19937 class (MT19937 stands for "Mersenne Twister" based on the Mersenne prime $2^{19937}−1$). This PRNG produces sequences of 32-bit integers with a very long period of $2^{19937}−1$, i.e., the sequence will repeat itself only after $2^{19937}−1$ numbers have been generated — an imaginably large number! This line initializes the PRNG with a seed produced by device, which is an object of type std::random_device:
std::mt19937 generator(device());
Let's now restate our initial goal: we need a uniform integer distribution which produces random values only in the closed interval $[1,6]$. The class std::uniform_int_distribution was designed for exactly this type of task. We first create an instance of this class which defines the closed interval over which we wish to sample integer values:
std::uniform_int_distribution<int> distribution(1,6);
Using its overloaded operator(), an object of type std::uniform_int_distribution can take a random number generator and use it to generate a number within its defined target interval. Indeed, the following expression in our code returns a number in $[1,6]$:
distribution(generator)
As a final note, the STL also contains an implementation of the Mersenne Twister PRNG which generates 64-bit pseudorandom integers through a class called std::mt19937_64. Although not strictly necessary, the seed for this PRNG should be a 64-bit integer as well.
If you wish to have your program always generate the same sequence of pseudorandom numbers (e.g. for reproducing scientific experiments), all you have to do is seed your PRNG with a fixed seed. The code below shows an example in which we always seed std::mt19937 with the same value to have it always generate the same sequence of pseudorandom numbers:
#include <random>
#include <iostream>
int main()
{
/* seed the PRNG (MT19937) using a fixed value (in our case, 0) */
std::mt19937 generator(0);
std::uniform_int_distribution<int> distribution(1,6);
/* generate ten numbers in [1,6] (always the same sequence!) */
for (size_t i = 0; i < 10; ++i)
{
std::cout << distribution(generator) << ' ';
}
std::cout << std::endl;
return 0;
}
On my laptop, this code consistently generates the following sequence:
4 4 5 6 4 6 4 6 3 4
|
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|
https://www.lessonplanet.com/teachers/school-home-links-writing-about-your-family
|
In this writing sentences learning exercise, students complete several sentences using the prompt on the lined writing paper. Students will write about their families.
Concepts
Resource Details
|
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|
http://smartonlineexam.com/general-english/passage/91/question-answer/Rearrangement%20of%20Jumbled%20Sentences%20in%20Para/?questionLanguage=
|
Q.1
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) An option is a contract, or a provision of a contract, that gives one party (the option holder) the right, but not the obligation, to perform a specified transaction with another party (the option issuer or option writer) according to the specified terms. (B) For every buyer of an option there most be a seller. As with futures, the process of closing out options positions will cause contracts to cease to exist, diminishing the total number. (C) The owner of a property might sell another party an option to purchase the property any time during the next three months at a specified price. The seller is often referred to as the writer. (D) As with futures, options are brought into existence by being traded, if none is traded, none exists; conversely, there is no limit to the number of option contracts that can be in existence at any time.
Q.2
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) Fortunately for all of us, nature has devised ways to capture new energy. (B) Food chains require constant supplies of new energy to make up for the continual losses (C) The most common way is through photosynthesis, the process by which green plants use the suns energy to build sugars out of carbon dioxide and water (D) Energy is passed through the food chain. But unlike nutrients, energy is continually being lost.
Q.3
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) They must be able to finance the expansion of airport capacity and facilities to meet demand over the long term, while providing quality of service for passengers and freight. (8) This applies to airport operators as well, wherein, continuity and stability is essential for effective performance. (C) Each state must decide on the extent to which, and how, it wishes to participate in the gradual process of liberalization. Adequate mechanisms must also be in place that can provide fast and effective dispute mediation or resolution. (D) Adequate and effective safeguards must be in place to ensure fair competition and sustained participation by airlines in industrialized and developing countries alike.
Q.4
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) The tank should be protected from unauthorized access to reduce the chance of intentional or accidental interference. The fence should allow natural air flow (e.g. made from wire mesh) and should be kept in good condition. (B) Any gates should be kept locked unless access to the tank is required (C) Absence of fence can only be justified where the risk of interference is low, and there is no uncontrolled public access - for example due to tank location or other accessibility factors. Tank valve covers should be kept locked whether or not the tank is fenced. (D) For larger tanks (i.e. four tonnes or higher LPG capacity) a security fence is required to keep it secure while for tanks below four tonnes LPG capacity, there may be certain circumstances where a fence may not be necessary.
Q.5
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) A high loss rate during maturation is accepted for the reduction in detailed plant maintenance costs (B) Although some processes have been mechanized and automated, others have not. (C) It remains highly unlikely that all plants treated in the same way at the same time will arrive at the same condition together, so plant care requires observation, judgment and personal skill; selection for sale requires comparison and judgment. (D) Nurseries are highly labour-intensive.
Q.6
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) The ecological effects of acid rain are most clearly seen in the aquatic or water environments such as streams, lakes, and marshes. (B) Acid rain flows into streams, lakes, and marshes after falling on forests, fields, buildings, and roads. Acid rain also falls directly on aquatic habitats. Most lakes and streams have a pH between 6 and 8, although some lakes are naturally acidic even without the effects of acid rain. (C) Acid rain primarily affects sensitive bodies of water, which are located in watersheds whose soils have a limited ability to neutralize acidic compounds (called "buffering capacity"). (D) Lakes and streams become acidic (pH value goes down) when the water itself and its surrounding soil cannot buffer the acid rain enough to neutralize it. In areas where buffering capacity is low, acid rain also releases aluminum from soils into lakes and streams.
Q.7
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) Unlike other fruits they lack firm pulp. Mostly citrus fruits are consumed as fresh fruits particularly sweet oranges, mandarins and grape fruit. The rind of the citrus fruits is rich in pectin and essential oils. (B) Citrus fruits are not only delicious and refreshing but they also provide vitamins, minerals and many other substances. (C) Importantly, these fruits contain considerable amounts of vitamin c. (D) Citrus fruits possess juice sacks. Fruits are also good sources of Vitamin and Protein. The mild bitterness in juice is due to the presence of glucoside called Naringin which is said to have medicinal value.
Q.8
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) If a country follows a fixed exchange rates and also runs a large fiscal deficit it could lead to speculative attacks on the currency. (B) Fiscal deficits play a role especially during currency crisis. This leads to lowering of the reserves and in case there is a speculation on the currency, the government may not have adequate reserves to protect the fixed value of the currency. (C) So, though fiscal deficits do not have a direct bearing on foreign exchange markets, they play a role in case there is a crisis. (D) Higher deficits imply government might resort to using forex reserves to finance its deficit. This pushes the government to devalue the currency.
Q.9
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) As a result, India captured an increased proportion of this market, and at present, India is the world's leading diamond cutting and polishing centre, (B) As compared with the traditional diamond cutting & polishing centres of Belgium, India, with its low labour cost, opened up new possibilities for the world diamond industry by making diamonds affordable for new, less affluent buyers. (C) The Indian diamond processing industry took roots in the 1960s. (D) India produces around 95 per cent of the world's cut and polished diamond pieces and by carat weight, India is estimated to process 80 per cent of world rough production by volume and 58 per cent by value.
Q.10
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) Inspired by the success of the experiments related to the cooperative movement in Britain and the co-operative credit movement in Germany, such societies were set up in India that provide credit to small scale industrialists, salaried employees, and other urban and semi-urban residents, (B) Co-operative societies are based on the principles of cooperation, mutual help, democratic decision making, and open membership. (C) Cooperatives represented anew and alternative approach to organization as against proprietary firms, partnership firms, and joint stock companies which represent the dominant form of commercial organization. (D) The origins of the when co-operative banking movement in India can be traced to the close of nineteenth century.
Q.11
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) However, the relevant provisions of the IRC were not available for production beyond 2007. (B) The alternative fuel production tax credit for refined coal was the largest tax expenditure related to coal use during FY 2007 (C) However, coal was estimated to be a relatively small recipient of tax expenditures in FY 2010, with an estimated value of $561 million in FY 2010, down from$3.3 billion in FY 2007. (D) Over 90 percent of coal is consumed by the electricity sector. Coal-fired generation accounted for 45 percent of total electricity generation in 2010.
Q.12
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) Neither the tenant farmer nor the land lord who owns/cultivates a small holding can afford to invest in technology, creation of infrastructure like irrigation systems in his farm land. (B) If significant growth has to be achieved in agriculture sector, technology, Infrastructure and other linkages have to be developed that can lead to increased production and productivity. (C) High growth in Sector cannot be brought in by micro level initiatives alone without providing them necessary infrastructure and logistical inputs. (D) Such linkages could be facilitated by corporates through Public Sector or Private Sector participation who in turn derive their financial resources from Banks.
Q.13
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) Areas for plantation in forest and non-forest lands will be carefully identified for the purpose (B) Planting Material will be arranged under the National Bamboo Mission and there will be centralized nurseries (public/private) and decentralized nurseries (mahila and kisan nurseries). (C) The plantation activities will be undertaken in compact areas so that the impact of the mission becomes visible. (D) Quality planting material will be raised through tissue culture units in the public sector.
Q.14
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) Florida coastline in the contiguous United States, encompassing approximately 1,350 miles (2,170 kin), and is the only state to border both the Gulf of Mexico and the Atlantic Ocean. (B) Much of Florida is situated on a peninsula between the Gulf of Mexico, the Atlantic Ocean, and the Straits of Florida. The climate varies from subtropical in the north to tropical in the south (C) Its geography is marked by a coastline, by the omnipresence of water and the threat of hurricanes. It's symbolic animals like the American alligator, crocodile, panther and the manatee, can be found in the Everglades, one of the most famous national parks in the world. (D) Much of the state is at or near sea level and its terrain is characterized by sedimentary.
Q.15
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) However, during the last 13 years of implementation, many impediments were encountered by policy makers, implementing banks and the farmers in the implementation of the scheme. (B) The Kisan Credit Card has emerged as an innovative credit delivery mechanism to meet the production credit requirements of the farmers in a timely and hassle-free manner. (C) It was, therefore, felt necessary to revisit the existing KCC Scheme to make it truly simple and hassle free for both the farmers and bankers. (D) Recommendations of various Committees appointed by (JOT and studies conducted by NABARD also corroborate this fact.
Q.16
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) Understanding these co-benefits has become important in seeking cost effective air pollution reduction strategies. (B) Another possible option is switching the fuels that are used by power plants. For instance, burning natural gas creates much less SO2 than burning coal. (C) There are several options for reducing SO2 emissions, including using coal containing less sulfur, washing the coal, and using devices called scrubbers to chemically remove the SO, from the gases leaving the smokestack. (D) Besides these, there are certain other approaches that would also have additional benefits of reducing other pollutants such as mercury and carbon dioxide.
Q.17
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) The global location of automotive production, including that by Japanese companies, has become increasingly dispersed in recent years. lndeed, even as the collapse in the domestic production levels of the major two Japanese car producers began to ease in May, their overseas production continued to weaken considerably. (B) In the aftermath of the natural disasters in Japan, it is clear that this has been the case. (C) The growth and changing location of foreign production thus means that a temporary supply-chain disruption from Japan could now have larger direct spillover effects in other countries than would have previously been the case. (D) By 2009, less than half of the passenger car production by the largest six Japanese producers was undertaken in Japan. The most notable change over the past decade has been the increasing share of final assembly undertaken in China.
Q.18
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) In one of the findings, it was seen that the world-famous company had a remarkable share in the market of the two wheeler industry of India. (B) Rest of the two wheeler manufacturer had a share of less than 10 per cent and it was due to the quality of the product and the services provided by them to the customers. (C) Overall, the company had recorded more than 41 per cent share in the segment during the period. (D) Third position was grabbed by the company in the segment which had a share of 18.14 per cent.
Q.19
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
(A) Hence, the company further strengthened its domination of the domestic Multi Utility Vehicle sub-segment during the year, increasing its market share to 57.2 per cent over the previous year's market share of 51.3 per cent. (B) In 2009, the company successfully launched a MUV model in South Africa and also formed a new joint venture with an Australian company to focus on the Australian Market. (C) This company then focused on expanding its footprint in the overseas market as well. (D) The company's domestic Multi Utility Vehicle sales volumes increased by 3.3 per cent, as against a decline of 7.4 per cent for industry Multi Utility Vehicle sales.
Q.20
The sentences given in each question when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.
|
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|
https://codereview.stackexchange.com/questions/90371/simple-grid-using-svg
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# Simple grid using SVG
I developed this grid which displays number of records for X & Y, user can click each number to see a list. (I didn't add list markup to fiddle yet - so lets not worried about it for now.)
What I believe is that I overcomplicated this simple project by choosing SVG, and it can be improved massively by using simple HTML, maybe in the future (years time I would like to add zooming to it, maybe which is why I used SVG).
Could you improve it to simplest level please, preferably using HTML and avoiding SVG?
function CreateHeatmap() {
$("#svgContainer").empty(); var width =$(window).innerWidth() - ($(window).innerWidth() / 50), height =$(window).innerHeight() - ($(window).innerHeight() / 40), sideRectW = width / 17, sideRectH = height / 17, boxW = (width - sideRectW) / (4 + 1), // getting number "4" from web services as number of boxes depends boxH = (height - sideRectH) / (4 + 1), // getting number "4" from web services as number of boxes depends boxSize = boxW + boxH; var svgContainer = d3.select("#mainContainer") .append("svg") .attr("id", "svgContainer") .attr("width", "100%") .attr("height", "100%") .attr("preserveAspectRatio", "none") .attr("viewBox", "0 0 " + width + " " + height) .attr("float", "right") .attr("overflow", "hidden"); svgContainer.append("rect") .attr("fill", "url(#svgLG1)") .attr("width", "100%") .attr("height", "100%"); var CreateGradient = function () { var gradient = svgContainer.append("svg:linearGradient").attr("id", "svgLG1").attr("x1", "0").attr("y1", "1").attr("x2", "1").attr("y2", "0"); gradient.append("svg:stop").attr("offset", "0").attr("stop-color", "#0f0"); gradient.append("svg:stop").attr("offset", "0.7").attr("stop-color", "#ff0"); gradient.append("svg:stop").attr("offset", "1").attr("stop-color", "#f00"); }; var ShowList = function (item) { var id =$(item).attr("id");
var quantity = id.charAt(1);
var quality = id.charAt(2);
};
var CreateRect = function (x, y, boxId) {
svgContainer.append("g").attr("id", "g" + boxId).on("click", function () {
ShowList(this);
}).append("rect").attr("x", x).attr("y", y).attr("id", "rectBoxNo" + boxId).attr("width", boxW).attr("height", boxH).attr("stroke", "black").attr("stroke-width", "1").attr("fill", "none");
};
var CreateRects = function () {
for (var i = 0; i <= 4; i++) { // getting number of x and y from web services, but for example let assume it's 4
var b = 4;
for (var j = 0; j <= 4; j++) {
CreateRect(sideRectW + (boxW * i), boxH * b, "" + i + j);
b--;
}
}
};
var CreateCoordinatesRect = function (x, y, w, h, boxColor) {
svgContainer.append("rect").attr("x", x).attr("y", y).attr("width", w).attr("height", h).attr("fill", boxColor);
};
var CreateText = function (x, y, text, textColor, size) {
svgContainer.append("text").attr("x", x).attr("y", y).attr("fill", textColor).attr("font-size", size).text(text);
};
var CreateText90Degree = function (x, y, text, textColor, size) {
svgContainer.append("text").attr("x", x).attr("y", y).attr("fill", textColor).attr("font-size", size).attr("transform", "rotate(-90," + x + 13 + ", " + y + 15 + ")").text(text);
};
var CreateCoordinatesNumbers = function () {
var j = 0;
for (var i = 0; i <= 4; i++) {
CreateText(sideRectW + (boxW * i) + (boxW / 2), height - sideRectH / 2, "" + (j++), "white", 12);
}
j = 4;
for (var i = 0; i <= 4; i++) {
CreateText(sideRectW / 2, (boxH * i) + (boxH / 2), "" + (j--), "white", 12);
}
};
CreateCoordinatesRect(0, 0, sideRectW, $("#mainContainer").height(), "Black"); CreateCoordinatesRect(0, height - sideRectH, width, sideRectH, "Black"); CreateText(((width - sideRectW) / 2) + 13, (height - sideRectH / 5) + 4, "X", "white", 16); CreateText90Degree(0, ((height - sideRectH) / 2) + 20, "Y", "white", 16); CreateCoordinatesNumbers(); CreateRects(); } function PopulateHeatmap(data) { var AddNumberOfFruitCratesToEachBox = function (text, xy) { var rectContainer = d3.selectAll("#rectBoxNo" + xy); var xDivider = 2.5, yDivider = 1.6; if (text >= 10 && text <= 99) xDivider = xDivider + (0.6); else if (text >= 100) yDivider = yDivider + (0.6); var w = Number(rectContainer.attr("width")); var h = Number(rectContainer.attr("height")); var x = Number(rectContainer.attr("x")) + (w / xDivider); var y = Number(rectContainer.attr("y")) + (h / yDivider); var svgContainer = d3.selectAll("#svgContainer"); svgContainer.selectAll("#g" + xy).append("text") .attr("x", x) .attr("y", y) .attr("fill", "white") .attr("font-size", 0.15 * (w + h)) .attr("class", "hover_grouptext").text(text); }; var fCount = {}; for (var i = 0; i < 4; i += 1) { for (var j = 0; j < 4; j += 1) { fCount["" + i + j] = 0; } }$.each(data, function (index, item) {
if (item.x > -1 && item.y > -1) {
fCount["" + item.x + item.y]++;
}
});
for (var i = 0; i < 4; i += 1) {
for (var j = 0; j < 4; j += 1) {
if (fCount["" + i + j] > 0) {
AddNumberOfFruitCratesToEachBox(fCount["" + i + j], "" + i + j);
}
}
}
}
function OwResize() {
$("#mainContainer").height($(window).innerHeight() - ($(window).innerHeight() / 40)); } var containerData = [ { "x": 0, "y": 0, "Title": "Crate Number 1", "Url": "http:www.fruitfactory.com\crates\1", "Comments": null, "ObjectOther1": [ ], "ObjectOther2": [ ] }, { "x": 0, "y": 0, "Title": "Crate Number 2", "Url": "http:www.fruitfactory.com\crates\2", "Comments": null, "ObjectOther1": [ ], "ObjectOther2": [ ] }, { "x": 3, "y": 3, "Title": "Crate Number 3", "Url": "http:www.fruitfactory.com\crates\3", "Comments": null, "ObjectOther1": [ ], "ObjectOther2": [ ] } ];$(window).resize(OwResize);
CreateHeatmap();
PopulateHeatmap(containerData);
.hover_group:hover {
opacity: 0.5;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.5/d3.min.js"></script>
<div id="mainContainer">
<div id="fruit-grid"></div>
</div>
You are free to use anything but it should work with IE-8 & Chrome.
Fiddle
http://jsfiddle.net/nhe613kt/388/
In example code I am adding heatmap and populating them one after another but in real, I am creating it at one point and populating at another, I can't do both at same time as I am getting data from ajax get request.
Bounty Edit
I would expect a better version of what I developed in html using any third party library you want, just one thing need to keep in mind is that, I am creating rectangles or boxes you can say by getting numbers from web services, so hard coding won't help here for number of boxes here as I can do that myself using a table. Thanks for your time :)
Indeed, D3 is perfectly suited for this task (besides being joy to work with). The following is a very simple implementation, which delegates to CSS as much as possible. Much of any further customisation one may need can be implemented simply by fiddling with CSS. The whole thing should be easy to wrap up as a module.
We'll append the result to the #grid-container div:
<div id="grid-container"></div>
We'll work with this fake data:
function rint(limit) { return Math.floor(Math.random() * limit); }
var rowCount = rint(3) + 3;
var colCount = rint(3) + 3;
var data = d3.range(25).map(function(){ // fake data (refresh few times for variety)
return {
x: rint(colCount),
y: rint(rowCount)
};
});
We'll map data into a three-dimensional array heat according to those x and y values – heat is what we'll visualise with the help of d3. Each heat[y][x] will contain an array of objects with corresponding x and y values:
var heat = d3.range(rowCount).map(function(){
return d3.range(colCount).map(function(){
return [];
});
});
data.forEach(function(d){
heat[heat.length - d.y - 1][d.x].push(d);
});
Find the "hottest" value for the heat map – we'll use this later to generate a full range of colours:
var maxHeat = d3.max([].concat.apply([], heat), function(box){
return box.length;
});
Now we do the d3 thing. First, generate row selection and populate it with heat data:
var row = d3.select("#grid-container").selectAll(".row").data(heat);
Append the missing div.rows:
row.enter().append("div").attr("class", "row");
Use row selection to create a nested box selection. Each box will inherit the corresponding datum from row's data:
var box = row.selectAll(".box").data(function(d) { return d; });
We now enter and append all the boxes in the grid:
box.enter().append("div")
.attr("class", function(d, x, y){
var klas = ["box"]
if (y == heat.length - 1) klas.push("bottom");
if (x == 0) klas.push("left");
return klas.join(" ");
})
.attr({
"data-row": function(d, x, y){ return heat.length - 1 - y; },
"data-col": function(d, x, y){ return x; }
})
.style("background-color", function(d) {
return d3.hsl( (1 - (d.length / maxHeat)) * 210, 0.8, 0.4 );
})
.text(function(d){
return d.length > 0 ? d.length : "";
});
Notice that we are tagging the left column and the bottom row of boxes with classes .left and .bottom, respectively. We are also appending data-row and data-col attributes that we can use to provide CSS content for pseudo elements which will serve as column and row numbers:
.box.left:before {
content: attr(data-row);
}
.box.bottom:after {
content: attr(data-col);
}
Importantly, note that I am here merely using the length of the datum d as the innerText of each box. Keep in mind that that d is a list of objects that share the same x and y. This means that the items of d contain all the information you need to enrich the interface of each div.box (with names, links, images, etc.), or, alternatively, to generate (say, on mouse over event) a second visualisation that would show the list of objects as a "detail" view into the data.
Complete code at: http://jsfiddle.net/vpgsLw1v/2/
|
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|
https://worldwidescience.org/topicpages/b/bright+single+photon.html
|
#### Sample records for bright single photon
1. Bright Single Photon Emitter in Silicon Carbide
Science.gov (United States)
Lienhard, Benjamin; Schroeder, Tim; Mouradian, Sara; Dolde, Florian; Trong Tran, Toan; Aharonovich, Igor; Englund, Dirk
Efficient, on-demand, and robust single photon emitters are of central importance to many areas of quantum information processing. Over the past 10 years, color centers in solids have emerged as excellent single photon emitters. Color centers in diamond are among the most intensively studied single photon emitters, but recently silicon carbide (SiC) has also been demonstrated to be an excellent host material. In contrast to diamond, SiC is a technologically important material that is widely used in optoelectronics, high power electronics, and microelectromechanical systems. It is commercially available in sizes up to 6 inches and processes for device engineering are well developed. We report on a visible-spectrum single photon emitter in 4H-SiC. The emitter is photostable at both room and low temperatures, and it enables 2 million photons/second from unpatterned bulk SiC. We observe two classes of orthogonally polarized emitters, each of which has parallel absorption and emission dipole orientations. Low temperature measurements reveal a narrow zero phonon line with linewidth < 0.1 nm that accounts for more than 30% of the total photoluminescence spectrum. To our knowledge, this SiC color emitter is the brightest stable room-temperature single photon emitter ever observed.
2. High brightness single photon sources based on photonic wires
DEFF Research Database (Denmark)
Claudon, J.; Bleuse, J.; Bazin, M.;
2009-01-01
We present a novel single-photon-source based on the emission of a semiconductor quantum dot embedded in a single-mode photonic wire. This geometry ensures a very large coupling (> 95%) of the spontaneous emission to the guided mode. Numerical simulations show that a photon collection efficiency as...
3. A bright on-demand source of indistinguishable single photons at telecom wavelengths
CERN Document Server
Kim, Je-Hyung; Richardson, Christopher J K; Leavitt, Richard P; Waks, Edo
2015-01-01
Long-distance quantum communication relies on the ability to efficiently generate and prepare single photons at telecom wavelengths. In many applications these photons must also be indistinguishable such that they exhibit interference on a beamsplitter, which implements effective photon-photon interactions. However, deterministic generation of indistinguishable single photons with high brightness remains a challenging problem. We demonstrate a telecom wavelength source of indistinguishable single photons using an InAs/InP quantum dot in a nanophotonic cavity. The cavity enhances the quantum dot emission, resulting in a nearly Gaussian transverse mode profile with high out-coupling efficiency exceeding 46%, leading to detected photon count rates that would exceed 1.5 million counts per second. We also observe Purcell enhanced spontaneous emission rate as large as 4. Using this source, we generate linearly polarized, high purity single photons at telecom-wavelength and demonstrate the indistinguishable nature o...
4. A bright single-photon source based on a photonic trumpet
OpenAIRE
Munsch, Mathieu; Malik, Nitin S.; Bleuse, Joël; Dupuy, Emmanuel; Gregersen, Niels; Mørk, Jesper; Gérard, Jean-Michel; Claudon, Julien
2012-01-01
Fiber-like photonic nanowires, which are optical waveguides made of a high refractive index material n, have recently emerged as non-resonant systems providing an efficient spontaneous emission (SE) control. When they embed a quantum emitter like a quantum dot (QD), they find application to the realization of bright sources of quantum light and, reversibly, provide an efficient interface between propagating photons and the QD. For a wire diameter ∼ λ/n (λ is the operation wavelength), the fra...
5. High brightness single mode source of correlated photon pairs using a photonic crystal fiber
CERN Document Server
Fulconis, J; Wadsworth, W J; Russell, P S J; Rarity, J G
2005-01-01
We demonstrate a picosecond source of correlated photon pairs using a micro-structured fibre with zero dispersion around 715 nm wavelength. The fibre is pumped in the normal dispersion regime at ~708 nm and phase matching is satisfied for widely spaced parametric wavelengths. Here we generate up to 10^7 photon pairs per second in the fibre at wavelengths of 587 nm and 897 nm. On collecting the light in single-mode-fibre-coupled Silicon avalanche diode photon counting detectors we detect ~3.2.10^5 coincidences per second at pump power 0.5 mW.
6. A bright single-photon source based on a photonic trumpet
DEFF Research Database (Denmark)
Munsch, Mathieu; Malik, Nitin S.; Bleuse, Joël;
be brought close to unity with a proper engineering of the wire ends. In particular, a tapering of the top wire end is necessary to achieve a directive far-field emission pattern [1]. Recently, we have realized a single-photon source featuring a needle-like taper. The source efficiency, though record...... with a divergence controlled by the top-facet diameter: for a top diameter of 1.5 µm, less than 5% of the light is scattered outside the collection cone of a lens with a 0.75 NA. iii) the large top facet also simplifies the implementation of a top electrode, to achieve an electrical driving of the device [3]. Using...
7. Single Semiconductor Quantum Dots in Microcavities: Bright sources of indistinguishable Photons
OpenAIRE
Schneider, C.; Gold, P.; Lu, C. -Y.; Höfling, S.; Pan, J. -W.; Kamp, M.
2015-01-01
In this chapter we will discuss the technology and experimental techniques to realize quantum dot (QD) single photon sources combining high outcoupling efficiencies and highest degrees of non-postselected photon indistinguishability. The system, which is based on ultra low density InAs QDs embedded in a quasi planar single sided microcavity with natural photonic traps is an ideal testbed to study quantum light emission from single QDs. We will discuss the influence of the excitation condition...
8. Bright single photon source based on self-aligned quantum dot-cavity systems
OpenAIRE
Maier, Sebastian; Gold, Peter; Forchel, Alfred; Gregersen, Niels; Mørk, Jesper; Höfling, Sven; Schneider, Christian; Kamp, Martin
2014-01-01
We report on a quasi-planar quantum-dot-based single-photon source that shows an unprecedented high extraction efficiency of 42% without complex photonic resonator geometries or post-growth nanofabrication. This very high efficiency originates from the coupling of the photons emitted by a quantum dot to a Gaussian shaped nanohill defect that naturally arises during epitaxial growth in a self-aligned manner. We investigate the morphology of these defects and characterize the photonic operation...
9. Bright quantum dot single photon source based on a low Q defect cavity
DEFF Research Database (Denmark)
Maier, Sebastian; Gold, Peter; Forchel, A.;
2014-01-01
The quasi-planar single photon source presented in this paper shows an extraction efficiency of 42% without complex photonic resonator geometries or lithography steps as well as a high purity with a g2(0) value of 0.023.......The quasi-planar single photon source presented in this paper shows an extraction efficiency of 42% without complex photonic resonator geometries or lithography steps as well as a high purity with a g2(0) value of 0.023....
10. Bright single photon source based on self-aligned quantum dot–cavity systems
DEFF Research Database (Denmark)
Maier, Sebastian; Gold, Peter; Forchel, Alfred;
2014-01-01
We report on a quasi-planar quantum-dot-based single-photon source that shows an unprecedented high extraction efficiency of 42% without complex photonic resonator geometries or post-growth nanofabrication. This very high efficiency originates from the coupling of the photons emitted by a quantum...... dot to a Gaussian shaped nanohill defect that naturally arises during epitaxial growth in a self-aligned manner. We investigate the morphology of these defects and characterize the photonic operation mechanism. Our results show that these naturally arising coupled quantum dot-defects provide a new...
11. Bright single photon source based on self-aligned quantum dot-cavity systems.
Science.gov (United States)
Maier, Sebastian; Gold, Peter; Forchel, Alfred; Gregersen, Niels; Mørk, Jesper; Höfling, Sven; Schneider, Christian; Kamp, Martin
2014-04-01
We report on a quasi-planar quantum-dot-based single-photon source that shows an unprecedented high extraction efficiency of 42% without complex photonic resonator geometries or post-growth nanofabrication. This very high efficiency originates from the coupling of the photons emitted by a quantum dot to a Gaussian shaped nanohill defect that naturally arises during epitaxial growth in a self-aligned manner. We investigate the morphology of these defects and characterize the photonic operation mechanism. Our results show that these naturally arising coupled quantum dot-defects provide a new avenue for efficient (up to 42% demonstrated) and pure (g(2)(0) value of 0.023) single-photon emission. PMID:24718190
12. Bright and stable visible-spectrum single photon emitter in silicon carbide
CERN Document Server
Lienhard, Benjamin; Mouradian, Sara; Dolde, Florian; Tran, Toan Trong; Aharonovich, Igor; Englund, Dirk R
2016-01-01
Single photon sources are of paramount importance in quantum communication, quantum computation, and quantum metrology. In particular, there is great interest to realize scalable solid state platforms that can emit triggered photons on demand to achieve scalable nanophotonic networks. We report on a visible-spectrum single photon emitter in 4H-silicon carbide (SiC). The emitter is photostable at room- and low-temperature enabling photon counts per second (cps) in excess of 2$\\times$10$^6$ from unpatterned, bulk SiC. It exists in two orthogonally polarized states, which have parallel absorption and emission dipole orientations. Low temperature measurements reveal a narrow zero phonon line (linewidth $30~$% of the total photoluminescence spectrum.
13. Bright Single-Photon Sources Based on Anti-Reflection Coated Deterministic Quantum Dot Microlenses
Directory of Open Access Journals (Sweden)
Peter Schnauber
2015-12-01
Full Text Available We report on enhancing the photon-extraction efficiency (PEE of deterministic quantum dot (QD microlenses via anti-reflection (AR coating. The AR-coating deposited on top of the curved microlens surface is composed of a thin layer of Ta2O5, and is found to effectively reduce back-reflection of light at the semiconductor-vacuum interface. A statistical analysis of spectroscopic data reveals, that the AR-coating improves the light out-coupling of respective microlenses by a factor of 1.57 ± 0.71, in quantitative agreement with numerical calculations. Taking the enhancement factor into account, we predict improved out-coupling of light with a PEE of up to 50%. The quantum nature of emission from QDs integrated into AR-coated microlenses is demonstrated via photon auto-correlation measurements revealing strong suppression of two-photon emission events with g(2(0 = 0.05 ± 0.02. As such, these bright non-classical light sources are highly attractive with respect to applications in the field of quantum cryptography.
14. Atmospheric CO2 remote sensing system based on high brightness semiconductor lasers and single photon counting detection
Science.gov (United States)
Pérez-Serrano, Antonio; Vilera, Maria Fernanda; Esquivias, Ignacio; Faugeron, Mickael; Krakowski, Michel; van Dijk, Frédéric; Kochem, Gerd; Traub, Martin; Adamiec, Pawel; Barbero, Juan; Ai, Xiao; Rarity, John G.; Quatrevalet, Mathieu; Ehret, Gerhard
2015-10-01
We propose an integrated path differential absorption lidar system based on all-semiconductor laser sources and single photon counting detection for column-averaged measurements of atmospheric CO2. The Random Modulated Continuous Wave (RM-CW) approach has been selected as the best suited to semiconductor lasers. In a RM-CW lidar, a pseudo random sequence is sent to the atmosphere and the received signal reflected from the target is correlated with the original sequence in order to retrieve the path length. The transmitter design is based on two monolithic Master Oscillator Power Amplifiers (MOPAs), providing the on-line and off-line wavelengths close to the selected absorption line around 1.57 µm. Each MOPA consists of a frequency stabilized distributed feedback master oscillator, a bent modulator section, and a tapered amplifier. This design allows the emitters to deliver high power and high quality laser beams with good spectral properties. An output power above 400 mW with a SMSR higher than 45 dB and modulation capability have been demonstrated. On the side of the receiver, our theoretical and experimental results indicate that the major noise contribution comes from the ambient light and detector noise. For this reason narrow band optical filters are required in the envisioned space-borne applications. In this contribution, we present the latest progresses regarding the design, modeling and characterization of the transmitter, the receiver, the frequency stabilization unit and the complete system.
15. Bright perspectives for nuclear photonics
International Nuclear Information System (INIS)
With the advent of new high-power, short-pulse laser facilities in combination with novel technologies for the production of highly brilliant, intense γ beams (like, e.g., Extreme Light Infrastructure - Nuclear Physics (ELI-NP) in Bucharest, MEGaRay in Livermore or a planned upgrade of the HIγS facility at Duke University), unprecedented perspectives will open up in the coming years for photonuclear physics both in basic sciences as in various fields of applications. Ultra-high sensitivity will be enabled by an envisaged increase of the γ-beam spectral density from the presently typical 102γ/eVs to about 104γ/eVs, thus enabling a new quality of nuclear photonics, assisted by new γ-optical elements. Photonuclear reactions with highly brilliant γ beams will allow to produce radioisotopes for nuclear medicine with much higher specific activity and/or more economically than with conventional methods. This will open the door for completely new clinical applications of radioisotopes. The isotopic, state-selective sensitivity of the well-established technique of nuclear resonance fluorescence (NRF) will be boosted by the drastically reduced energy bandwidth (<0.1%) of the novel γ beams. Together with a much higher intensity of these beams, this will pave the road towards a γ-beam based non-invasive tomography and microscopy, assisting the management of nuclear materials, such as radioactive waste management, the detection of nuclear fissile material in the recycling process or the detection of clandestine fissile materials. Moreover, also secondary sources like low-energy, pulsed, polarized neutron beams of high intensity and high brilliance or a new type of positron source with significantly increased brilliance, for the first time fully polarized, can be realized and lead to new applications in solid state physics or material sciences. (authors)
16. Ultra-bright and efficient single photon generation based on N-V centres in nanodiamonds on a solid immersion lens
OpenAIRE
Schröder, Tim; Gädeke, Friedemann; Banholzer, Moritz Julian; Benson, Oliver
2010-01-01
Single photons are fundamental elements for quantum information technologies such as quantum cryptography, quantum information storage and optical quantum computing. Colour centres in diamond have proven to be stable single photon sources and thus essential components for reliable and integrated quantum information technology. A key requirement for such applications is a large photon flux and a high efficiency. Paying tribute to various attempts to maximise the single photon flux we show that...
17. Silicon-chip source of bright photon pairs.
Science.gov (United States)
Jiang, Wei C; Lu, Xiyuan; Zhang, Jidong; Painter, Oskar; Lin, Qiang
2015-08-10
Integrated quantum photonics relies critically on the purity, scalability, integrability, and flexibility of a photon source to support diverse quantum functionalities on a single chip. Here we report a chip-scale photon-pair source on the silicon-on-insulator platform that utilizes dramatic cavity-enhanced four-wave mixing in a high-Q silicon microdisk resonator. The device is able to produce high-quality photon pairs at different wavelengths with a high spectral brightness of 6.24×10(7) pairs/s/mW(2)/GHz and photon-pair correlation with a coincidence-to-accidental ratio of 1386 ± 278 while pumped with a continuous-wave laser. The superior performance, together with the structural compactness and CMOS compatibility, opens up a great avenue towards quantum silicon photonics with capability of multi-channel parallel information processing for both integrated quantum computing and long-haul quantum communication. PMID:26367942
18. Bright Solid State Source of Photon Triplets
CERN Document Server
Khoshnegar, Milad; Predojević, Ana; Dalacu, Dan; Prilmüller, Maximilian; Lapointe, Jean; Wu, Xiaohua; Tamarat, Philippe; Lounis, Brahim; Poole, Philip; Weihs, Gregor; Majedi, Hamed
2015-01-01
Producing advanced quantum states of light is a priority in quantum information technologies. While remarkable progress has been made on single photons and photon pairs, multipartite correlated photon states are usually produced in purely optical systems by post-selection or cascading, with extremely low efficiency and exponentially poor scaling. Multipartite states enable improved tests of the foundations of quantum mechanics as well as implementations of complex quantum optical networks and protocols. It would be favorable to directly generate these states using solid state systems, for better scaling, simpler handling, and the promise of reversible transfer of quantum information between stationary and flying qubits. Here we use the ground states of two optically active coupled quantum dots to directly produce photon triplets. The wavefunctions of photogenerated excitons localized in these ground states are correlated via molecular hybridization and Coulomb interactions. The formation of a triexciton leads...
19. Ultra-bright and efficient single photon generation based on N-V centres in nanodiamonds on a solid immersion lens
CERN Document Server
Schröder, Tim; Banholzer, Moritz Julian; Benson, Oliver
2010-01-01
Single photons are fundamental elements for quantum information technologies such as quantum cryptography, quantum information storage and optical quantum computing. Colour centres in diamond have proven to be stable single photon sources and thus essential components for reliable and integrated quantum information technology. A key requirement for such applications is a large photon flux and a high efficiency. Paying tribute to various attempts to maximise the single photon flux we show that collection efficiencies of photons from colour centres can be increased with a rather simple experimental setup. To do so we spin-coated nanodiamonds containing single nitrogen-vacancy colour centres on the flat surface of a ZrO2 solid immersion lens. We found stable single photon count rates of up to 853 kcts/s at saturation under continuous wave excitation while having excess to more than 100 defect centres with count rates from 400 kcts/s to 500 kcts/s. For a blinking defect centre we found count rates up to 2.4 Mcts/...
20. Bright Photon Pair Source with High Spectral and Spatial Purity
International Nuclear Information System (INIS)
Spontaneous parametric down-conversion (SPDC) is a reliable and robust source of photons for quantum information applications. For applications that involve operations such as entanglement swapping or single-photon heralding, two-photon states are required to be factorable (uncorrelated) in their spectral and spatial degrees of freedom. We report the design and experimental characterization of an SPDC source that has been optimized for high spectral and spatial purity. The source is pumped by the 776 nm output of a mode-locked Ti:Sapphire laser and consists of a periodically-poled Potassium Titanyl Phosphate (PPKTP) crystal phase-matched for collinear type-II SPDC. The dispersive properties of PPKTP at these wavelengths is such that it is possible to minimize the spectral entanglement by matching the widths of the pump to the spectral phase-matching function. The spatial entanglement is minimized through careful control of the pump focus, yielding nearly single-mode emission. An advantage of this approach is that the emission rate into the collection modes is very high, resulting in a very bright SPDC source. We also report a scheme that employs the output of collinear sources such as these to produce polarization-entangled photon pairs. The scheme, which requires only simple polarization elements, can be scaled to N-photon GHZ states.
1. Single-photon imaging
CERN Document Server
Seitz, Peter
2011-01-01
The acquisition and interpretation of images is a central capability in almost all scientific and technological domains. In particular, the acquisition of electromagnetic radiation, in the form of visible light, UV, infrared, X-ray, etc. is of enormous practical importance. The ultimate sensitivity in electronic imaging is the detection of individual photons. With this book, the first comprehensive review of all aspects of single-photon electronic imaging has been created. Topics include theoretical basics, semiconductor fabrication, single-photon detection principles, imager design and applications of different spectral domains. Today, the solid-state fabrication capabilities for several types of image sensors has advanced to a point, where uncoooled single-photon electronic imaging will soon become a consumer product. This book is giving a specialist´s view from different domains to the forthcoming “single-photon imaging” revolution. The various aspects of single-photon imaging are treated by internati...
2. Single photon quantum cryptography
OpenAIRE
Beveratos, Alexios; Brouri, Rosa; Gacoin, Thierry; Villing, André; Poizat, Jean-Philippe; Grangier, Philippe
2002-01-01
We report the full implementation of a quantum cryptography protocol using a stream of single photon pulses generated by a stable and efficient source operating at room temperature. The single photon pulses are emitted on demand by a single nitrogen-vacancy (NV) color center in a diamond nanocrystal. The quantum bit error rate is less that 4.6% and the secure bit rate is 9500 bits/s. The overall performances of our system reaches a domain where single photons have a measurable advantage over ...
3. Single-photon imaging
International Nuclear Information System (INIS)
The acquisition and interpretation of images is a central capability in almost all scientific and technological domains. In particular, the acquisition of electromagnetic radiation, in the form of visible light, UV, infrared, X-ray, etc. is of enormous practical importance. The ultimate sensitivity in electronic imaging is the detection of individual photons. With this book, the first comprehensive review of all aspects of single-photon electronic imaging has been created. Topics include theoretical basics, semiconductor fabrication, single-photon detection principles, imager design and applications of different spectral domains. Today, the solid-state fabrication capabilities for several types of image sensors has advanced to a point, where uncooled single-photon electronic imaging will soon become a consumer product. This book is giving a specialist's view from different domains to the forthcoming ''single-photon imaging'' revolution. The various aspects of single-photon imaging are treated by internationally renowned, leading scientists and technologists who have all pioneered their respective fields. (orig.)
4. Single photons on demand
International Nuclear Information System (INIS)
Quantum cryptography and information processing are set to benefit from developments in novel light sources that can emit photons one by one. Quantum mechanics has gained a reputation for making counter-intuitive predictions. But we rarely get the chance to witness these effects directly because, being humans, we are simply too big. Take light, for example. The light sources that are familiar to us, such as those used in lighting and imaging or in CD and DVD players, are so huge that they emit billions and billions of photons. But what if there was a light source that emitted just one photon at a time? Over the past few years, new types of light source that are able to emit photons one by one have been emerging from laboratories around the world. Pulses of light composed of a single photon correspond to power flows in the femtowatt range - a million billion times less than that of a table lamp. The driving force behind the development of these single-photon sources is a range of novel applications that take advantage of the quantum nature of light. Quantum states of superposed and entangled photons could lead the way to guaranteed-secure communication, to information processing with unprecedented speed and efficiency, and to new schemes for quantum teleportation. (U.K.)
5. Single-photon spectroscopy of a single molecule
CERN Document Server
Rezus, Y L A; Lettow, R; Renn, A; Zumofen, G; Goetzinger, S; Sandoghdar, V
2011-01-01
Exploring the interaction of light and matter at the ultimate limit of single photons and single emitters is of great interest both from a fundamental point of view and for emerging applications in quantum engineering. However, the difficulty of generating single photons with specific wavelengths, bandwidths and brightness as well as the weak interaction probability of a single photon with an optical emitter pose a formidable challenge toward this goal. Here, we demonstrate a general approach based on the creation of single photons from a single emitter and their use for performing spectroscopy on a second emitter situated at a distance. Although we used organic molecules as emitters, our strategy is readily extendable to other material systems such as quantum dots and color centers. Our work ushers in a new line of experiments that provide access to the coherent and nonlinear couplings of few emitters and few propagating photons.
6. Design of bright, fiber-coupled and fully factorable photon pair sources
International Nuclear Information System (INIS)
From quantum computation to quantum key distribution, many quantum-enhanced applications rely on the ability to generate pure single photons. Even though the process of spontaneous parametric downconversion (SPDC) is widely used as the basis for photon-pair sources, the conditions for pure heralded single-photon generation, taking into account both spectral and spatial degrees of freedom, have not been fully described. We present an analysis of the spatio-temporal correlations present in photon pairs produced by type-I, non-collinear SPDC. We derive a set of conditions for full factorability in all degrees of freedom-required for the heralding of pure single photons-between the signal and idler modes. In this paper, we consider several possible approaches for the design of bright, fiber-coupled and factorable photon-pair sources. We show through numerical simulations of the exact equations that sources based on: (i) the suppression of spatio-temporal entanglement according to our derived conditions and (ii) a tightly focused pump beam together with optimized fiber-collection modes and spectral filtering of the signal and idler photon pairs, lead to a source brightness of the same order of magnitude. Likewise, we find that both of these sources lead to a drastically higher factorable photon-pair flux, compared to an unengineered source.
OpenAIRE
Jie-Qiao Liao; Franco Nori
2013-01-01
We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in quadratic optomechanics. We consider single-photon emission and scattering when the photon is initially inside the cavity and in the fields outside the cavity, respectively. Using our solutions, we calculate the single-photon emission and scattering spectra, and find relations between the spectral features and the system's inherent parameters, such as: the...
8. Transform-limited single photons from a single quantum dot
Science.gov (United States)
Kuhlmann, Andreas V.; Prechtel, Jonathan H.; Houel, Julien; Ludwig, Arne; Reuter, Dirk; Wieck, Andreas D.; Warburton, Richard J.
2015-09-01
Developing a quantum photonics network requires a source of very-high-fidelity single photons. An outstanding challenge is to produce a transform-limited single-photon emitter to guarantee that single photons emitted far apart in the time domain are truly indistinguishable. This is particularly difficult in the solid-state as the complex environment is the source of noise over a wide bandwidth. A quantum dot is a robust, fast, bright and narrow-linewidth emitter of single photons; layer-by-layer growth and subsequent nano-fabrication allow the electronic and photonic states to be engineered. This represents a set of features not shared by any other emitter but transform-limited linewidths have been elusive. Here, we report transform-limited linewidths measured on second timescales, primarily on the neutral exciton but also on the charged exciton close to saturation. The key feature is control of the nuclear spins, which dominate the exciton dephasing via the Overhauser field.
9. Nonlinear interaction between single photons.
Science.gov (United States)
Guerreiro, T; Martin, A; Sanguinetti, B; Pelc, J S; Langrock, C; Fejer, M M; Gisin, N; Zbinden, H; Sangouard, N; Thew, R T
2014-10-24
Harnessing nonlinearities strong enough to allow single photons to interact with one another is not only a fascinating challenge but also central to numerous advanced applications in quantum information science. Here we report the nonlinear interaction between two single photons. Each photon is generated in independent parametric down-conversion sources. They are subsequently combined in a nonlinear waveguide where they are converted into a single photon of higher energy by the process of sum-frequency generation. Our approach results in the direct generation of photon triplets. More generally, it highlights the potential for quantum nonlinear optics with integrated devices and, as the photons are at telecom wavelengths, it opens the way towards novel applications in quantum communication such as device-independent quantum key distribution. PMID:25379916
10. Ramsey interference with single photons
CERN Document Server
Clemmen, Stéphane; Ramelow, Sven; Gaeta, Alexander L
2016-01-01
Interferometry using discrete energy levels in nuclear, atomic or molecular systems is the foundation for a wide range of physical phenomena and enables powerful techniques such as nuclear magnetic resonance, electron spin resonance, Ramsey-based spectroscopy and laser/maser technology. It also plays a unique role in quantum information processing as qubits are realized as energy superposition states of single quantum systems. Here, we demonstrate quantum interference of different energy states of single quanta of light in full analogy to energy levels of atoms or nuclear spins and implement a Ramsey interferometer with single photons. We experimentally generate energy superposition states of a single photon and manipulate them with unitary transformations to realize arbitrary projective measurements, which allows for the realization a high-visibility single-photon Ramsey interferometer. Our approach opens the path for frequency-encoded photonic qubits in quantum information processing and quantum communicati...
11. Photophysics of single silicon vacancy centers in diamond: implications for single photon emission
CERN Document Server
Neu, Elke; Becher, Christoph
2012-01-01
Single silicon vacancy (SiV) color centers in diamond have recently shown the ability for high brightness, narrow bandwidth, room temperature single photon emission. This work develops a model describing the three level population dynamics of single SiV centers in diamond nanocrystals on iridium surfaces including an intensity dependent de-shelving process. Furthermore, we investigate the brightness and photostability of single centers and find maximum single photon rates of 6.2 Mcps under continuous excitation. We investigate the collection efficiency of the fluorescence and estimate quantum efficiencies of the SiV centers.
12. Single-photon decision maker
OpenAIRE
Makoto Naruse; Martin Berthel; Aurélien Drezet; Serge Huant; Masashi Aono; Hirokazu Hori; Song-Ju Kim
2015-01-01
Decision making is critical in our daily lives and for society in general and is finding evermore practical applications in information and communication technologies. Herein, we demonstrate experimentally that single photons can be used to make decisions in uncertain, dynamically changing environments. Using a nitrogen-vacancy in a nanodiamond as a single-photon source, we demonstrate the decision-making capability by solving the multi-armed bandit problem. This capability is directly and im...
13. Single-photon Sagnac interferometer
OpenAIRE
Bertocchi, Guillaume; Alibart, Olivier; Ostrowsky, Daniel Barry; Tanzilli, Sébastien; Baldi, Pascal
2006-01-01
We present the first experimental demonstration of the optical Sagnac effect at the single-photon level. Using a high quality guided-wave heralded single- photon source at 1550 nm and a fibre optics setup, we obtain an interference pattern with net visibilities up to (99.2 $\\pm$ 0.4%). On the basis of this high visibility and the compactness of the setup, the interest of such a system for fibre optics gyroscope is discussed.
14. Single photon from a single trapped atom
International Nuclear Information System (INIS)
Full text: A quantum treatment of the interaction between atoms and light usually begins with the simplest model system: a two-level atom interacting with a monochromatic light wave. Here we demonstrate an elegant experimental realization of this system using an optically trapped single rubidium atom illuminated by resonant light pulses. We observe Rabi oscillations, and show that this system can be used as a highly efficient triggered source of single photons with a well-defined polarisation. In contrast to other sources based on neutral atoms and trapped ions, no optical cavity is required. We achieved a flux of single photons of about 104 s-1 at the detector, and observe complete antibunching. This source has potential applications for distributed atom-atom entanglement using single photons. (author)
15. Spectral compression of single photons
CERN Document Server
Lavoie, Jonathan; Wright, Logan G; Fedrizzi, Alessandro; Resch, Kevin J
2013-01-01
Photons are critical to quantum technologies since they can be used for virtually all quantum information tasks: in quantum metrology, as the information carrier in photonic quantum computation, as a mediator in hybrid systems, and to establish long distance networks. The physical characteristics of photons in these applications differ drastically; spectral bandwidths span 12 orders of magnitude from 50 THz for quantum-optical coherence tomography to 50 Hz for certain quantum memories. Combining these technologies requires coherent interfaces that reversibly map centre frequencies and bandwidths of photons to avoid excessive loss. Here we demonstrate bandwidth compression of single photons by a factor 40 and tunability over a range 70 times that bandwidth via sum-frequency generation with chirped laser pulses. This constitutes a time-to-frequency interface for light capable of converting time-bin to colour entanglement and enables ultrafast timing measurements. It is a step toward arbitrary waveform generatio...
16. Single-photon decision maker
Science.gov (United States)
Naruse, Makoto; Berthel, Martin; Drezet, Aurélien; Huant, Serge; Aono, Masashi; Hori, Hirokazu; Kim, Song-Ju
2015-08-01
Decision making is critical in our daily lives and for society in general and is finding evermore practical applications in information and communication technologies. Herein, we demonstrate experimentally that single photons can be used to make decisions in uncertain, dynamically changing environments. Using a nitrogen-vacancy in a nanodiamond as a single-photon source, we demonstrate the decision-making capability by solving the multi-armed bandit problem. This capability is directly and immediately associated with single-photon detection in the proposed architecture, leading to adequate and adaptive autonomous decision making. This study makes it possible to create systems that benefit from the quantum nature of light to perform practical and vital intelligent functions.
17. Photon Statistics of Single-Photon Quantum States in Real Single Photon Detection
Institute of Scientific and Technical Information of China (English)
李刚; 李园; 王军民; 彭堃墀; 张天才
2004-01-01
@@ Single photon detection (SPD) with high quantum efficiency has been widely used for measurement of different quantum states with different photon distributions.Based on the direct single SPD and double-SPD of HBT configuration, we discuss the effect of a real SPD on the photon statistics measurement and it shows that the measured photon distributions for different quantum states are corrected in different forms.The results are confirmed by experiment with the strongly attenuated coherent light and thermal light.This system can be used to characterize the photon statistics of the fluorescence light from single atom or single molecular.
18. Single photon and nonlocality
Aurelien Drezet
2007-03-01
In a paper by Home and Agarwal [1], it is claimed that quantum nonlocality can be revealed in a simple interferometry experiment using only single particles. A critical analysis of the concept of hidden variable used by the authors of [1] shows that the reasoning is not correct.
19. Creation of multiple identical single photon emitters in diamond
CERN Document Server
Rogers, Lachlan J; Marseglia, Luca; Müller, Christoph; Naydenov, Boris; Schauffert, Hardy; Kranz, C; Teraji, T; Isoya, Junichi; McGuinness, Liam P; Jelezko, Fedor
2013-01-01
Emitters of indistinguishable single photons are crucial for the growing field of quantum technologies. To realize scalability and increase the complexity of quantum optics technologies, multiple independent yet identical single photon emitters are also required. However typical solid-state single photon sources are dissimilar, necessitating the use of electrical feedback or optical cavities to improve spectral overlap between distinct emitters. Here, we present controllable growth of bright silicon-vacancy (SiV-) centres in bulk diamond which intrinsically show almost identical emission (spectral overlap of up to 83%) and near transform-limited excitation linewidths. We measure the photo-physical properties of defects at room and cryogenic temperatures, and demonstrate incorporation into a solid immersion lens (SIL). Our results have impact upon the application of single photon sources for quantum optics and cryptography, and the production of next generation fluorophores for bio-imaging.
20. On the brightness of diluted photon source in synchrotron light facilities
Energy Technology Data Exchange (ETDEWEB)
Ivanyan, M. E-mail: [email protected]; Martirosyan, Y.; Tsakanov, V
2004-10-01
The undulator radiation spectral brightness in storage ring is studied taking into account the effects of the electron beam oscillating trajectory and the beam transverse size variation along the undulator. The modified optimal beta function at the source point to reach maximum brightness is obtained that is in direct relation with the emitted photons wavelength. It is shown that the maximum spectral brightness in long wavelength range is achieved with low beta lattice, while in short wavelength range with larger beta.
1. Teleportation using squeezed single photons
OpenAIRE
Branczyk, Agata M.; Ralph, T. C.
2008-01-01
We present an analysis of squeezed single photon states as a resource for teleportation of coherent state qubits and propose proof-of-principle experiments for the demonstration of coherent state teleportation and entanglement swapping. We include an analysis of the squeezed vacuum as a simpler approximation to small-amplitude cat states. We also investigate the effects of imperfect sources and inefficient detection on the proposed experiments.
2. Photonic wires and trumpets for ultrabright single photon sources
DEFF Research Database (Denmark)
Gérard, Jean-Michel; Claudon, Julien; Bleuse, Joël;
2013-01-01
Photonic wires have recently demonstrated very attractive assets in the field of high-efficiency single photon sources. After presenting the basics of spontaneous emission control in photonic wires, we compare the two possible tapering strategies that can be applied to their output end so as to...... tailor their radiation diagram in the far-field. We highlight the novel “photonic trumpet” geometry, which provides a clean Gaussian beam, and is much less sensitive to fabrication imperfections than the more common needle-like taper geometry. S4Ps based on a single QD in a PW with integrated bottom...... mirror and tapered tip display jointly a record-high efficiency (0.75±0.1 photon per pulse) and excellent single photon purity. Beyond single photon sources, photonic wires and trumpets appear as a very attractive resource for solid-state quantum optics experiments....
3. Highly anisotropic decay rate of single quantum dots in photonic crystal membranes
DEFF Research Database (Denmark)
Wang, Qin; Stobbe, Søren; Nielsen, Henri Thyrrestrup; Hofmann, Holger; Kamp, Martin; Friess, Benedikt; Worschech, Lukas; Schlereth, Thomas; Hofling, Sven; Lodahl, Peter
We measured the variation of spontaneous emission rates with polarization for self-assembled single quantum-dots in photonic crystal membranes, and obtained a maximum anisotropy factor of 6 between decay rates of the two nondegenerate bright states....
4. Engineered Quantum Dot Single Photon Sources
CERN Document Server
Buckley, Sonia; Vuckovic, Jelena
2012-01-01
Fast, high efficiency, and low error single photon sources are required for implementation of a number of quantum information processing applications. The fastest triggered single photon sources to date have been demonstrated using epitaxially grown semiconductor quantum dots (QDs), which can be conveniently integrated with optical microcavities. Recent advances in QD technology, including demonstrations of high temperature and telecommunications wavelength single photon emission, have made QD single photon sources more practical. Here we discuss the applications of single photon sources and their various requirements, before reviewing the progress made on a quantum dot platform in meeting these requirements.
5. The photonic nanowire: an emerging platform for highly efficient single-photon sources for quantum information applications
DEFF Research Database (Denmark)
Gregersen, Niels; Munsch, Mathieu; Malik, Nitin S.; Bleuse, Joël; Dupuy, Emmanuel; Delga, Adrien; Mørk, Jesper; Gérard, Jean-Michel; Claudon, Julien
2013-01-01
Efficient coupling between a localized quantum emitter and a well defined optical channel represents a powerful route to realize single-photon sources and spin-photon interfaces. The tailored fiber-like photonic nanowire embedding a single quantum dot has recently demonstrated an appealing...... first implementation of this strategy has lead to an ultra-bright single-photon source with a first-lens external efficiency of 0.75 ± 0.1 and a predicted coupling to a Gaussian beam of 0.61 ± 0.08....
6. Dark and bright modes manipulation for plasmon-triggered photonic devices
KAUST Repository
Panaro, S.
2014-09-10
In the last decade, several efforts have been spent in the study of near-field coupled systems, in order to induce hybridization of plasmonic modes. Within this context, particular attention has been recently paid on the possibility to couple conventional bright and dark modes. As a result of such phenomenon, a Fano resonance appears as a characteristic sharp dip in the scattering spectra. Here we show how, gradually coupling a single rod-like nanostructure to an aligned nanoantenna dimer, it is possible to induce the near-field activation of an anti-bonding dark mode. The high polarization sensitivity presented by the far-field response of T-shape trimer, combined with the sharp Fano resonance sustained by this plasmonic device, opens interesting perspectives towards a new era of photonic devices. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).
7. Optimised quantum hacking of superconducting nanowire single-photon detectors
OpenAIRE
2013-01-01
We explore bright-light control of superconducting nanowire single-photon detectors (SNSPDs) in the shunted configuration (a practical measure to avoid latching). In an experiment, we simulate an illumination pattern the SNSPD would receive in a typical quantum key distribution system under hacking attack. We show that it effectively blinds and controls the SNSPD. The transient blinding illumination lasts for a fraction of a microsecond and produces several deterministic fake clicks during th...
8. Improved photon counting efficiency calibration using superconducting single photon detectors
Science.gov (United States)
Gan, Haiyong; Xu, Nan; Li, Jianwei; Sun, Ruoduan; Feng, Guojin; Wang, Yanfei; Ma, Chong; Lin, Yandong; Zhang, Labao; Kang, Lin; Chen, Jian; Wu, Peiheng
2015-10-01
The quantum efficiency of photon counters can be measured with standard uncertainty below 1% level using correlated photon pairs generated through spontaneous parametric down-conversion process. Normally a laser in UV, blue or green wavelength range with sufficient photon energy is applied to produce energy and momentum conserved photon pairs in two channels with desired wavelengths for calibration. One channel is used as the heralding trigger, and the other is used for the calibration of the detector under test. A superconducting nanowire single photon detector with advantages such as high photon counting speed (responsivity (UV to near infrared) is used as the trigger detector, enabling correlated photons calibration capabilities into shortwave visible range. For a 355nm single longitudinal mode pump laser, when a superconducting nanowire single photon detector is used as the trigger detector at 1064nm and 1560nm in the near infrared range, the photon counting efficiency calibration capabilities can be realized at 532nm and 460nm. The quantum efficiency measurement on photon counters such as photomultiplier tubes and avalanche photodiodes can be then further extended in a wide wavelength range (e.g. 400-1000nm) using a flat spectral photon flux source to meet the calibration demands in cutting edge low light applications such as time resolved fluorescence and nonlinear optical spectroscopy, super resolution microscopy, deep space observation, and so on.
9. Study of narrowband single photon emitters in polycrystalline diamond films
Energy Technology Data Exchange (ETDEWEB)
Sandstrom, Russell G.; Shimoni, Olga; Martin, Aiden A.; Aharonovich, Igor, E-mail: [email protected] [School of Physics and Advanced Materials, University of Technology, Sydney, P.O. Box 123, Broadway, New South Wales 2007 (Australia)
2014-11-03
Quantum information processing and integrated nanophotonics require robust generation of single photon emitters on demand. In this work, we demonstrate that diamond films grown on a silicon substrate by microwave plasma chemical vapor deposition can host bright, narrowband single photon emitters in the visible—near infra-red spectral range. The emitters possess fast lifetime (∼several ns), absolute photostability, and exhibit full polarization at excitation and emission. Pulsed and continuous laser excitations confirm their quantum behaviour at room temperature, while low temperature spectroscopy is performed to investigate inhomogeneous broadening. Our results advance the knowledge of solid state single photon sources and open pathways for their practical implementation in quantum communication and quantum information processing.
10. Single photon emission computerized tomography
International Nuclear Information System (INIS)
In this thesis two single-photon emission tomographic techniques are presented: (a) longitudinal tomography with a rotating slanting-hole collimator, and (b) transversal tomography with a rotating gamma camera. These methods overcome the disadvantages of conventional scintigraphy. Both detection systems and the image construction methods are explained and comparisons with conventional scintigraphy are drawn. One chapter is dedicated to the determination of system parameters like spatial resolution, contrast, detector uniformity, and size of the object, by phantom studies. In separate chapters the results are presented of detection of tumors and metastases in the liver and the liver hilus; skeletal diseases; various pathological aberrations of the brain; and myocardial perfusion. The possible use of these two ect's for other organs and body areas is discussed in the last chapter. (Auth.)
11. Single photon response of photomultiplier tubes
International Nuclear Information System (INIS)
Beta or gamma rays, when directly incident on the window of an optically shielded photomultiplier tube, yield a typical single photon spectrum. The single photons are possibly generated in the glass window of the photomultiplier tube through excitation of atoms in glass by electrons. The coincidence resolving time has also been measured with a 60Co gamma source and a pair of optically shielded photomultiplier tubes detecting single photons. (orig.)
12. Photon statistics characterization of a single photon source
OpenAIRE
Alleaume, Romain; Treussart, Francois; Courty, Jean-Michel; Roch, Jean-Francois
2003-01-01
n a recent experiment, we reported the time-domain intensity noise measurement of a single photon source relying on single molecule fluorescence control. In this article we present data processing, starting from photocount timestamps. The theoretical analytical expression of the time-dependent Mandel parameter Q(T) of an intermittent single photon source is derived from ONOFF dynamics . Finally, source intensity noise analysis using the Mandel parameter is quantitatively compared to the usual...
13. Continuous variable teleportation of single photon states
OpenAIRE
Ide, Toshiki; Hofmann, Holger Friedrich; Kobayashi, Takayoshi; Furusawa, Akira
2001-01-01
The properties of continuous-variable teleportation of single-photon states are investigated. The output state is different from the input state due to the nonmaximal entanglement in the Einstein-Podolsky-Rosen beams. The photon statistics of the teleportation output are determined and the correlation between the field information b obtained in the teleportation process and the change in photon number is discussed. The results of the output photon statistics are applied to the transmission of...
14. Optimized Heralding Schemes for Single Photons
CERN Document Server
Huang, Yu-Ping; Kumar, Prem
2011-01-01
A major obstacle to a practical, heralded source of single photons is the fundamental trade-off between high heralding efficiency and high production rate. To overcome this difficulty, we propose applying sequential spectral and temporal filtering on the signal photons before they are detected for heralding. Based on a multimode theory that takes into account the effect of simultaneous multiple photon-pair emission, we find that these filters can be optimized to yield both a high heralding efficiency and a high production rate. While the optimization conditions vary depending on the underlying photon-pair spectral correlations, all correlation profiles can lead to similarly high performance levels when optimized filters are employed. This suggests that a better strategy for improving the performance of heralded single-photon sources is to adopt an appropriate measurement scheme for the signal photons, rather than tailoring the properties of the photon-pair generation medium.
15. Single-photon emission tomography.
Science.gov (United States)
Goffin, Karolien; van Laere, Koen
2016-01-01
Single-photon emission computed tomography (SPECT) is a functional nuclear imaging technique that allows visualization and quantification of different in vivo physiologic and pathologic features of brain neurobiology. It has been used for many years in diagnosis of several neurologic and psychiatric disorders. In this chapter, we discuss the current state-of-the-art of SPECT imaging of brain perfusion and dopamine transporter (DAT) imaging. Brain perfusion SPECT imaging plays an important role in the localization of the seizure onset zone in patients with refractory epilepsy. In cerebrovascular disease, it can be useful in determining the cerebrovascular reserve. After traumatic brain injury, SPECT has shown perfusion abnormalities despite normal morphology. In the context of organ donation, the diagnosis of brain death can be made with high accuracy. In neurodegeneration, while amyloid or (18)F-fluorodeoxyglucose positron emission tomography (FDG-PET) are the nuclear diagnostic tools of preference for early and differential diagnosis of dementia, perfusion SPECT imaging can be useful, albeit with slightly lower accuracy. SPECT imaging of the dopamine transporter system is widely available in Europe and Asia, but since recently also in the USA, and has been accepted as an important diagnostic tool in the early and differential diagnosis of parkinsonism in patients with unclear clinical features. The combination of perfusion SPECT (or FDG-PET) and DAT imaging provides differential diagnosis between idiopathic Parkinson's disease, Parkinson-plus syndromes, dementia with Lewy bodies, and essential tremor. PMID:27432669
16. What are single photons good for?
Science.gov (United States)
Sangouard, Nicolas; Zbinden, Hugo
2012-10-01
In a long-held preconception, photons play a central role in present-day quantum technologies. But what are sources producing photons one by one good for precisely? Well, in opposition to what many suggest, we show that single-photon sources are not helpful for point to point quantum key distribution because faint laser pulses do the job comfortably. However, there is no doubt about the usefulness of sources producing single photons for future quantum technologies. In particular, we show how single-photon sources could become the seed of a revolution in the framework of quantum communication, making the security of quantum key distribution device-independent or extending quantum communication over many hundreds of kilometers. Hopefully, these promising applications will provide a guideline for researchers to develop more and more efficient sources, producing narrowband, pure and indistinguishable photons at appropriate wavelengths.
17. What are single photons good for?
CERN Document Server
Sangouard, Nicolas
2012-01-01
In a long-held preconception, photons play a central role in present-day quantum technologies. But what are sources producing photons one by one good for precisely? Well, in opposition to what many suggest, we show that single-photon sources are not helpful for point to point quantum key distribution because faint laser pulses do the job comfortably. However, there is no doubt about the usefulness of sources producing single photons for future quantum technologies. In particular, we show how single-photon sources could become the seed of a revolution in the framework of quantum communication, making the security of quantum key distribution device independent or extending quantum communication over many hundreds of kilometers. Hopefully, these promising applications will provide a guideline for researchers to develop more and more efficient sources, producing narrowband, pure and indistinguishable photons at appropriate wavelengths.
18. Hybrid photonic circuit for multiplexed heralded single photons
CERN Document Server
Meany, Thomas; Collins, Matthew J; Clark, Alex S; Williams, Robert J; Eggleton, Benjamin J; Steel, M J; Withford, Michael J; Alibart, Olivier; Tanzilli, Sébastien
2014-01-01
A key resource for quantum optics experiments is an on-demand source of single and multiple photon states at telecommunication wavelengths. This letter presents a heralded single photon source based on a hybrid technology approach, combining high efficiency periodically poled lithium niobate waveguides, low-loss laser inscribed circuits, and fast (>1 MHz) fibre coupled electro-optic switches. Hybrid interfacing different platforms is a promising route to exploiting the advantages of existing technology and has permitted the demonstration of the multiplexing of four identical sources of single photons to one output. Since this is an integrated technology, it provides scalability and can immediately leverage any improvements in transmission, detection and photon production efficiencies.
19. Interfacing superconducting qubits and single optical photons
CERN Document Server
Das, Sumanta; Sørensen, Anders S
2016-01-01
We propose an efficient light-matter interface at optical frequencies between a superconducting qubit and a single photon. The desired interface is based on a hybrid architecture composed of an organic molecule embedded inside an optical waveguide and electrically coupled to a superconducting qubit far from the optical axis. We show that high fidelity, photon-mediated, entanglement between distant superconducting qubits can be achieved with incident pulses at the single photon level. Such low light level is highly sought for to overcome the decoherence of the superconducting qubit caused by absorption of optical photons.
20. The Single-Photon Router
OpenAIRE
Hoi, Io-Chun; Wilson, C. M.; Johansson, Göran; Palomaki, Tauno; Peropadre, Borja; Delsing, Per
2011-01-01
We have embedded an artificial atom, a superconducting "transmon" qubit, in an open transmission line and investigated the strong scattering of incident microwave photons ($\\sim6$ GHz). When an input coherent state, with an average photon number $N\\ll1$ is on resonance with the artificial atom, we observe extinction of up to 90% in the forward propagating field. We use two-tone spectroscopy to study scattering from excited states and we observe electromagnetically induced transparency (EIT). ...
1. Photon statistics characterization of a single-photon source
International Nuclear Information System (INIS)
In a recent experiment, we reported the time-domain intensity noise measurement of a single-photon source relying on single-molecule fluorescence control. In this paper, we present data processing starting from photocount timestamps. The theoretical analytical expression of the time-dependent Mandel parameter Q(T) of an intermittent single-photon source is derived from ON↔OFF dynamics. Finally, source intensity noise analysis, using the Mandel parameter, is quantitatively compared with the usual approach relying on the time autocorrelation function, both methods yielding the same molecular dynamical parameters
2. Superconducting Nanowire Single Photon Detector on Diamond
CERN Document Server
Atikian, Haig A; Salim, A Jafari; Burek, Michael J; Choy, Jennifer T; Majedi, A Hamed; Loncar, Marko
2014-01-01
Superconducting nanowire single photon detectors (SNSPDs) are fabricated directly on diamond substrates and their optical and electrical properties are characterized. Dark count performance and photon count rates are measured at varying temperatures for 1310nm and 632nm photons. The procedure to prepare diamond substrate surfaces suitable for the deposition and patterning of thin film superconducting layers is reported. Using this approach, diamond substrates with less than 300pm RMS surface roughness are obtained.
3. Sharp and Bright Photoluminescence Emission of Single Crystalline Diacetylene Nanoparticles
CERN Document Server
Kima, Seokho; Kima, Hyeong Tae; Cuic, Chunzhi; Park, Dong Hyuk
2016-01-01
Amorphous nanoparticles (NPs) of diacetylene (DA) molecules were prepared by using a reprecipitation method. After crystallization through solvent-vapor annealing process, the highly crystalline DA NPs show different structural and optical characteristics compared with the amorphous DA NPs. The single crystal structure of DA NPs was confirmed by high-resolution transmission electron microscopy (HR-TEM) and wide angle X-ray scattering (WAXS). The luminescence color and photoluminescence (PL) characteristics of the DA NPs were measured using color charge-coupled device (CCD) images and high-resolution laser confocal microscope (LCM). The crystalline DA NPs emit bright green light emission compared with amorphous DA NPs and the main PL peak of the crystalline DA NPs exhibits relative narrow and blue shift phenomena due to enhanced interaction between DA molecular in the nano-size crystal structure.
4. Computational Modeling of Photonic Crystal Microcavity Single-Photon Emitters
Science.gov (United States)
Saulnier, Nicole A.
Conventional cryptography is based on algorithms that are mathematically complex and difficult to solve, such as factoring large numbers. The advent of a quantum computer would render these schemes useless. As scientists work to develop a quantum computer, cryptographers are developing new schemes for unconditionally secure cryptography. Quantum key distribution has emerged as one of the potential replacements of classical cryptography. It relics on the fact that measurement of a quantum bit changes the state of the bit and undetected eavesdropping is impossible. Single polarized photons can be used as the quantum bits, such that a quantum system would in some ways mirror the classical communication scheme. The quantum key distribution system would include components that create, transmit and detect single polarized photons. The focus of this work is on the development of an efficient single-photon source. This source is comprised of a single quantum dot inside of a photonic crystal microcavity. To better understand the physics behind the device, a computational model is developed. The model uses Finite-Difference Time-Domain methods to analyze the electromagnetic field distribution in photonic crystal microcavities. It uses an 8-band k · p perturbation theory to compute the energy band structure of the epitaxially grown quantum dots. We discuss a method that combines the results of these two calculations for determining the spontaneous emission lifetime of a quantum dot in bulk material or in a microcavity. The computational models developed in this thesis are used to identify and characterize microcavities for potential use in a single-photon source. The computational tools developed are also used to investigate novel photonic crystal microcavities that incorporate 1D distributed Bragg reflectors for vertical confinement. It is found that the spontaneous emission enhancement in the quasi-3D cavities can be significantly greater than in traditional suspended slab
5. Efficient generation of indistinguishable single photons on-demand at telecom wavelengths
Science.gov (United States)
Kim, Jehyung; Cai, Tao; Richardson, Christopher; Leavitt, Richard; Waks, Edo
Highly efficient single photon sources are important building blocks for optical quantum information processing. For practical use and long-distance quantum communication, single photons should have fiber-compatible telecom wavelengths. In addition, most quantum communication applications require high degree of indistinguishability of single photons, such that they exhibit interference on a beam splitter. However, deterministic generation of indistinguishable single photons with high brightness remains a challenging problem in particular at telecom wavelengths. We demonstrate a telecom wavelength source of indistinguishable single photons using an InAs/InP quantum dot in a nanophotonic cavity. To obtain the efficient single quantum dot emission, we employ the higher order mode in L3 photonic crystal cavity that shows a nearly Gaussian transverse mode profile and results in out-coupling efficiency exceeding 46 % and unusual bright single quantum dot emission exceeding 1.5 million counts per second at a detector. We also observe Purcell enhanced spontaneous emission rate as large as 4 and high linear polarization ratio of 0.96 for the coupled dots. Using this source, we generate high purity single photons at 1.3 μm wavelength and demonstrate the indistinguishable nature of the emission using a two-photon interference measurement.
6. Superconducting nanowire single-photon imager
CERN Document Server
Zhao, Qing-Yuan; Calandri, Niccolò; Dane, Andrew E; McCaughan, Adam N; Bellei, Francesco; Wang, Hao-Zhu; Santavicca, Daniel F; Berggren, Karl K
2016-01-01
Detecting spatial and temporal information of individual photons is a crucial technology in today's quantum information science. Among the existing single-photon detectors, superconducting nanowire single-photon detectors (SNSPDs) have been demonstrated with a sub-50 ps timing jitter, near unity detection efficiency1, wide response spectrum from visible to infrared and ~10 ns reset time. However, to gain spatial sensitivity, multiple SNSPDs have to be integrated into an array, whose spatial and temporal resolutions are limited by the multiplexing circuit. Here, we add spatial sensitivity to a single nanowire while preserving the temporal resolution from an SNSPD, thereby turning an SNSPD into a superconducting nanowire single-photon imager (SNSPI). To achieve an SNSPI, we modify a nanowire's electrical behavior from a lumped inductor to a transmission line, where the signal velocity is slowed down to 0.02c (where c is the speed of light). Consequently, we are able to simultaneously read out the landing locati...
7. Single Photon Emission Computed Tomography (SPECT)
Science.gov (United States)
... Tools & Resources Stroke More Single Photon Emission Computed Tomography (SPECT) Updated:Sep 11,2015 What is a ... Heart Attack Myocardial Perfusion Imaging (MPI) Positron Emission Tomography (PET) Radionuclide Ventriculography, Radionuclide Angiography, MUGA Scan Heart ...
8. Optimised quantum hacking of superconducting nanowire single-photon detectors
Science.gov (United States)
2014-03-01
We explore bright-light control of superconducting nanowire single-photon detectors (SNSPDs) in the shunted configuration (a practical measure to avoid latching). In an experiment, we simulate an illumination pattern the SNSPD would receive in a typical quantum key distribution system under hacking attack. We show that it effectively blinds and controls the SNSPD. The transient blinding illumination lasts for a fraction of a microsecond and produces several deterministic fake clicks during this time. This attack does not lead to elevated timing jitter in the spoofed output pulse, and hence does not introduce significant errors. Five different SNSPD chip designs were tested. We consider possible countermeasures to this attack.
9. Simple microcavity for single-photon generation.
Science.gov (United States)
Plakhotnik, Taras
2005-04-18
A new design of an optical resonator for generation of single-photon pulses is proposed. The resonator is made of a cylindrical or spherical piece of a polymer squeezed between two flat dielectric mirrors. The mode characteristics of this resonator are calculated numerically. The numerical analysis is backed by a physical explanation. The decay time and the mode volume of the fundamental mode are sufficient for achieving more than 96% probability of generating a single-photon in a single-mode. The corresponding requirement for the reflectivity of the mirrors (~99.9%) and the losses in the polymer (100 dB/m) are quite modest. The resonator is suitable for single-photon generation based on optical pumping of a single quantum system such as an organic molecule, a diamond nanocrystal, or a semiconductor quantum dot if they are imbedded in the polymer. PMID:19495201
10. Photon statistics measurement by use of single photon detection
Institute of Scientific and Technical Information of China (English)
XIAO Liantuan; JIANG Yuqiang; ZHAO Yanting; YIN Wangbao; ZHAO Jianming; JIA Suotang
2004-01-01
The direct measurement of the Mandel para- meter of weak laser pulses, with 10 ns pulse duration time and the mean number of photon per pulsebeing approximately 0.1, is investigated by recording every photocount event. With the Hanbury Brown and Twiss detection scheme, and not more than one photon per pulse being detected during the sample time by single-photon counters, we have found that the single mode diode laser with driving current lower than the threshold yields a sub-Poissonian statistics. In addition, when the diode laser driving current is much higher than the threshold, it is validated that the Mandel parameter QC of the Poissonian coherent state is nearly The experimental results are in good agreement with theoretical prediction considering the measurement error.
11. High brightness fiber laser pump sources based on single emitters and multiple single emitters
Science.gov (United States)
Scheller, Torsten; Wagner, Lars; Wolf, Jürgen; Bonati, Guido; Dörfel, Falk; Gabler, Thomas
2008-02-01
Driven by the potential of the fiber laser market, the development of high brightness pump sources has been pushed during the last years. The main approaches to reach the targets of this market had been the direct coupling of single emitters (SE) on the one hand and the beam shaping of bars and stacks on the other hand, which often causes higher cost per watt. Meanwhile the power of single emitters with 100μm emitter size for direct coupling increased dramatically, which also pushed a new generation of wide stripe emitters or multi emitters (ME) of up to 1000μm emitter size respectively "minibars" with apertures of 3 to 5mm. The advantage of this emitter type compared to traditional bars is it's scalability to power levels of 40W to 60W combined with a small aperture which gives advantages when coupling into a fiber. We show concepts using this multiple single emitters for fiber coupled systems of 25W up to 40W out of a 100μm fiber NA 0.22 with a reasonable optical efficiency. Taking into account a further efficiency optimization and an increase in power of these devices in the near future, the EUR/W ratio pushed by the fiber laser manufacturer will further decrease. Results will be shown as well for higher power pump sources. Additional state of the art tapered fiber bundles for photonic crystal fibers are used to combine 7 (19) pump sources to output powers of 100W (370W) out of a 130μm (250μm) fiber NA 0.6 with nominal 20W per port. Improving those TFB's in the near future and utilizing 40W per pump leg, an output power of even 750W out of 250μm fiber NA 0.6 will be possible. Combined Counter- and Co-Propagated pumping of the fiber will then lead to the first 1kW fiber laser oscillator.
12. Near-optimal single-photon sources in the solid state
Science.gov (United States)
Somaschi, N.; Giesz, V.; de Santis, L.; Loredo, J. C.; Almeida, M. P.; Hornecker, G.; Portalupi, S. L.; Grange, T.; Antón, C.; Demory, J.; Gómez, C.; Sagnes, I.; Lanzillotti-Kimura, N. D.; Lemaítre, A.; Auffeves, A.; White, A. G.; Lanco, L.; Senellart, P.
2016-05-01
The scaling of optical quantum technologies requires efficient, on-demand sources of highly indistinguishable single photons. Semiconductor quantum dots inserted into photonic structures are ultrabright single-photon sources, yet the indistinguishability is limited by charge noise. Parametric downconversion sources provide highly indistinguishable photons but are operated at very low brightness to maintain high single-photon purity. To date, no technology has provided a bright source generating near-unity indistinguishability and pure single photons. Here, we report such devices made of quantum dots in electrically controlled cavities. Application of an electrical bias on the deterministically fabricated structures is shown to strongly reduce charge noise. Under resonant excitation, an indistinguishability of 0.9956 ± 0.0045 is demonstrated with g(2)(0) = 0.0028 ± 0.0012. The photon extraction of 65% and measured brightness of 0.154 ± 0.015 make this source 20 times brighter than any source of equal quality. This new generation of sources opens the way to new levels of complexity and scalability in optical quantum technologies.
13. Measurement of Ultra-Short Single-Photon Pulse Duration with Two-Photon Interference
Institute of Scientific and Technical Information of China (English)
LV Fan; SUN Fang-Wen; ZOU Chang-Ling; HAN Zheng-Fu; GUO Guang-Can
2011-01-01
We proposed a protocol of measuring the duration of ultra-short single-photon pulse with two-photon interference.The pulse duration can be obtained from the width of the visibility of two-photon Hong-Ou-Mandel interference or the indistinguishability of the two photons. Moreover, the shape of a single-photon pulse can be measured with ultra-short single-photon pulses through the two-photon interference.%@@ We proposed a protocol of measuring the duration of ultra-short single-photon pulse with two-photon interference.The pulse duration can be obtained from the width of the visibility of two-photon Hong-Ou-Mandel interference or the indistinguishability of the two photons.Moreover, the shape of a single-photon pulse can be measured with ultra-short single-photon pulses through the two-photon interference.
14. Multiple intrinsically identical single-photon emitters in the solid state.
Science.gov (United States)
Rogers, L J; Jahnke, K D; Teraji, T; Marseglia, L; Müller, C; Naydenov, B; Schauffert, H; Kranz, C; Isoya, J; McGuinness, L P; Jelezko, F
2014-01-01
Emitters of indistinguishable single photons are crucial for the growing field of quantum technologies. To realize scalability and increase the complexity of quantum optics technologies, multiple independent yet identical single-photon emitters are required. However, typical solid-state single-photon sources are inherently dissimilar, necessitating the use of electrical feedback or optical cavities to improve spectral overlap between distinct emitters. Here we demonstrate bright silicon vacancy (SiV(-)) centres in low-strain bulk diamond, which show spectral overlap of up to 91% and nearly transform-limited excitation linewidths. This is the first time that distinct single-photon emitters in the solid state have shown intrinsically identical spectral properties. Our results have impact on the application of single-photon sources for quantum optics and cryptography. PMID:25162729
15. Superconducting nanowire single photon detector on diamond
International Nuclear Information System (INIS)
Superconducting nanowire single photon detectors are fabricated directly on diamond substrates and their optical and electrical properties are characterized. Dark count performance and photon count rates are measured at varying temperatures for 1310 nm and 632 nm photons. A multi-step diamond surface polishing procedure is reported, involving iterative reactive ion etching and mechanical polishing to create a suitable diamond surface for the deposition and patterning of thin film superconducting layers. Using this approach, diamond substrates with less than 300 pm Root Mean Square surface roughness are obtained
16. Superconducting nanowire single photon detector on diamond
Energy Technology Data Exchange (ETDEWEB)
Atikian, Haig A.; Burek, Michael J.; Choy, Jennifer T.; Lončar, Marko, E-mail: [email protected] [School of Engineering and Applied Sciences, Harvard University, 33 Oxford Street, Cambridge, Massachusetts 02138 (United States); Eftekharian, Amin; Jafari Salim, A.; Hamed Majedi, A. [University of Waterloo, 200 University Ave West, Waterloo, Ontario N2L 3G1 (Canada); Institute for Quantum Computing, University of Waterloo, 200 University Ave West, Waterloo, Ontario N2L 3G1 (Canada)
2014-03-24
Superconducting nanowire single photon detectors are fabricated directly on diamond substrates and their optical and electrical properties are characterized. Dark count performance and photon count rates are measured at varying temperatures for 1310 nm and 632 nm photons. A multi-step diamond surface polishing procedure is reported, involving iterative reactive ion etching and mechanical polishing to create a suitable diamond surface for the deposition and patterning of thin film superconducting layers. Using this approach, diamond substrates with less than 300 pm Root Mean Square surface roughness are obtained.
17. Selective excitation of bright and dark plasmonic resonances of single gold nanorods
CERN Document Server
Demichel, O; Francs, G Colas des; Bouhelier, A; Hertz, E; Billard, F; de Fornel, F; Cluzel, B
2015-01-01
Plasmonic dark modes are pure near-field resonances since their dipole moments are vanishing in far field. These modes are particularly interesting to enhance nonlinear light-matter interaction at the nanometer scale because radiative losses are mitigated therefore increasing the intrinsic lifetime of the resonances. However, the excitation of dark modes by standard far field approaches is generally inefficient because the symmetry of the electromagnetic near-field distribution has a poor overlap with the excitation field. Here, we demonstrate the selective optical excitation of bright and dark plasmonic modes of single gold nanorods by spatial phase-shaping the excitation beam. Using two-photon luminescence measurements, we unambiguously identify the symmetry and the order of the emitting modes and analyze their angular distribution by Fourier-space imaging.
18. A bright triggered twin-photon source in the solid state
CERN Document Server
Thoma, Alexander; Schlehahn, Alexander; Gschrey, Manuel; Schnauber, Peter; Schulze, Jan-Hindrik; Strittmatter, André; Rodt, Sven; Carmele, Alexander; Knorr, Andreas; Reitzenstein, Stephan
2016-01-01
A non-classical light source emitting pairs of identical photons represents a versatile resource of interdisciplinary importance with applications in quantum optics and quantum biology. Emerging research fields, which benefit from such type of quantum light source, include quantum-optical spectroscopy or experiments on photoreceptor cells sensitive to photon statistics. To date, photon twins have mostly been generated using parametric downconversion sources, relying on Poissonian number distributions, or atoms, exhibiting low emission rates. Here, we propose and experimentally demonstrate the efficient, triggered generation of photon twins using the energy-degenerate biexciton-exciton radiative cascade of a single semiconductor quantum dot. Deterministically integrated within a microlens, this nanostructure emits highly-correlated photon pairs, degenerate in energy and polarization, at a rate of up to (2.8 $\\pm$ 0.4) MHz. Two-photon interference experiments reveal a significant degree of indistinguishability ...
19. Gated Mode Superconducting Nanowire Single Photon Detectors
CERN Document Server
Akhlaghi, Mohsen K
2011-01-01
Single Photon Detectors (SPD) are fundamental to quantum optics and quantum information. Superconducting Nanowire SPDs (SNSPD) [1] provide high performance in terms of quantum efficiency (QE), dark count rate (DCR) and timing jitter [2], but have limited maximum count rate (MCR) when operated as a free-running mode (FM) detector [3, 4]. However, high count rates are needed for many applications like quantum computing [5] and communication [6], and laser ranging [7]. Here we report the first operation of SNSPDs in a gated mode (GM) that exploits a single photon triggered latching phenomenon to detect photons. We demonstrate operation of a large active area single element GM-SNSPD at 625MHz, one order of magnitude faster than its FM counterpart. Contrary to FM-SNSPDs, the MCR in GM can be pushed to GHz range without a compromise on the active area or QE, while reducing the DCR.
20. Multidimensional time-correlated single photon counting
Science.gov (United States)
Becker, Wolfgang; Bergmann, Axel
2006-10-01
Time-correlated single photon counting (TCSPC) is based on the detection of single photons of a periodic light signal, measurement of the detection time of the photons, and the build-up of the photon distribution versus the time in the signal period. TCSPC achieves a near ideal counting efficiency and transit-time-spread-limited time resolution for a given detector. The drawback of traditional TCSPC is the low count rate, long acquisition time, and the fact that the technique is one-dimensional, i.e. limited to the recording of the pulse shape of light signals. We present an advanced TCSPC technique featuring multi-dimensional photon acquisition and a count rate close to the capability of currently available detectors. The technique is able to acquire photon distributions versus wavelength, spatial coordinates, and the time on the ps scale, and to record fast changes in the fluorescence lifetime and fluorescence intensity of a sample. Biomedical applications of advanced TCSPC techniques are time-domain optical tomography, recording of transient phenomena in biological systems, spectrally resolved fluorescence lifetime imaging, FRET experiments in living cells, and the investigation of dye-protein complexes by fluorescence correlation spectroscopy. We demonstrate the potential of the technique for selected applications.
1. Quantum Information Processing with Single Photons
CERN Document Server
Lim, Y L
2005-01-01
Photons are natural carriers of quantum information due to their ease of distribution and long lifetime. This thesis concerns various related aspects of quantum information processing with single photons. Firstly, we demonstrate N-photon entanglement generation through a generalised N X N symmetric beam splitter known as the Bell multiport. A wide variety of 4-photon entangled states as well as the N-photon W-state can be generated with an unexpected non-monotonic decreasing probability of success with N. We also show how the same setup can be used to generate multiatom entanglement. A further study of multiports also leads us to a multiparticle generalisation of the Hong-Ou-Mandel dip which holds for all Bell multiports of even number of input ports. Next, we demonstrate a generalised linear optics based photon filter that has a constant success probability regardless of the number of photons involved. This filter has the highest reported success probability and is interferometrically robust. Finally, we dem...
2. Single perylene diimide dendrimers as single-photon sources
International Nuclear Information System (INIS)
Single-molecule fluorescence spectroscopy was performed on a number of perylene diimide multichromophores with different dendritic geometries, with the particular goal of characterizing their performance as single-photon sources at room temperature. The quality of the different perylene diimide-containing dendrimers as single-photon sources was evaluated by determining the Mandel parameter. Values similar to ones reported previously for perylene monoimide dendrimers were found. The different arrangements of the chromophores in the different dendrimers do not noticeably affect their efficiency as single-photon emitters. Due to the formation of oxygen-enhanced long dark states, anaerobic conditions are found to be the best for optimizing their performance, which is in contrast with the case for perylene monoimide containing dendrimers
3. Experimental demonstration of highly anisotropic decay rates of single quantum dots inside photonic crystals
DEFF Research Database (Denmark)
Wang, Qin; Stobbe, Søren; Nielsen, Henri Thyrrestrup; Hofmann, Holger; Kamp, Martin; Schlereth, thomas; Höfling, Sven; Lodahl, Peter
We have systematically measured the variation of the spontaneous emission rate with polarization for self-assembled single quantum dots in two-dimensional photonic crystal membranes and obtained a maximum anisotropy factor of 6 between the decay rates of the two nondegenerate bright exciton states....
4. Highly anisotropic decay rates of single quantum dots in photonic crystal membranes
DEFF Research Database (Denmark)
Wang, Qin; Stobbe, Søren; Nielsen, Henri Thyrrestrup; Hofmann, H.; Kamp, M.; Schlereth, T.W.; Höfling, S.; Lodahl, Peter
We have measured the variation of the spontaneous emission rate with polarization for self-assembled single quantum dots in two-dimensional photonic crystal membranes. We observe a maximum anisotropy factor of 6 between the decay rates of the two bright exciton states. This large anisotropy is at...
5. Single Photon Experiments and Quantum Complementarity
Directory of Open Access Journals (Sweden)
Georgiev D. D.
2007-04-01
Full Text Available Single photon experiments have been used as one of the most striking illustrations of the apparently nonclassical nature of the quantum world. In this review we examine the mathematical basis of the principle of complementarity and explain why the Englert-Greenberger duality relation is not violated in the configurations of Unruh and of Afshar.
6. Interactive Screen Experiments with Single Photons
Science.gov (United States)
Bronner, Patrick; Strunz, Andreas; Silberhorn, Christine; Meyn, Jan-Peter
2009-01-01
Single photons are used for fundamental quantum physics experiments as well as for applications. Originally being a topic of advance courses, such experiments are increasingly a subject of undergraduate courses. We provide interactive screen experiments (ISE) for supporting the work in a real laboratory, and for students who do not have access to…
7. Very Efficient Single-Photon Sources Based on Quantum Dots in Photonic Wires
DEFF Research Database (Denmark)
Gerard, Jean-Michel; Claudon, Julien; Bleuse, Joel;
2014-01-01
We review the recent development of high efficiency single photon sources based on a single quantum dot in a photonic wire. Unlike cavity-based devices, very pure single photon emission and efficiencies exceeding 0.7 photon per pulse are jointly demonstrated under non-resonant pumping conditions...... optical properties of "one-dimensional atoms"....
8. Efficacy of a single sequence of intermittent bright light pulses for delaying circadian phase in humans
OpenAIRE
Gronfier, Claude; Wright, Kenneth P.; Kronauer, Richard E.; Jewett, Megan E.; Czeisler, Charles A.
2004-01-01
It has been shown in animal studies that exposure to brief pulses of bright light can phase shift the circadian pacemaker, and that the resetting action of light is most efficient during the first minutes of light exposure. In humans, multiple consecutive days of exposure to brief bright light pulses have been shown to phase shift the circadian pacemaker. The aim of the present study was to determine if a single sequence of brief bright light pulses administered during the early biological ni...
9. Single-Photon Imaging and Efficient Coupling to Single Plasmons
CERN Document Server
Celebrano, M; Kukura, P; Agio, M; Renn, A; Goetzinger, S; Sandoghdar, V
2009-01-01
We demonstrate strong coupling of single photons emitted by individual molecules at cryogenic and ambient conditions to individual nanoparticles. We provide images obtained both in transmission and reflection, where an efficiency greater than 55% was achieved in converting incident narrow-band photons to plasmon-polaritons (plasmons) of a silver nanoparticle. Our work paves the way to spectroscopy and microscopy of nano-objects with sub-shot noise beams of light and to triggered generation of single plasmons and electrons in a well-controlled manner.
10. Deterministic Single-Phonon Source Triggered by a Single Photon
Science.gov (United States)
Söllner, Immo; Midolo, Leonardo; Lodahl, Peter
2016-06-01
We propose a scheme that enables the deterministic generation of single phonons at gigahertz frequencies triggered by single photons in the near infrared. This process is mediated by a quantum dot embedded on chip in an optomechanical circuit, which allows for the simultaneous control of the relevant photonic and phononic frequencies. We devise new optomechanical circuit elements that constitute the necessary building blocks for the proposed scheme and are readily implementable within the current state-of-the-art of nanofabrication. This will open new avenues for implementing quantum functionalities based on phonons as an on-chip quantum bus.
11. Deterministic Single-Phonon Source Triggered by a Single Photon
CERN Document Server
Söllner, Immo; Lodahl, Peter
2016-01-01
We propose a scheme that enables the deterministic generation of single phonons at GHz frequencies triggered by single photons in the near infrared. This process is mediated by a quantum dot embedded on-chip in an opto-mechanical circuit, which allows for the simultaneous control of the relevant photonic and phononic frequencies. We devise new opto-mechanical circuit elements that constitute the necessary building blocks for the proposed scheme and are readily implementable within the current state-of-the-art of nano-fabrication. This will open new avenues for implementing quantum functionalities based on phonons as an on-chip quantum bus.
12. Single-Photon Detection at Telecom Wavelengths
Institute of Scientific and Technical Information of China (English)
SUN Zhi-Bin; MA Hai-Qiang; LEI Ming; WANG Di; LIU Zhao-Jie; YANG Han-Dong; WU Ling-An; ZHAI Guang-Jie; FENG Ji
2007-01-01
A single-photon detector based on an InGaAs avalanche photodiode has been developed for use at telecom wavelengths. A suitable delay and sampling gate modulation circuit are used to prevent positive and negative transient pulses from influencing the detection of true photon induced avalanches. A monostable trigger circuit eliminates the influence of avalanche peak jitter, and a dead time modulation feedback control circuit decreases the afterpulsing. From performance tests we find that at the optimum operation point, the quantum efficiency is 12% and the dark count rate 1.5 × 10-6 ns-1, with a detection rate of 500 kHz.
13. Purification of a single photon nonlinearity
CERN Document Server
Snijders, H; Norman, J; Bakker, M P; Gossard, A; Bowers, J E; van Exter, M P; Bouwmeester, D; Löffler, W
2016-01-01
We show that the lifetime-reduced fidelity of a semiconductor quantum dot-cavity single photon nonlinearity can be restored by polarization pre- and postselection. This is realized with a polarization degenerate microcavity in the weak coupling regime, where an output polarizer enables quantum interference of the two orthogonally polarized transmission amplitudes. This allows us to transform incident coherent light into a stream of strongly correlated photons with a second-order correlation function of g2(0)~40, larger than previous experimental results even in the strong-coupling regime. This purification technique might also be useful to improve the fidelity of quantum dot based logic gates.
14. Diamond-based single-photon emitters
International Nuclear Information System (INIS)
The exploitation of emerging quantum technologies requires efficient fabrication of key building blocks. Sources of single photons are extremely important across many applications as they can serve as vectors for quantum information-thereby allowing long-range (perhaps even global-scale) quantum states to be made and manipulated for tasks such as quantum communication or distributed quantum computation. At the single-emitter level, quantum sources also afford new possibilities in terms of nanoscopy and bio-marking. Color centers in diamond are prominent candidates to generate and manipulate quantum states of light, as they are a photostable solid-state source of single photons at room temperature. In this review, we discuss the state of the art of diamond-based single-photon emitters and highlight their fabrication methodologies. We present the experimental techniques used to characterize the quantum emitters and discuss their photophysical properties. We outline a number of applications including quantum key distribution, bio-marking and sub-diffraction imaging, where diamond-based single emitters are playing a crucial role. We conclude with a discussion of the main challenges and perspectives for employing diamond emitters in quantum information processing.
15. Single-Photon Technologies Based on Quantum-Dots in Photonic Crystals
DEFF Research Database (Denmark)
Lehmann, Tau Bernstorff
In this thesis, the application of semiconductor quantum-dots in photonic crystals is explored as aresource for single-photon technology.Two platforms based on photonic crystals, a cavity and a waveguide, are examined as platformssingle-photon sources. Both platforms demonstrate strong single-photon...... purity under quasi-resonantexcitation. Furthermore the waveguide based platform demonstrates indistinguishable single-photonsat timescales up to 13 ns.A setup for active demultiplexing of single-photons to a three-fold single-photon state is proposed.Using a fast electro-optical modulator, single-photons...... from a quantum-dot are routed on timescalesof the exciton lifetime. Using active demultiplexing a three-fold single-photon state is generated at anextracted rate of 2:03 ±0:49 Hz.An on-chip power divider integrated with a quantum-dot is investigated. Correlation measurementof the photon statistic...
16. Atomic metasurfaces for manipulation of single photons
CERN Document Server
Zhou, Ming; Kats, Mikhail; Yu, Zongfu
2016-01-01
Metasurfaces are an emerging platform for the manipulation of light on a two-dimensional plane. Existing metasurfaces comprise arrays of optical resonators such as plasmonic antennas or high-index nanoparticles. In this letter, we describe a new type of metasurface based on electronic transitions in two-level systems (TLSs). Specifically, we investigated a sheet of rubidium (Rb) atoms, whose energy levels can be tuned with structured illumination from a control laser, which enables dynamically tunable single-photon steering. These metasurface elements are lossless and orders of magnitude smaller than conventional optical resonators, which allows for the overlapping of multiple metasurfaces in a single plane, enabling multi-band operation. We demonstrate that atomic metasurfaces can be passive optical elements, and can also be utilized for beaming of spontaneously emitted photons. Though conceptually similar to conventional metasurfaces, the use of TLSs, which are inherently Fermionic, will lead to numerous ne...
17. T-shaped single-photon router.
Science.gov (United States)
Lu, Jing; Wang, Z H; Zhou, Lan
2015-09-01
We study the transport properties of a single photon scattered by a two-level system (TLS) in a T-shaped waveguide, which is made of two coupled-resonator waveguides (CRWs)- an infinite CRW and a semi-infinite CRW. The spontaneous emission of the TLS directs single photons from one CRW to the other. Although the transfer rate is different for the wave incident from different CRWs, due to the boundary breaking the translational symmetry, the boundary can enhance the transfer rate found in Phys. Rev. Lett. 111, 103604 (2013) and Phys. Rev. A 89, 013805 (2014), as the transfer rate could be unity for the wave incident from the semi-infinite CRW. PMID:26368401
18. Advantages of gated silicon single photon detectors
Science.gov (United States)
Legré, Matthieu; Lunghi, Tommaso; Stucki, Damien; Zbinden, Hugo
2013-05-01
We present gated silicon single photon detectors based on two commercially available avalanche photodiodes (APDs) and one customised APD from ID Quantique SA. This customised APD is used in a commercially available device called id110. A brief comparison of the two commercial APDs is presented. Then, the charge persistence effect of all of those detectors that occurs just after a strong illumination is shown and discussed.
19. Noiseless Conditional Teleportation of a Single Photon.
Science.gov (United States)
Fuwa, Maria; Toba, Shunsuke; Takeda, Shuntaro; Marek, Petr; Mišta, Ladislav; Filip, Radim; van Loock, Peter; Yoshikawa, Jun-Ichi; Furusawa, Akira
2014-11-28
We experimentally demonstrate the noiseless teleportation of a single photon by conditioning on quadrature Bell measurement results near the origin in phase space and thereby circumventing the photon loss that otherwise occurs even in optimal gain-tuned continuous-variable quantum teleportation. In general, thanks to this loss suppression, the noiseless conditional teleportation can preserve the negativity of the Wigner function for an arbitrary pure input state and an arbitrary pure entangled resource state. In our experiment, the positive value of the Wigner function at the origin for the unconditional output state, W(0,0)=0.015±0.001, becomes clearly negative after conditioning, W(0,0)=-0.025±0.005, illustrating the advantage of noiseless conditional teleportation. PMID:25494071
20. On Chip Manipulation of Single Photons from a Diamond Defect
CERN Document Server
Kennard, J E; Marseglia, L; Aharonovich, I; Castelletto, S; Patton, B R; Politi, A; Matthews, J C F; Sinclair, A G; Gibson, B C; Prawer, S; Rarity, J G; O'Brien, J L
2013-01-01
Operating reconfigurable quantum circuits with single photon sources is a key goal of photonic quantum information science and technology. We use an integrated waveguide device comprising of directional couplers and a reconfigurable thermal phase controller to manipulate single photons emitted from a chromium related colour centre in diamond. Observation of both a wave-like interference pattern and particle-like sub-Poissionian autocorrelation functions demonstrates coherent manipulation of single photons emitted from the chromium related centre and verifies wave particle duality.
1. Efficacy of a single sequence of intermittent bright light pulses for delaying circadian phase in humans. : Phase delaying efficacy of intermittent bright light
OpenAIRE
Gronfier, Claude; Wright, Kenneth,; Kronauer, Richard,; Jewett, Megan,; Czeisler, Charles,
2004-01-01
International audience It has been shown in animal studies that exposure to brief pulses of bright light can phase shift the circadian pacemaker and that the resetting action of light is most efficient during the first minutes of light exposure. In humans, multiple consecutive days of exposure to brief bright light pulses have been shown to phase shift the circadian pacemaker. The aim of the present study was to determine whether a single sequence of brief bright light pulses administered ...
2. Limitations on building single-photon-resolution detection devices
CERN Document Server
Kok, P
2003-01-01
Single-photon resolution (SPR) detectors can tell the difference between incoming wave packets of n and n+1 photons. Such devices are especially important for linear optical quantum computing with projective measurements. However, in this paper I show that it is impossible to construct a photodetector with single-photon resolution when we are restricted to single-photon sources, linear optical elements and projective measurements with standard (non-photon-number discriminating) photodetectors. These devices include SPR detectors that sometimes fail to distinguish one- and two-photon inputs, but at the same time indicate this failure.
Institute of Scientific and Technical Information of China (English)
TAN Yong-Gang; CAI Qing-Yu; SHI Ting-Yun
2007-01-01
@@ Using the single-photon nonlocality, we propose a quantum novel overloading cryptography scheme, in which a single photon carries two bits information in one-way quantum channel. Two commutative modes of the single photon, the polarization mode and the spatial mode, are used to encode secret information. Strict time windows are set to detect the impersonation attack. The spatial mode which denotes the existence of photons is noncommutative with the phase of the photon, so that our scheme is secure against photon-number-splitting attack. Our protocol may be secure against individual attack.
4. Single-photon absorber based on strongly interacting Rydberg atoms
CERN Document Server
Tresp, Christoph; Mirgorodskiy, Ivan; Gorniaczyk, Hannes; Paris-Mandoki, Asaf; Hofferberth, Sebastian
2016-01-01
Removing exactly one photon from an arbitrary input pulse is an elementary operation in quantum optics and enables applications in quantum information processing and quantum simulation. Here we demonstrate a deterministic single-photon absorber based on the saturation of an optically thick free-space medium by a single photon due to Rydberg blockade. Single-photon subtraction adds a new component to the Rydberg quantum optics toolbox, which already contains photonic logic building-blocks such as single-photon sources, switches, transistors, and conditional $\\pi$-phase shifts. Our approach is scalable to multiple cascaded absorbers, essential for preparation of non-classical light states for quantum information and metrology applications, and, in combination with the single-photon transistor, high-fidelity number-resolved photon detection.
5. A search for single photons at PETRA
International Nuclear Information System (INIS)
A search for single photons, produced in e+e- collisions together with particles interacting only weakly with matter, has been performed using the CELLO detector operating at the PETRA storage ring. From the absence of any signal, an upper limit is set at 15 (90% CL) on the number of light neutrino species, and lower limits on various supersymmetric particle masses are derived. For massless photinos, mass degenerate scalar partners of the left- and right-handed electrons are excluded below 37.7 GeV/c2 (90% CL). (orig.)
6. Single-photon imaging in complementary metal oxide semiconductor processes
NARCIS (Netherlands)
Charbon, E.
2014-01-01
This paper describes the basics of single-photon counting in complementary metal oxide semiconductors, through single-photon avalanche diodes (SPADs), and the making of miniaturized pixels with photon-counting capability based on SPADs. Some applications, which may take advantage of SPAD image senso
7. Single-photon source engineering using a Modal Method
DEFF Research Database (Denmark)
Gregersen, Niels
Solid-state sources of single indistinguishable photons are of great interest for quantum information applications. The semiconductor quantum dot embedded in a host material represents an attractive platform to realize such a single-photon source (SPS). A near-unity efficiency, defined as the num...... photonic nanowire SPSs...
8. Single-photon indistinguishability: influence of phonons
DEFF Research Database (Denmark)
Nielsen, Per Kær; Lodahl, Peter; Jauho, Antti-Pekka;
2012-01-01
indistinguishability, absent in the approximate theories. The maximum arises due to virtual processes in the highly non-Markovian short-time regime, which dominate the decoherence for small QD-cavity coupling, and phonon-mediated real transitions between the upper and lower polariton branches in the long-time regime......Recent years have demonstrated that the interaction with phonons plays an important role in semiconductor based cavity QED systems [2], consisting of a quantum dot (QD) coupled to a single cavity mode [Fig. 1(a)], where the phonon interaction is the main decoherence mechanism. Avoiding decoherence...... effects is important in linear optical quantum computing [1], where a device emitting fully coherent indistinguishable single photons on demand, is the essential ingredient. In this contribution we present a numerically exact simulation of the effect of phonons on the degree of indistinguishability of...
9. Higgs boson decays into single photon plus unparticle
International Nuclear Information System (INIS)
The decay of the standard model Higgs boson into a single photon and a vector unparticle through a one-loop process is studied. For an intermediate-mass Higgs boson, this single photon plus unparticle mode can have a branching ratio comparable with the two-photon discovery mode. The emitted photon has a continuous energy spectrum encoding the nature of the recoil unparticle. It can be measured in precision studies of the Higgs boson after its discovery.
10. Quantum Logic with Cavity Photons From Single Atoms
Science.gov (United States)
Holleczek, Annemarie; Barter, Oliver; Rubenok, Allison; Dilley, Jerome; Nisbet-Jones, Peter B. R.; Langfahl-Klabes, Gunnar; Marshall, Graham D.; Sparrow, Chris; O'Brien, Jeremy L.; Poulios, Konstantinos; Kuhn, Axel; Matthews, Jonathan C. F.
2016-07-01
We demonstrate quantum logic using narrow linewidth photons that are produced with an a priori nonprobabilistic scheme from a single 87Rb atom strongly coupled to a high-finesse cavity. We use a controlled-not gate integrated into a photonic chip to entangle these photons, and we observe nonclassical correlations between photon detection events separated by periods exceeding the travel time across the chip by 3 orders of magnitude. This enables quantum technology that will use the properties of both narrow-band single photon sources and integrated quantum photonics.
11. Generation and Detection of Infrared Single Photons and their Applications
Institute of Scientific and Technical Information of China (English)
ZENG He-ping; WU Guang; WU E; PAN Hai-feng; ZHOU Chun-yuan; WU E.,F.Treussart; J.-F.Roch
2006-01-01
Unbreakable secret communication has been a dream from ancient time.It is quantum physics that gives us hope to turn this wizardly dream into reality.The rapid development of quantum cryptography may put an end to the history of eavesdropping.This will be largely due to the advanced techniques related to single quanta,especially infrared single photons.In this paper,we report on our research works on single-photon control for quantum cryptography,ranging from single-photon generation to single-photon detection and their applications.
12. Spontaneous two photon emission from a single quantum dot
CERN Document Server
Ota, Y; Kumagai, N; Arakawa, Y
2011-01-01
Spontaneous two photon emission from a solid-state single quantum emitter is observed. We investigated photoluminescence from the neutral biexciton in a single semiconductor quantum dot coupled with a high Q photonic crystal nanocavity. When the cavity is resonant to the half energy of the biexciton, the strong vacuum field in the cavity inspires the biexciton to simultaneously emit two photons into the mode, resulting in clear emission enhancement of the mode. Meanwhile, suppression was observed of other single photon emission from the biexciton, as the two photon emission process becomes faster than the others at the resonance.
13. A universal setup for active control of a single-photon detector
Energy Technology Data Exchange (ETDEWEB)
Liu, Qin; Skaar, Johannes [Department of Electronics and Telecommunications, Norwegian University of Science and Technology, NO-7491 Trondheim (Norway); Lamas-Linares, Antía; Kurtsiefer, Christian [Centre for Quantum Technologies and Department of Physics, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Makarov, Vadim, E-mail: [email protected] [Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1 (Canada); Gerhardt, Ilja, E-mail: [email protected] [Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart (Germany)
2014-01-15
The influence of bright light on a single-photon detector has been described in a number of recent publications. The impact on quantum key distribution (QKD) is important, and several hacking experiments have been tailored to fully control single-photon detectors. Special attention has been given to avoid introducing further errors into a QKD system. We describe the design and technical details of an apparatus which allows to attack a quantum-cryptographic connection. This device is capable of controlling free-space and fiber-based systems and of minimizing unwanted clicks in the system. With different control diagrams, we are able to achieve a different level of control. The control was initially targeted to the systems using BB84 protocol, with polarization encoding and basis switching using beamsplitters, but could be extended to other types of systems. We further outline how to characterize the quality of active control of single-photon detectors.
14. Low emittance pion beams generation from bright photons and relativistic protons
CERN Document Server
Serafini, L; Petrillo, V
2015-01-01
Present availability of high brilliance photon beams as those produced by X-ray Free Electron Lasers in combination with intense TeV proton beams typical of the Large Hadron Collider makes it possible to conceive the generation of pion beams via photo-production in a highly relativistic Lorentz boosted frame: the main advantage is the low emittance attainable and a TeV-class energy for the generated pions, that may be an interesting option for the production of low emittance muon and neutrino beams. We will describe the kinematics of the two classes of dominant events, i.e. the pion photo-production and the electron/positron pair production, neglecting other small cross-section possible events like Compton and muon pair production. Based on the phase space distributions of the pion and muon beams we will analyze the pion beam brightness achievable in three examples, based on advanced high efficiency high repetition rate FELs coupled to LHC or Future Circular Collider (FCC) proton beams, together with the stud...
15. Controllable single photon stimulation of retinal rod cells
CERN Document Server
Phan, Nam Mai; Bessarab, Dmitri A; Krivitsky, Leonid A
2013-01-01
Retinal rod cells are commonly assumed to be sensitive to single photons [1, 2, 3]. Light sources used in prior experiments exhibit unavoidable fluctuations in the number of emitted photons [4]. This leaves doubt about the exact number of photons used to stimulate the rod cell. In this letter, we interface rod cells of Xenopus laevis with a light source based on Spontaneous Parametric Down Conversion (SPDC) [5], which provides one photon at a time. Precise control of generation of single photons and directional delivery enables us to provide unambiguous proof of single photon sensitivity of rod cells without relying on the statistical assumptions. Quantum correlations between single photons in the SPDC enable us to determine quantum efficiency of the rod cell without pre-calibrated reference detectors [6, 7, 8]. These results provide the path for exploiting resources offered by quantum optics in generation and manipulation of light in visual studies. From a more general perspective, this method offers the ult...
16. A Versatile Source of Single Photons for Quantum Information Processing
CERN Document Server
Förtsch, Michael; Wittmann, Christoffer; Strekalov, Dmitry; Aiello, Andrea; Chekhova, Maria V; Silberhorn, Christine; Leuchs, Gerd; Marquardt, Christoph
2012-01-01
The quantum state of a single photon stands amongst the most fundamental and intriguing manifestations of quantum physics. At the same time single photons and pairs of single photons are important building blocks in the fields of linear optical based quantum computation and quantum repeater infrastructure. These fields possess enormous potential and much scientific and technological progress has been made in developing individual components, like quantum memories and photon sources using various physical implementations. However, further progress suffers from the lack of compatibility between these different components. Ultimately, one aims for a versatile source of single photons and photon pairs in order to overcome this hurdle of incompatibility. Such a photon source should allow for tuning of the spectral properties (wide wavelength range and narrow bandwidth) to address different implementations while retaining high efficiency. In addition, it should be able to bridge different wavelength regimes to make...
17. Circuit electromechanics with single photon strong coupling
International Nuclear Information System (INIS)
In circuit electromechanics, the coupling strength is usually very small. Here, replacing the capacitor in circuit electromechanics by a superconducting flux qubit, we show that the coupling among the qubit and the two resonators can induce effective electromechanical coupling which can attain the strong coupling regime at the single photon level with feasible experimental parameters. We use dispersive couplings among two resonators and the qubit while the qubit is also driven by an external classical field. These couplings form a three-wave mixing configuration among the three elements where the qubit degree of freedom can be adiabatically eliminated, and thus results in the enhanced coupling between the two resonators. Therefore, our work constitutes the first step towards studying quantum nonlinear effect in circuit electromechanics
18. Circuit electromechanics with single photon strong coupling
Energy Technology Data Exchange (ETDEWEB)
Xue, Zheng-Yuan, E-mail: [email protected]; Yang, Li-Na [Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006 (China); Zhou, Jian, E-mail: [email protected] [Department of Electronic Communication Engineering, Anhui Xinhua University, Hefei 230088 (China); Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006 (China)
2015-07-13
In circuit electromechanics, the coupling strength is usually very small. Here, replacing the capacitor in circuit electromechanics by a superconducting flux qubit, we show that the coupling among the qubit and the two resonators can induce effective electromechanical coupling which can attain the strong coupling regime at the single photon level with feasible experimental parameters. We use dispersive couplings among two resonators and the qubit while the qubit is also driven by an external classical field. These couplings form a three-wave mixing configuration among the three elements where the qubit degree of freedom can be adiabatically eliminated, and thus results in the enhanced coupling between the two resonators. Therefore, our work constitutes the first step towards studying quantum nonlinear effect in circuit electromechanics.
19. Experimental generation of single photons via active multiplexing
International Nuclear Information System (INIS)
An on-demand single-photon source is a fundamental building block in quantum science and technology. We experimentally demonstrate the proof of concept for a scheme to generate on-demand single photons via actively multiplexing several heralded photons probabilistically produced from pulsed spontaneous parametric down-conversions (SPDCs). By utilizing a four-photon-pair source, an active feed-forward technique, and an ultrafast single-photon router, we show a fourfold enhancement of the output photon rate. Simultaneously, we maintain the quality of the output single-photon states, confirmed by correlation measurements. We also experimentally verify, via Hong-Ou-Mandel interference, that the router does not affect the indistinguishability of the single photons. Furthermore, we give numerical simulations, which indicate that photons based on multiplexing of four SPDC sources can outperform the heralding based on highly advanced photon-number-resolving detectors. Our results show a route for on-demand single-photon generation and the practical realization of scalable linear optical quantum-information processing.
20. Coherent single-photon absorption by single emitters coupled to 1D nanophotonic waveguides
DEFF Research Database (Denmark)
Chen, Yuntian; Wubs, Martijn; Mørk, Jesper;
2012-01-01
We have derived an efficient model that allows calculating the dynamical single-photon absorption of an emitter coupled to a waveguide. We suggest a novel and simple structure that leads to strong single-photon absorption.......We have derived an efficient model that allows calculating the dynamical single-photon absorption of an emitter coupled to a waveguide. We suggest a novel and simple structure that leads to strong single-photon absorption....
1. Combined Effects of Gain and Two-photon Absorption on Dark-bright Vector Soliton Propagation and Interaction
Directory of Open Access Journals (Sweden)
Hong Li
2014-02-01
Full Text Available Interaction as well as dynamics of the dark-bright vector solitons induced by incorporation of gain and two-photon absorption are investigated by the numerical method in a birefringent fiber. The numerical results show that the gain and the two-photon absorption may lead to the destructive effects on the soliton propagation and interaction. Their combined effects play a crucial role in the dynamics and depend strictly on the sign and magnitude of their coefficients, so the proper incorporation may reduce effectively their destructive effects. The nonlinear gain combined with the filter can be used to suppress effectively the disadvantaged effects and the stabilization mechanism is demonstrated.
2. The photonic nanowire: A highly efficient single-photon source
DEFF Research Database (Denmark)
Gregersen, Niels
2014-01-01
The photonic nanowire represents an attractive platform for a quantum light emitter. However, careful optical engineering using the modal method, which elegantly allows access to all relevant physical parameters, is crucial to ensure high efficiency.......The photonic nanowire represents an attractive platform for a quantum light emitter. However, careful optical engineering using the modal method, which elegantly allows access to all relevant physical parameters, is crucial to ensure high efficiency....
3. Two-order Interference of Single Photon
Institute of Scientific and Technical Information of China (English)
JIANG Yunkun; LI Jian; SHI Baosen; FAN Xiaofeng; GUO Guangcan
2000-01-01
A pair of photons called signal and idler photons, respectively, are produced through the nonlinear process of type-I spontaneous parametric downconversion in BBO crystal pumped by the second-harmonic wave of a Ti:sapphire femtosecond laser pulse. The two-order interference phenomenon of the signal photon in Michelson interferometer is observed and give an analysis in detail.
4. Electromagnetic fields, size, and copy of a single photon
CERN Document Server
Liu, Shan-Liang
2016-01-01
We propose the expressions of electromagnetic fields of a single photon which properly describe the known characteristics of a photon, derive the relations between the photon size and wavelength on basis of the expressions, reveal the differences between a photon and its copy, and give the specific expressions of annihilation and creation operators of a photon. The results show that a photon has length of half the wavelength, and its radius is proportional to square root of the wavelength; a photon and its copy have the phase difference of {\\pi} and constitute a phase-entangled state; the N-photon phase-entangled state, which is formed by the sequential stimulated emission and corresponds to the wave train in optics, is not a coherent state, but it is the eigenstate of the number operator of photons.
5. Extremely High Brightness from Polymer-Encapsulated Quantum Dots for Two-photon Cellular and Deep-tissue Imaging
OpenAIRE
Fan, Yanyan; Liu, Helin; Han, Rongcheng; Huang, Lu; Shi, Hao; Sha, Yinlin; Jiang, Yuqiang
2015-01-01
Materials possessing high two photon absorption (TPA) are highly desirable for a range of fields, such as three-dimensional data storage, TP microscopy (TPM) and photodynamic therapy (PDT). Specifically, for TPM, high TP excitation (TPE) brightness (σ × ϕ, where σ is TPA cross-sections and ϕ is fluorescence quantum yield), excellent photostability and minimal cytotoxicity are highly desirable. However, when TPA materials are transferred to aqueous media through molecule engineering or nanopar...
6. The mystery of spectral breaks: Lyman continuum absorption by photon-photon pair production in the Fermi GeV spectra of bright blazars
International Nuclear Information System (INIS)
We re-analyze Fermi/LAT γ-ray spectra of bright blazars using the new Pass 7 version of the detector response files and detect breaks at ∼5 GeV in the rest-frame spectra of 3C 454.3 and possibly also 4C +21.35, associated with the photon-photon pair production absorption by the He II Lyman continuum (LyC). We also detect significant breaks at ∼20 GeV associated with hydrogen LyC in both the individual spectra and the stacked redshift-corrected spectrum of several bright blazars. The detected breaks in the stacked spectra univocally prove that they are associated with atomic ultraviolet emission features of the quasar broad-line region (BLR). The dominance of the absorption by the hydrogen Ly complex over He II, a small detected optical depth, and break energy consistent with head-on collisions with LyC photons imply that the γ-ray emission site is located within the BLR, but most of the BLR emission comes from a flat disk-like structure producing little opacity. Alternatively, the LyC emission region size might be larger than the BLR size measured from reverberation mapping, and/or the γ-ray emitting region is extended. These solutions would resolve the long-standing issue of how the multi-hundred GeV photons can escape from the emission zone without being absorbed by softer photons.
7. Interferometric Quantum-Nondemolition Single-Photon Detectors
Science.gov (United States)
Kok, Peter; Lee, Hwang; Dowling, Jonathan
2007-01-01
Two interferometric quantum-nondemolition (QND) devices have been proposed: (1) a polarization-independent device and (2) a polarization-preserving device. The prolarization-independent device works on an input state of up to two photons, whereas the polarization-preserving device works on a superposition of vacuum and single- photon states. The overall function of the device would be to probabilistically generate a unique detector output only when its input electromagnetic mode was populated by a single photon, in which case its output mode would also be populated by a single photon. Like other QND devices, the proposed devices are potentially useful for a variety of applications, including such areas of NASA interest as quantum computing, quantum communication, detection of gravity waves, as well as pedagogical demonstrations of the quantum nature of light. Many protocols in quantum computation and quantum communication require the possibility of detecting a photon without destroying it. The only prior single- photon-detecting QND device is based on quantum electrodynamics in a resonant cavity and, as such, it depends on the photon frequency. Moreover, the prior device can distinguish only between one photon and no photon. The proposed interferometric QND devices would not depend on frequency and could distinguish between (a) one photon and (b) zero or two photons. The first proposed device is depicted schematically in Figure 1. The input electromagnetic mode would be a superposition of a zero-, a one-, and a two-photon quantum state. The overall function of the device would be to probabilistically generate a unique detector output only when its input electromagnetic mode was populated by a single photon, in which case its output mode also would be populated by a single photon.
8. Direct fiber-coupled single photon source based on a photonic crystal waveguide
International Nuclear Information System (INIS)
A single photon source plays a key role in quantum applications such as quantum computers and quantum communications. Epitaxially grown quantum dots are one of the promising platforms to implement a good single photon source. However, it is challenging to realize an efficient single photon source based on semiconductor materials due to their high refractive index. Here we demonstrate a direct fiber coupled single photon source with high collection efficiency by employing a photonic crystal (PhC) waveguide and a tapered micro-fiber. To confirm the single photon nature, the second-order correlation function g(2)(τ) is measured with a Hanbury Brown-Twiss setup. The measured g(2)(0) value is 0.15, and we can estimate 24% direct collection efficiency from a quantum dot to the fiber
9. Direct fiber-coupled single photon source based on a photonic crystal waveguide
Energy Technology Data Exchange (ETDEWEB)
Ahn, Byeong-Hyeon, E-mail: [email protected]; Lee, Chang-Min; Lim, Hee-Jin [Department of Physics, KAIST, Daejeon 305-701 (Korea, Republic of); Schlereth, Thomas W.; Kamp, Martin [Technische Physik, Physikalisches Institut and Wilhelm Conrad Röntgen-Center for Complex Material Systems, Universität Würzburg, Am Hubland, D-97074 Würzburg (Germany); Höfling, Sven [Technische Physik, Physikalisches Institut and Wilhelm Conrad Röntgen-Center for Complex Material Systems, Universität Würzburg, Am Hubland, D-97074 Würzburg (Germany); SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS (United Kingdom); Lee, Yong-Hee [Department of Physics, KAIST, Daejeon 305-701 (Korea, Republic of); Graduate School of Nanoscience and Technology (WCU), KAIST, Daejeon 305-701 (Korea, Republic of)
2015-08-24
A single photon source plays a key role in quantum applications such as quantum computers and quantum communications. Epitaxially grown quantum dots are one of the promising platforms to implement a good single photon source. However, it is challenging to realize an efficient single photon source based on semiconductor materials due to their high refractive index. Here we demonstrate a direct fiber coupled single photon source with high collection efficiency by employing a photonic crystal (PhC) waveguide and a tapered micro-fiber. To confirm the single photon nature, the second-order correlation function g{sup (2)}(τ) is measured with a Hanbury Brown-Twiss setup. The measured g{sup (2)}(0) value is 0.15, and we can estimate 24% direct collection efficiency from a quantum dot to the fiber.
10. Quasi-secure quantum dialogue using single photons
Institute of Scientific and Technical Information of China (English)
2007-01-01
A quasi-secure quantum dialogue protocol using single photons was proposed. Different from the previous entanglement-based protocols, the present protocol uses batches of single photons which run back and forth between the two parties. A round run for each photon makes the two parties each obtain a classical bit of information. So the efficiency of information transmission can be increased. The present scheme is practical and well within the present-day technology.
11. Single pairs of time-bin entangled photons
CERN Document Server
Versteegh, Marijn A M; Berg, Aafke A van den; Juska, Gediminas; Dimastrodonato, Valeria; Gocalinska, Agnieszka; Pelucchi, Emanuele; Zwiller, Val
2015-01-01
Time-bin entangled photons are ideal for long-distance quantum communication via optical fibers. Here we present a source where, even at high creation rates, each excitation pulse generates at most one time-bin entangled pair. This is important for the accuracy and security of quantum communication. Our site-controlled quantum dot generates single polarization-entangled photon pairs, which are then converted, without loss of entanglement strength, into single time-bin entangled photon pairs.
12. All-Optical Routing of Single Photons by a One-Atom Switch Controlled by a Single Photon
CERN Document Server
Shomroni, Itay; Lovsky, Yulia; Bechler, Orel; Guendelman, Gabriel; Dayan, Barak
2014-01-01
The prospect of quantum networks, in which quantum information is carried by single photons in photonic circuits, has long been the driving force behind the effort to achieve all-optical routing of single photons. Here we realize the most basic unit of such a photonic circuit: a single-photon activated switch, capable of routing a photon from any of its two inputs to any of its two outputs. Our device is based on a single 87Rb atom coupled to a fiber-coupled, chip-based microresonator, and is completely all-optical, requiring no other fields beside the in-fiber single-photon pulses. Nonclassical statistics of the control pulse confirm that a single reflected photon toggles the switch from high reflection (65%) to high transmission (90%), with average of ~1.5 control photons per switching event (~3 including linear losses). The fact that the control and target photons are both in-fiber and practically identical makes this scheme compatible with scalable architectures for quantum information processing.
13. High-efficiency WSi superconducting nanowire single-photon detectors for quantum state engineering in the near infrared
CERN Document Server
Jeannic, H Le; Cavaillès, A; Marsili, F; Shaw, M D; Huang, K; Morin, O; Nam, S W; Laurat, J
2016-01-01
We report on high-efficiency superconducting nanowire single-photon detectors based on amorphous WSi and optimized at 1064 nm. At an operating temperature of 1.8 K, we demonstrated a 93% system detection efficiency at this wavelength with a dark noise of a few counts per second. Combined with cavity-enhanced spontaneous parametric down-conversion, this fiber-coupled detector enabled us to generate narrowband single photons with a heralding efficiency greater than 90% and a high spectral brightness of $0.6\\times10^4$ photons/(s$\\cdot$mW$\\cdot$MHz). Beyond single-photon generation at large rate, such high-efficiency detectors open the path to efficient multiple-photon heralding and complex quantum state engineering.
14. Quantum Communication with Continuum Single-Photon Pulses
OpenAIRE
Rios, F. F. S.; Ramos, R. V.
2014-01-01
In this work, we analyze the behavior of continuum single-photon pulses in some quantum communication schemes. In particular, we consider the single-photon interference in a Mach-Zenhder interferometer, the HOM interference and the quantum bit commitment protocol.
15. Quantum dot single-photon switches of resonant tunneling current for discriminating-photon-number detection
OpenAIRE
Qianchun Weng; Zhenghua An; Bo Zhang; Pingping Chen; Xiaoshuang Chen; Ziqiang Zhu; Wei Lu
2015-01-01
Low-noise single-photon detectors that can resolve photon numbers are used to monitor the operation of quantum gates in linear-optical quantum computation. Exactly 0, 1 or 2 photons registered in a detector should be distinguished especially in long-distance quantum communication and quantum computation. Here we demonstrate a photon-number-resolving detector based on quantum dot coupled resonant tunneling diodes (QD-cRTD). Individual quantum-dots (QDs) coupled closely with adjacent quantum we...
16. On improving single photon sources via linear optics and photodetection
CERN Document Server
Berry, D W; Sanders, B C; Knight, P L; Berry, Dominic W.; Scheel, Stefan; Sanders, Barry C.; Knight, Peter L.
2004-01-01
In practice, single photons are generated as a mixture of vacuum with a single photon with weights 1-p and p, respectively; here we are concerned with increasing p by directing multiple copies of the single photon-vacuum mixture into a linear optic device and applying photodetection on some outputs to conditionally prepare single photon states with larger p. We prove that it is impossible, under certain conditions, to increase p via linear optics and conditional preparation based on photodetection, and we also establish a class of photodetection events for which p can be improved. In addition we prove that it is not possible to obtain perfect (p=1) single photon states via this method from imperfect (p<1) inputs.
17. Telecom-heralded single-photon absorption by a single atom
Science.gov (United States)
Lenhard, Andreas; Bock, Matthias; Becher, Christoph; Kucera, Stephan; Brito, José; Eich, Pascal; Müller, Philipp; Eschner, Jürgen
2015-12-01
We present, characterize, and apply the architecture of a photonic quantum interface between the near infrared and telecom spectral regions. A singly resonant optical parametric oscillator (OPO) operated below threshold, in combination with external filters, generates high-rate (>2.5 ×106s-1 ) narrowband photon pairs (˜7 MHz bandwidth); the signal photons are tuned to resonance with an atomic transition in Ca+, while the idler photons are at telecom wavelength. Interface operation is demonstrated through high-rate absorption of single photons by a single trapped ion (˜670 s-1 ), heralded by coincident telecom photons.
18. Single photon emission computed tomography (SPECT)
International Nuclear Information System (INIS)
The functional state of organs can be imaged by their accumulation of single photon emitter like 99mTc (γ-ray energy 140 keV), 201Tl (73 keV) and 201I (159 keV) with computed tomography. The emitted γ-ray is collimated to reach the NaI (Tl) detector for specifying its direction, which is called as the scintillation camera or gamma camera. The camera rotating around the patient gives the SPECT images. The NaI (Tl) detector is suitable for converting 60-300 keV γ-ray to fluorescence through the photoelectric effect. Photomultiplier receiving the fluorescence outputs X/Y signals for the emitting position and Z signal (energy) separately, giving imaging data. 3D images can be re-constructed by either method of the filtered back projection or maximum likelihood-expectation maximization. For quantitative reconstruction, correction of γ-ray absorption in water, of scattering and of collimator opening is necessary. Recently, semiconductor-detectors like CdZnTe and CdTe are being utilized in place of NaI for better resolution, which will reduce the size of the camera. Further, a camera with coincidence circuit for positron has appeared and will be applicable for both SPECT and PET. Compton camera having 2-step detectors without collimator is now under development. (N.I.)
19. A stable, single-photon emitter in a thin organic crystal for application to quantum-photonic devices
CERN Document Server
Polisseni, Claudio; Boissier, Sebastien; Grandi, Samuele; Clark, Alex S; Hinds, E A
2016-01-01
Single organic molecules offer great promise as bright, reliable sources of identical single photons on demand, capable of integration into solid-state devices. It has been proposed that such molecules in a crystalline organic matrix might be placed close to an optical waveguide for this purpose, but so far there have been no demonstrations of sufficiently thin crystals, with a controlled concentration of suitable dopant molecules. Here we present a method for growing very thin anthracene crystals from super-saturated vapour, which produces crystals of extreme flatness and controlled thickness. We show how this crystal can be doped with a widely adjustable concentration of dibenzoterrylene (DBT) molecules and we examine the optical properties of these molecules to demonstrate their suitability as quantum emitters in nanophotonic devices. Our measurements show that the molecules are available in the crystal as single quantum emitters, with a well-defined polarisation relative to the crystal axes, making them a...
20. Single photon laser altimeter data processing, analysis and experimental validation
Science.gov (United States)
Vacek, Michael; Peca, Marek; Michalek, Vojtech; Prochazka, Ivan
2015-10-01
Spaceborne laser altimeters are common instruments on-board the rendezvous spacecraft. This manuscript deals with the altimeters using a single photon approach, which belongs to the family of time-of-flight range measurements. Moreover, the single photon receiver part of the altimeter may be utilized as an Earth-to-spacecraft link enabling one-way ranging, time transfer and data transfer. The single photon altimeters evaluate actual altitude through the repetitive detections of single photons of the reflected laser pulses. We propose the single photon altimeter signal processing and data mining algorithm based on the Poisson statistic filter (histogram method) and the modified Kalman filter, providing all common altimetry products (altitude, slope, background photon flux and albedo). The Kalman filter is extended for the background noise filtering, the varying slope adaptation and the non-causal extension for an abrupt slope change. Moreover, the algorithm partially removes the major drawback of a single photon altitude reading, namely that the photon detection measurement statistics must be gathered. The developed algorithm deduces the actual altitude on the basis of a single photon detection; thus, being optimal in the sense that each detected signal photon carrying altitude information is tracked and no altitude information is lost. The algorithm was tested on the simulated datasets and partially cross-probed with the experimental data collected using the developed single photon altimeter breadboard based on the microchip laser with the pulse energy on the order of microjoule and the repetition rate of several kilohertz. We demonstrated that such an altimeter configuration may be utilized for landing or hovering a small body (asteroid, comet).
1. The mystery of spectral breaks: Lyman continuum absorption by photon-photon pair production in the Fermi GeV spectra of bright blazars
CERN Document Server
Stern, Boris E
2014-01-01
We reanalyze Fermi/LAT gamma-ray spectra of bright blazars with a higher photon statistics than in previous works and with new Pass 7 data representation. In the spectra of the brightest blazar 3C 454.3 and possibly of 4C +21.35 we detect breaks at 5 GeV (in the rest frame) associated with the photon-photon pair production absorption by He II Lyman continuum (LyC). We also detect confident breaks at 20 GeV associated with hydrogen LyC both in the individual spectra and in the stacked redshift-corrected spectrum of several bright blazars. The detected breaks in the stacked spectra univocally prove that they are associated with atomic ultraviolet emission features of the quasar broad-line region (BLR). The dominance of the absorption by hydrogen Ly complex over He II, rather small detected optical depth, and the break energy consistent with the head-on collisions with LyC photons imply that the gamma-ray emission site is located within the BLR, but most of the BLR emission comes from a flat disk-like structure ...
2. Efficient generation of single and entangled photons on a silicon photonic integrated chip
OpenAIRE
Mower, Jacob; Englund, Dirk
2011-01-01
We present a protocol for generating on-demand, indistinguishable single photons on a silicon photonic integrated chip. The source is a time-multiplexed spontaneous parametric down-conversion element that allows optimization of single-photon versus multiphoton emission while realizing high output rate and indistinguishability. We minimize both the scaling of active elements and the scaling of active element loss with multiplexing. We then discuss detection strategies and data processing to fu...
3. Room-temperature single-photon sources based on nanocrystal fluorescence in photonic/plasmonic nanostructures
Science.gov (United States)
Lukishova, S. G.; Winkler, J. M.; Bissell, L. J.; Mihaylova, D.; Liapis, Andreas C.; Shi, Z.; Goldberg, D.; Menon, V. M.; Boyd, R. W.; Chen, G.; Prasad, P.
2014-10-01
Results are presented here towards robust room-temperature SPSs based on fluorescence in nanocrystals: colloidal quantum dots, color-center diamonds and doped with trivalent rare-earth ions (TR3+). We used cholesteric chiral photonic bandgap and Bragg-reflector microcavities for single emitter fluorescence enhancement. We also developed plasmonic bowtie nanoantennas and 2D-Si-photonic bandgap microcavities. The paper also provides short outlines of other technologies for room-temperature single-photon sources.
4. A highly efficient single-photon source based on a quantum dot in a photonic nanowire
DEFF Research Database (Denmark)
Claudon, Julien; Bleuse, Joel; Malik, Nitin Singh; Bazin, Maela; Jaffrennou, Perine; Gregersen, Niels; Sauvan, Christophe; Lalanne, Philippe; Gerard, Jean-Michel
2010-01-01
The development of efficient solid-state sources of single photons is a major challenge in the context of quantum communication,optical quantum information processing and metrology1. Such a source must enable the implementation of a stable, single-photon emitter, like a colour centre in diamond2...
5. Coherent single-photon absorption by single emitters coupled to one-dimensional nanophotonic waveguides
DEFF Research Database (Denmark)
Chen, Yuntian; Wubs, Martijn; Mørk, Jesper; Koenderink, A. Femius
2011-01-01
We study the dynamics of single-photon absorption by a single emitter coupled to a one-dimensional waveguide that simultaneously provides channels for spontaneous emission (SE) decay and a channel for the input photon. We have developed a time-dependent theory that allows us to specify any input ...... can be improved by a further 4% by engineering the dispersion. Efficient single-photon absorption by a single emitter has potential applications in quantum communication and quantum computation....
6. Engineering single photon emitters by ion implantation in diamond
OpenAIRE
Naydenov, B.; Kolesov, R.; Batalov, A.; Meijer, J; Pezzagna, S.; Rogalla, D.; Jelezko, F.; Wrachtrup, J.
2009-01-01
Diamond provides unique technological platform for quantum technologies including quantum computing and communication. Controlled fabrication of optically active defects is a key element for such quantum toolkit. Here we report the production of single color centers emitting in the blue spectral region by high energy implantation of carbon ions. We demonstrate that single implanted defects show sub-poissonian statistics of the emitted photons and can be explored as single photon source in qua...
7. Single photon, spin, and charge manipulation of diamond quantum register
International Nuclear Information System (INIS)
Single-photon sources that provide non-classical light states on demand have a broad range of application in quantum communication, quantum computing, and metrology. Recently, significant progresses have been shown in semiconductor quantum-dots. However, a major obstacle is the requirement of cryogenic temperatures. Here we show the realization of a stable room temperature electrically driven single-photon source based on a single NV centre in a diode structure. (author)
8. Quantum dot single-photon switches of resonant tunneling current for discriminating-photon-number detection.
Science.gov (United States)
Weng, Qianchun; An, Zhenghua; Zhang, Bo; Chen, Pingping; Chen, Xiaoshuang; Zhu, Ziqiang; Lu, Wei
2015-01-01
Low-noise single-photon detectors that can resolve photon numbers are used to monitor the operation of quantum gates in linear-optical quantum computation. Exactly 0, 1 or 2 photons registered in a detector should be distinguished especially in long-distance quantum communication and quantum computation. Here we demonstrate a photon-number-resolving detector based on quantum dot coupled resonant tunneling diodes (QD-cRTD). Individual quantum-dots (QDs) coupled closely with adjacent quantum well (QW) of resonant tunneling diode operate as photon-gated switches- which turn on (off) the RTD tunneling current when they trap photon-generated holes (recombine with injected electrons). Proposed electron-injecting operation fills electrons into coupled QDs which turn "photon-switches" to "OFF" state and make the detector ready for multiple-photons detection. With proper decision regions defined, 1-photon and 2-photon states are resolved in 4.2 K with excellent propabilities of accuracy of 90% and 98% respectively. Further, by identifying step-like photon responses, the photon-number-resolving capability is sustained to 77 K, making the detector a promising candidate for advanced quantum information applications where photon-number-states should be accurately distinguished. PMID:25797442
9. Quantum dot single-photon switches of resonant tunneling current for discriminating-photon-number detection
Science.gov (United States)
Weng, Qianchun; An, Zhenghua; Zhang, Bo; Chen, Pingping; Chen, Xiaoshuang; Zhu, Ziqiang; Lu, Wei
2015-03-01
Low-noise single-photon detectors that can resolve photon numbers are used to monitor the operation of quantum gates in linear-optical quantum computation. Exactly 0, 1 or 2 photons registered in a detector should be distinguished especially in long-distance quantum communication and quantum computation. Here we demonstrate a photon-number-resolving detector based on quantum dot coupled resonant tunneling diodes (QD-cRTD). Individual quantum-dots (QDs) coupled closely with adjacent quantum well (QW) of resonant tunneling diode operate as photon-gated switches- which turn on (off) the RTD tunneling current when they trap photon-generated holes (recombine with injected electrons). Proposed electron-injecting operation fills electrons into coupled QDs which turn photon-switches'' to OFF'' state and make the detector ready for multiple-photons detection. With proper decision regions defined, 1-photon and 2-photon states are resolved in 4.2 K with excellent propabilities of accuracy of 90% and 98% respectively. Further, by identifying step-like photon responses, the photon-number-resolving capability is sustained to 77 K, making the detector a promising candidate for advanced quantum information applications where photon-number-states should be accurately distinguished.
10. Photon-counting single-molecule spectroscopy for studying conformational dynamics and macromolecular interactions
Energy Technology Data Exchange (ETDEWEB)
Laurence, Ted Alfred
2002-07-30
Single-molecule methods have the potential to provide information about conformational dynamics and molecular interactions that cannot be obtained by other methods. Removal of ensemble averaging provides several benefits, including the ability to detect heterogeneous populations and the ability to observe asynchronous reactions. Single-molecule diffusion methodologies using fluorescence resonance energy transfer (FRET) are developed to monitor conformational dynamics while minimizing perturbations introduced by interactions between molecules and surfaces. These methods are used to perform studies of the folding of Chymotrypsin Inhibitor 2, a small, single-domain protein, and of single-stranded DNA (ssDNA) homopolymers. Confocal microscopy is used in combination with sensitive detectors to detect bursts of photons from fluorescently labeled biomolecules as they diffuse through the focal volume. These bursts are analyzed to extract fluorescence resonance energy transfer (FRET) efficiency. Advances in data acquisition and analysis techniques that are providing a more complete picture of the accessible molecular information are discussed. Photon Arrival-time Interval Distribution (PAID) analysis is a new method for monitoring macromolecular interactions by fluorescence detection with simultaneous determination of coincidence, brightness, diffusion time, and occupancy (proportional to concentration) of fluorescently-labeled molecules undergoing diffusion in a confocal detection volume. This method is based on recording the time of arrival of all detected photons, and then plotting the two-dimensional histogram of photon pairs, where one axis is the time interval between each pair of photons 1 and 2, and the second axis is the number of other photons detected in the time interval between photons 1 and 2. PAID is related to Fluorescence Correlation Spectroscopy (FCS) by a collapse of this histogram onto the time interval axis. PAID extends auto- and cross-correlation FCS
11. Photon-counting single-molecule spectroscopy for studying conformational dynamics and macromolecular interactions
International Nuclear Information System (INIS)
Single-molecule methods have the potential to provide information about conformational dynamics and molecular interactions that cannot be obtained by other methods. Removal of ensemble averaging provides several benefits, including the ability to detect heterogeneous populations and the ability to observe asynchronous reactions. Single-molecule diffusion methodologies using fluorescence resonance energy transfer (FRET) are developed to monitor conformational dynamics while minimizing perturbations introduced by interactions between molecules and surfaces. These methods are used to perform studies of the folding of Chymotrypsin Inhibitor 2, a small, single-domain protein, and of single-stranded DNA (ssDNA) homopolymers. Confocal microscopy is used in combination with sensitive detectors to detect bursts of photons from fluorescently labeled biomolecules as they diffuse through the focal volume. These bursts are analyzed to extract fluorescence resonance energy transfer (FRET) efficiency. Advances in data acquisition and analysis techniques that are providing a more complete picture of the accessible molecular information are discussed. Photon Arrival-time Interval Distribution (PAID) analysis is a new method for monitoring macromolecular interactions by fluorescence detection with simultaneous determination of coincidence, brightness, diffusion time, and occupancy (proportional to concentration) of fluorescently-labeled molecules undergoing diffusion in a confocal detection volume. This method is based on recording the time of arrival of all detected photons, and then plotting the two-dimensional histogram of photon pairs, where one axis is the time interval between each pair of photons 1 and 2, and the second axis is the number of other photons detected in the time interval between photons 1 and 2. PAID is related to Fluorescence Correlation Spectroscopy (FCS) by a collapse of this histogram onto the time interval axis. PAID extends auto- and cross-correlation FCS
12. A photon-photon quantum gate based on a single atom in an optical resonator.
Science.gov (United States)
Hacker, Bastian; Welte, Stephan; Rempe, Gerhard; Ritter, Stephan
2016-08-11
That two photons pass each other undisturbed in free space is ideal for the faithful transmission of information, but prohibits an interaction between the photons. Such an interaction is, however, required for a plethora of applications in optical quantum information processing. The long-standing challenge here is to realize a deterministic photon-photon gate, that is, a mutually controlled logic operation on the quantum states of the photons. This requires an interaction so strong that each of the two photons can shift the other's phase by π radians. For polarization qubits, this amounts to the conditional flipping of one photon's polarization to an orthogonal state. So far, only probabilistic gates based on linear optics and photon detectors have been realized, because "no known or foreseen material has an optical nonlinearity strong enough to implement this conditional phase shift''. Meanwhile, tremendous progress in the development of quantum-nonlinear systems has opened up new possibilities for single-photon experiments. Platforms range from Rydberg blockade in atomic ensembles to single-atom cavity quantum electrodynamics. Applications such as single-photon switches and transistors, two-photon gateways, nondestructive photon detectors, photon routers and nonlinear phase shifters have been demonstrated, but none of them with the ideal information carriers: optical qubits in discriminable modes. Here we use the strong light-matter coupling provided by a single atom in a high-finesse optical resonator to realize the Duan-Kimble protocol of a universal controlled phase flip (π phase shift) photon-photon quantum gate. We achieve an average gate fidelity of (76.2 ± 3.6) per cent and specifically demonstrate the capability of conditional polarization flipping as well as entanglement generation between independent input photons. This photon-photon quantum gate is a universal quantum logic element, and therefore could perform most existing two-photon operations
13. Video recording true single-photon double-slit interference
CERN Document Server
Aspden, Reuben S; Spalding, Gabriel C
2016-01-01
As normally used, no commercially available camera has a low-enough dark noise to directly produce video recordings of double-slit interference at the photon-by-photon level, because readout noise significantly contaminates or overwhelms the signal. In this work, noise levels are significantly reduced by turning on the camera only when the presence of a photon has been heralded by the arrival, at an independent detector, of a time-correlated photon produced via parametric down-conversion. This triggering scheme provides the improvement required for direct video imaging of Young's double-slit experiment with single photons, allowing clarified versions of this foundational demonstration. Further, we introduce variations on this experiment aimed at promoting discussion of the role spatial coherence plays in such a measurement. We also emphasize complementary aspects of single-photon measurement, where imaging yields (transverse) position information, while diffraction yields the transverse momentum, and highligh...
14. Controlling light emission from single-photon sources using photonic nanowires
DEFF Research Database (Denmark)
Gregersen, Niels; Chen, Yuntian; Mørk, Jesper;
2012-01-01
The photonic nanowire has recently emerged as an promising alternative to microcavity-based single-photon source designs. In this simple structure, a geometrical effect ensures a strong coupling between an embedded emitter and the optical mode of interest and a combination of tapers and mirrors are...... used to tailor the far-field emission pattern. This non-resonant approach relaxes the demands to fabrication perfection, allowing for record-high measured efficiency of fabricated nanowire single-photon sources. We review recent progress in photonic nanowire technology and present next generation...
15. QUANTUM KEY DISTRIBUTION WITH REALISTIC HERALDED SINGLE-PHOTON SOURCES
OpenAIRE
Lasota, Mikolaj; Demkowicz-Dobrzanski, Rafal; Banaszek, Konrad
2013-01-01
We analyze theoretically performance of four-state quantum key distribution protocols implemented with a realistic heralded single-photon source. The analysis assumes a noisy model for the detector heralding generation of individual photons via spontaneous parametric down-conversion, including dark counts and imperfect photon number resolution. We identify characteristics of the heralding detector that defines the attainable cryptographic key rate and the maximum secure distance. Approximate ...
16. High-Brightness Beams from a Light Source Injector The Advanced Photon Source Low-Energy Undulator Test Line Linac
CERN Document Server
Travish, G; Borland, M; Hahne, M; Harkay, K C; Lewellen, J W; Lumpkin, Alex H; Milton, S V; Sereno, N S
2000-01-01
The use of existing linacs, and in particular light source injectors, for free-electron laser (FEL) experiments is becoming more common due to the desire to test FELs at ever shorter wavelengths. The high-brightness, high-current beams required by high-gain FELs impose technical specifications that most existing linacs were not designed to meet. Moreover, the need for specialized diagnostics, especially shot-to-shot data acquisition, demands substantial modification and upgrade of conventional linacs. Improvements have been made to the Advanced Photon Source (APS) injector linac in order to produce and characterize high-brightness beams. Specifically, effort has been directed at generating beams suitable for use in the low-energy undulator test line (LEUTL) FEL in support of fourth-generation light source research. The enhancements to the linac technical and diagnostic capabilities that allowed for self-amplified spontaneous emission (SASE) operation of the FEL at 530 nm are described. Recent results, includi...
17. An integral gated mode single photon detector at telecom wavelengths
International Nuclear Information System (INIS)
We demonstrate an integral gated mode single photon detector at telecom wavelengths. The charge number of an avalanche pulse rather than the peak current is monitored for single photon detection. The transient spikes in conventional gated mode operation are cancelled completely by integrating, which enables one to effectively improve the performance of single photon detector with the same avalanche photodiode. This method achieved a detection efficiency of 29.9% at the dark count probability per gate equal to 5.57 x 10-6/gate (1.11 x 10-6 ns-1) at 1550 nm
18. Coupling of single quantum dots to a photonic crystal waveguide
DEFF Research Database (Denmark)
Lund-Hansen, Toke; Stobbe, Søren; Julsgaard, Brian; Lodahl, Peter
is coupled efficiently to a single enhanced mode. One popular approach has been to couple single quantum dots to a nanocavity but a limiting factor in this configuration is that in order to apply the photon it should subsequently be coupled out of the cavity, reducing the overall efficiency...... significantly. An alternative approach is to couple the quantum dot directly to the propagating mode of a photonic waveguide. We demonstrate the coupling of single quantum dots to a photonic crystal waveguide using time-resolved spontaneous emission measurements. A pronounced effect is seen in the decay rates...
19. Superconducting single photon detectors integrated with diamond nanophotonic circuits
CERN Document Server
Rath, Patrik; Ferrari, Simone; Sproll, Fabian; Lewes-Malandrakis, Georgia; Brink, Dietmar; Ilin, Konstantin; Siegel, Michael; Nebel, Christoph; Pernice, Wolfram
2015-01-01
Photonic quantum technologies promise to repeat the success of integrated nanophotonic circuits in non-classical applications. Using linear optical elements, quantum optical computations can be performed with integrated optical circuits and thus allow for overcoming existing limitations in terms of scalability. Besides passive optical devices for realizing photonic quantum gates, active elements such as single photon sources and single photon detectors are essential ingredients for future optical quantum circuits. Material systems which allow for the monolithic integration of all components are particularly attractive, including III-V semiconductors, silicon and also diamond. Here we demonstrate nanophotonic integrated circuits made from high quality polycrystalline diamond thin films in combination with on-chip single photon detectors. Using superconducting nanowires coupled evanescently to travelling waves we achieve high detection efficiencies up to 66 % combined with low dark count rates and timing resolu...
20. Dissipation-enabled efficient excitation transfer from a single photon to a single quantum emitter
Science.gov (United States)
Trautmann, N.; Alber, G.
2016-05-01
We propose a scheme for triggering a dissipation-dominated highly efficient excitation transfer from a single-photon wave packet to a single quantum emitter. This single-photon-induced optical pumping turns dominant dissipative processes, such as spontaneous photon emission by the emitter or cavity decay, into valuable tools for quantum information processing and quantum communication. It works for an arbitrarily shaped single-photon wave packet with sufficiently small bandwidth provided a matching condition is satisfied which balances the dissipative rates involved. Our scheme does not require additional laser pulses or quantum feedback and does not rely on high finesse optical resonators. In particular, it can be used to enhance significantly the coupling of a single photon to a single quantum emitter implanted in a one-dimensional waveguide or even in a free space scenario. We demonstrate the usefulness of our scheme for building a deterministic quantum memory and a deterministic frequency converter between photonic qubits of different wavelengths.
1. Multiple-Event, Single-Photon Counting Imaging Sensor
Science.gov (United States)
Zheng, Xinyu; Cunningham, Thomas J.; Sun, Chao; Wang, Kang L.
2011-01-01
The single-photon counting imaging sensor is typically an array of silicon Geiger-mode avalanche photodiodes that are monolithically integrated with CMOS (complementary metal oxide semiconductor) readout, signal processing, and addressing circuits located in each pixel and the peripheral area of the chip. The major problem is its single-event method for photon count number registration. A single-event single-photon counting imaging array only allows registration of up to one photon count in each of its pixels during a frame time, i.e., the interval between two successive pixel reset operations. Since the frame time can t be too short, this will lead to very low dynamic range and make the sensor merely useful for very low flux environments. The second problem of the prior technique is a limited fill factor resulting from consumption of chip area by the monolithically integrated CMOS readout in pixels. The resulting low photon collection efficiency will substantially ruin any benefit gained from the very sensitive single-photon counting detection. The single-photon counting imaging sensor developed in this work has a novel multiple-event architecture, which allows each of its pixels to register as more than one million (or more) photon-counting events during a frame time. Because of a consequently boosted dynamic range, the imaging array of the invention is capable of performing single-photon counting under ultra-low light through high-flux environments. On the other hand, since the multiple-event architecture is implemented in a hybrid structure, back-illumination and close-to-unity fill factor can be realized, and maximized quantum efficiency can also be achieved in the detector array.
2. Single Photon Ignition of Two-photon Super-fluorescence through the Vacuum of Electromagnetic Field
OpenAIRE
Enaki, Nicolae A.
2010-01-01
The ignition of two-quantum collective emission of inverted sub-ensemble of radiators due to mutual interaction of this sub-ensemble with other two dipole active atomic subsystems in process of two-photon exchanges between the atoms through the vacuum field is proposed. The three particle resonances between two-photon and single quantum transitions of inverted radiators from the ensemble are proposed for acceleration of collective decay rate of bi-photons, obtained relatively dipole-forbidden...
3. Total teleportation of a single-photon state
Science.gov (United States)
Humble, Travis S.; Bennink, Ryan S.; Grice, Warren P.
2008-08-01
Recent demonstrations of teleportation have transferred quantum information encoded into either polarization or fieldquadrature degrees of freedom (DOFs), but an outstanding question is how to simultaneously teleport quantum information encoded into multiple DOFs. We describe how the transverse-spatial, spectral and polarization states of a single photon can be simultaneously teleported using a pair of multimode, polarization-entangled photons derived from spontaneous parametric down-conversion. Furthermore, when the initial photon pair is maximally entangled in the spatial, spectral, and polarization DOFs then the photon's full quantum state can be reliably teleported using a Bell-state measurement based on sum-frequency generation.
4. Total teleportation of a single-photon state
Energy Technology Data Exchange (ETDEWEB)
Humble, Travis S [ORNL; Bennink, Ryan S [ORNL; Grice, Warren P [ORNL
2008-01-01
Recent demonstrations of teleportation have transferred quantum information encoded into either polarization or field-quadrature degrees of freedom (DOFs), but an outstanding question is how to simultaneously teleport quantum information encoded into multiple DOFs. We describe how the transverse-spatial, spectral and polarization states of a single photon can be simultaneously teleported using a pair of multimode, polarization-entangled photons derived from spontaneous parametric down-conversion. Furthermore, when the initial photon pair is maximally entangled in the spatial, spectral, and polarization DOFs then the photon s full quantum state can be reliably teleported using a Bell-state measurement based on sum-frequency generation.
5. Quantum teleportation of a single-photon wave packet
OpenAIRE
Molotkov, S. N.
1998-01-01
A quantum teleportation scheme based on the EPR-pair entangled with respect to the energy+time'' variables is proposed. Teleportation of the multimode state of a single-photon wave packet is considered.
6. Continuous variable teleportation of single photon states (Proceedings version)
OpenAIRE
Ide, Toshiki; Hofmann, Holger F.; Kobayashi, Takayoshi; Furusawa, Akira
2001-01-01
We investigate the changes to a single photon state caused by the non-maximal entanglement in continuous variable quantum teleportation. It is shown that the teleportation measurement introduces field coherence in the output.
7. Single Photon Avalanche Diodes: Towards the Large Bidimensional Arrays
Directory of Open Access Journals (Sweden)
Emilio Sciacca
2008-08-01
Full Text Available Single photon detection is one of the most challenging goals of photonics. In recent years, the study of ultra-fast and/or low-intensity phenomena has received renewed attention from the academic and industrial communities. Intense research activity has been focused on bio-imaging applications, bio-luminescence, bio-scattering methods, and, more in general, on several applications requiring high speed operation and high timing resolution. In this paper we present design and characterization of bi-dimensional arrays of a next generation of single photon avalanche diodes (SPADs. Single photon sensitivity, dark noise, afterpulsing and timing resolution of the single SPAD have been examined in several experimental conditions. Moreover, the effects arising from their integration and the readout mode have also been deeply investigated.
8. Correction of ultraviolet single photon counting image distortion
Institute of Scientific and Technical Information of China (English)
Xinghua Zhang; Baosheng Zhao; Zhenhua Miao; Wei Li; Xiangping Zhu; Yong'an Liu; Wei Zou
2008-01-01
Single photon counting imaging technology has been widely used in space environment detection, astronomy observation, nuclear physics, and ultraweak bioluminescence. However, the distortion of the single photon counting image will badly affect the measurement results. Therefore, the correction of distortion for single photon counting image is very significant. Ultraviolet single photon imaging system with wedge and strip anode is introduced and the influence factor leading to image distortion is analyzed. To correct original distorted image, three different image correction methods, namely, the physical correction, the global correction, and the local correction, are applied. In addition, two parameters, i.e, the position index and the linearity index, are defined to evaluate the performance of the three methods. The results suggest that the correction methods can improve the quality of the initial image without losing gray information of each counting light spot. And the local correction can provide the best visual inspections and performance evaluation among the three methods.
9. Category theoretic analysis of single-photon decision maker
CERN Document Server
Kim, Makoto Naruse Song-Ju; Berthel, Martin; Drezet, Aurélien; Huant, Serge; Hori, Hirokazu
2016-01-01
Decision making is a vital function in the era of artificial intelligence; however, its physical realizations and their theoretical fundamentals are not yet known. In our former study [Sci. Rep. 5, 513253 (2015)], we demonstrated that single photons can be used to make decisions in uncertain, dynamically changing environments. The multi-armed bandit problem was successfully solved using the dual probabilistic and particle attributes of single photons. Herein, we present the category theoretic foundation of the single-photon-based decision making, including quantitative analysis that agrees well with the experimental results. The category theoretic model unveils complex interdependencies of the entities of the subject matter in the most simplified manner, including a dynamically changing environment. In particular, the octahedral structure in triangulated categories provides a clear understanding of the underlying mechanisms of the single-photon decision maker. This is the first demonstration of a category the...
10. Single-photon quantum router with multiple output ports.
Science.gov (United States)
Yan, Wei-Bin; Fan, Heng
2014-01-01
The routing capability is a requisite in quantum network. Although the quantum routing of signals has been investigated in various systems both in theory and experiment, the general form of quantum routing with many output terminals still needs to be explored. Here we propose a scheme to achieve the multi-channel quantum routing of the single photons in a waveguide-emitter system. The channels are composed by the waveguides and are connected by intermediate two-level emitters. By adjusting the intermediate emitters, the output channels of the input single photons can be controlled. This is demonstrated in the cases of one output channel, two output channels and the generic N output channels. The results show that the multi-channel quantum routing of single photons can be well achieved in the proposed system. This offers a scheme for the experimental realization of general quantum routing of single photons. PMID:24769619
11. Raman-Free, Noble-Gas-Filled Photonic-Crystal Fiber Source for Ultrafast, Very Bright Twin-Beam Squeezed Vacuum.
Science.gov (United States)
Finger, Martin A; Iskhakov, Timur Sh; Joly, Nicolas Y; Chekhova, Maria V; Russell, Philip St J
2015-10-01
We report a novel source of twin beams based on modulational instability in high-pressure argon-filled hollow-core kagome-style photonic-crystal fiber. The source is Raman-free and manifests strong photon-number correlations for femtosecond pulses of squeezed vacuum with a record brightness of ∼2500 photons per mode. The ultra-broadband (∼50 THz) twin beams are frequency tunable and contain one spatial and less than 5 frequency modes. The presented source outperforms all previously reported squeezed-vacuum twin-beam sources in terms of brightness and low mode content. PMID:26551812
12. Potential of semiconductor nanowires for single photon sources
NARCIS (Netherlands)
Harmand, J.-C.; Liu, L.; Patriarche, G.; Tchernycheva, M.; Akopian, N.; Perinetti, U.; Zwiller, V.
2009-01-01
The catalyst-assisted growth of semiconductor nanowires heterostructures offers a very flexible way to design and fabricate single photon emitters. The nanowires can be positioned by organizing the catalyst prior to growth. Single quantum dots can be formed in the core of single nanowires which can
13. Ultrafast Room-Temperature Single Photon Emission from Quantum Dots Coupled to Plasmonic Nanocavities.
Science.gov (United States)
Hoang, Thang B; Akselrod, Gleb M; Mikkelsen, Maiken H
2016-01-13
Efficient and bright single photon sources at room temperature are critical components for quantum information systems such as quantum key distribution, quantum state teleportation, and quantum computation. However, the intrinsic radiative lifetime of quantum emitters is typically ∼10 ns, which severely limits the maximum single photon emission rate and thus entanglement rates. Here, we demonstrate the regime of ultrafast spontaneous emission (∼10 ps) from a single quantum emitter coupled to a plasmonic nanocavity at room temperature. The nanocavity integrated with a single colloidal semiconductor quantum dot produces a 540-fold decrease in the emission lifetime and a simultaneous 1900-fold increase in the total emission intensity. At the same time, the nanocavity acts as a highly efficient optical antenna directing the emission into a single lobe normal to the surface. This plasmonic platform is a versatile geometry into which a variety of other quantum emitters, such as crystal color centers, can be integrated for directional, room-temperature single photon emission rates exceeding 80 GHz. PMID:26606001
14. Continuous monitoring can improve single-photon probability
OpenAIRE
Raghunathan, Shesha; Brun, Todd
2010-01-01
An engineering technique using continuous quantum measurement together with a change detection algorithm is proposed to improve the probability of single photon emission for a quantum-dot based single-photon source. The technique involves continuous monitoring of the emitter, integrating the measured signal, and a simple change detection circuit to decide when to stop pumping. The idea is to pump just long enough such that the emitter $+$ cavity system is in a state that can emit at most one ...
15. Multiboson Correlation Interferometry with arbitrary single-photon pure states
OpenAIRE
Tamma, Vincenzo; Laibacher, Simon
2014-01-01
We provide a compact full description of multiboson correlation measurements of arbitrary order N in passive linear interferometers with arbitrary input single-photon pure states. This allows us to physically analyze the novel problem of multiboson correlation sampling at the output of random linear interferometers. Our results also describe general multiboson correlation landscapes for an arbitrary number of input single photons and arbitrary interferometers. In particular, we use two differ...
16. Spectral-hole memory for light at the single-photon level
Science.gov (United States)
Kutluer, Kutlu; Pascual-Winter, María Florencia; Dajczgewand, Julian; Ledingham, Patrick M.; Mazzera, Margherita; Chanelière, Thierry; de Riedmatten, Hugues
2016-04-01
We demonstrate a solid-state spin-wave optical memory based on stopped light in a spectral hole. A long-lived narrow spectral hole is created by optical pumping in the inhomogeneous absorption profile of a Pr3 +:Y2SiO5 crystal. Optical pulses sent through the spectral hole experience a strong reduction of their group velocity and are spatially compressed in the crystal. A short Raman pulse transfers the optical excitation to the spin state before the light pulse exits the crystal, effectively stopping the light. After a controllable delay, a second Raman pulse is sent, which leads to the emission of the stored photons. We reach storage and retrieval efficiencies for bright pulses of up to 39 % in a 5-mm-long crystal. We also show that our device works at the single-photon level by storing and retrieving 3 -μ s -long weak coherent pulses with efficiencies up to 31 % , demonstrating the most efficient spin-wave solid-state optical memory at the single-photon level so far. We reach an unconditional noise level of (9 ±1 ) ×10-3 photons per pulse in a detection window of 4 μ s , leading to a signal-to-noise ratio of 33 ±4 for an average input photon number of 1, making our device promising for long-lived storage of nonclassical light.
17. Single photon frequency up-conversion and its applications
International Nuclear Information System (INIS)
Optical frequency up-conversion is a technique, based on sum frequency generation in a non-linear optical medium, in which signal light from one frequency (wavelength) is converted to another frequency. By using this technique, near infrared light can be converted to light in the visible or near visible range and therefore detected by commercially available visible detectors with high efficiency and low noise. The National Institute of Standards and Technology (NIST) has adapted the frequency up-conversion technique to develop highly efficient and sensitive single photon detectors and a spectrometer for use at telecommunication wavelengths. The NIST team used these single photon up-conversion detectors and spectrometer in a variety of pioneering research projects including the implementation of a quantum key distribution system; the demonstration of a detector with a temporal resolution beyond the jitter limitation of commercial single photon detectors; the characterization of an entangled photon pair source, including a direct spectrum measurement for photons generated in spontaneous parametric down-conversion; the characterization of single photons from quantum dots including the measurement of carrier lifetime with escalated high accuracy and the demonstration of the converted quantum dot photons preserving their non-classical features; the observation of 2nd, 3rd and 4th order temporal correlations of near infrared single photons from coherent and pseudo-thermal sources following frequency up-conversion; a study on the time-resolving measurement capability of the detectors using a short pulse pump and; evaluating the modulation of a single photon wave packet for better interfacing of independent sources. In this article, we will present an overview of the frequency up-conversion technique, introduce its applications in quantum information systems and discuss its unique features and prospects for the future.
18. Near-unity efficiency, single-photon sources based on tapered photonic nanowires
DEFF Research Database (Denmark)
Bleuse, Joël; Munsch, Mathieu; Claudon, Julien;
2012-01-01
Single-photon emission from excitons in InAs Quantum Dots (QD) embedded in GaAs Tapered Photonic Wires (TPW) already demonstrated a 0.72 collection efficiency, with TPWs were the apex is the sharp end of the cone. Going to alternate designs, still based on the idea of the adiabatic deconfinement ...
19. Quantum computing with distant single photon sources with insurance
CERN Document Server
Lim, Y L; Kwek, L C; Lim, Yuan Liang; Beige, Almut; Kwek, Leong Chuan
2004-01-01
We demonstrate the possibility to perform quantum computations using only single photon sources, linear optics elements and photon detectors. In contrast to common linear optics quantum computing proposals, the described scheme can be operated with insurance without relying on highly entangled ancilla photons. Universality is achieved by employing the properties of certain single photon sources, namely the fact that it is possible to encode the logical qubit within the state of a source as well as in the state of the generated photon. The proposed Ising gate allows to build cluster states for one-way quantum computing. Furthermore we describe the implementation of the quantum parity filter, enabling teleportation with insurance, and the generation of multiphoton entanglement on demand.
20. Demonstration of the angular uncertainty principle for single photons
International Nuclear Information System (INIS)
We present an experimental demonstration of a form of the angular uncertainty principle for single photons. Producing light from type I down-conversion, we use spatial light modulators to perform measurements on signal and idler photons. By measuring states in the angle and orbital angular momentum basis, we demonstrate the uncertainty relation of Franke-Arnold et al (2004 New J. Phys. 6 103). We consider two manifestations of the uncertainty relation. In the first we herald the presence of a photon by detection of its paired partner and demonstrate the uncertainty relation on this single photon. In the second, we perform orbital angular momentum measurements on one photon and angular measurements on its correlated partner exploring, in this way, the uncertainty relation through non-local measurements
1. Heralded Single-Magnon Quantum Memory for Photon Polarization States
International Nuclear Information System (INIS)
We demonstrate a heralded quantum memory where a photon announces the mapping of a light polarization state onto a single collective-spin excitation (magnon) shared between two atomic ensembles. The magnon can be converted at a later time into a single polarized photon with polarization fidelity over 90(2)% for all fiducial input states, well above the classical limit of (2/3). The process can be viewed as a nondestructive quantum probe where a photon is detected, stored, and regenerated without touching its - potentially undetermined - polarization.
2. How bright is the proton? A precise determination of the photon PDF
CERN Document Server
Manohar, Aneesh; Salam, Gavin P; Zanderighi, Giulia
2016-01-01
It has become apparent in recent years that it is important, notably for a range of physics studies at the Large Hadron Collider, to have accurate knowledge on the distribution of photons in the proton. We show how the photon parton distribution function (PDF) can be determined in a model-independent manner, using electron-proton ($ep$) scattering data, in effect viewing the $ep\\to e+X$ process as an electron scattering off the photon field of the proton. To this end, we consider an imaginary BSM process with a flavour changing photon-lepton vertex. We write its cross section in two ways, one in terms of proton structure functions, the other in terms of a photon distribution. Requiring their equivalence yields the photon distribution as an integral over proton structure functions. As a result of the good precision of $ep$ data, we constrain the photon PDF at the level of 1-2% over a wide range of $x$ values.
3. Entanglement-preserving absorption of single SPDC photons by a single atom
CERN Document Server
Huwer, J; Piro, N; Schug, M; Dubin, F; Eschner, J
2011-01-01
We study the controlled interaction between a single trapped Ca40+ ion and single photons belonging to entangled photon pairs. The ion is prepared as a polarization-sensitive single-photon absorber; the absorption of one photon from a pair is marked by a quantum jump of the atomic state and heralded by the coincident detection of the entangled partner photon. For three polarization basis settings of absorption and detection of the herald, we find maximum coincidences always for orthogonal polarizations. Tomographic reconstruction of the biphoton quantum state from the absorption-herald coincidences reveals 93% overlap with the maximally entangled state. This proves that the polarization entanglement shared by the photon pair is preserved in the absorption process and converted to transient photon-atom entanglement.
4. Picosecond Lifetimes with High Quantum Yields from Single-Photon-Emitting Colloidal Nanostructures at Room Temperature.
Science.gov (United States)
Bidault, Sébastien; Devilez, Alexis; Maillard, Vincent; Lermusiaux, Laurent; Guigner, Jean-Michel; Bonod, Nicolas; Wenger, Jérôme
2016-04-26
Minimizing the luminescence lifetime while maintaining a high emission quantum yield is paramount in optimizing the excitation cross-section, radiative decay rate, and brightness of quantum solid-state light sources, particularly at room temperature, where nonradiative processes can dominate. We demonstrate here that DNA-templated 60 and 80 nm diameter gold nanoparticle dimers, featuring one fluorescent molecule, provide single-photon emission with lifetimes that can fall below 10 ps and typical quantum yields in a 45-70% range. Since these colloidal nanostructures are obtained as a purified aqueous suspension, fluorescence spectroscopy can be performed on both fixed and freely diffusing nanostructures to quantitatively estimate the distributions of decay rate and fluorescence intensity enhancements. These data are in excellent agreement with theoretical calculations and demonstrate that millions of bright fluorescent nanostructures, with radiative lifetimes below 100 ps, can be produced in parallel. PMID:26972678
5. Witnessing trustworthy single-photon entanglement with local homodyne measurements.
Science.gov (United States)
Morin, Olivier; Bancal, Jean-Daniel; Ho, Melvyn; Sekatski, Pavel; D'Auria, Virginia; Gisin, Nicolas; Laurat, Julien; Sangouard, Nicolas
2013-03-29
Single-photon entangled states, i.e., states describing two optical paths sharing a single photon, constitute the simplest form of entanglement. Yet they provide a valuable resource in quantum information science. Specifically, they lie at the heart of quantum networks, as they can be used for quantum teleportation, swapped, and purified with linear optics. The main drawback of such entanglement is the difficulty in measuring it. Here, we present and experimentally test an entanglement witness allowing one to say whether a given state is path entangled and also that entanglement lies in the subspace, where the optical paths are each filled with one photon at most, i.e., refers to single-photon entanglement. It uses local homodyning only and relies on no assumption about the Hilbert space dimension of the measured system. Our work provides a simple and trustworthy method for verifying the proper functioning of future quantum networks. PMID:23581297
6. NIR-emitting molecular-based nanoparticles as new two-photon absorbing nanotools for single particle tracking
Science.gov (United States)
Daniel, J.; Godin, A. G.; Clermont, G.; Lounis, B.; Cognet, L.; Blanchard-Desce, M.
2015-07-01
In order to provide a green alternative to QDs for bioimaging purposes and aiming at designing bright nanoparticles combining both large one- and two-photon brightness, a bottom-up route based on the molecular engineering of dedicated red to NIR emitting dyes that spontaneously form fluorescent organic nanoparticles (FONs) has been implemented. These fully organic nanoparticles built from original quadrupolar dyes are prepared using a simple, expeditious and green protocol that yield very small molecular-based nanoparticles (radius ~ 7 nm) suspension in water showing a nice NIR emission (λem=710 nm). These FONs typically have absorption coefficient more than two orders larger than popular NIR-emitting dyes (such as Alexa Fluor 700, Cy5.5 ….) and much larger Stokes shift values (i.e. up to over 5500 cm-1). They also show very large two-photon absorption response in the 800-1050 nm region (up to about 106 GM) of major promise for two-photon excited fluorescence microscopy. Thanks to their brightness and enhanced photostability, these FONs could be imaged as isolated nanoparticles and tracked using wide-field imaging. As such, thanks to their size and composition (absence of heavy metals), they represent highly promising alternatives to NIR-emitting QDs for use in bioimaging and single particle tracking applications. Moreover, efficient FONs coating was achieved by using a polymeric additive built from a long hydrophobic (PPO) and a short hydrophilic (PEO) segment and having a cationic head group able to interact with the highly negative surface of FONs. This electrostatically-driven interaction promotes both photoluminescence and two-photon absorption enhancement leading to an increase of two-photon brightness of about one order of magnitude. This opens the way to wide-field single particle tracking under two-photon excitation
7. Highly efficient photonic nanowire single-photon sources for quantum information applications
DEFF Research Database (Denmark)
Gregersen, Niels; Claudon, J.; Munsch, M.;
2013-01-01
must feature near-unity efficiency, where the efficiency is defined as the number of detected photons per trigger, the probability g(2)(τ=0) of multi-photon emission events should be 0 and the emitted photons are required to be indistinguishable. An optically or electrically triggered quantum light......Within the emerging field of optical quantum information processing, the current challenge is to construct the basic building blocks for the quantum computing and communication systems. A key component is the singlephoton source (SPS) capable of emitting single photons on demand. Ideally, the SPS...... emitter, e.g. a nitrogen-vacancy center or a semiconductor quantum dot (QD), embedded in a solid-state semiconductor host material appears as an attractive platform for generating such single photons. However, for a QD in bulk material, the large index contrast at the semiconductor-air interface leads to...
8. Localized Polymerization Using Single Photon Photoinitiators in Two-photon process for Fabricating Subwavelength Structures
CERN Document Server
Ummethala, Govind; Chaudhary, Raghvendra P; Hawal, Suyog; Saxena, Sumit; Shukla, Shobha
2016-01-01
Localized polymerization in subwavelength volumes using two photon dyes has now become a well-established method for fabrication of subwavelength structures. Unfortunately, the two photon absorption dyes used in such process are not only expensive but also proprietary. LTPO-L is an inexpensive, easily available single photon photoinitiator and has been used extensively for single photon absorption of UV light for polymerization. These polymerization volumes however are not localized and extend to micron size resolution having limited applications. We have exploited high quantum yield of radicals of LTPO-Lfor absorption of two photons to achieve localized polymerization in subwavelength volumes, much below the diffraction limit. Critical concentration (10wt%) of LTPO-Lin acrylate (Sartomer) was found optimal to achieve subwavelength localized polymerization and has been demonstrated by fabricating 2D/3D complex nanostructures and functional devices such as variable polymeric gratings with nanoscaled subwavelen...
9. Localised excitation of a single photon source by a nanowaveguide
Science.gov (United States)
Geng, Wei; Manceau, Mathieu; Rahbany, Nancy; Sallet, Vincent; de Vittorio, Massimo; Carbone, Luigi; Glorieux, Quentin; Bramati, Alberto; Couteau, Christophe
2016-01-01
Nowadays, integrated photonics is a key technology in quantum information processing (QIP) but achieving all-optical buses for quantum networks with efficient integration of single photon emitters remains a challenge. Photonic crystals and cavities are good candidates but do not tackle how to effectively address a nanoscale emitter. Using a nanowire nanowaveguide, we realise an hybrid nanodevice which locally excites a single photon source (SPS). The nanowire acts as a passive or active sub-wavelength waveguide to excite the quantum emitter. Our results show that localised excitation of a SPS is possible and is compared with free-space excitation. Our proof of principle experiment presents an absolute addressing efficiency ηa ~ 10-4 only ~50% lower than the one using free-space optics. This important step demonstrates that sufficient guided light in a nanowaveguide made of a semiconductor nanowire is achievable to excite a single photon source. We accomplish a hybrid system offering great potentials for electrically driven SPSs and efficient single photon collection and detection, opening the way for optimum absorption/emission of nanoscale emitters. We also discuss how to improve the addressing efficiency of a dipolar nanoscale emitter with our system.
10. Efficient generation of single and entangled photons on a silicon photonic integrated chip
International Nuclear Information System (INIS)
We present a protocol for generating on-demand, indistinguishable single photons on a silicon photonic integrated chip. The source is a time-multiplexed spontaneous parametric down-conversion element that allows optimization of single-photon versus multiphoton emission while realizing high output rate and indistinguishability. We minimize both the scaling of active elements and the scaling of active element loss with multiplexing. We then discuss detection strategies and data processing to further optimize the procedure. We simulate an improvement in single-photon-generation efficiency over previous time-multiplexing protocols, assuming existing fabrication capabilities. We then apply this system to generate heralded Bell states. The generation efficiency of both nonclassical states could be increased substantially with improved fabrication procedures.
11. Engineering single photon emitters by ion implantation in diamond.
Science.gov (United States)
Naydenov, B; Kolesov, R; Batalov, A; Meijer, J; Pezzagna, S; Rogalla, D; Jelezko, F; Wrachtrup, J
2009-11-01
Diamond provides unique technological platform for quantum technologies including quantum computing and communication. Controlled fabrication of optically active defects is a key element for such quantum toolkit. Here we report the production of single color centers emitting in the blue spectral region by high energy implantation of carbon ions. We demonstrate that single implanted defects show sub-poissonian statistics of the emitted photons and can be explored as single photon source in quantum cryptography. Strong zero phonon line at 470.5 nm allows unambiguous identification of this defect as interstitial-related TR12 color center. PMID:19956415
12. Deterministic teleportation using single-photon entanglement as a resource
DEFF Research Database (Denmark)
Björk, Gunnar; Laghaout, Amine; Andersen, Ulrik L.
2012-01-01
We outline a proof that teleportation with a single particle is, in principle, just as reliable as with two particles. We thereby hope to dispel the skepticism surrounding single-photon entanglement as a valid resource in quantum information. A deterministic Bell-state analyzer is proposed which...
13. Quantum interference of independently generated telecom-band single photons
International Nuclear Information System (INIS)
We report on high-visibility quantum interference of independently generated telecom O-band (1310 nm) single photons using standard single-mode fibers. The experimental data are shown to agree well with the results of simulations using a comprehensive quantum multimode theory without the need for any fitting parameter
14. Quantum interference of independently generated telecom-band single photons
Energy Technology Data Exchange (ETDEWEB)
Patel, Monika [Center for Photonic Communication and Computing, Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3112 (United States); Altepeter, Joseph B.; Huang, Yu-Ping; Oza, Neal N. [Center for Photonic Communication and Computing, Department of Electrical Engineering and Computer Science, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3118 (United States); Kumar, Prem [Center for Photonic Communication and Computing, Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3112, USA and Center for Photonic Communication and Computing, Department of Electrical Engineering (United States)
2014-12-04
We report on high-visibility quantum interference of independently generated telecom O-band (1310 nm) single photons using standard single-mode fibers. The experimental data are shown to agree well with the results of simulations using a comprehensive quantum multimode theory without the need for any fitting parameter.
15. Single-photon production at the CERN ISR
International Nuclear Information System (INIS)
A measurement of single photon production from p-p collisions at ISR energies is presented. A signal comparable to single π0 production is found at large p/sub T/. A study of associated particles favors production dominated by the first-order QCD process of gluon-valence quark production q g → q γ
16. Single mode dye-doped polymer photonic crystal lasers
DEFF Research Database (Denmark)
Christiansen, Mads Brøkner; Buss, Thomas; Smith, Cameron; Petersen, Sidsel Rübner; Jørgensen, Mette Marie; Kristensen, Anders
2010-01-01
Dye-doped polymer photonic crystal (PhC) lasers fabricated by combined nanoimprint and photolithography are studied for their reproducibility and stability characteristics. We introduce a phase shift in the PhC lattice that substantially improves the yield of single wavelength emission. Single mode...
17. Remote preparation of complex spatial states of single photons and verification by two-photon coincidence experiment.
Science.gov (United States)
Kang, Yoonshik; Cho, Kiyoung; Noh, Jaewoo; Vitullo, Dashiell L P; Leary, Cody; Raymer, M G
2010-01-18
We propose and provide experimental evidence in support of a theory for the remote preparation of a complex spatial state of a single photon. An entangled two-photon source was obtained by spontaneous parametric down-conversion, and a double slit was placed in the path of the signal photon as a scattering object. The signal photon was detected after proper spatial filtering so that the idler photon was prepared in the corresponding single-photon state. By using a two-photon coincidence measurement, we obtained the Radon transform, at several longitudinal distances, of the single-photon Wigner distribution function modified by the double slit. The experimental results are consistent with the idler photon being in a pure state. An inverse Radon transformation can, in principle, be applied to the measured data to reconstruct the modified single-photon Wigner function, which is a complete representation of the amplitude and phase structure of the scattering object. PMID:20173945
18. SIMULTANEOUS TELEPORTATION OF MULTIPLE SINGLE-PHOTON DEGREES OF FREEDOM
Energy Technology Data Exchange (ETDEWEB)
Humble, Travis S [ORNL; Bennink, Ryan S [ORNL; Grice, Warren P [ORNL
2011-01-01
We report how quantum information encoded into multiple photonic degrees of freedom may be simultaneously teleported using a single, common physical process. The application of teleportation to the complete quantum state of a photon, i.e., the spectral, spatial, and polarization component states, permits the full photonic Hilbert space to be used for encoding information while simultaneously enabling subspaces to be addressed individually, e.g., for quantum information processing. We analyze the feasibility of teleporting the full quantum state through numerical analysis of the fidelity under nominal experimental conditions and for different types of input states, e.g., single-photon states that are separable and entangled in the physical degrees of freedom.
19. A high-brightness source of polarization-entangled photons optimized for applications in free space
CERN Document Server
Steinlechner, Fabian; Jofre, Marc; Weier, Henning; Perez, Daniel; Jennewein, Thomas; Ursin, Rupert; Rarity, John; Mitchell, Morgan W; Torres, Juan P; Weinfurter, Harald; Pruneri, Valerio; 10.1364/OE.20.009640
2012-01-01
We present a simple but highly efficient source of polarization-entangled photons based on spontaneous parametric down-conversion (SPDC) in bulk periodically poled potassium titanyl phosphate crystals (PPKTP) pumped by a 405 nm laser diode. Utilizing one of the highest available nonlinear coefficients in a non-degenerate, collinear type-0 phase-matching configuration, we generate polarization entanglement via the crossed-crystal scheme and detect 0.64 million photon pair events/s/mW, while maintaining an overlap fidelity with the ideal Bell state of 0.98 at a pump power of 0.025 mW.
20. Plasmonic nanoantenna based triggered single-photon source
Science.gov (United States)
Straubel, J.; Filter, R.; Rockstuhl, C.; Słowik, K.
2016-05-01
Highly integrated single-photon sources are key components in future quantum-optical circuits. Whereas the probabilistic generation of single photons can routinely be done by now, their triggered generation is a much greater challenge. Here, we describe the triggered generation of single photons in a hybrid plasmonic device. It consists of a lambda-type quantum emitter coupled to a multimode optical nanoantenna. For moderate interaction strengths between the subsystems, the description of the quantum optical evolution can be simplified by an adiabatic elimination of the electromagnetic fields of the nanoantenna modes. This leads to an insightful analysis of the emitter's dynamics, entails the opportunity to understand the physics of the device, and to identify parameter regimes for a desired operation. Even though the approach presented in this work is general, we consider a simple exemplary design of a plasmonic nanoantenna, made of two silver nanorods, suitable for triggered generation of single photons. The investigated device realizes single photons, triggered, potentially at high rates, and using low device volumes.
1. Nanoantenna enhancement for telecom-wavelength superconducting single photon detectors
CERN Document Server
Heath, Robert M; Drysdale, Timothy D; Miki, Shigehito; Giannini, Vincenzo; Maier, Stefan A; Hadfield, Robert H
2015-01-01
Superconducting nanowire single photon detectors are rapidly emerging as a key infrared photon-counting technology. Two front-side-coupled silver dipole nanoantennas, simulated to have resonances at 1480 nm and 1525 nm, were fabricated in a two-step process. An enhancement of 50% to 130% in the system detection efficiency was observed when illuminating the antennas. This offers a pathway to increasing absorption into superconducting nanowires, creating larger active areas, and achieving more efficient detection at longer wavelengths.
2. Triangular nanobeam photonic cavities in single crystal diamond
OpenAIRE
Bayn, Igal; Meyler, Boris; Salzman, Joseph; Kalish, Rafi
2011-01-01
Diamond photonics provides an attractive architecture to explore room temperature cavity quantum electrodynamics and to realize scalable multi-qubit computing. Here we review the present state of diamond photonic technology. The design, fabrication and characterization of a novel triangular cross section nanobeam cavity produced in a single crystal diamond is demonstrated. The present cavity design, based on a triangular cross section allows vertical confinement and better signal collection e...
3. Automated characterization of single-photon avalanche photodiode
OpenAIRE
2012-01-01
We report an automated characterization of a single-photon detector based on commercial silicon avalanche photodiode (PerkinElmer C30902SH). The photodiode is characterized by I-V curves at different illumination levels (darkness, 10 pW and 10 µW), dark count rate and photon detection efficiency at different bias voltages. The automated characterization routine is implemented in C++ running on a Linux computer. ABSTRAK: Kami melaporkan pencirian pengesan foton tunggal secara automatik b...
4. Quasi free mechanism in single photon double ionization of helium
International Nuclear Information System (INIS)
Double ionization of Helium by a single photon is widely believed to proceed through two mechanisms: knock-off (TS1) or shake-off, with the last one dominating at high photon energies. A new mechanism, termed ''Quasi Free Mechanism'' (QFM) was predicted 35 years ago by Amusia and coworkers, but escaped experimental observation till today. Here we provide the first proof of this mechanism using 800 eV photons from the Advanced Light Source. Fragments (electrons and ions) were measured in coincidence using momentum spectroscopy (COLTRIMS). He(2+) ions with zero momentum were found - the fingerprint for the QFM.
Science.gov (United States)
Jen, H. H.; Chang, M.-S.; Chen, Y.-C.
2016-07-01
We propose a set of subradiant states which can be prepared and detected in a one-dimensional optical lattice. We find that the decay rates are highly dependent on the spatial phases imprinted on the atomic chain, which allows systematic investigations of the subradiance in fluorescence experiments. The time evolution of these states can have a long decay time where up to 100 ms of lifetime is predicted for 100 atoms. They can also show decayed Rabi-like oscillations with a beating frequency determined by the difference of the cooperative Lamb shift in the subspace. Experimental requirements are also discussed for practical implementation of the subradiant states. Our proposal provides a scheme for quantum storage of photons in arrays of two-level atoms through the preparation and detection of subradiant states, which offers opportunities for quantum many-body state preparation and quantum information processing in optical lattices.
6. Utra-bright compact sources of correlated photons based on SPDC in periodically-poled KTP
Science.gov (United States)
Beausoleil, Ray; Fiorentino, Marco; Spillane, Sean; Roberts, Tony; Battle, Phil; Munroe, Mark
2007-05-01
Photon pairs generated using spontaneous parametric down- conversion (SPDC) have been a central ingredient for a number of quantum optics experiments ranging from the generation of entanglement to demonstrations of quantum information processing protocols. The flux of pairs generated by SPDC sources has been steadily growing over the years opening the door to practical applications of correlated and entangled photon pairs. SPDC sources based on periodically poled waveguides have shown a great potential to generate large numbers of correlated pairs with a few μW of pump. These works, however, lack a clear explanation of the increased pair rate in waveguides and do not directly compare the waveguide result with bulk. Na"ively, field confinement in waveguides is not expected to enhance pair generation rate, since SPDC is a scattering phenomenon that only involves one pump photon and therefore does not benefit from higher photon densities created by focussing. In this talk we present a theoretical and experimental comparison of spontaneous parametric down-conversion in periodically poled waveguides and bulk KTP crystals. We measured a waveguide pair generation rate of 2.9 .10^6 pairs/s per mW of pump in a 1-nm band: more than 50 times higher than the bulk crystal generation rate. To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2007.NWS07.E3.4
7. Single-crystal phosphors for high-brightness white LEDs/LDs
Science.gov (United States)
Víllora, Encarnación G.; Arjoca, Stelian; Inomata, Daisuke; Shimamura, Kiyoshi
2016-03-01
White light-emitting diodes (wLEDs) are the new environmental friendly sources for general lighting purposes. For applications requiring a high-brightness, current wLEDs present overheating problems, which drastically decrease their emission efficiency, color quality and lifetime. This work gives an overview of the recent investigations on single-crystal phosphors (SCPs), which are proposed as novel alternative to conventional ceramic powder phosphors (CPPs). This totally new approach takes advantage of the superior properties of single-crystals in comparison with ceramic materials. SCPs exhibit an outstanding conversion efficiency and thermal stability up to 300°C. Furthermore, compared with encapsulated CPPs, SCPs possess a superior thermal conductivity, so that generated heat can be released efficiently. The conjunction of all these characteristics results in a low temperature rise of SCPs even under high blue irradiances, where conventional CPPs are overheated or even burned. Therefore, SCPs represent the ideal, long-demanded all-inorganic phosphors for high-brightness white light sources, especially those involving the use of high-density laser-diode beams.
8. Photonics
CERN Document Server
Andrews, David L
2015-01-01
Discusses the basic physical principles underlying Biomedical Photonics, spectroscopy and microscopy This volume discusses biomedical photonics, spectroscopy and microscopy, the basic physical principles underlying the technology and its applications. The topics discussed in this volume are: Biophotonics; Fluorescence and Phosphorescence; Medical Photonics; Microscopy; Nonlinear Optics; Ophthalmic Technology; Optical Tomography; Optofluidics; Photodynamic Therapy; Image Processing; Imaging Systems; Sensors; Single Molecule Detection; Futurology in Photonics. Comprehensive and accessible cov
9. Single-photon observables and preparation uncertainty relations
International Nuclear Information System (INIS)
We propose a procedure to define all single-photon observables in a consistent and unified picture based on operational approach to quantum mechanics. We identify the suppression of zero-helicity states as a projection from an extended Hilbert space onto the physical single-photon Hilbert space. We show that all single-photon observables are in general described by positive-operator valued measures (POVMs), obtained by applying this projection to opportune projection-valued measures (PVMs) defined on the extended Hilbert space. The POVMs associated to momentum and helicity reduce to PVMs, unlike those associated to position and spin. This fact reflects the intrinsic unsharpness of these observables. We apply this formalism to study the preparation uncertainty relations for position and momentum and to compute the probability distribution of spin, for a broad class of Gaussian states. Results show quantitatively the enhancement of the statistical character of the theory. (paper)
10. Jitter analysis of a superconducting nanowire single photon detector
Directory of Open Access Journals (Sweden)
Lixing You
2013-07-01
Full Text Available Jitter is one of the key parameters for a superconducting nanowire single photon detector (SNSPD. Using an optimized time-correlated single photon counting system for jitter measurement, we extensively studied the dependence of system jitter on the bias current and working temperature. The signal-to-noise ratio of the single-photon-response pulse was proven to be an important factor in system jitter. The final system jitter was reduced to 18 ps by using a high-critical-current SNSPD, which showed an intrinsic SNSPD jitter of 15 ps. A laser ranging experiment using a 15-ps SNSPD achieved a record depth resolution of 3 mm at a wavelength of 1550 nm.
11. Single-photon interference experiment for high schools
Science.gov (United States)
Bondani, Maria
2014-07-01
We follow the reductio ad absurdum reasoning described in the book "Sneaking a Look at God's Cards" by Giancarlo Ghirardi to demonstrate the wave-particle duality of light in a Mach-Zehnder interferometric setup analog to the conventional Young double-slit experiment. We aim at showing the double nature of light by measuring the existence of interference fringes down to the single-photon level. The setup includes a strongly attenuated laser, polarizing beam splitters, half-waveplates, polarizers and single-photon detectors.
12. Investigation of Hamamatsu H8500 phototubes as single photon detectors
Energy Technology Data Exchange (ETDEWEB)
Montgomery, R.A. [INFN Laboratori Nazionali di Frascati, Via Enrico Fermi, 40, 00044 Frascati (Italy); Hoek, M. [Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, Johann-Joachim-Becher-Weg 45, D 55128 Mainz (Germany); Lucherini, V.; Mirazita, M.; Orlandi, A.; Anefalos Pereira, S.; Pisano, S. [INFN Laboratori Nazionali di Frascati, Via Enrico Fermi, 40, 00044 Frascati (Italy); Rossi, P. [INFN Laboratori Nazionali di Frascati, Via Enrico Fermi, 40, 00044 Frascati (Italy); Jefferson Laboratory, Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, VA 23606 (United States); Viticchiè, A. [INFN Laboratori Nazionali di Frascati, Via Enrico Fermi, 40, 00044 Frascati (Italy); Witchger, A. [Department of Physics, Duquesne University, 317 Fisher Hall, Pittsburgh, PA 15282 (United States)
2015-08-01
We have investigated the response of a significant sample of Hamamatsu H8500 MultiAnode PhotoMultiplier Tubes (MAPMTs) as single photon detectors, in view of their use in a ring imaging Cherenkov counter for the CLAS12 spectrometer at the Thomas Jefferson National Accelerator Facility. For this, a laser working at 407.2 nm wavelength was employed. The sample is divided equally into standard window type, with a spectral response in the visible light region, and UV-enhanced window type MAPMTs. The studies confirm the suitability of these MAPMTs for single photon detection in such a Cherenkov imaging application.
13. Investigation of Hamamatsu H8500 phototubes as single photon detectors
CERN Document Server
Hoek, M; Mirazita, M; Montgomery, R A; Orlandi, A; Pereira, S Anefalos; Pisano, S; Rossi, P; Viticchiè, A; Witchger, A
2014-01-01
We have investigated the response of a significant sample of Hamamatsu H8500 MultiAnode PhotoMultiplier Tubes (MAPMTs) as single photon detectors, in view of their use in a ring imaging Cherenkov counter for the CLAS12 spectrometer at the Thomas Jefferson National Accelerator Facility. For this, a laser working at 407.2nm wavelength was employed. The sample is divided equally into standard window type, with a spectral response in the visible light region, and UV-enhanced window type MAPMTs. The studies confirm the suitability of these MAPMTs for single photon detection in such a Cherenkov imaging application.
14. A Variable Single Photon Plasmonic Beamsplitter
DEFF Research Database (Denmark)
Israelsen, Niels Møller; Kumar, Shailesh; Huck, Alexander; Neergaard-Nielsen, Jonas Schou; Andersen, Ulrik Lund
Plasmonic structures can both be exploited for scaling down optical components beyond the diffraction limit and enhancing andcollecting the emission from a single dipole emitter. Here, we experimentally demonstrate adiabatic coupling between two silvernanowires using a nitrogen vacancy center as a...
15. Measuring ultrafast protein folding rates from photon-by-photon analysis of single molecule fluorescence trajectories
Energy Technology Data Exchange (ETDEWEB)
Chung, Hoi Sung, E-mail: [email protected] [Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892-0520 (United States); Cellmer, Troy; Louis, John M. [Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892-0520 (United States); Eaton, William A., E-mail: [email protected] [Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892-0520 (United States)
2013-08-30
Highlights: ► Photon trajectories were measured for an ultrafast folding protein using single molecule FRET. ► Folding rates were obtained from a photon-by-photon analysis using a maximum likelihood method. ► Incorporating acceptor blinking into the analysis improved the accuracy of the extracted rates. ► The rates agree with the results from both the correlation analysis and ensemble laser temperature-jump. - Abstract: Folding and unfolding rates for the ultrafast folding villin subdomain were determined from a photon-by-photon analysis of fluorescence trajectories in single molecule FRET experiments. One of the obstacles to measuring fast kinetics in single molecule fluorescence experiments is blinking of the fluorophores on a timescale that is not well separated from the process of interest. By incorporating acceptor blinking into a two-state kinetics model, we show that it is possible to extract accurate rate coefficients on the microsecond time scale for folding and unfolding using the maximum likelihood method of Gopich and Szabo. This method yields the most likely parameters of a given model that can reproduce the observed photon trajectories. The extracted parameters agree with both the decay rate of the donor–acceptor cross correlation function and the results of ensemble equilibrium and kinetic experiments using nanosecond laser temperature jump.
16. Measuring ultrafast protein folding rates from photon-by-photon analysis of single molecule fluorescence trajectories
International Nuclear Information System (INIS)
Highlights: ► Photon trajectories were measured for an ultrafast folding protein using single molecule FRET. ► Folding rates were obtained from a photon-by-photon analysis using a maximum likelihood method. ► Incorporating acceptor blinking into the analysis improved the accuracy of the extracted rates. ► The rates agree with the results from both the correlation analysis and ensemble laser temperature-jump. - Abstract: Folding and unfolding rates for the ultrafast folding villin subdomain were determined from a photon-by-photon analysis of fluorescence trajectories in single molecule FRET experiments. One of the obstacles to measuring fast kinetics in single molecule fluorescence experiments is blinking of the fluorophores on a timescale that is not well separated from the process of interest. By incorporating acceptor blinking into a two-state kinetics model, we show that it is possible to extract accurate rate coefficients on the microsecond time scale for folding and unfolding using the maximum likelihood method of Gopich and Szabo. This method yields the most likely parameters of a given model that can reproduce the observed photon trajectories. The extracted parameters agree with both the decay rate of the donor–acceptor cross correlation function and the results of ensemble equilibrium and kinetic experiments using nanosecond laser temperature jump
17. Single-Photon Transistor Using a Förster Resonance
Science.gov (United States)
Tiarks, Daniel; Baur, Simon; Schneider, Katharina; Duerr, Stephan; Rempe, Gerhard
2015-05-01
An all-optical transistor is a device in which a gate light pulse switches the transmission of a target light pulse with a gain above unity. The gain quantifies the change of the transmitted target photon number per incoming gate photon. We study the quantum limit of one incoming gate photon and observe a gain of 20. The gate pulse is stored as a Rydberg excitation in an ultracold gas. The transmission of the subsequent target pulse is suppressed by Rydberg blockade which is enhanced by a Förster resonance. The detected target photons reveal in a single shot with a fidelity above 0.86 whether a Rydberg excitation was created during the gate pulse. The gain offers the possibility to distribute the transistor output to the inputs of many transistors, thus making complex computational tasks possible.
18. Interfering Heralded Single Photons from Two Separate Silicon Nanowires Pumped at Different Wavelengths
Directory of Open Access Journals (Sweden)
Xiang Zhang
2016-08-01
Full Text Available Practical quantum photonic applications require on-demand single photon sources. As one possible solution, active temporal and wavelength multiplexing has been proposed to build an on-demand single photon source. In this scheme, heralded single photons are generated from different pump wavelengths in many temporal modes. However, the indistinguishability of these heralded single photons has not yet been experimentally confirmed. In this work, we achieve 88% ± 8% Hong–Ou–Mandel quantum interference visibility from heralded single photons generated from two separate silicon nanowires pumped at different wavelengths. This demonstrates that active temporal and wavelength multiplexing could generate indistinguishable heralded single photons.
19. Single photon in hierarchical architecture for physical reinforcement learning: Photon intelligence
CERN Document Server
Naruse, Makoto; Drezet, Aurélien; Huant, Serge; Hori, Hirokazu; Kim, Song-Ju
2016-01-01
Understanding and using natural processes for intelligent functionalities, referred to as natural intelligence, has recently attracted interest from a variety of fields, including post-silicon computing for artificial intelligence and decision making in the behavioural sciences. In a past study, we successfully used the wave-particle duality of single photons to solve the two-armed bandit problem, which constitutes the foundation of reinforcement learning and decision making. In this study, we propose and confirm a hierarchical architecture for single-photon-based reinforcement learning and decision making that verifies the scalability of the principle. Specifically, the four-armed bandit problem is solved given zero prior knowledge in a two-layer hierarchical architecture, where polarization is autonomously adapted in order to effect adequate decision making using single-photon measurements. In the hierarchical structure, the notion of layer-dependent decisions emerges. The optimal solutions in the coarse la...
20. Comparison between two types of photonic-crystal cavities for single-photon emitters
International Nuclear Information System (INIS)
The properties of photonic-crystal (PhC) cavity modes are investigated for applications in single-photon emitters. Hexagonal-lattice PhC H1 and L3 cavities are fabricated in a GaAs slab containing InAs quantum dots. The cavity modes are characterized by polarization-dependent micro-photoluminescence measurements. Split and nearly degenerate dipole modes in H1 cavities are demonstrated in the same batch of samples, and a single L3 cavity mode with specific polarization is clearly observed. The results reveal that the L3 PhC cavity exhibits fairly excellent performance even with remarkable distortion and is favorable for single-photon emitters. Finite-difference time-domain simulations show that the verticality of the air-hole sidewall has a significant influence on the properties of PhC cavity modes
1. Evaluation of the ID220 single photon avalanche diode for extended spectral range of photon time-of-flight spectroscopy
DEFF Research Database (Denmark)
Nielsen, Otto Højager Attermann; Dahl, Anders Bjorholm; Anderson-Engels, Stefan;
This paper describe the performance of the ID220 single photon avalanche diode for single photon counting, and investigates its performance for photon time-of-flight (PToF) spectroscopy. At first this report will serve as a summary to the group for PToF spectroscopy at the Department of Physics...
2. Hyperbolic Metamaterial Nano-Resonators Make Poor Single Photon Sources
CERN Document Server
Axelrod, Simon; Wong, Herman M K; Helmy, Amr S; Hughes, Stephen
2016-01-01
We study the optical properties of quantum dipole emitters coupled to hyperbolic metamaterial nano-resonators using a semi-analytical quasinormal mode approach. We show that coupling to metamaterial nano-resonators can lead to significant Purcell enhancements that are nearly an order of magnitude larger than those of plasmonic resonators with comparable geometry. However, the associated single photon output $\\beta$-factors are extremely low (around 10%), far smaller than those of comparable sized metallic resonators (70%). Using a quasinormal mode expansion of the photon Green function, we describe how the low $\\beta$-factors are due to increased Ohmic quenching arising from redshifted resonances, larger quality factors and stronger confinement of light within the metal. In contrast to current wisdom, these results suggest that hyperbolic metamaterial nano-structures make poor choices for single photon sources.
3. Advanced active quenching circuits for single-photon avalanche photodiodes
Science.gov (United States)
Stipčević, M.; Christensen, B. G.; Kwiat, P. G.; Gauthier, D. J.
2016-05-01
Commercial photon-counting modules, often based on actively quenched solid-state avalanche photodiode sensors, are used in wide variety of applications. Manufacturers characterize their detectors by specifying a small set of parameters, such as detection efficiency, dead time, dark counts rate, afterpulsing probability and single photon arrival time resolution (jitter), however they usually do not specify the conditions under which these parameters are constant or present a sufficient description. In this work, we present an in-depth analysis of the active quenching process and identify intrinsic limitations and engineering challenges. Based on that, we investigate the range of validity of the typical parameters used by two commercial detectors. We identify an additional set of imperfections that must be specified in order to sufficiently characterize the behavior of single-photon counting detectors in realistic applications. The additional imperfections include rate-dependence of the dead time, jitter, detection delay shift, and "twilighting." Also, the temporal distribution of afterpulsing and various artifacts of the electronics are important. We find that these additional non-ideal behaviors can lead to unexpected effects or strong deterioration of the system's performance. Specifically, we discuss implications of these new findings in a few applications in which single-photon detectors play a major role: the security of a quantum cryptographic protocol, the quality of single-photon-based random number generators and a few other applications. Finally, we describe an example of an optimized avalanche quenching circuit for a high-rate quantum key distribution system based on time-bin entangled photons.
4. Directional emission of single photons from small atomic samples
DEFF Research Database (Denmark)
Miroshnychenko, Yevhen; V. Poulsen, Uffe; Mølmer, Klaus
2013-01-01
We provide a formalism to describe deterministic emission of single photons with tailored spatial and temporal profiles from a regular array of multi-level atoms. We assume that a single collective excitation is initially shared by all the atoms in a metastable atomic state, and that this state i...... coupled by a classical laser field to an optically excited state which rapidly decays to the ground atomic state. Our model accounts for the different field polarization components via re-absorption and emission of light by the Zeeman manifold of optically excited states.......We provide a formalism to describe deterministic emission of single photons with tailored spatial and temporal profiles from a regular array of multi-level atoms. We assume that a single collective excitation is initially shared by all the atoms in a metastable atomic state, and that this state is...
5. Enhanced Single Photon Emission from a Diamond-Silver Aperture
CERN Document Server
Choy, Jennifer T; Babinec, Thomas M; Bulu, Irfan; Khan, Mughees; Maletinsky, Patrick; Yacoby, Amir; Lončar, Marko
2011-01-01
We have developed a scalable method for coupling single color centers in diamond to plasmonic resonators and demonstrated Purcell enhancement of the single photon emission rate of nitrogen-vacancy (NV) centers. Our structures consist of single nitrogen-vacancy (NV) center-containing diamond nanoposts embedded in a thin silver film. We have utilized the strong plasmon resonances in the diamond-silver apertures to enhance the spontaneous emission of the enclosed dipole. The devices were realized by a combination of ion implantation and top-down nanofabrication techniques, which have enabled deterministic coupling between single NV centers and the plasmonic modes for multiple devices in parallel. The plasmon-enhanced NV centers exhibited over six-fold improvements in spontaneous emission rate in comparison to bare nanoposts and up to a factor of 3.6 in radiative lifetime reduction over bulk samples, with comparable increases in photon counts. The hybrid diamond-plasmon system presented here could provide a stabl...
6. Fiber-pigtailed optical tweezer for single-atom trapping and single-photon generation
CERN Document Server
Garcia, Sébastien; Hohmann, Leander; Reichel, Jakob; Long, Romain
2013-01-01
We demonstrate a miniature, fiber-coupled optical tweezer to trap a single atom. The same fiber is used to trap a single atom and to read out its fluorescence. To obtain a low background level, the tweezer light is chopped, and we measure the influence of the chopping frequency on the atom's lifetime. We use the single atom as a single-photon source at 780 nm and measure the second-order correlation function of the emitted photons. Because of its miniature, robust, fiber-pigtailed design, this tweezer can be implemented in a broad range of experiments where single atoms are used as a resource.
7. Quantum cryptography based on realistic "single-photon" source
Czech Academy of Sciences Publication Activity Database
Peřina, Jan; Haderka, Ondřej; Soubusta, Jan
Rochester: Optical Society of America, 2004 - (Bigelow, N.; Eberly, J.; Stroud, C.; Walmsley, I.), --- [International Conference on Quantum Information. Rochester (US), 10.06.2003-13.06.2003] R&D Projects: GA MŠk(CZ) LN00A015 Keywords : quantum cryptography * single-photon source Subject RIV: BH - Optics, Masers, Lasers
8. Programming Single-Photon Wavefronts for Quantum Authentication
NARCIS (Netherlands)
Pinkse, P.W.H.; Huisman, T.J.; Huisman, S.R.; Wolterink, T.A.W.; Mosk, A.P.
2014-01-01
We demonstrate the ability to program the wavefront of single-photon states produced by spontaneous parametric down conversion into complex two-dimensional patterns with a spatial light modulator for application in quantum authentication and quantum communication. © 2014 OSA
9. Single photon emission computed tomography (SPECT): Fundamentals, technique, clinical applications
International Nuclear Information System (INIS)
The fundamentals of SPECT (Single Photon Emission Computed Tomography) are presented, and the requirements on rotating SPECT systems are listed. SPECT with a rotating gamma camera has found general acceptance as an imaging method in nuclear medicine. Compared with conventional, two-dimensional imaging techniques, SPECT offers higher contrast and three-dimensional transversal, sagittal, coronal or oblique sectional images. (orig./MG)
10. Photonic nanowire-based single-photon source with polarization control
CERN Document Server
Gregersen, Niels
2016-01-01
This document describes a modal method for optical simulations of structures with elliptical cross sections and its application to the design of the photonic nanowire (NW)-based single-photon source (SPS). The work was carried out in the framework of the EMRP SIQUTE project ending May 31st 2016. The document summarizes the new method used to treat the elliptical cross section in an efficient manner and additionally presents design parameters for the photonic NW SPS with elliptical cross section for polarization control. The document does not introduce the new method and the elliptical photonic NW SPS design in the context of existing literature but instead dives directly into the equations. Additionally, the document assumes that the reader possess expert knowledge of general modal expansion techniques. The presented formalism does not implement Li's factorization rules nor the recently proposed open boundary geometry formalism with fast convergence towards the open geometry limit but instead relies on (older...
11. Telecom-wavelength single-photon sources for quantum communications
International Nuclear Information System (INIS)
This paper describes the progress towards the realization of efficient single-photon sources based on semiconductor quantum dots (QDs), for application in quantum key distribution and, more generally, quantum communications. We describe the epitaxial growth of QD arrays with low areal density and emitting in the telecom wavelength range, the nanofabrication of single-QD structures and devices, and their optical and electro-optical characterization. The potential for integration with monolithic microcavities is also discussed
12. Single photon detection with self-quenching multiplication
Science.gov (United States)
Zheng, Xinyu (Inventor); Cunningham, Thomas J. (Inventor); Pain, Bedabrata (Inventor)
2011-01-01
A photoelectronic device and an avalanche self-quenching process for a photoelectronic device are described. The photoelectronic device comprises a nanoscale semiconductor multiplication region and a nanoscale doped semiconductor quenching structure including a depletion region and an undepletion region. The photoelectronic device can act as a single photon detector or a single carrier multiplier. The avalanche self-quenching process allows electrical field reduction in the multiplication region by movement of the multiplication carriers, thus quenching the avalanche.
13. Fabrication of bright and small size semiconducting polymer nanoparticles for cellular labelling and single particle tracking
Science.gov (United States)
Wei, Lin; Zhou, Peng; Yang, Qingxiu; Yang, Qiaoyu; Ma, Ming; Chen, Bo; Xiao, Lehui
2014-09-01
In this work, we demonstrate a convenient and robust strategy for efficient fabrication of high fluorescence quantum yield (QY, 49.8 +/- 3%) semiconducting polymer nanoparticles (SPNs), with size comparable with semiconductor quantum dots (Qdots). The SPNs were synthesized by co-precipitation of hydrophobic semiconducting polymer together with amphiphilic multidentate polymer. Comprehensive spectroscopic and microscopic characterizations showed that the SPNs possess superior photophysical performance, with excellent fluorescence brightness and reduced photoblinking in contrast with Qdots, as well as good photostability compared to a fluorescent protein of a similar size, phycoerythrin. More importantly, by conjugating membrane biomarkers onto the surface of SPNs, it was found that they were not only suitable for specific cellular labelling but also for single particle tracking because of the improved optical performance.In this work, we demonstrate a convenient and robust strategy for efficient fabrication of high fluorescence quantum yield (QY, 49.8 +/- 3%) semiconducting polymer nanoparticles (SPNs), with size comparable with semiconductor quantum dots (Qdots). The SPNs were synthesized by co-precipitation of hydrophobic semiconducting polymer together with amphiphilic multidentate polymer. Comprehensive spectroscopic and microscopic characterizations showed that the SPNs possess superior photophysical performance, with excellent fluorescence brightness and reduced photoblinking in contrast with Qdots, as well as good photostability compared to a fluorescent protein of a similar size, phycoerythrin. More importantly, by conjugating membrane biomarkers onto the surface of SPNs, it was found that they were not only suitable for specific cellular labelling but also for single particle tracking because of the improved optical performance. Electronic supplementary information (ESI) available: Experimental section and additional supporting results as noted in the text
14. SiPM time resolution: From single photon to saturation
Energy Technology Data Exchange (ETDEWEB)
Gundacker, S., E-mail: [email protected] [European Organization for Nuclear Research (CERN), 1211 Geneva 23 (Switzerland); Auffray, E.; Di Vara, N.; Frisch, B.; Hillemanns, H.; Jarron, P. [European Organization for Nuclear Research (CERN), 1211 Geneva 23 (Switzerland); Lang, B. [Physical Chemistry Department - Sciences II - University of Geneva 30, Quai Ernest Ansermet, 1211 Geneva 4 (Switzerland); Meyer, T. [European Organization for Nuclear Research (CERN), 1211 Geneva 23 (Switzerland); Mosquera-Vazquez, S.; Vauthey, E. [Physical Chemistry Department - Sciences II - University of Geneva 30, Quai Ernest Ansermet, 1211 Geneva 4 (Switzerland); Lecoq, P. [European Organization for Nuclear Research (CERN), 1211 Geneva 23 (Switzerland)
2013-08-01
The time resolution of photon detection systems is important for a wide range of applications in physics and chemistry. It impacts the quality of time-resolved spectroscopy of ultrafast processes and has a direct influence on the best achievable time resolution of time-of-flight detectors in high-energy and medical physics. For the characterization of photon detectors, it is important to measure their exact timing properties in dependence of the photon flux and the operational parameters of the photodetector and its accompanying electronics. We report on the timing of silicon photomultipliers (SiPM) as a function of their bias voltage, electronics threshold settings and the number of impinging photons. We used ultrashort laser pulses at 400 nm wavelength with pulse duration below 200 fs. We focus our studies on different types of SiPMs (Hamamatsu MPPC S10931-025P, S10931-050P and S10931-100P) with different SPAD sizes (25μm, 50μm and 100μm) coupled to the ultrafast discriminator amplifier NINO. For the SiPMs, an optimum in the time resolution regarding bias and threshold settings can be reached. For the 50μm type, we achieve a single photon time resolution of 80 ps sigma, and for saturating photon fluxes better than 10 ps sigma.
15. Operational path-phase complementarity in single-photon interferometry
International Nuclear Information System (INIS)
We examine two set-ups that reveal different operational implications of path-phase complementarity for single photons in a Mach-Zehnder interferometer (MZI). In both set-ups, the which-way (WW) information is recorded in the polarization state of the photon serving as a 'flying which-way detector'. In the 'predictive' variant, using a fixed initial state, one obtains duality relation between the probability to correctly predict the outcome of either a which-way (WW) or which-phase (WP) measurement (equivalent to the conventional path-distinguishability-visibility). In this set-up, only one or the other (WW or WP) prediction has operational meaning in a single experiment. In the second, 'retrodictive' protocol, the initial state is secretly selected for each photon by one party, Alice, among a set of initial states which may differ in the amplitudes and phases of the photon in each arm of the MZI. The goal of the other party, Bob, is to retrodict the initial state by measurements on the photon. Here, a similar duality relation between WP and WW probabilities governs their simultaneous guesses in each experimental run.
16. An all-silicon single-photon source by unconventional photon blockade
CERN Document Server
Flayac, H; Savona, V
2015-01-01
The lack of suitable quantum emitters in silicon and silicon-based materials has prevented the realization of room temperature, compact, stable, and integrated sources of single photons in a scalable on-chip architecture, so far. Current approaches rely on exploiting the enhanced optical nonlinearity of silicon through light confinement or slow-light propagation, and are based on parametric processes that typically require substantial input energy and spatial footprint to reach a reasonable output yield. Here we propose an alternative all-silicon device that employs a different paradigm, namely the interplay between quantum interference and the third-order intrinsic nonlinearity in a system of two coupled optical cavities. This unconventional photon blockade allows to produce antibunched radiation at extremely low input powers. We demonstrate a reliable protocol to operate this mechanism under pulsed optical excitation, as required for device applications, thus implementing a true single-photon source. We fin...
17. Quantum Secure Direct Communication with Authentication Expansion Using Single Photons
International Nuclear Information System (INIS)
In this paper we propose two quantum secure direct communication (QSDC) protocols with authentication. The authentication key expansion method is introduced to improve the life of the keys with security. In the first scheme, the third party, called Trent is introduced to authenticate the users that participate in the communication. He sends the polarized photons in blocks to authenticate communication parties Alice and Bob using the authentication keys. In the communication process, polarized single photons are used to serve as the carriers, which transmit the secret messages directly. The second QSDC process with authentication between two parties is also discussed.
18. Unified single-photon and single-electron counting statistics: From cavity QED to electron transport
International Nuclear Information System (INIS)
A key ingredient of cavity QED is the coupling between the discrete energy levels of an atom and photons in a single-mode cavity. The addition of periodic ultrashort laser pulses allows one to use such a system as a source of single photons--a vital ingredient in quantum information and optical computing schemes. Here we analyze and time-adjust the photon-counting statistics of such a single-photon source and show that the photon statistics can be described by a simple transport-like nonequilibrium model. We then show that there is a one-to-one correspondence of this model to that of nonequilibrium transport of electrons through a double quantum dot nanostructure, unifying the fields of photon-counting statistics and electron-transport statistics. This correspondence empowers us to adapt several tools previously used for detecting quantum behavior in electron-transport systems (e.g., super-Poissonian shot noise and an extension of the Leggett-Garg inequality) to single-photon-source experiments.
19. Trapping a single atom with a fraction of a photon using a photonic crystal nanocavity
NARCIS (Netherlands)
van Oosten, D.; Kuipers, L.
2011-01-01
We consider the interaction between a single rubidium atom and a photonic crystal nanocavity. Because of the ultrasmall mode volume of the nanocavity, an extremely strong coupling regime can be achieved in which the atom can shift the cavity resonance by many cavity linewidths. We show that this shi
20. High-efficiency single-photon source: The photonic wire geometry
DEFF Research Database (Denmark)
Claudon, J.; Bazin, Maela; Malik, Nitin S.;
2009-01-01
We present a single-photon-source design based on the emission of a quantum dot embedded in a semiconductor (GaAs) nanowire. The nanowire ends are engineered (efficient metallic mirror and tip taper) to reach a predicted record-high collection efficiency of 90% with a realistic design. Preliminary...
1. Few-photon coherent nonlinear optics with a single molecule
CERN Document Server
Maser, Andreas; Utikal, Tobias; Götzinger, Stephan; Sandoghdar, Vahid
2015-01-01
The pioneering experiments of linear spectroscopy were performed using flames in the 1800s, but nonlinear optical measurements had to wait until lasers became available in the twentieth century. Because the nonlinear cross section of materials is very small, usually macroscopic bulk samples and pulsed lasers are used. Numerous efforts have explored coherent nonlinear signal generation from individual nanoparticles or small atomic ensembles with millions of atoms. Experiments on a single semiconductor quantum dot have also been reported, albeit with a very small yield. Here, we report on coherent nonlinear spectroscopy of a single molecule under continuous-wave single-pass illumination, where efficient photon-molecule coupling in a tight focus allows switching of a laser beam by less than a handful of pump photons nearly resonant with the sharp molecular transition. Aside from their fundamental importance, our results emphasize the potential of organic molecules for applications such as quantum information pro...
2. Apparent superluminal advancement of a single photon far beyond its coherence length
OpenAIRE
Cialdi, S; Boscolo, I.; CASTELLI, F.; Petrillo, V.
2008-01-01
We present experimental results relative to superluminal propagation based on a single photon traversing an optical system, called 4f-system, which acts singularly on the photon's spectral component phases. A single photon is created by a CW laser light down{conversion process. The introduction of a linear spectral phase function will lead to the shift of the photon peak far beyond the coherence length of the photon itself (an apparent superluminal propagation of the photon). Superluminal gro...
3. On-Chip Detection of Entangled Photons by Scalable Integration of Single-Photon Detectors
CERN Document Server
Najafi, Faraz; Harris, Nicholas; Bellei, Francesco; Dane, Andrew; Lee, Catherine; Kharel, Prashanta; Marsili, Francesco; Assefa, Solomon; Berggren, Karl K; Englund, Dirk
2014-01-01
Photonic integrated circuits (PICs) have emerged as a scalable platform for complex quantum technologies using photonic and atomic systems. A central goal has been to integrate photon-resolving detectors to reduce optical losses, latency, and wiring complexity associated with off-chip detectors. Superconducting nanowire single-photon detectors (SNSPDs) are particularly attractive because of high detection efficiency, sub-50-ps timing jitter, nanosecond-scale reset time, and sensitivity from the visible to the mid-infrared spectrum. However, while single SNSPDs have been incorporated into individual waveguides, the system efficiency of multiple SNSPDs in one photonic circuit has been limited below 0.2% due to low device yield. Here we introduce a micrometer-scale flip-chip process that enables scalable integration of SNSPDs on a range of PICs. Ten low-jitter detectors were integrated on one PIC with 100% device yield. With an average system efficiency beyond 10% for multiple SNSPDs on one PIC, we demonstrate h...
4. Multi-photon creation and single-photon annihilation of electron-positron pairs
International Nuclear Information System (INIS)
In this thesis we study multi-photon e+e- pair production in a trident process, and singlephoton e+e- pair annihilation in a triple interaction. The pair production is considered in the collision of a relativistic electron with a strong laser beam, and calculated within the theory of laser-dressed quantum electrodynamics. A regularization method is developed systematically for the resonance problem arising in the multi-photon process. Total production rates, positron spectra, and relative contributions of different reaction channels are obtained in various interaction regimes. Our calculation shows good agreement with existing experimental data from SLAC, and adds further insights into the experimental findings. Besides, we study the process in a manifestly nonperturbative domain, whose accessibility to future all-optical experiments based on laser acceleration is shown. In the single-photon e+e- pair annihilation, the recoil momentum is absorbed by a spectator particle. Various kinematic configurations of the three incoming particles are examined. Under certain conditions, the emitted photon exhibits distinct angular and polarization distributions which could facilitate the detection of the process. Considering an equilibrium relativistic e+e- plasma, it is found that the single-photon process becomes the dominant annihilation channel for plasma temperatures above 3 MeV. Multi-particle correlation effects are therefore essential for the e+e- dynamics at very high density. (orig.)
5. Multi-photon creation and single-photon annihilation of electron-positron pairs
Energy Technology Data Exchange (ETDEWEB)
Hu, Huayu
2011-04-27
In this thesis we study multi-photon e{sup +}e{sup -} pair production in a trident process, and singlephoton e{sup +}e{sup -} pair annihilation in a triple interaction. The pair production is considered in the collision of a relativistic electron with a strong laser beam, and calculated within the theory of laser-dressed quantum electrodynamics. A regularization method is developed systematically for the resonance problem arising in the multi-photon process. Total production rates, positron spectra, and relative contributions of different reaction channels are obtained in various interaction regimes. Our calculation shows good agreement with existing experimental data from SLAC, and adds further insights into the experimental findings. Besides, we study the process in a manifestly nonperturbative domain, whose accessibility to future all-optical experiments based on laser acceleration is shown. In the single-photon e{sup +}e{sup -} pair annihilation, the recoil momentum is absorbed by a spectator particle. Various kinematic configurations of the three incoming particles are examined. Under certain conditions, the emitted photon exhibits distinct angular and polarization distributions which could facilitate the detection of the process. Considering an equilibrium relativistic e{sup +}e{sup -} plasma, it is found that the single-photon process becomes the dominant annihilation channel for plasma temperatures above 3 MeV. Multi-particle correlation effects are therefore essential for the e{sup +}e{sup -} dynamics at very high density. (orig.)
6. QUPID, a single photon sensor for extremely low radioactivity
International Nuclear Information System (INIS)
We have successfully developed a new photon sensor, the Quartz Photon Intensifying Detector (QUPID), for experiments such as dark matter searches and observation of double beta decay. The QUPID is a type of hybrid-photo-detector (HPD), consisting of a special bialkali photocathode considering the operation under extremely low temperature such as the temperature of liquid xenon, -108 oC, and a special avalanche photodiode for electron bombardment. The QUPID is constructed solely from extremely low radioactive materials, such as quartz and Si-avalanche photodiodes (APDs), which allows it to reach radiation levels of less than 1 mBq while being able to detect single photons. In this paper, we report superior characteristics of the QUPID confirmed by the evaluation.
7. Single Photon studies in ATLAS with Run 2 dataset
CERN Document Server
Aparisi Pozo, Javier Alberto; Solans Sanchez, Carlos; CERN. Geneva. EP Department
2016-01-01
We present a performance study of photon reconstruction within the Higgs working group of the ATLAS experiment. The analysis use a data sample of proton-proton collisions at center-of-mass energy of $\\sqrt{s} = 13~TeV$, recorded with the ATLAS detector at the LHC in 2015+2016, corresponding to a total integrated luminosity of 14.5 $fb^{-1}$ (at the moment). The performance of electron and photon reconstruction plays a critical role in the reach of many analysis, including $H\\rightarrow \\gamma \\gamma$ and $H\\rightarrow 4l$ concerning Higgs searches. This work is a study of single photon conversions with the ATLAS detector.
8. Photonic Quantum Logic with Narrowband Light from Single Atoms
Science.gov (United States)
Rubenok, Allison; Holleczek, Annemarie; Barter, Oliver; Dilley, Jerome; Nisbet-Jones, Peter B. R.; Langfahl-Klabes, Gunnar; Kuhn, Axel; Sparrow, Chris; Marshall, Graham D.; O'Brien, Jeremy L.; Poulios, Konstantinos; Matthews, Jonathan C. F.
Atom-cavity sources of narrowband photons are a promising candidate for the future development of quantum technologies. Likewise, integrated photonic circuits have established themselves as a fore-running contender in quantum computing, security, and communication. Here we report on recent achievements to interface these two technologies: Atom-cavity sources coupled to integrated photonic circuits. Using narrow linewidth photons emitted from a single 87 Rb atom strongly coupled to a high-finesse cavity we demonstrate the successful operation of an integrated control-not gate. Furthermore, we are able to verify the generation of post-selected entanglement upon successful operation of the gate. We are able to see non-classical correlations in detection events that are up to three orders of magnitude farther apart than the time needed for light to travel across the chip. Our hybrid approach will facilitate the future development of technologies that benefit from the advantages of both integrated quantum circuits and atom-cavity photon sources. Now at: National Physics Laboratory.
9. Limits on the deterministic creation of pure single-photon states using parametric down-conversion
CERN Document Server
Christ, Andreas
2011-01-01
Parametric down-conversion (PDC) is one of the most widely used methods to create pure single-photon states for quantum information applications. However little attention has been paid to higher-order photon components in the PDC process, yet these ultimately limit the prospects of generating single-photons of high quality. In this paper we investigate the impacts of higher-order photon components and multiple frequency modes on the heralding rates and single-photon fidelities. This enables us to determine the limits of PDC sources for single-photon generation. Our results show that a perfectly single-mode PDC source in conjunction with a photon-number resolving detector is ultimately capable of creating single-photon Fock states with unit fidelity and a maximal state creation probability of 25%. Hence an array of 17 switched sources is required to build a deterministic (>99% emission probability) pure single-photon source.
10. Automated Characterization of Single-Photon Avalanche Photodiode
Directory of Open Access Journals (Sweden)
Aina Mardhiyah M. Ghazali
2012-01-01
Full Text Available We report an automated characterization of a single-photon detector based on commercial silicon avalanche photodiode (PerkinElmer C30902SH. The photodiode is characterized by I-V curves at different illumination levels (darkness, 10 pW and 10 µW, dark count rate and photon detection efficiency at different bias voltages. The automated characterization routine is implemented in C++ running on a Linux computer. ABSTRAK: Kami melaporkan pencirian pengesan foton tunggal secara automatik berdasarkan kepada diod foto runtuhan silikon (silicon avalanche photodiode (PerkinElmer C30902SH komersial. Pencirian diod foto adalah berdasarkan kepada plot arus-voltan (I-V pada tahap pencahayaan yang berbeza (kelam - tanpa cahaya, 10pW, dan 10µW, kadar bacaan latar belakang, kecekapan pengesanan foton pada voltan picuan yang berbeza. Pengaturcaraan C++ digunakan di dalam rutin pencirian automatik melalui komputer dengan sistem pengendalian LINUX.KEYWORDS: avalanche photodiode (APD; single photon detector; photon counting; experiment automation
11. All-optical tailoring of single-photon spectra in a quantum-dot microcavity system
CERN Document Server
Breddermann, Dominik; Binder, Rolf; Zrenner, Artur; Schumacher, Stefan
2016-01-01
Semiconductor quantum-dot cavity systems are promising sources for solid-state based on-demand generation of single photons for quantum communication. Commonly, the spectral characteristics of the emitted single photon are fixed by system properties such as electronic transition energies and spectral properties of the cavity. In the present work we study single-photon generation from the quantum-dot biexciton through a partly stimulated non-degenerate two-photon emission. We show that frequency and linewidth of the single photon can be fully controlled by the stimulating laser pulse, ultimately allowing for efficient all-optical spectral shaping of the single photon.
12. Research in absolute calibration of single photon detectors by means of correlated photons
Institute of Scientific and Technical Information of China (English)
Yu Feng; Xiaobing Zheng; Jianjun Li; Wei Zhang
2006-01-01
There are two general methods in radiometric calibration of detectors, one is based on radiation sources and the other based on detectors. Because the two methods need to establish a primary standard of high precision and a transfer chain, precision of the standard will be reduced by extension of the chain. A new calibration method of detectors can be realized by using correlated photons generated in spontaneous parametric down-conversion (SPDC) effect of nonlinear crystal, without needing transfer chain. Using 351.1-nm output of a tunable laser to pump β-barium borate (BBO) crystal, an absolute calibration experimental system of single photon detectors based on correlated photons is performed. The quantum efficiency of photomultiplier (PMT) at 702.2 nm is measured by the setup. Advantages of this method over traditional methods are also pointed out by comparison.
13. Advanced time-correlated single photon counting techniques
CERN Document Server
Becker, Wolfgang
2005-01-01
Time-correlated single photon counting (TCSPC) is a remarkable technique for recording low-level light signals with extremely high precision and picosecond-time resolution. TCSPC has developed from an intrinsically time-consuming and one-dimensional technique into a fast, multi-dimensional technique to record light signals. So this reference and text describes how advanced TCSPC techniques work and demonstrates their application to time-resolved laser scanning microscopy, single molecule spectroscopy, photon correlation experiments, and diffuse optical tomography of biological tissue. It gives practical hints about constructing suitable optical systems, choosing and using detectors, detector safety, preamplifiers, and using the control features and optimising the operating conditions of TCSPC devices. Advanced TCSPC Techniques is an indispensable tool for everyone in research and development who is confronted with the task of recording low-intensity light signals in the picosecond and nanosecond range.
14. Localization of Narrowband Single Photon Emitters in Nanodiamonds.
Science.gov (United States)
Bray, Kerem; Sandstrom, Russell; Elbadawi, Christopher; Fischer, Martin; Schreck, Matthias; Shimoni, Olga; Lobo, Charlene; Toth, Milos; Aharonovich, Igor
2016-03-23
Diamond nanocrystals that host room temperature narrowband single photon emitters are highly sought after for applications in nanophotonics and bioimaging. However, current understanding of the origin of these emitters is extremely limited. In this work, we demonstrate that the narrowband emitters are point defects localized at extended morphological defects in individual nanodiamonds. In particular, we show that nanocrystals with defects such as twin boundaries and secondary nucleation sites exhibit narrowband emission that is absent from pristine individual nanocrystals grown under the same conditions. Critically, we prove that the narrowband emission lines vanish when extended defects are removed deterministically using highly localized electron beam induced etching. Our results enhance the current understanding of single photon emitters in diamond and are directly relevant to fabrication of novel quantum optics devices and sensors. PMID:26937848
15. Quantum private query based on single-photon interference
Science.gov (United States)
Xu, Sheng-Wei; Sun, Ying; Lin, Song
2016-08-01
Quantum private query (QPQ) has become a research hotspot recently. Specially, the quantum key distribution (QKD)-based QPQ attracts lots of attention because of its practicality. Various such kind of QPQ protocols have been proposed based on different technologies of quantum communications. Single-photon interference is one of such technologies, on which the famous QKD protocol GV95 is just based. In this paper, we propose two QPQ protocols based on single-photon interference. The first one is simpler and easier to realize, and the second one is loss tolerant and flexible, and more practical than the first one. Furthermore, we analyze both the user privacy and the database privacy in the proposed protocols.
16. Localization of narrowband single photon emitters in nanodiamonds
CERN Document Server
Bray, Kerem; Elbadawi, Christopher; Fischer, Martin; Schreck, Matthias; Shimoni, Olga; Lobo, Charlene; Toth, Milos; Aharonovich, Igor
2016-01-01
Diamond nanocrystals that host room temperature narrowband single photon emitters are highly sought after for applications in nanophotonics and bio-imaging. However, current understanding of the origin of these emitters is extremely limited. In this work we demonstrate that the narrowband emitters are point defects localized at extended morphological defects in individual nanodiamonds. In particular, we show that nanocrystals with defects such as twin boundaries and secondary nucleation sites exhibit narrowband emission that is absent from pristine individual nanocrystals grown under the same conditions. Critically, we prove that the narrowband emission lines vanish when extended defects are removed deterministically using highly localized electron beam induced etching. Our results enhance the current understanding of single photon emitters in diamond, and are directly relevant to fabrication of novel quantum optics devices and sensors.
17. Photon Cascade from a Single Crystal Phase Nanowire Quantum Dot
DEFF Research Database (Denmark)
Bouwes Bavinck, Maaike; Jöns, Klaus D; Zieliński, Michal; Patriarche, Gilles; Harmand, Jean-Christophe; Akopian, Nika; Zwiller, Val
2016-01-01
unprecedented potential to be controlled with atomic layer accuracy without random alloying. We show for the first time that crystal phase quantum dots are a source of pure single-photons and cascaded photon-pairs from type II transitions with excellent optical properties in terms of intensity and line width......We report the first comprehensive experimental and theoretical study of the optical properties of single crystal phase quantum dots in InP nanowires. Crystal phase quantum dots are defined by a transition in the crystallographic lattice between zinc blende and wurtzite segments and therefore offer....... We notice that the emission spectra consist often of two peaks close in energy, which we explain with a comprehensive theory showing that the symmetry of the system plays a crucial role for the hole levels forming hybridized orbitals. Our results state that crystal phase quantum dots have promising...
18. Authenticated Quantum Key Distribution with Collective Detection using Single Photons
Science.gov (United States)
Huang, Wei; Xu, Bing-Jie; Duan, Ji-Tong; Liu, Bin; Su, Qi; He, Yuan-Hang; Jia, Heng-Yue
2016-05-01
We present two authenticated quantum key distribution (AQKD) protocols by utilizing the idea of collective (eavesdropping) detection. One is a two-party AQKD protocol, the other is a multiparty AQKD protocol with star network topology. In these protocols, the classical channels need not be assumed to be authenticated and the single photons are used as the quantum information carriers. To achieve mutual identity authentication and establish a random key in each of the proposed protocols, only one participant should be capable of preparing and measuring single photons, and the main quantum ability that the rest of the participants should have is just performing certain unitary operations. Security analysis shows that these protocols are free from various kinds of attacks, especially the impersonation attack and the man-in-the-middle (MITM) attack.
19. Quantum private query based on single-photon interference
Science.gov (United States)
Xu, Sheng-Wei; Sun, Ying; Lin, Song
2016-05-01
Quantum private query (QPQ) has become a research hotspot recently. Specially, the quantum key distribution (QKD)-based QPQ attracts lots of attention because of its practicality. Various such kind of QPQ protocols have been proposed based on different technologies of quantum communications. Single-photon interference is one of such technologies, on which the famous QKD protocol GV95 is just based. In this paper, we propose two QPQ protocols based on single-photon interference. The first one is simpler and easier to realize, and the second one is loss tolerant and flexible, and more practical than the first one. Furthermore, we analyze both the user privacy and the database privacy in the proposed protocols.
20. Single-photon ultrashort-lived radionuclides: symposium proceedings
Energy Technology Data Exchange (ETDEWEB)
Paras, P.; Thiessen, J.W. (eds.)
1985-01-01
The purpose was to define the current role and state-of-the-art regarding the development, clinical applications, and usefulness of generator-produced single-photon ultrashort-lived radionuclides (SPUSLR's) and to predict their future impact on medicine. Special emphasis was placed on the generator production of iridium-191, gold-195, and krypton-81. This report contains expanded summaries of the included papers. (ACR)
1. Single Photon Emission Tomography Imaging in Parkinsonian Disorders: A Review
OpenAIRE
Acton, Paul D.; P. David Mozley
2000-01-01
Parkinsonian symptoms are associated with a number of neurodegenerative disorders, such as Parkinson’s disease, multiple system atrophy and progressive supranuclear palsy. Pathological evidence has shown clearly that these disorders are associated with a loss of neurons, particularly in the nigrostriatal dopaminergic pathway. Positron emission tomography (PET) and single photon emission tomography (SPECT) now are able to visualise and quantify changes in cerebral blood flow, glucose metabolis...
2. Clinical results of quantitative single photon emission tomography
International Nuclear Information System (INIS)
In addition to the traditional skills of pattern recognition in the interpretation of images, it is necessary to add quantitative techniques, particularly in difficult problems, to determine normal and abnormal variation. Single photon emission tomography, SPET, overcomes the problems of tissue background and superficial tissue overlying a suspect lesion. Nevertheless, the goal of absolute quantitation is important in the solution to several clinical problems. The use and success of quantitative SPET in the liver, heart, adrenal and pituitary glands are reviewed. (author)
3. Superconducting nanowire single photon detectors for quantum information and communications
OpenAIRE
Wang, Zhen; Miki, Shigehito; Fujiwara, Mikio
2010-01-01
Superconducting nanowire single photon detectors (SNSPD or SSPD) are highly promising devices in the growing field of quantum information and communications technology. We have developed a practical SSPD system with our superconducting thin films and devices fabrication, optical coupling packaging, and cryogenic technology. The SSPD system consists of six-channel SSPD devices and a compact Gifford-McMahon (GM) cryocooler, and can operate continuously on 100 V ac power without the need for any...
4. Fabrication and test of Superconducting Single Photon Detectors
International Nuclear Information System (INIS)
We report here on the state of our fabrication process for Superconducting Single Photon Detectors (SSPDs). We have fabricated submicrometer SSPD structures by electron beam lithography using very thin (10 nm) NbN films deposited by DC-magnetron sputtering on different substrates and at room substrate temperature. The structures show a fast optical response (risetime <500 ps limited by readout electronics) and interesting self-resetting features
5. Secure authentication of classical messages with single photons
International Nuclear Information System (INIS)
This paper proposes a scheme for secure authentication of classical messages with single photons and a hashed function. The security analysis of this scheme is also given, which shows that anyone cannot forge valid message authentication codes (MACs). In addition, the lengths of the authentication key and the MACs are invariable and shorter, in comparison with those presented authentication schemes. Moreover, quantum data storage and entanglement are not required in this scheme. Therefore, this scheme is more efficient and economical. (general)
6. Coherence measures for heralded single-photon sources
OpenAIRE
Bocquillon, E.; Couteau, C.; Razavi, M.; Laflamme, R.; Weihs, G.
2008-01-01
Single-photon sources (SPSs) are mainly characterized by the minimum value of their second-order coherence function, viz. their $g^{(2)}$ function. A precise measurement of $g^{(2)}$ may, however, require high time-resolution devices, in whose absence, only time-averaged measurements are accessible. These time-averaged measures, standing alone, do not carry sufficient information for proper characterization of SPSs. Here, we develop a theory, corroborated by an experiment, that allows us to s...
7. Single-Photon Emission Computed Tomography in Neurotherapeutics
OpenAIRE
Devous, Michael D.
2005-01-01
Summary: The measurement of regional cerebral blood flow (rCBF) by single-photon emission computed tomography (SPECT) is a powerful clinical and research tool. There are several clinical applications now documented, a substantial number under active investigation, and a larger number yet to be studied. Standards regarding patient imaging environment and image presentation are becoming established. This article reviews key aspects of SPECT functional brain imaging in clinical practice, with a ...
8. Single-photon imaging in complementary metal oxide semiconductor processes.
Science.gov (United States)
Charbon, E
2014-03-28
9. A Search for Single Photon Events in Neutrino Interactions
CERN Document Server
Kullenberg, C T; Dimmery, D; Tian, X C; Autiero, D; Gninenko, S; Rubbia, A; Alekhin, S; Astier, P; Baldisseri, A; Baldo-Ceolin, M; Banner, M; Bassompierre, G; Benslama, K; Besson, N; Bird, I; Blumenfeld, B; Bobisut, F; Bouchez, J; Boyd, S; Bueno, A; Bunyatov, S; Camilleri, L; Cardini, A; Cattaneo, P W; Cavasinni, V; Cervera-Villanueva, A; Challis, R; Chukanov, A; Collazuol, G; Conforto, G; Conta, C; Contalbrigo, M; Cousins, R; Degaudenzi, H; De Santo, A; Del Prete, T.; Di Lella, L; do Couto e Silva, E; Dumarchez, J; Ellis, M; Feldman, G J; Ferrari, R; Ferrere, D.; Flaminio, V; Fraternali, M; Gaillard, J M; Gangler, E; Geiser, A; Geppert, D; Gibin, D; Godley, A; Gomez-Cadenas, J J; Gosset, J; Gossling, C; Gouanere, M.; Grant, A; Graziani, G; Guglielmi, A; Hagner, C; Hernando, J; Hurst, P; Hyett, N; Iacopini, E; Joseph, C; Juget, F; Kent, N; Klimov, O; Kokkonen, J; Kovzelev, A; Krasnoperov, A; Kim, J J; Kirsanov, M.; Kulagin, S; Lacaprara, S; Lachaud, C; Lakic, B; Lanza, A; La Rotonda, L; Laveder, M; Letessier-Selvon, A; Levy, J M; Ling, J; Linssen, L; Ljubicic, A; Long, J; Lupi, A; Lyubushkin, V; Marchionni, A; Martelli, F; Mechain, X; Mendiburu, J P; Meyer, J P; Mezzetto, M; Moorhead, G F; Naumov, D; Nedelec, P; Nefedov, Yu; Nguyen-Mau, C; Orestano, D; Pastore, F; Peak, L S; Pennacchio, E; Pessard, H; Petti, R.; Placci, A; Polesello, G; Pollmann, D; Polyarush, A; Poulsen, C; Popov, B; Rebuffi, L; Rico, J; Riemann, P; Roda, C; Salvatore, F; Samoylov, O; Schahmaneche, K; Schmidt, B; Schmidt, T; Sconza, A; Scott, A.M.; Seaton, M.B.; Sevior, M; Sillou, D; Soler, F.J.P.; Sozzi, G; Steele, D; Stiegler, U; Stipcevic, M; Stolarczyk, Th.; Tareb-Reyes, M.; Taylor, G.N.; Tereshchenko, V.; Toropin, A.; Touchard, A.-M.; Tovey, S.N.; Tran, M.-T.; Tsesmelis, E.; Ulrichs, J.; Vacavant, L.; Valdata-Nappi, M.; Valuev, V.; Vannucci, F.; Varvell, K.E.; Veltri, M.; Vercesi, V.; Vidal-Sitjes, G.; Vieira, J.-M.; Vinogradova, T.; Weber, F.V.; Weisse, T.; Wilson, F.F.; Winton, L.J.; Wu, Q.; Yabsley, B.D.; Zaccone, H.; Zuber, K.; Zuccon, P.
2012-01-01
We present a search for neutrino-induced events containing a single, exclusive photon using data from the NOMAD experiment at the CERN SPS where the average energy of the neutrino flux is $\\simeq 25$ GeV. The search is motivated by an excess of electron-like events in the 200--475 MeV energy region as reported by the MiniBOONE experiment. In NOMAD, photons are identified via their conversion to $e^+e^-$ in an active target embedded in a magnetic field. The background to the single photon signal is dominated by the asymmetric decay of neutral pions produced either in a coherent neutrino-nucleus interaction, or in a neutrino-nucleon neutral current deep inelastic scattering, or in an interaction occurring outside the fiducial volume. All three backgrounds are determined {\\it in situ} using control data samples prior to opening the `signal-box'. In the signal region, we observe {\\bf 155} events with a predicted background of {\\bf 129.2 $\\pm$ 8.5 $\\pm$ 3.3}. We interpret this as null evidence for excess of single...
10. High-fidelity frequency down-conversion of visible entangled photon pairs with superconducting single-photon detectors
Energy Technology Data Exchange (ETDEWEB)
Ikuta, Rikizo; Kato, Hiroshi; Kusaka, Yoshiaki; Yamamoto, Takashi; Imoto, Nobuyuki [Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531 (Japan); Miki, Shigehito; Yamashita, Taro; Terai, Hirotaka; Wang, Zhen [Advanced ICT Research Institute, National Institute of Information and Communications Technology (NICT), Kobe 651-2492 (Japan); Fujiwara, Mikio; Sasaki, Masahide [Advanced ICT Research Institute, National Institute of Information and Communications Technology (NICT), Koganei, Tokyo 184-8795 (Japan); Koashi, Masato [Photon Science Center, The University of Tokyo, Bunkyo-ku, 113-8656 (Japan)
2014-12-04
We experimentally demonstrate a high-fidelity visible-to-telecommunicationwavelength conversion of a photon by using a solid-state-based difference frequency generation. In the experiment, one half of a pico-second visible entangled photon pair at 780 nm is converted to a 1522-nm photon. Using superconducting single-photon detectors with low dark count rates and small timing jitters, we observed a fidelity of 0.93±0.04 after the wavelength conversion.
11. Feasibility of detecting single atoms using photonic bandgap cavities
CERN Document Server
Lev, B I; Barclay, P; Painter, O J; Mabuchi, H; Lev, Benjamin; Srinivasan, Kartik; Barclay, Paul; Painter, Oskar; Mabuchi, Hideo
2004-01-01
We propose an atom-cavity chip that combines laser cooling and trapping of neutral atoms with magnetic microtraps and waveguides to deliver a cold atom to the mode of a fiber taper coupled photonic bandgap (PBG) cavity. The feasibility of this device for detecting single atoms is analyzed using both a semi-classical treatment and an unconditional master equation approach. Single-atom detection seems achievable in an initial experiment involving the non-deterministic delivery of weakly trapped atoms into the mode of the PBG cavity.
12. Molecular single photon double K-shell ionization
Energy Technology Data Exchange (ETDEWEB)
Penent, F., E-mail: [email protected] [UPMC, Université Paris 06, LCPMR, 11 rue P. et M. Curie, 75231 Paris Cedex 05 (France); CNRS, LCPMR (UMR 7614), 11 rue P. et M. Curie, 75231 Paris Cedex 05 (France); Nakano, M. [Photon Factory, Institute of Materials Structure Science, Oho, Tsukuba 305-0801 (Japan); Department of Chemistry, Tokyo Institute of Technology, O-okayama, Tokyo 152-8551 (Japan); Tashiro, M. [Institute for Molecular Science, Okazaki 444-8585 (Japan); Grozdanov, T.P. [Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade (Serbia); Žitnik, M. [Jožef Stefan Institute, P.O. Box 3000, SI-1001 Ljubljana (Slovenia); Carniato, S.; Selles, P.; Andric, L.; Lablanquie, P.; Palaudoux, J. [UPMC, Université Paris 06, LCPMR, 11 rue P. et M. Curie, 75231 Paris Cedex 05 (France); CNRS, LCPMR (UMR 7614), 11 rue P. et M. Curie, 75231 Paris Cedex 05 (France); Shigemasa, E.; Iwayama, H. [Institute for Molecular Science, Okazaki 444-8585 (Japan); Hikosaka, Y.; Soejima, K. [Department of Environmental Science, Niigata University, Niigata 950-2181 (Japan); Suzuki, I.H. [Photon Factory, Institute of Materials Structure Science, Oho, Tsukuba 305-0801 (Japan); Kouchi, N. [Department of Chemistry, Tokyo Institute of Technology, O-okayama, Tokyo 152-8551 (Japan); Ito, K. [Photon Factory, Institute of Materials Structure Science, Oho, Tsukuba 305-0801 (Japan)
2014-10-15
We have studied single photon double K-shell ionization of small molecules (N{sub 2}, CO, C{sub 2}H{sub 2n} (n = 1–3), …) and the Auger decay of the resulting double core hole (DCH) molecular ions thanks to multi-electron coincidence spectroscopy using a magnetic bottle time-of-flight spectrometer. The relative cross-sections for single-site (K{sup −2}) and two-site (K{sup −1}K{sup −1}) double K-shell ionization with respect to single K-shell (K{sup −1}) ionization have been measured that gives important information on the mechanisms of single photon double ionization. The spectroscopy of two-site (K{sup −1}K{sup −1}) DCH states in the C{sub 2}H{sub 2n} (n = 1–3) series shows important chemical shifts due to a strong dependence on the C-C bond length. In addition, the complete cascade Auger decay following single site (K{sup −2}) ionization has been obtained.
13. Efficient and robust fiber coupling of superconducting single photon detectors
CERN Document Server
Dorenbos, S N; Driessen, E F C; Zwiller, V
2011-01-01
We applied a recently developed fiber coupling technique to superconducting single photon detectors (SSPDs). As the detector area of SSPDs has to be kept as small as possible, coupling to an optical fiber has been either inefficient or unreliable. Etching through the silicon substrate allows fabrication of a circularly shaped chip which self aligns to the core of a ferrule terminated fiber in a fiber sleeve. In situ alignment at cryogenic temperatures is unnecessary and no thermal stress during cooldown, causing misalignment, is induced. We measured the quantum efficiency of these devices with an attenuated tunable broadband source. The combination of a lithographically defined chip and high precision standard telecommunication components yields near unity coupling efficiency and a system detection efficiency of 34% at a wavelength of 1200 nm. This quantum efficiency measurement is confirmed by an absolute efficiency measurement using correlated photon pairs (with $\\lambda$ = 1064 nm) produced by spontaneous ...
14. A single probe for imaging photons, electrons and physical forces
Science.gov (United States)
Pilet, Nicolas; Lisunova, Yuliya; Lamattina, Fabio; Stevenson, Stephanie E.; Pigozzi, Giancarlo; Paruch, Patrycja; Fink, Rainer H.; Hug, Hans J.; Quitmann, Christoph; Raabe, Joerg
2016-06-01
The combination of complementary measurement techniques has become a frequent approach to improve scientific knowledge. Pairing of the high lateral resolution scanning force microscopy (SFM) with the spectroscopic information accessible through scanning transmission soft x-ray microscopy (STXM) permits assessing physical and chemical material properties with high spatial resolution. We present progress from the NanoXAS instrument towards using an SFM probe as an x-ray detector for STXM measurements. Just by the variation of one parameter, the SFM probe can be utilised to detect either sample photo-emitted electrons or transmitted photons. This allows the use of a single probe to detect electrons, photons and physical forces of interest. We also show recent progress and demonstrate the current limitations of using a high aspect ratio coaxial SFM probe to detect photo-emitted electrons with very high lateral resolution. Novel probe designs are proposed to further progress in using an SFM probe as a STXM detector.
15. Modal coupling of single photons to a nanofibre
CERN Document Server
Gaio, Michele; Castro-Lopez, Marta; Pisignano, Dario; Camposeo, Andrea; Sapienza, Riccardo
2015-01-01
Nanoscale quantum optics of individual light emitters placed in confined geometries is developing as an exciting new research field aiming at efficient manipulation of single-photons . This requires selective channelling of light into specific optical modes of nanophotonic structures. Hybrid photonic systems combining emitters with nanostructured media can yield this functionality albeit limited by the required nanometre-scale spatial and spectral coupling. Furthermore, assessing the coupling strength presents significant challenges and disentangling the different modal contribution is often impossible. Here, we show that momentum spectroscopy of individually addressed emitters, embedded in a nanofibre, can be used to quantify the modal coupling efficiency to the nanofibre modes. For free-standing polymer nanofibres doped with colloidal quantum dots, we report broadband coupling to the fundamental mode of up $\\beta_{01}=31\\pm2\\%$, in robust agreement with theoretical calculations. Electrospun soft-matter nano...
16. Proposal for calibration of a single-photon counting detector without the need of input photon flux calibration
International Nuclear Information System (INIS)
A method for calibration of single-photon detectors without the need of input photon flux calibration is presented. The method relies on the use of waveguide-coupled single photon detectors and a series of photon-counting measurements using a single-photon source. It is shown that the method can yield relative uncertainties of less than 1% including counting statistics and fiber splice loss uncertainties with a total measurement time of about 1 h under the assumptions that the fractional losses of the waveguide-coupled detectors are known or zero and the loss along the waveguide is constant. It is also shown that the fractional losses of the waveguide-coupled detectors can be determined if they are equal. However, in this case an input photon flux calibration is required. (paper)
17. All-optical tailoring of single-photon spectra in a quantum-dot microcavity system
OpenAIRE
Breddermann, Dominik; Heinze, Dirk; Binder, Rolf; Zrenner, Artur; Schumacher, Stefan
2016-01-01
Semiconductor quantum-dot cavity systems are promising sources for solid-state based on-demand generation of single photons for quantum communication. Commonly, the spectral characteristics of the emitted single photon are fixed by system properties such as electronic transition energies and spectral properties of the cavity. In the present work we study single-photon generation from the quantum-dot biexciton through a partly stimulated non-degenerate two-photon emission. We show that frequen...
18. Non-blinking single-photon emitters in silica
Science.gov (United States)
Rabouw, Freddy T.; Cogan, Nicole M. B.; Berends, Anne C.; Stam, Ward van der; Vanmaekelbergh, Daniel; Koenderink, A. Femius; Krauss, Todd D.; Donega, Celso de Mello
2016-01-01
Samples for single-emitter spectroscopy are usually prepared by spin-coating a dilute solution of emitters on a microscope cover slip of silicate based glass (such as quartz). Here, we show that both borosilicate glass and quartz contain intrinsic defect colour centres that fluoresce when excited at 532 nm. In a microscope image the defect emission is indistinguishable from spin-coated emitters. The emission spectrum is characterised by multiple peaks with the main peak between 2.05 and 2.20 eV, most likely due to coupling to a silica vibration with an energy that varies between 160 and 180 meV. The defects are single-photon emitters, do not blink, and have photoluminescence lifetimes of a few nanoseconds. Photoluminescence from such defects may previously have been misinterpreted as originating from single nanocrystal quantum dots. PMID:26892489
19. Quantum dots as single-photon sources for quantum information processing
Energy Technology Data Exchange (ETDEWEB)
2005-07-01
Semiconductor pillar microcavities containing quantum dots have shown promise as efficient sources of single and correlated pairs of photons, which may find applications in quantum information processing. In this paper we discuss the use of these sources to generate single photons and the use of pillars with elliptical cross-section to enhance and select a particular photon state. Single-photon interference measurements are also performed and show coherence times of up to 180 ps for quasi-resonantly pumped dots. Hong-Ou-Mandel-type two-photon interference measurements using a fibre interferometer indicate that individually created photons display a large degree of indistinguishability.
20. Strong coupling between single atoms and non-transversal photons
International Nuclear Information System (INIS)
Full text: We investigate the interaction between single quantum emitters and non-transversally polarized photons for which the electric field vector amplitude has a significant component in the direction of propagation. Even though this situation seems to be at odds with the description of light as a transverse wave, it regularly occurs when inter-facing or manipulating emitters with non-paraxial, guided, or evanescent light. Here, we quantitatively investigate this phenomenon for the case of single 85Rb atoms that strongly interact with a bottle-micro resonator - a novel type of whispering-gallery-mode (WGM) micro resonator. Our experimental results show that the non-transversal polarization decisively alters the physics of light–matter interaction. In addition they demonstrate that WGM resonators constitute a novel class of micro resonators that can, e.g., simultaneously sustain three orthogonally polarized eigenmodes. Building on our improved understanding, we investigate pathways to future WGM resonator based photonic devices. As a first example, we simultaneously interface the resonator with two coupling fibers, and use a single atom to route the incoming light between the optical fibers. (author)
1. Single-Photon Switching and Entanglement of Solid-State Qubits in an Integrated Nanophotonic System
CERN Document Server
Sipahigil, Alp; Sukachev, Denis D; Burek, Michael J; Borregaard, Johannes; Bhaskar, Mihir K; Nguyen, Christian T; Pacheco, Jose L; Atikian, Haig A; Meuwly, Charles; Camacho, Ryan M; Jelezko, Fedor; Bielejec, Edward; Park, Hongkun; Lončar, Marko; Lukin, Mikhail D
2016-01-01
Efficient interfaces between photons and quantum emitters form the basis for quantum networks and enable nonlinear optical devices operating at the single-photon level. We demonstrate an integrated platform for scalable quantum nanophotonics based on silicon-vacancy (SiV) color centers coupled to nanoscale diamond devices. By placing SiV centers inside diamond photonic crystal cavities, we realize a quantum-optical switch controlled by a single color center. We control the switch using SiV metastable orbital states and verify optical switching at the single-photon level by using photon correlation measurements. We use Raman transitions to realize a single-photon source with a tunable frequency and bandwidth in a diamond waveguide. Finally, we create entanglement between two SiV centers by detecting indistinguishable Raman photons emitted into a single waveguide. Entanglement is verified using a novel superradiant feature observed in photon correlation measurements, paving the way for the realization of quantu...
2. Single photon detector tests for the LHC synchrotron light diagnostics
International Nuclear Information System (INIS)
A synchrotron light detector using a Single-Photon Avalanche Detector (SPAD) is planned for the LHC longitudinal diagnostics monitor, an application which requires high count rate, low noise and good time resolution. SPAD detectors have been developed at Milan Polytechnic with active quenching circuits. Initial tests of these detectors and currently available commercial time-to-digital data acquisition equipment were made at the ESRF. We present the results of those tests, an estimation of the performance that can be expected for the LHC case and an analysis of the difficulties, constraints and potential of this type of detector. (authors)
3. Multi-group dynamic quantum secret sharing with single photons
Science.gov (United States)
Liu, Hongwei; Ma, Haiqiang; Wei, Kejin; Yang, Xiuqing; Qu, Wenxiu; Dou, Tianqi; Chen, Yitian; Li, Ruixue; Zhu, Wu
2016-07-01
In this letter, we propose a novel scheme for the realization of single-photon dynamic quantum secret sharing between a boss and three dynamic agent groups. In our system, the boss can not only choose one of these three groups to share the secret with, but also can share two sets of independent keys with two groups without redistribution. Furthermore, the security of communication is enhanced by using a control mode. Compared with previous schemes, our scheme is more flexible and will contribute to a practical application.
4. High bit rate germanium single photon detectors for 1310nm
Science.gov (United States)
Seamons, J. A.; Carroll, M. S.
2008-04-01
5. Secure authentication of classical messages with single photons
Institute of Scientific and Technical Information of China (English)
Wang Tian-Yin; Wen Qiao-Yan; Zhu Fu-Chen
2009-01-01
This paper proposes a scheme for secure authentication of classical messages with single photons and a hashed function.The security analysis of this scheme is also given,which shows that anyone cannot forge valid message authentication codes (MACs).In addition,the lengths of the authentication key and the MACs are invariable and shorter,in comparison with those presented authentication schemes.Moreover,quantum data storage and entanglement are not required in this scheme.Therefore,this scheme is more efficient and economical.
6. Strong Single-Photon Coupling in Superconducting Quantum Magnetomechanics
Science.gov (United States)
Via, Guillem; Kirchmair, Gerhard; Romero-Isart, Oriol
2015-04-01
We show that the inductive coupling between the quantum mechanical motion of a superconducting microcantilever and a flux-dependent microwave quantum circuit can attain the strong single-photon nanomechanical coupling regime with feasible experimental parameters. We propose to use a superconducting strip, which is in the Meissner state, at the tip of a cantilever. A pickup coil collects the flux generated by the sheet currents induced by an external quadrupole magnetic field centered at the strip location. The position-dependent magnetic response of the superconducting strip, enhanced by both diamagnetism and demagnetizing effects, leads to a strong magnetomechanical coupling to quantum circuits.
7. cGMP in Mouse Rods: the spatiotemporal dynamics underlying single photon responses
Directory of Open Access Journals (Sweden)
Owen P. Gross
2015-03-01
Full Text Available Vertebrate vision begins when retinal photoreceptors transduce photons into membrane hyperpolarization, which reduces glutamate release onto second-order neurons. In rod photoreceptors, transduction of single photons is achieved by a well-understood G-protein cascade that modulates cGMP levels, and in turn, cGMP-sensitive inward current. The spatial extent and depth of the decline in cGMP during the single photon response have been major issues in phototransduction research since the discovery that single photons elicit substantial and reproducible changes in membrane current. The spatial profile of cGMP decline during the single photon response affects signal gain, and thus may contribute to reduction of trial-to-trial fluctuations in the single photon response. Here we summarize the general principles of rod phototransduction, emphasizing recent advances in resolving the spatiotemporal dynamics of cGMP during the single photon response.
8. Single-Photon Superradiance from a Quantum Dot.
Science.gov (United States)
Tighineanu, Petru; Daveau, Raphaël S; Lehmann, Tau B; Beere, Harvey E; Ritchie, David A; Lodahl, Peter; Stobbe, Søren
2016-04-22
We report on the observation of single-photon superradiance from an exciton in a semiconductor quantum dot. The confinement by the quantum dot is strong enough for it to mimic a two-level atom, yet sufficiently weak to ensure superradiance. The electrostatic interaction between the electron and the hole comprising the exciton gives rise to an anharmonic spectrum, which we exploit to prepare the superradiant quantum state deterministically with a laser pulse. We observe a fivefold enhancement of the oscillator strength compared to conventional quantum dots. The enhancement is limited by the base temperature of our cryostat and may lead to oscillator strengths above 1000 from a single quantum emitter at optical frequencies. PMID:27152804
9. Single-Photon Superradiance from a Quantum Dot
Science.gov (United States)
Tighineanu, Petru; Daveau, Raphaël S.; Lehmann, Tau B.; Beere, Harvey E.; Ritchie, David A.; Lodahl, Peter; Stobbe, Søren
2016-04-01
We report on the observation of single-photon superradiance from an exciton in a semiconductor quantum dot. The confinement by the quantum dot is strong enough for it to mimic a two-level atom, yet sufficiently weak to ensure superradiance. The electrostatic interaction between the electron and the hole comprising the exciton gives rise to an anharmonic spectrum, which we exploit to prepare the superradiant quantum state deterministically with a laser pulse. We observe a fivefold enhancement of the oscillator strength compared to conventional quantum dots. The enhancement is limited by the base temperature of our cryostat and may lead to oscillator strengths above 1000 from a single quantum emitter at optical frequencies.
10. Single-electron pulse selector for a photon counting system
International Nuclear Information System (INIS)
A basic circuit of a single-electron pulse selector used in a low-intensity photon detection system is described. The selector is used integrally with photomultipliers of the FEU-79 and FEU-106 types with a fast response ranging from 10 to 15 ns. It discriminates pulses with amplitudes most likely for single-electron condition. The selector consists of a differential discriminator and a preamplifier with an amplification factor exceeding 30. The selector can operate with input pulses with a duration of more than 5 ns. The output pulse duration is 5 ns and it does not depend on the input pulse diration. The discrimination threshold can be controlled in the range from 0.1 to 10 mV
11. Sensitivity to the Gravitino mass from single-photon spectrum at TESLA Linear Collider
OpenAIRE
Checchia, P
1999-01-01
The spectrum of single-photon events detected in the forward and in the barrel region of a TESLA linear collider detector was studied in order to investigate the production of superlight Gravitino pairs associated with a photon.
12. Generation and efficient measurement of single photons from fixed frequency superconducting qubits
OpenAIRE
Kindel, William F.; Schroer, M. D.; Lehnert, K. W.
2015-01-01
We demonstrate and evaluate an on-demand source of single itinerant microwave photons. Photons are generated using a highly coherent, fixed-frequency qubit-cavity system, and a protocol where the microwave control field is far detuned from the photon emission frequency. By using a Josephson parametric amplifier (JPA), we perform efficient single-quadrature detection of the state emerging from the cavity. We characterize the imperfections of the photon generation and detection, including detec...
13. Collaborative single target detection for depth imaging from sparse single-photon data
CERN Document Server
Altmann, Yoann; McCarthy, Aongus; Buller, Gerald S; McLaughlin, Steve
2016-01-01
This paper presents a new Bayesian model and associated algorithm for depth and intensity profiling using full waveforms from time-correlated single-photon counting (TCSPC) measurements in the limit of very low photon counts (i.e., typically less than $20$ photons per pixel). The model represents each Lidar waveform as an unknown constant background level, which is combined in the presence of a target, to a known impulse response weighted by the target intensity and finally corrupted by Poisson noise. The joint target detection and depth imaging problem is expressed as a pixel-wise model selection and estimation problem which is solved using Bayesian inference. Prior knowledge about the problem is embedded in a hierarchical model that describes the dependence structure between the model parameters while accounting for their constraints. In particular, Markov random fields (MRFs) are used to model the joint distribution of the background levels and of the target presence labels, which are both expected to exhi...
14. High-quality asynchronous heralded single-photon source at telecom wavelength
International Nuclear Information System (INIS)
We report on the experimental realization and characterization of an asynchronous heralded single-photon source based on spontaneous parametric down-conversion. Photons at 1550 nm are heralded as being inside a single-mode fibre with more than 60% probability, and the multi-photon emission probability is reduced by a factor of up to more than 500 compared to Poissonian light sources. These figures of merit, together with the choice of telecom wavelength for the heralded photons, are compatible with practical applications needing very efficient and robust single-photon sources
15. Radiation burst from a single γ-photon field
International Nuclear Information System (INIS)
16. Experimental studies of single-photon photodetachment of atomic anions
Science.gov (United States)
Duvvuri, Srividya S.
Laser photodetachment electron spectroscopy (LPES) has been used to study the structure of the terbium anion. The data was analyzed assuming that the terbium anion forms in dysprosium-like states. Using this assumption, the electron affinity of Tb([Xe]4f96s 2 6 Ho15/2 ) equals 1.98 +/- 0.10 eV, and the ground state of the terbium anion is assigned to the Dy-like Tb-([Xe]4f 106s2 5I 8) electronic configuration. At lust two bound excited states of Tb - are also evident in the photoelectron kinetic energy spectra, with binding energies of 0.449 +/- 0.01 and 1.67 +/- 0.07 eV relative to the Tb(6 Ho15/2 ) ground state. The energy scale of each Tb- photoelectron spectrum way calibrated using reference photoelectron peaks from 12 C-, 16O- and 23Na-, which have well known binding energies [1]. Photoelectron angular distribution measurements following the single-photon photodetachment of the lanthanide anions Tb- and Lu - are also presented. The asymmetry parameters were determined from the non-linear least-square fits of the photoelectron yields as a function of the angle between the photon polarization vector and the photoelectron momentum vector of the collected photoelectrons. The measurements indicated the single-photon photodetachment process hnu + Tb -([Xe]4f106s 2 5I8) → Tb([Xe]4 f96s2 6) Ho15/2 + e - has beta values of 1.51 +/- 0.08 and 1.35 +/- 0.08 at wavelengths of 514.5 and 488 nm, respectively. For Lu -, the fine-structure resolved photodetachment process hnu +Lu-([Xe]4f146s 26p5d 1D 2) → Lu([Xe]4f145 d6s2 2D 3/2) + e-, has been measured at wavelength of 532 nm yielding beta = 0.8 +/- 0.1, supporting the assertion that Lu - forms via the attachment of a 6p-electron to the neutral Lu atom [2]. Finally, photodetachment cross sections and the angular distributions of photo-electrons produced by the single-photon detachment of the Fe - and Cu- have also been measured at discrete visible photon wavelengths. From the measured photodetachment cross sections, the
17. Triangular nanobeam photonic cavities in single crystal diamond
CERN Document Server
Bayn, Igal; Salzman, Joseph; Kalish, Rafi
2011-01-01
Diamond photonics provides an attractive architecture to explore room temperature cavity quantum electrodynamics and to realize scalable multi-qubit computing. Here we review the present state of diamond photonic technology. The design, fabrication and characterization of a novel triangular cross section nanobeam cavity produced in a single crystal diamond is demonstrated. The present cavity design, based on a triangular cross section allows vertical confinement and better signal collection efficiency than that of slab-based nanocavities, and eliminates the need for a pre-existing membrane. The nanobeam is fabricated by Focused-Ion-Beam (FIB) patterning. The cavity is characterized by a confocal photoluminescence. The modes display quality factors of Q ~220 and are deviated in wavelength by only ~1.7nm from the NV- color center zero phonon line (ZPL). The measured results are found in good agreement with 3D Finite-Difference-Time-Domain (FDTD) calculations. A more advanced cavity design with Q=22,000 is model...
18. Triangular nanobeam photonic cavities in single-crystal diamond
International Nuclear Information System (INIS)
Diamond photonics provides an attractive architecture to explore room temperature cavity quantum electrodynamics and to realize scalable multi-qubit computing. Here, we review the present state of diamond photonic technology. The design, fabrication and characterization of a novel nanobeam cavity produced in a single crystal diamond are demonstrated. The present cavity design, based on a triangular cross-section, allows vertical confinement and better signal collection efficiency than that of slab-based nanocavities and eliminates the need for a pre-existing membrane. The nanobeam is fabricated by focused-ion-beam (FIB) patterning. The cavity is characterized by confocal photoluminescence. The modes display quality factors of Q∼220 and deviate in wavelength by only ∼1.7 nm from the nitrogen-vacancy (NV-) color center zero phonon line (ZPL). The measured results are found to be in good agreement with three-dimensional finite-difference-time-domain (FDTD) calculations. A more advanced cavity design with Q=22 000 is modeled, showing the potential for high-Q implementations using the triangular geometry. The prospects of this concept and its application in spin non-demolition measurement and quantum computing are discussed.
19. Room temperature mid-IR single photon spectral imaging
CERN Document Server
Dam, Jeppe Seidelin; Tidemand-Lichtenberg, Peter
2012-01-01
Spectral imaging and detection of mid-infrared (mid-IR) wavelengths are emerging as an enabling technology of great technical and scientific interest; primarily because important chemical compounds display unique and strong mid-IR spectral fingerprints revealing valuable chemical information. While modern Quantum cascade lasers have evolved as ideal coherent mid-IR excitation sources, simple, low noise, room temperature detectors and imaging systems still lag behind. We address this need presenting a novel, field-deployable, upconversion system for sensitive, 2-D, mid-IR spectral imaging. Measured room temperature dark noise is 0.2 photons/spatial element/second, which is a billion times below the dark noise level of cryogenically cooled InSb cameras. Single photon imaging and up to 200 x 100 spatial elements resolution is obtained reaching record high continuous wave quantum efficiency of about 20 % for polarized incoherent light at 3 \\mum. The proposed method is relevant for existing and new mid-IR applicat...
20. Direct Photonic-Plasmonic Coupling and Routing in Single Nanowires
Energy Technology Data Exchange (ETDEWEB)
Yan, Rouxue; Pausauskie, Peter; Huang, Jiaxing; Yang, Piedong
2009-10-20
Metallic nanoscale structures are capable of supporting surface plasmon polaritons (SPPs), propagating collective electron oscillations with tight spatial confinement at the metal surface. SPPs represent one of the most promising structures to beat the diffraction limit imposed by conventional dielectric optics. Ag nano wires have drawn increasing research attention due to 2D sub-100 nm mode confinement and lower losses as compared with fabricated metal structures. However, rational and versatile integration of Ag nanowires with other active and passive optical components, as well as Ag nanowire based optical routing networks, has yet to be achieved. Here, we demonstrate that SPPs can be excited simply by contacting a silver nanowire with a SnO2 nanoribbon that serves both as an unpolarized light source and a dielectric waveguide. The efficient coupling makes it possible to measure the propagation-distance-dependent waveguide spectra and frequency-dependent propagation length on a single Ag nanowire. Furthermore, we have demonstrated prototypical photonic-plasmonic routing devices, which are essential for incorporating low-loss Ag nanowire waveguides as practical components into high-capacity photonic circuits.
1. Two-photon interference at telecom wavelengths for time-bin-encoded single photons from quantum-dot spin qubits
Science.gov (United States)
Yu, Leo; Natarajan, Chandra M.; Horikiri, Tomoyuki; Langrock, Carsten; Pelc, Jason S.; Tanner, Michael G.; Abe, Eisuke; Maier, Sebastian; Schneider, Christian; Höfling, Sven; Kamp, Martin; Hadfield, Robert H.; Fejer, Martin M.; Yamamoto, Yoshihisa
2015-11-01
Practical quantum communication between remote quantum memories rely on single photons at telecom wavelengths. Although spin-photon entanglement has been demonstrated in atomic and solid-state qubit systems, the produced single photons at short wavelengths and with polarization encoding are not suitable for long-distance communication, because they suffer from high propagation loss and depolarization in optical fibres. Establishing entanglement between remote quantum nodes would further require the photons generated from separate nodes to be indistinguishable. Here, we report the observation of correlations between a quantum-dot spin and a telecom single photon across a 2-km fibre channel based on time-bin encoding and background-free frequency downconversion. The downconverted photon at telecom wavelengths exhibits two-photon interference with another photon from an independent source, achieving a mean wavepacket overlap of greater than 0.89 despite their original wavelength mismatch (900 and 911 nm). The quantum-networking operations that we demonstrate will enable practical communication between solid-state spin qubits across long distances.
2. Two-photon interference at telecom wavelengths for time-bin-encoded single photons from quantum-dot spin qubits.
Science.gov (United States)
Yu, Leo; Natarajan, Chandra M; Horikiri, Tomoyuki; Langrock, Carsten; Pelc, Jason S; Tanner, Michael G; Abe, Eisuke; Maier, Sebastian; Schneider, Christian; Höfling, Sven; Kamp, Martin; Hadfield, Robert H; Fejer, Martin M; Yamamoto, Yoshihisa
2015-01-01
Practical quantum communication between remote quantum memories rely on single photons at telecom wavelengths. Although spin-photon entanglement has been demonstrated in atomic and solid-state qubit systems, the produced single photons at short wavelengths and with polarization encoding are not suitable for long-distance communication, because they suffer from high propagation loss and depolarization in optical fibres. Establishing entanglement between remote quantum nodes would further require the photons generated from separate nodes to be indistinguishable. Here, we report the observation of correlations between a quantum-dot spin and a telecom single photon across a 2-km fibre channel based on time-bin encoding and background-free frequency downconversion. The downconverted photon at telecom wavelengths exhibits two-photon interference with another photon from an independent source, achieving a mean wavepacket overlap of greater than 0.89 despite their original wavelength mismatch (900 and 911 nm). The quantum-networking operations that we demonstrate will enable practical communication between solid-state spin qubits across long distances. PMID:26597223
3. Heralded single-photon source utilizing highly nondegenerate, spectrally factorable spontaneous parametric downconversion.
Science.gov (United States)
Kaneda, Fumihiro; Garay-Palmett, Karina; U'Ren, Alfred B; Kwiat, Paul G
2016-05-16
We report on the generation of an indistinguishable heralded single-photon state, using highly nondegenerate spontaneous parametric downconversion (SPDC). Spectrally factorable photon pairs can be generated by incorporating a broadband pump pulse and a group-velocity matching (GVM) condition in a periodically-poled potassium titanyl phosphate (PPKTP) crystal. The heralding photon is in the near IR, close to the peak detection efficiency of off-the-shelf Si single-photon detectors; meanwhile, the heralded photon is in the telecom L-band where fiber losses are at a minimum. We observe spectral factorability of the SPDC source and consequently high purity (90%) of the produced heralded single photons by several different techniques. Because this source can also realize a high heralding efficiency (> 90%), it would be suitable for time-multiplexing techniques, enabling a pseudo-deterministic single-photon source, a critical resource for optical quantum information and communication technology. PMID:27409894
4. Quantum dot single photon sources: prospects for applications in linear optics quantum information processing
CERN Document Server
Kiraz, A; Imamoglu, A
2003-01-01
An optical source that produces single photon pulses on demand has potential applications in linear optics quantum information processing, provided that stringent requirements on indistinguishability and collection efficiency of the generated photons are met. We show that these are conflicting requirements for anharmonic emitters that are incoherently pumped via reservoirs. As a model for a coherently pumped single photon source, we consider cavity-assisted spin-flip Raman transitions in a single charged quantum dot embedded in a microcavity. We demonstrate that using such a source, arbitrarily high collection efficiency and indistinguishability of the generated photons can be obtained simultaneously with increased cavity coupling. We analyze the role of errors that arise from distinguishability of the single photon pulses in linear optics quantum gates by relating the gate fidelity to the strength of the two-photon interference dip in photon cross-correlation measurements. We find that performing controlled ...
5. All-fibre multiplexed source of high-purity heralded single photons
CERN Document Server
Francis-Jones, Robert J A; Mosley, Peter J
2016-01-01
Single photon sources based on spontaneous photon-pair generation have enabled pioneering experiments in quantum optics. However, their non-determinism presents a bottleneck to scaling up photonic and hybrid quantum-enhanced technologies. Furthermore, photon pairs are typically emitted into many correlated frequency modes, producing an undesirable mixed state on heralding. Here we present a complete fibre-integrated heralded single photon source that addresses both these difficulties simultaneously. We use active switching to provide a path to deterministic operation by multiplexing separate spontaneous sources, and dispersion engineering to minimise frequency correlation for high-purity single photon generation. All the essential elements -- nonlinear material with dispersion control, wavelength isolation, optical delay, and fast switching -- are incorporated in a low-loss alignment-free package that heralds photons in telecoms single-mode fibre. Our results demonstrate a scalable approach to delivering pure...
6. SPECT single photon emission computed tomography: A primer
International Nuclear Information System (INIS)
This book aims to assist nuclear medicine technologists in expanding their knowledge of nuclear medicine to include SPECT. The text of this primer is written with the assumption that the reader is proficient in most elements of nuclear medicine technology; therefore, the information is limited to data that will answer the basic questions of single-photon emission computed tomography .... The authors' goal is to bring the basics of this material together in a manner that would answer the technologist's fundamental questions. The authors have designed this primer in a generic manner to be used as an extension of the manufacturer's operating manual .... A glossary is included which contains some of the terminology relevant to the specialty, and reading lists are provided at the end of each chapter to direct the reader to more comprehensive text on specific subjects
7. Technology development for a single-photon source
International Nuclear Information System (INIS)
m to 1.5 μm was obtained. To achieve high collection efficiency, the quantum dots should be embedded into photonic crystals. An ArCl2-etch-process was developed which enables the etch of small features in AlxGayIn1-x-yAs material system to transfer the Si3N4-pattern into the semiconductor. Using this process the fabricated photonic crystals with L3-cavities had Q-factors around 2200. Any concept using a cavity needs a mechanism to control the frequency-detuning between the mode and the quantum dots, due to the inhomogeneous frequency broadening of the quantum dots. Thus an in-situ tuning mechanism is required for adjusting the emission wavelength of the quantum dot or cavity mode, respectively. This concept intents to use the quantum confined Stark effect (QCSE) to force the emission of a single photon out of a quantum dot into the photonic crystal mode. This is realized using a reversed biased Schottky contact to cause a red-shift of the emission of a single quantum dot. Electroluminescence measurements on the device show, that even with very low currents of 14.5 μA the saturation intensity of single quantum dots could be reached. (orig.)
8. Signs of cerebral atrophy on single-photon emission tomography.
Science.gov (United States)
Wong, C O; Meyerrose, G E; Sostre, S
1994-05-01
Cerebral atrophy often coexists with other brain disorders and by itself may alter the pattern of cerebral perfusion. If unrecognized, it may confound diagnoses based on brain single-photon emission tomography (SPET). In this retrospective study, we describe and evaluate criteria for the diagnosis of cerebral atrophy on technetium-99m hexamethylpropylene amine oxime brain SPET studies. The SPET scans of 11 patients with cerebral atrophy and ten controls were evaluated for the presence of a prominent interhemispheric fissure, presence of prominent cerebral sulci, separation of thalamic nuclei, and pronounced separation of caudate nuclei. The SPET studies were interpreted by two independent observers blind to the findings of magnetic resonance imaging, which provided the final diagnosis of cerebral atrophy. The combination of the four scintigraphic signs was accurate in the diagnosis of cerebral atrophy in 95% of the cases and had a sensitivity of 91% and a specificity of 100%. PMID:8062851
9. Collective magnetic splitting in single-photon superradiance
CERN Document Server
Kong, Xiangjin
2016-01-01
In an ensemble of identical atoms, cooperative effects like sub- or superradiance may alter the decay rates and the energy of specific transitions may be shifted from the single-atom value by the so-called collective Lamb shift. So far, one has considered these effects in ensembles of two-level systems only. In this work we show that in a system with atoms or nuclei under the action of an external magnetic field, an additional, so far unaccounted for collective contribution to the level shifts appears that can amount to seizable deviations from the single-atom Zeeman or magnetic hyperfine splitting. We develop a formalism to describe single-photon superradiance in multi-level systems and quantify the parameter regime for which the collective Lamb shift leads to measurable deviations in the magnetic-field-induced splitting. In particular, we show that this effect should be observable in the nuclear magnetic hyperfine splitting in M\\"ossbauer nuclei embedded in thin-film x-ray cavities.
10. Single-Photon Avalanche Diodes (SPAD) in CMOS 0.35 µm technology
OpenAIRE
Pellion, D; Jradi, K; Brochard, Nicolas; Prêle, D.; Ginhac, Dominique
2015-01-01
Some decades ago single photon detection used to be the terrain of photomultiplier tube (PMT), thanks to its characteristics of sensitivity and speed. However, PMT has several disadvantages such as low quantum efficiency, overall dimensions, and cost, making them unsuitable for compact design of integrated systems. So, the past decade has seen a dramatic increase in interest in new integrated single-photon detectors called Single-Photon Avalanche Diodes (SPAD) or Geiger-mode APD. SPAD are wor...
11. Single Photon Subradiance: Quantum control of spontaneous emission and ultrafast readout
OpenAIRE
Scully, Marlan O.
2015-01-01
Recent work has shown that collective single photon emission from an ensemble of resonate two-level atoms, i.e. single photon superradiance, is a rich field of study. The present paper addresses the flip side of superradiance, i.e. subradiance. Single photon subradiant states are potentially stable against collective spontaneous emission and can have ultrafast readout. In particular it is shown how many atom collective effects provide a new way to control spontaneous emission by preparing and...
12. Single photon time transfer link model for GNSS satellites
Science.gov (United States)
Vacek, Michael; Michalek, Vojtech; Peca, Marek; Prochazka, Ivan; Blazej, Josef
2015-05-01
13. Source of single photons and interferometry with one photon. From the Young's slit experiment to the delayed choice
International Nuclear Information System (INIS)
This manuscript is divided in two independent parts. In the first part, we study the wave-particle duality for a single photon emitted by the triggered photoluminescence of a single NV color center in a diamond nano-crystal. We first present the realization of a single-photon interference experiment using a Fresnel's bi-prism, in a scheme equivalent to the standard Young's double-slit textbook experiment. We then discuss the complementarity between interference and which-path information in this two-path interferometer. We finally describe the experimental realization of Wheeler's delayed-choice Gedanken experiment, which is a fascinating and subtle illustration of wave-particle duality. The second part of the manuscript is devoted to the efficiency improvement of single-photon sources. We first describe the implementation of a new single-photon source based on the photoluminescence of a single nickel-related defect center in diamond. The photophysical properties of such defect make this single-photon source well adapted to open-air quantum cryptography. We finally demonstrate an original method that leads to an improvement of single-molecule photo stability at room temperature. (author)
14. Direct writing of large-area plasmonic photonic crystals using single-shot interference ablation
International Nuclear Information System (INIS)
We report direct writing of metallic photonic crystals (MPCs) through a single-shot exposure of a thin film of colloidal gold nanoparticles to the interference pattern of a single UV laser pulse before a subsequent annealing process. This is defined as interference ablation, where the colloidal gold nanoparticles illuminated by the bright interference fringes are removed instantly within a timescale of about 6 ns, which is actually the pulse length of the UV laser, whereas the gold nanoparticles located within the dark interference fringes remain on the substrate and form grating structures. This kind of ablation has been proven to have a high spatial resolution and thus enables successful fabrication of waveguided MPC structures with the optical response in the visible spectral range. The subsequent annealing process transforms the grating structures consisting of ligand-covered gold nanoparticles into plasmonic MPCs. The annealing temperature is optimized to a range from 250 to 300 deg. C to produce MPCs of gold nanowires with a period of 300 nm and an effective area of 5 mm in diameter. If the sample of the spin-coated gold nanoparticles is rotated by 900 after the first exposure, true two-dimensional plasmonic MPCs are produced through a second exposure to the interference pattern. Strong plasmonic resonance and its coupling with the photonic modes of the waveguided MPCs verifies the success of this new fabrication technique. This is the simplest and most efficient technique so far for the construction of large-area MPC devices, which enables true mass fabrication of plasmonic devices with high reproducibility and high success rate.
15. Experimental open-air quantum key distribution with a single-photon source
International Nuclear Information System (INIS)
We describe the implementation of a quantum key distribution (QKD) system using a single-photon source, operating at night in open air. The single-photon source at the heart of the functional and reliable set-up relies on the pulsed excitation of a single nitrogen-vacancy colour centre in a diamond nanocrystal. We tested the effect of attenuation on the polarized encoded photons for inferring the longer distance performance of our system. For strong attenuation, the use of pure single-photon states gives measurable advantage over systems relying on weak attenuated laser pulses. The results are in good agreement with theoretical models developed to assess QKD security
16. Time-division phase modulated single-photon interference in a Sagnac interferometer
Institute of Scientific and Technical Information of China (English)
WU Guang; ZHOU Chunyuan; ZENG Heping
2003-01-01
We introduce a stable, long-distance single- photon Sagnac interferometer, which has a balanced configuration to efficiently compensate phase drift caused by change of the fiber-optic path. By using time-division phase modulation, single-photon interference was realized at 1550 nm in a 5-km-long as well as 27-km-long Sagnac fiber loops, with a fringe visibility higher than 90% and long-term stability. The stable performance of the single-photon interference indicated that the time-division phase-modulated Sag- nac interferometer might readily lead to practical applications in single-photon routing and quantum cryptography.
17. Custom single-photon avalanche diode with integrated front-end for parallel photon timing applications.
Science.gov (United States)
Cammi, C; Panzeri, F; Gulinatti, A; Rech, I; Ghioni, M
2012-03-01
Emerged as a solid state alternative to photo multiplier tubes (PMTs), single-photon avalanche diodes (SPADs) are nowadays widely used in the field of single-photon timing applications. Custom technology SPADs assure remarkable performance, in particular a 10 counts/s dark count rate (DCR) at low temperature, a high photon detection efficiency (PDE) with a 50% peak at 550 nm and a 30 ps (full width at half maximum, FWHM) temporal resolution, even with large area devices, have been obtained. Over the past few years, the birth of novel techniques of analysis has led to the parallelization of the measurement systems and to a consequent increasing demand for the development of monolithic arrays of detectors. Unfortunately, the implementation of a multidimensional system is a challenging task from the electrical point of view; in particular, the avalanche current pick-up circuit, used to obtain the previously reported performance, has to be modified in order to enable high parallel temporal resolution, while minimizing the electrical crosstalk probability between channels. In the past, the problem has been solved by integrating the front-end electronics next to the photodetector, in order to reduce the parasitic capacitances and consequently the filtering action on the current signal of the SPAD, leading to an improvement of the timing jitter at higher threshold. This solution has been implemented by using standard complementary metal-oxide-semiconductor (CMOS) technologies, which, however, do not allow a complete control on the SPAD structure; for this reason the intrinsic performance of CMOS SPADs, such as DCR, PDE, and afterpulsing probability, are worse than those attainable with custom detectors. In this paper, we propose a pixel architecture, which enables the development of custom SPAD arrays in which every channel maintains the performance of the best single photodetector. The system relies on the integration of the timing signal pick-up circuit next to the
18. Custom single-photon avalanche diode with integrated front-end for parallel photon timing applications
Science.gov (United States)
Cammi, C.; Panzeri, F.; Gulinatti, A.; Rech, I.; Ghioni, M.
2012-03-01
Emerged as a solid state alternative to photo multiplier tubes (PMTs), single-photon avalanche diodes (SPADs) are nowadays widely used in the field of single-photon timing applications. Custom technology SPADs assure remarkable performance, in particular a 10 counts/s dark count rate (DCR) at low temperature, a high photon detection efficiency (PDE) with a 50% peak at 550 nm and a 30 ps (full width at half maximum, FWHM) temporal resolution, even with large area devices, have been obtained. Over the past few years, the birth of novel techniques of analysis has led to the parallelization of the measurement systems and to a consequent increasing demand for the development of monolithic arrays of detectors. Unfortunately, the implementation of a multidimensional system is a challenging task from the electrical point of view; in particular, the avalanche current pick-up circuit, used to obtain the previously reported performance, has to be modified in order to enable high parallel temporal resolution, while minimizing the electrical crosstalk probability between channels. In the past, the problem has been solved by integrating the front-end electronics next to the photodetector, in order to reduce the parasitic capacitances and consequently the filtering action on the current signal of the SPAD, leading to an improvement of the timing jitter at higher threshold. This solution has been implemented by using standard complementary metal-oxide-semiconductor (CMOS) technologies, which, however, do not allow a complete control on the SPAD structure; for this reason the intrinsic performance of CMOS SPADs, such as DCR, PDE, and afterpulsing probability, are worse than those attainable with custom detectors. In this paper, we propose a pixel architecture, which enables the development of custom SPAD arrays in which every channel maintains the performance of the best single photodetector. The system relies on the integration of the timing signal pick-up circuit next to the
19. Efficient multi-mode to single-mode conversion in a 61 port photonic lantern
DEFF Research Database (Denmark)
Noordegraaf, Danny; Skovgaard, Peter M. W.; Dybendahl Maack, Martin;
2010-01-01
We demonstrate the fabrication of a multi-mode (MM) to 61 port single-mode (SM) splitter or "Photonic Lantern". Low port count Photonic Lanterns were first described by Leon-Saval et al. (2005). These are based on a photonic crystal fiber type design, with air-holes defining the multi-mode fiber ...
20. Fast Path and Polarization Manipulation of Telecom Wavelength Single Photons in Lithium Niobate Waveguide Devices
NARCIS (Netherlands)
Bonneau, D.; Lobino, M.; Jiang, P.; Natarajan, C.M.; Tanner, M.G.; Hadfield, R.H.; Dorenbos, S.N.; Zwiller, V.; Thompson, M.G.; O'Brien, J.L.
2012-01-01
We demonstrate fast polarization and path control of photons at 1550 nm in lithium niobate waveguide devices using the electro-optic effect. We show heralded single photon state engineering, quantum interference, fast state preparation of two entangled photons, and feedback control of quantum interf
1. High Count Rate Single Photon Counting Detector Array Project
Data.gov (United States)
National Aeronautics and Space Administration — An optical communications receiver requires efficient and high-rate photon-counting capability so that the information from every photon, received at the aperture,...
2. Video recording true single-photon double-slit interference
OpenAIRE
Aspden, Reuben S.; Padgett, Miles J.; Spalding, Gabriel C.
2016-01-01
As normally used, no commercially available camera has a low-enough dark noise to directly produce video recordings of double-slit interference at the photon-by-photon level, because readout noise significantly contaminates or overwhelms the signal. In this work, noise levels are significantly reduced by turning on the camera only when the presence of a photon has been heralded by the arrival, at an independent detector, of a time-correlated photon produced via parametric down-conversion. Thi...
3. Interference with a quantum dot single-photon source and a laser at telecom wavelength
Energy Technology Data Exchange (ETDEWEB)
Felle, M. [Toshiba Research Europe Limited, Cambridge Research Laboratory, 208 Cambridge Science Park, Milton Road, Cambridge CB4 0GZ (United Kingdom); Centre for Advanced Photonics and Electronics, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0FA (United Kingdom); Huwer, J., E-mail: [email protected]; Stevenson, R. M.; Skiba-Szymanska, J.; Ward, M. B.; Shields, A. J. [Toshiba Research Europe Limited, Cambridge Research Laboratory, 208 Cambridge Science Park, Milton Road, Cambridge CB4 0GZ (United Kingdom); Farrer, I.; Ritchie, D. A. [Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Penty, R. V. [Centre for Advanced Photonics and Electronics, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0FA (United Kingdom)
2015-09-28
The interference of photons emitted by dissimilar sources is an essential requirement for a wide range of photonic quantum information applications. Many of these applications are in quantum communications and need to operate at standard telecommunication wavelengths to minimize the impact of photon losses and be compatible with existing infrastructure. Here, we demonstrate for the first time the quantum interference of telecom-wavelength photons from an InAs/GaAs quantum dot single-photon source and a laser; an important step towards such applications. The results are in good agreement with a theoretical model, indicating a high degree of indistinguishability for the interfering photons.
4. Interference with a quantum dot single-photon source and a laser at telecom wavelength
International Nuclear Information System (INIS)
The interference of photons emitted by dissimilar sources is an essential requirement for a wide range of photonic quantum information applications. Many of these applications are in quantum communications and need to operate at standard telecommunication wavelengths to minimize the impact of photon losses and be compatible with existing infrastructure. Here, we demonstrate for the first time the quantum interference of telecom-wavelength photons from an InAs/GaAs quantum dot single-photon source and a laser; an important step towards such applications. The results are in good agreement with a theoretical model, indicating a high degree of indistinguishability for the interfering photons
5. Photonic crystal fibre source of photon pairs for quantum information processing
CERN Document Server
Fulconis, J; O'Brien, J L; Rarity, J G; Wadsworth, W J; Alibart, Olivier; Brien, Jeremy L. O'; Fulconis, Jeremie; Rarity, John G.; Wadsworth, William J.
2006-01-01
We demonstrate two key components for optical quantum information processing: a bright source of heralded single photons; and a bright source of entangled photon pairs. A pair of pump photons produces a correlated pair of photons at widely spaced wavelengths (583 nm and 900 nm), via a $\\chi^{(3)}$ four-wave mixing process. We demonstrate a non-classical interference between heralded photons from independent sources with a visibility of 95%, and an entangled photon pair source, with a fidelity of 89% with a Bell state.
6. Electrically pumped single-photon emission at room temperature from a single InGaN/GaN quantum dot
International Nuclear Information System (INIS)
We demonstrate a semiconductor quantum dot based electrically pumped single-photon source operating at room temperature. Single photons emitted in the red spectral range from single In0.4Ga0.6N/GaN quantum dots exhibit a second-order correlation value g(2)(0) of 0.29, and fast recombination lifetime ∼1.3 ±0.3 ns at room temperature. The single-photon source can be driven at an excitation repetition rate of 200 MHz.
7. Controlling Single-Photon Transport along an Optical Waveguide by using a Three-Level Atom
Institute of Scientific and Technical Information of China (English)
TIAN Wei; CHEN Bin; XU Wei-Dong
2012-01-01
We theoretically investigate the single-photon transport properties in an optical waveguide embedded with a V-type three-level atom (VTLA) based on symmetric and asymmetric couplings between the photon and the VTLA.Our numerical results show that the transmission spectrum of the incident photon can be well controlled by virtue of both symmetric and asymmetric coupling interactions.A multifrequency photon attenuator is realized by controlling the asymmetric coupling interactions.Furthermore,the influences of dissipation of the VTLA for the realistic physical system on single-photon transport properties are also analyzed.
8. Wide-field single photon counting imaging with an ultrafast camera and an image intensifier
International Nuclear Information System (INIS)
We are reporting a method for wide-field photon counting imaging using a CMOS camera with a 40 kHz frame rate coupled with a three-stage image intensifier mounted on a standard fluorescence microscope. This system combines high frame rates with single photon sensitivity. The output of the phosphor screen, consisting of single-photon events, is collected by a CMOS camera allowing to create a wide-field image with parallel positional and timing information of each photon. Using a pulsed excitation source and a luminescent sample, the arrival time of hundreds of photons can be determined simultaneously in many pixels with microsecond resolution.
9. High Speed Travelling Wave Single-Photon Detectors With Near-Unity Quantum Efficiency
CERN Document Server
Pernice, W; Minaeva, O; Li, M; Goltsman, G N; Sergienko, A V; Tang, H X
2011-01-01
Ultrafast, high quantum efficiency single photon detectors are among the most sought-after elements in modern quantum optics and quantum communication. Close-to-unity photon detection efficiency is essential for scalable measurement-based quantum computation, quantum key distribution, and loophole-free Bell experiments. However, imperfect modal matching and finite photon absorption rates have usually limited the maximum attainable detection efficiency of single photon detectors. Here we demonstrate a superconducting nanowire detector atop nanophotonic waveguides and achieve single photon detection efficiency up to 94% at telecom wavelengths. Our detectors are fully embedded in a scalable, low loss silicon photonic circuit and provide ultrashort timing jitter of 18ps at multi-GHz detection rates. Exploiting this high temporal resolution we demonstrate ballistic photon transport in silicon ring resonators. The direct implementation of such a detector with high quantum efficiency, high detection speed and low ji...
10. Photon counting imaging and centroiding with an electron-bombarded CCD using single molecule localisation software
Science.gov (United States)
Hirvonen, Liisa M.; Barber, Matthew J.; Suhling, Klaus
2016-06-01
Photon event centroiding in photon counting imaging and single-molecule localisation in super-resolution fluorescence microscopy share many traits. Although photon event centroiding has traditionally been performed with simple single-iteration algorithms, we recently reported that iterative fitting algorithms originally developed for single-molecule localisation fluorescence microscopy work very well when applied to centroiding photon events imaged with an MCP-intensified CMOS camera. Here, we have applied these algorithms for centroiding of photon events from an electron-bombarded CCD (EBCCD). We find that centroiding algorithms based on iterative fitting of the photon events yield excellent results and allow fitting of overlapping photon events, a feature not reported before and an important aspect to facilitate an increased count rate and shorter acquisition times.
11. Radiation dose to small infants from single-photon absorptiometry
International Nuclear Information System (INIS)
12. Superconducting nanowire single photon detectors for quantum information and communications
CERN Document Server
Wang, Zhen; Fujiwara, Mikio
2010-01-01
Superconducting nanowire single photon detectors (SNSPD or SSPD) are highly promising devices in the growing field of quantum information and communications technology. We have developed a practical SSPD system with our superconducting thin films and devices fabrication, optical coupling packaging, and cryogenic technology. The SSPD system consists of six-channel SSPD devices and a compact Gifford-McMahon (GM) cryocooler, and can operate continuously on 100 V ac power without the need for any cryogens. The SSPD devices were fabricated from high-quality niobium nitride (NbN) ultra-thin films that were epitaxially grown on single-crystal MgO substrates. The packaged SSPD devices were temperature stabilized to 2.96 K +/- 10 mK. The system detection efficiency for an SSPD device with an area of 20x20 $\\mu m^2$ was found to be 2.6% and 4.5% at wavelengths of 1550 and 1310 nm, respectively, at a dark count rate of 100 c/s, and a jitter of 100 ps full width at half maximum (FWHM). We also performed ultra-fast BB84 q...
13. Proceedings of clinical SPECT [single photon emission computed tomography] symposium
International Nuclear Information System (INIS)
It has been five years since the last in-depth American College of Nuclear Physicians/Society of Nuclear Medicine Symposium on the subject of single photon emission computed tomography (SPECT) was held. Because this subject was nominated as the single most desired topic we have selected SPECT imaging as the basis for this year's program. The objectives of this symposium are to survey the progress of SPECT clinical applications that have taken place over the last five years and to provide practical and timely guidelines to users of SPECT so that this exciting imaging modality can be fully integrated into the evaluation of pathologic processes. The first half was devoted to a consideration of technical factors important in SPECT acquisition and the second half was devoted to those organ systems about which sufficient clinical SPECT imaging data are available. With respect to the technical aspect of the program we have selected the key areas which demand awareness and attention in order to make SPECT operational in clinical practice. These include selection of equipment, details of uniformity correction, utilization of phantoms for equipment acceptance and quality assurance, the major aspect of algorithms, an understanding of filtered back projection and appropriate choice of filters and an awareness of the most commonly generated artifacts and how to recognize them. With respect to the acquisition and interpretation of organ images, the faculty will present information on the major aspects of hepatic, brain, cardiac, skeletal, and immunologic imaging techniques. Individual papers are processed separately for the data base
14. Single-photon transport through an atomic chain coupled to a one-dimensional nanophotonic waveguide
Science.gov (United States)
Liao, Zeyang; Zeng, Xiaodong; Zhu, Shi-Yao; Zubairy, M. Suhail
2015-08-01
We study the dynamics of a single-photon pulse traveling through a linear atomic chain coupled to a one-dimensional (1D) single mode photonic waveguide. We derive a time-dependent dynamical theory for this collective many-body system which allows us to study the real time evolution of the photon transport and the atomic excitations. Our analytical result is consistent with previous numerical calculations when there is only one atom. For an atomic chain, the collective interaction between the atoms mediated by the waveguide mode can significantly change the dynamics of the system. The reflectivity of a photon can be tuned by changing the ratio of coupling strength and the photon linewidth or by changing the number of atoms in the chain. The reflectivity of a single-photon pulse with finite bandwidth can even approach 100 % . The spectrum of the reflected and transmitted photon can also be significantly different from the single-atom case. Many interesting physical phenomena can occur in this system such as the photonic band-gap effects, quantum entanglement generation, Fano-like interference, and superradiant effects. For engineering, this system may serve as a single-photon frequency filter, single-photon modulation, and may find important applications in quantum information.
15. Bridging visible and telecom wavelengths with a single-mode broadband photon pair source
International Nuclear Information System (INIS)
We present a spectrally decorrelated photon pair source bridging the visible and telecom wavelength regions. Tailored design and fabrication of a solid-core photonic crystal fiber (PCF) lead to the emission of signal and idler photons into only a single spectral and spatial mode. Thus no narrowband filtering is necessary and the heralded generation of pure photon number states in ultrafast wave packets at telecom wavelengths becomes possible.
16. High fidelity transfer and storage of photon states in a single nuclear spin
OpenAIRE
Yang, Sen; Wang, Ya; Rao, D. D. Bhaktavatsala; Tran, Thai Hien; Momenzadeh, S. Ali; Nagy, Roland; Markham, M.; Twitchen, D. J.; Ping WANG; Yang, Wen; Stoehr, Rainer; Neumann, Philipp; Kosaka, Hideo; Wrachtrup, Joerg
2015-01-01
Building a quantum repeater network for long distance quantum communication requires photons and quantum registers that comprise qubits for interaction with light, good memory capabilities and processing qubits for storage and manipulation of photons. Here we demonstrate a key step, the coherent transfer of a photon in a single solid-state nuclear spin qubit with an average fidelity of 98% and storage over 10 seconds. The storage process is achieved by coherently transferring a photon to an e...
17. Probing the Hotspot Interaction Length in NbN Nanowire Superconducting Single-Photon Detectors
CERN Document Server
Renema, J J; Wang, Q; van Exter, M P; Fiore, A; de Dood, M J A
2016-01-01
We measure the maximal distance at which two absorbed photons can jointly trigger a detection event in NbN nanowire superconducting single photon detector (SSPD) microbridges by comparing the one-photon and two-photon efficiency of bridges of different overall lengths, from 0 to 400 nm. We find a length of $23 \\pm 2$ nm. This value is in good agreement with to size of the quasiparticle cloud at the time of the detection event.
18. Single-Photon Depth Imaging Using a Union-of-Subspaces Model
OpenAIRE
Shin, Dongeek; Shapiro, Jeffrey H.; Goyal, Vivek K
2015-01-01
Light detection and ranging systems reconstruct scene depth from time-of-flight measurements. For low light-level depth imaging applications, such as remote sensing and robot vision, these systems use single-photon detectors that resolve individual photon arrivals. Even so, they must detect a large number of photons to mitigate Poisson shot noise and reject anomalous photon detections from background light. We introduce a novel framework for accurate depth imaging using a small number of dete...
19. Vitamin B12 enhances the phase-response of circadian melatonin rhythm to a single bright light exposure in humans.
Science.gov (United States)
Hashimoto, S; Kohsaka, M; Morita, N; Fukuda, N; Honma, S; Honma, K
1996-12-13
Eight young males were subjected to a single blind cross-over test to see the effects of vitamin B12 (methylcobalamin; VB12) on the phase-response of the circadian melatonin rhythm to a single bright light exposure. VB12 (0.5 mg/day) or vehicle was injected intravenously at 1230 h for 11 days, which was followed by oral administration (2 mg x 3/day) for 7 days. A serial blood sampling was performed under dim light condition (less than 200 lx) and plasma melatonin rhythm was determined before and after a single bright light exposure (2500 lx for 3 h) at 0700 h. The melatonin rhythm before the light exposure showed a smaller amplitude in the VB12 trial than in the placebo. The light exposure phase-advanced the melatonin rhythm significantly in the VB12 trail, but not in the placebo. These findings indicate that VB12 enhances the light-induced phase-shift in the human circadian rhythm. PMID:8981490
20. Bias-free true random number generation using superconducting nanowire single-photon detectors
Science.gov (United States)
He, Yuhao; Zhang, Weijun; Zhou, Hui; You, Lixing; Lv, Chaolin; Zhang, Lu; Liu, Xiaoyu; Wu, Junjie; Chen, Sijing; Ren, Min; Wang, Zhen; Xie, Xiaoming
2016-08-01
We demonstrate a bias-free true random number generator (TRNG) based on single photon detection using superconducting nanowire single photon detectors (SNSPDs). By comparing the photon detection signals of two consecutive laser pulses and extracting the random bits by the von Neumann correction method, we achieved a random number generation efficiency of 25% (a generation rate of 3.75 Mbit s‑1 at a system clock rate of 15 MHz). Using a multi-channel superconducting nanowire single photon detector system with controllable pulse signal amplitudes, we detected the single photons with photon number resolution and positional sensitivity, which could further increase the random number generation efficiency. In a three-channel SNSPD system, the random number bit generation efficiency was improved to 75%, corresponding to a generation rate of 7.5 Mbit s‑1 with a 10 MHz system clock rate. All of the generated random numbers successfully passed the statistical test suite.
1. Quantum Optics with Quantum Dots in Photonic Wires: Basics and Application to “Ultrabright” Single Photon Sources
DEFF Research Database (Denmark)
Gérard, J. M.; Claudon, J.; Bleuse, J.; Malik, N. S.; Munsch, M.; Dupuy, E.; Lalanne, P.; Gregersen, Niels
2011-01-01
, we have noticeably observed a very strong (16 fold) inhibition of their spontaneous emission rate in the thin-wire limit, and a nearly perfect funnelling of their spontaneous emission into the guided mode for larger PWs. We present a novel single -photon-source based on the emission of a quantum dot......We review recent experimental and theoretical results, which highlight the strong interest of the photonic wire (PW) geometry for quantum optics experiments with solid-state emitters, and for quantum optoelectronic devices. By studying single InAs QDs embedded within single-mode cylindrical GaAs PW...
2. Waveguide-integrated single- and multi-photon detection at telecom wavelengths using superconducting nanowires
Energy Technology Data Exchange (ETDEWEB)
Ferrari, Simone; Kahl, Oliver [Institute of Nanotechnology, Karlsruhe Institute of Technology, Karlsruhe 76132 (Germany); Kovalyuk, Vadim [Institute of Nanotechnology, Karlsruhe Institute of Technology, Karlsruhe 76132 (Germany); Department of Physics, Moscow State Pedagogical University, Moscow 119992 (Russian Federation); Goltsman, Gregory N. [Department of Physics, Moscow State Pedagogical University, Moscow 119992 (Russian Federation); National Research University Higher School of Economics, 20 Myasnitskaya Ulitsa, Moscow 101000 (Russian Federation); Korneev, Alexander [Department of Physics, Moscow State Pedagogical University, Moscow 119992 (Russian Federation); Moscow Institute of Physics and Technology (State University), Moscow 141700 (Russian Federation); Pernice, Wolfram H. P., E-mail: [email protected] [Institute of Nanotechnology, Karlsruhe Institute of Technology, Karlsruhe 76132 (Germany); Department of Physics, University of Münster, 48149 Münster (Germany)
2015-04-13
We investigate single- and multi-photon detection regimes of superconducting nanowire detectors embedded in silicon nitride nanophotonic circuits. At near-infrared wavelengths, simultaneous detection of up to three photons is observed for 120 nm wide nanowires biased far from the critical current, while narrow nanowires below 100 nm provide efficient single photon detection. A theoretical model is proposed to determine the different detection regimes and to calculate the corresponding internal quantum efficiency. The predicted saturation of the internal quantum efficiency in the single photon regime agrees well with plateau behavior observed at high bias currents.
3. Waveguide-integrated single- and multi-photon detection at telecom wavelengths using superconducting nanowires
International Nuclear Information System (INIS)
We investigate single- and multi-photon detection regimes of superconducting nanowire detectors embedded in silicon nitride nanophotonic circuits. At near-infrared wavelengths, simultaneous detection of up to three photons is observed for 120 nm wide nanowires biased far from the critical current, while narrow nanowires below 100 nm provide efficient single photon detection. A theoretical model is proposed to determine the different detection regimes and to calculate the corresponding internal quantum efficiency. The predicted saturation of the internal quantum efficiency in the single photon regime agrees well with plateau behavior observed at high bias currents
4. Monolithic on-chip integration of semiconductor waveguides, beamsplitters and single-photon sources
International Nuclear Information System (INIS)
The implementation of fully integrated single-photon sources and detectors into waveguide structures such as photonic crystals or a slab and ridge waveguide is currently one of the major goals in the linear optics quantum computation and communication community. Here, we present an implementation of a single-photon on-chip experiment based on a III–V semiconductor platform. Individual semiconductor quantum dots were used as pulsed single-photon sources integrated in ridge waveguides, and the on-chip waveguide-beamsplitter operation is verified on the single-photon level by performing off-chip photon cross-correlation measurements between the two output ports of the beamsplitter. A degree of polarization of the emitted photons above 90% is observed and a careful characterization of the waveguide propagation losses in straight (< 1.5 dB mm−1) and bent (∼ (8.5 ± 2.2) dB mm−1) sections documents the applicability of such GaAs-based waveguide structures in more complex photonic integrated circuits. The presented work marks an important step towards the realization of fully integrated photonic quantum circuits including on-demand single-photon emitters. (paper)
5. InGaAs/InAlAs single photon avalanche diode for 1550 nm photons
Science.gov (United States)
Xie, Shiyu; Zhou, Xinxin; Calandri, Niccolò; Sanzaro, Mirko; Tosi, Alberto; Tan, Chee Hing; Ng, Jo Shien
2016-01-01
A single photon avalanche diode (SPAD) with an InGaAs absorption region, and an InAlAs avalanche region was designed and demonstrated to detect 1550 nm wavelength photons. The characterization included leakage current, dark count rate and single photon detection efficiency as functions of temperature from 210 to 294 K. The SPAD exhibited good temperature stability, with breakdown voltage dependence of approximately 45 mV K−1. Operating at 210 K and in a gated mode, the SPAD achieved a photon detection probability of 26% at 1550 nm with a dark count rate of 1 × 108 Hz. The time response of the SPAD showed decreasing timing jitter (full width at half maximum) with increasing overbias voltage, with 70 ps being the smallest timing jitter measured. PMID:27069647
6. Observation of the quantum paradox of separation of a single photon from one of its properties
OpenAIRE
Ashby, James M.; Schwarz, Peter D.; Schlosshauer, Maximilian
2016-01-01
We report an experimental realization of the quantum paradox of the separation of a single photon from one of its properties (the so-called "quantum Cheshire cat"). We use a modified Sagnac interferometer with displaced paths to produce appropriately pre- and postselected states of heralded single photons. Weak measurements of photon presence and circular polarization are performed in each arm of the interferometer by introducing weak absorbers and small polarization rotations and analyzing c...
7. Energy Relaxtation and Hot Spot Formation in Superconducting Single Photon Detectors SSPDS
Directory of Open Access Journals (Sweden)
Florya I.N.
2015-01-01
Full Text Available We have studied the mechanism of energy relaxation and resistive state formation after absorption of a single photon for different wavelengths and materials of single photon detectors. Our results are in good agreement with the hot spot model.
8. Single-photon quantum error rejection and correction with linear optics
OpenAIRE
Kalamidas, Demetrios
2005-01-01
We present single-photon schemes for quantum error rejection and correction with linear optics. In stark contrast to other known proposals, our schemes do not require multi-photon entangled states, are not probabilistic, and their application is not restricted to single bit-flip errors.
9. Young's double-slit experiment with single photons and quantum eraser
Science.gov (United States)
Rueckner, Wolfgang; Peidle, Joseph
2013-12-01
An apparatus for a double-slit interference experiment in the single-photon regime is described. The apparatus includes a which-path marker that destroys the interference as well as a quantum eraser that restores it. We present data taken with several light sources, coherent and incoherent and discuss the efficacy of these as sources of single photons.
10. Single spontaneous photon as a coherent beamsplitter for an atomic matter-wave
Energy Technology Data Exchange (ETDEWEB)
Tomkovič, Jiří; Welte, Joachim; Oberthaler, Markus K. [Kirchhoff-Institut für Physik, Universität Heidelberg, Heidelberg (Germany); Schreiber, Michael [Ludwig-Maximilians-Universität, München (Germany); Kiffner, Martin [Physik Department I, Technische Universität München, Garching (Germany); Schmiedmayer, Jörg [Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Vienna (Austria)
2014-12-04
In free space the spontaneous emission of a single photon destroys motional coherence. Close to a mirror surface the reflection erases the which-path information and the single emitted photon can be regarded as a coherent beam splitter for an atomic matter-wavewhich can be verified by atom interferometry. Our experiment is a realization of the recoiling slit Gedanken experiment by Einstein.
11. Evaluation of a fast single-photon avalanche photodiode for measurement of early transmitted photons through diffusive media.
Science.gov (United States)
Mu, Ying; Valim, Niksa; Niedre, Mark
2013-06-15
We tested the performance of a fast single-photon avalanche photodiode (SPAD) in measurement of early transmitted photons through diffusive media. In combination with a femtosecond titanium:sapphire laser, the overall instrument temporal response time was 59 ps. Using two experimental models, we showed that the SPAD allowed measurement of photon-density sensitivity functions that were approximately 65% narrower than the ungated continuous wave case at very early times. This exceeds the performance that we have previously achieved with photomultiplier-tube-based systems and approaches the theoretical maximum predicted by time-resolved Monte Carlo simulations. PMID:23938989
12. Low-noise low-jitter 32-pixels CMOS single-photon avalanche diodes array for single-photon counting from 300 nm to 900 nm
Energy Technology Data Exchange (ETDEWEB)
Scarcella, Carmelo; Tosi, Alberto, E-mail: [email protected]; Villa, Federica; Tisa, Simone; Zappa, Franco [Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy)
2013-12-15
We developed a single-photon counting multichannel detection system, based on a monolithic linear array of 32 CMOS SPADs (Complementary Metal-Oxide-Semiconductor Single-Photon Avalanche Diodes). All channels achieve a timing resolution of 100 ps (full-width at half maximum) and a photon detection efficiency of 50% at 400 nm. Dark count rate is very low even at room temperature, being about 125 counts/s for 50 μm active area diameter SPADs. Detection performance and microelectronic compactness of this CMOS SPAD array make it the best candidate for ultra-compact time-resolved spectrometers with single-photon sensitivity from 300 nm to 900 nm.
13. Low-noise low-jitter 32-pixels CMOS single-photon avalanche diodes array for single-photon counting from 300 nm to 900 nm.
Science.gov (United States)
Scarcella, Carmelo; Tosi, Alberto; Villa, Federica; Tisa, Simone; Zappa, Franco
2013-12-01
We developed a single-photon counting multichannel detection system, based on a monolithic linear array of 32 CMOS SPADs (Complementary Metal-Oxide-Semiconductor Single-Photon Avalanche Diodes). All channels achieve a timing resolution of 100 ps (full-width at half maximum) and a photon detection efficiency of 50% at 400 nm. Dark count rate is very low even at room temperature, being about 125 counts/s for 50 μm active area diameter SPADs. Detection performance and microelectronic compactness of this CMOS SPAD array make it the best candidate for ultra-compact time-resolved spectrometers with single-photon sensitivity from 300 nm to 900 nm. PMID:24387425
14. Experimental single-photon exchange along a space link of 7000 km
Science.gov (United States)
Dequal, Daniele; Vallone, Giuseppe; Bacco, Davide; Gaiarin, Simone; Luceri, Vincenza; Bianco, Giuseppe; Villoresi, Paolo
2016-01-01
Extending the single-photon transmission distance is a basic requirement for the implementation of quantum communication on a global scale. In this work we report the single-photon exchange from a medium Earth orbit satellite (MEO) at more than 7000 km of slant distance to the ground station at the Matera Laser Ranging Observatory. The single-photon transmitter was realized by exploiting the corner cube retroreflectors mounted on the LAGEOS-2 satellite. Long duration of data collection is possible with such altitude, up to 43 min in a single passage. The mean number of photons per pulse (μsat) has been limited to 1 for 200 s, resulting in an average detection rate of 3.0 counts/s and a signal-to-noise ratio of 1.5. The feasibility of single-photon exchange from MEO satellites paves the way to tests of quantum mechanics in moving frames and to global quantum Information.
15. Up-conversion single-photon detector using multi-wavelength sampling techniques.
Science.gov (United States)
Ma, Lijun; Bienfang, Joshua C; Slattery, Oliver; Tang, Xiao
2011-03-14
The maximum achievable data-rate of a quantum communication system can be critically limited by the efficiency and temporal resolution of the system's single-photon detectors. Frequency up-conversion technology can be used to increase detection efficiency for IR photons. In this paper we describe a scheme to improve the temporal resolution of an up-conversion single-photon detector using multi-wavelength optical-sampling techniques, allowing for increased transmission rates in single-photon communications systems. We experimentally demonstrate our approach with an up-conversion detector using two spectrally and temporally distinct pump pulses, and show that it allows for high-fidelity single-photon detection at twice the rate supported by a conventional single-pump up-conversion detector. We also discuss the limiting factors of this approach and identify important performance-limiting trade offs. PMID:21445185
16. Experimental single photon exchange along a space link of 7000 km
DEFF Research Database (Denmark)
Dequal, Daniele; Vallone, Giuseppe; Bacco, Davide;
2015-01-01
the Matera Laser Ranging Observatory. The single photon transmitter was realized by exploiting the corner cube retro-reflectors mounted on the LAGEOS-2 satellite. Long duration of data collection is possible with such altitude, up to 43 minutes in a single passage. The mean number of photons per pulse......Extending the single photon transmission distance is a basic requirement for the implementation of quantum communication on a global scale. In this work we report the single photon exchange from a medium Earth orbit satellite (MEO) at more than 7000 km of slanted distance to the ground station at...... (µsat) has been limited to 1 for 200 seconds, resulting in an average detection rate of 3.0 cps and a signal to noise ratio of 1.5. The feasibility of single photon exchange from MEO satellites paves the way to tests of Quantum Mechanics in moving frames and to global Quantum Information....
17. Tracking hidden objects with a single-photon camera
CERN Document Server
Gariepy, Genevieve; Henderson, Robert; Leach, Jonathan; Faccio, Daniele
2015-01-01
The ability to know what is hidden around a corner or behind a wall provides a crucial advantage when physically going around the obstacle is impossible or dangerous. Previous solutions to this challenge were constrained e.g. by their physical size, the requirement of reflective surfaces or long data acquisition times. These impede both the deployment of the technology outside the laboratory and the development of significant advances, such as tracking the movement of large-scale hidden objects. We demonstrate a non-line-of-sight laser ranging technology that relies upon the ability, using only a floor surface, to send and detect light that is scattered around an obstacle. A single-photon avalanche diode (SPAD) camera detects light back-scattered from a hidden object that can then be located with centimetre precision, simultaneously tracking its movement. This non-line-of-sight laser ranging system is also shown to work at human length scales, paving the way for a variety of real-life situations.
18. Single photon emission tomography imaging in parkinsonian disorders: a review.
Science.gov (United States)
Acton, P D; Mozley, P D
2000-01-01
Parkinsonian symptoms are associated with a number of neurodegenerative disorders, such as Parkinson's disease, multiple system atrophy and progressive supranuclear palsy. Pathological evidence has shown clearly that these disorders are associated with a loss of neurons, particularly in the nigrostriatal dopaminergic pathway. Positron emission tomography (PET) and single photon emission tomography (SPECT) now are able to visualise and quantify changes in cerebral blood flow, glucose metabolism, and dopaminergic function produced by parkinsonian disorders. Both PET and SPECT have become important tools in the differential diagnosis of these diseases, and may have sufficient sensitivity to detect neuronal changes before the onset of clinical symptoms. Imaging is now being utilised to elucidate the genetic contribution to Parkinson's disease, and in longitudinal studies to assess the efficacy and mode of action of neuroprotective drug and surgical treatments. This review summarises recent applications of SPECT imaging in the study of parkinsonian disorders, with particular reference to the increasing role it is playing in the understanding, diagnosis and management of these diseases. PMID:11455039
19. Single photon emission computed tomography in periatric frontal epilepsy
International Nuclear Information System (INIS)
Neuroradiological examinations were made in 9 pediatric patients with frontal epilepsy by using single photon emission computed tomography (SPECT), cat scanning (CT) and magnetic resonance imaging (MRI). Two patients (22%) had abnormal findings on both CT and MRI; and 6 patients (67%) had them on SPECT, two of whom had findings corresponding to focal sites on EEG. Among the 6 patients, 5 were suspected of having decreased regional cerebral blood flow (rCBF), corresponding to 84%-94% of the contralateral blood flow. Two patients were evaluable before and after seizures; one had increased rCBF at the time of frequent seizures and returned to normal after seizures; and the other had no abnormality in the early stage of epilepsy, but had decreased rCBF after seizures. SPECT appears to provide a simple, useful tool in evaluating cerebral hemodynamics in infantile epilepsy, although serial hemodynamic changes with developmental process of central nerves and the time of examination must be considered according to individual patients. (N.K.)
20. Single-Photon Emission Computed Tomography (SPECT) in childhood epilepsy
International Nuclear Information System (INIS)
The success of epilepsy surgery is determined strongly by the precise location of the epileptogenic focus. The information from clinical electrophysiological data needs to be strengthened by functional neuroimaging techniques. Single photon emission computed tomography (SPECT) available locally has proved useful as a localising investigation. It evaluates the regional cerebral blood flow and the comparison between ictal and interictal blood flow on SPECT has proved to be a sensitive nuclear marker for the site of seizure onset. Many studies justify the utility of SPECT in localising lesions to possess greater precision than interictal scalp EEG or anatomic neuroimaging. SPECT is of definitive value in temporal lobe epilepsy. Its role in extratemporal lobe epilepsy is less clearly defined. It is useful in various other generalized and partial seizure disorders including epileptic syndromes and helps in differentiating pseudoseizures from true seizures. The need for newer radiopharmaceutical agents with specific neurochemical properties and longer shelf life are under investigation. Subtraction ictal SPECT co-registered to MRI is a promising new modality. (author)
1. Single photon emission computed tomography-guided Cerenkov luminescence tomography
Science.gov (United States)
Hu, Zhenhua; Chen, Xueli; Liang, Jimin; Qu, Xiaochao; Chen, Duofang; Yang, Weidong; Wang, Jing; Cao, Feng; Tian, Jie
2012-07-01
Cerenkov luminescence tomography (CLT) has become a valuable tool for preclinical imaging because of its ability of reconstructing the three-dimensional distribution and activity of the radiopharmaceuticals. However, it is still far from a mature technology and suffers from relatively low spatial resolution due to the ill-posed inverse problem for the tomographic reconstruction. In this paper, we presented a single photon emission computed tomography (SPECT)-guided reconstruction method for CLT, in which a priori information of the permissible source region (PSR) from SPECT imaging results was incorporated to effectively reduce the ill-posedness of the inverse reconstruction problem. The performance of the method was first validated with the experimental reconstruction of an adult athymic nude mouse implanted with a Na131I radioactive source and an adult athymic nude mouse received an intravenous tail injection of Na131I. A tissue-mimic phantom based experiment was then conducted to illustrate the ability of the proposed method in resolving double sources. Compared with the traditional PSR strategy in which the PSR was determined by the surface flux distribution, the proposed method obtained much more accurate and encouraging localization and resolution results. Preliminary results showed that the proposed SPECT-guided reconstruction method was insensitive to the regularization methods and ignored the heterogeneity of tissues which can avoid the segmentation procedure of the organs.
2. Monitoring cellular mechanosensing using time-correlated single photon counting
Science.gov (United States)
Tabouillot, Tristan; Gullapalli, Ramachandra; Butler, Peter J.
2006-10-01
Endothelial cells (ECs) convert mechanical stimuli into chemical signaling pathways to regulate their functions and properties. It is hypothesized that perturbation of cellular structures by force is accompanied by changes in molecular dynamics. In order to address these fundamental issues in mechanosensation and transduction, we have developed a hybrid multimodal microscopy - time-correlated single photon counting (TCSPC) spectroscopy system intended to determine time- and position dependent mechanically-induced changes in the dynamics of molecules in live cells as determined from fluorescence lifetimes and autocorrelation analysis (fluorescence correlation spectroscopy). Colocalization of cell-structures and mechanically-induced changes in molecular dynamics can be done in post-processing by comparing TCSPC data with 3-D models generated from total internal reflection fluorescence (TIRF), differential interference contrast (DIC), epifluorescence, and deconvolution. We present control experiments in which the precise location of the apical cell membrane with respect to a confocal probe is assessed using information obtainable only from TCSPC. Such positional accuracy of TCSPC measurements is essential to understanding the role of the membrane in mechanotransduction. We predict that TCSPC will become a useful method to obtain high temporal and spatial resolution information on localized mechanical phenomena in living endothelial cells. Such insight into mechanotransduction phenomenon may uncover the origins of mechanically-related diseases such as atherosclerosis.
3. Single Photon Emission Tomography Imaging in Parkinsonian Disorders: A Review
Directory of Open Access Journals (Sweden)
Paul D. Acton
2000-01-01
Full Text Available Parkinsonian symptoms are associated with a number of neurodegenerative disorders, such as Parkinson’s disease, multiple system atrophy and progressive supranuclear palsy. Pathological evidence has shown clearly that these disorders are associated with a loss of neurons, particularly in the nigrostriatal dopaminergic pathway. Positron emission tomography (PET and single photon emission tomography (SPECT now are able to visualise and quantify changes in cerebral blood flow, glucose metabolism, and dopaminergic function produced by parkinsonian disorders. Both PET and SPECT have become important tools in the differential diagnosis of these diseases, and may have sufficient sensitivity to detect neuronal changes before the onset of clinical symptoms. Imaging is now being utilised to elucidate the genetic contribution to Parkinson’s disease, and in longitudinal studies to assess the efficacy and mode of action of neuroprotective drug and surgical treatments. This review summarises recent applications of SPECT imaging in the study of parkinsonian disorders, with particular reference to the increasing role it is playing in the understanding, diagnosis and management of these diseases.
4. Single photon radionuclide computed tomography with Tomogscanner II, (1)
International Nuclear Information System (INIS)
The single photon radionuclide computed tomography (RCT) was examined in 214 patients with the Tomogscanner-II. The RCT of brain was superior to the conventional brain scan, especially in the detection of lesions at the base of brain or the postoperated condition. The blood pool RCT of brain depicted an arterio-venous malformation and a giant aneurysma at the base of brain. The RCT of cisternography was useful to understand the anatomical relationship of the activity. The RCT of cerebral blood perfusion was possible with a method of continuous infusion of sup(81m)Kr into an internal carotid artery. In the body study, the reconstructed image of the Tomogscanner was excellent. The area of myocardial infarction showed clear defect in the horse-shaped myocardial section image after injection of 4 mCi of 201TlCl. The RCT of liver was available to detect defects and evaluated the activity and size of spleen. The RCT of kidney, lung or bone also showed good image, respectively. The Tomogscanner-II gave very good images in clinical examination of body as well as brain. (author)
5. Single Photon Atomic Sorting: Isotope Separation with Maxwell's Demon
CERN Document Server
Raizen, M G; Jerkins, M
2010-01-01
Isotope separation is one of the grand challenges of modern society and holds great potential for basic science, medicine, energy, and defense. We consider here a new and general approach to isotope separation. The method is based on an irreversible change of the mass-to-magnetic moment ratio of a particular isotope in an atomic beam, followed by deflection in a magnetic field gradient. The underlying mechanism is a reduction of the entropy of the beam by the information of a single-scattered photon for each atom that is separated. We numerically simulate isotope separation for a range of examples. The first class of atoms we consider are those that have zero magnetic moment in their ground electronic state. A laser induces an irreversible transition to a metastable state, followed by magnetic deflection. The second (larger) class of atoms we consider are those that have a magnetic moment in their ground state. The magnetic stretch-state is deflected in one zone of a magnetic field gradient, followed by a las...
6. Brain single photon emission computed tomography in neonates
Energy Technology Data Exchange (ETDEWEB)
Denays, R.; Van Pachterbeke, T.; Tondeur, M.; Spehl, M.; Toppet, V.; Ham, H.; Piepsz, A.; Rubinstein, M.; Nol, P.H.; Haumont, D. (Free Universities of Brussels (Belgium))
1989-08-01
This study was designed to rate the clinical value of ({sup 123}I)iodoamphetamine (IMP) or ({sup 99m}Tc) hexamethyl propylene amine oxyme (HM-PAO) brain single photon emission computed tomography (SPECT) in neonates, especially in those likely to develop cerebral palsy. The results showed that SPECT abnormalities were congruent in most cases with structural lesions demonstrated by ultrasonography. However, mild bilateral ventricular dilatation and bilateral subependymal porencephalic cysts diagnosed by ultrasound were not associated with an abnormal SPECT finding. In contrast, some cortical periventricular and sylvian lesions and all the parasagittal lesions well visualized in SPECT studies were not diagnosed by ultrasound scans. In neonates with subependymal and/or intraventricular hemorrhage the existence of a parenchymal abnormality was only diagnosed by SPECT. These results indicate that ({sup 123}I)IMP or ({sup 99m}Tc)HM-PAO brain SPECT shows a potential clinical value as the neurodevelopmental outcome is clearly related to the site, the extent, and the number of cerebral lesions. Long-term clinical follow-up is, however, mandatory in order to define which SPECT abnormality is associated with neurologic deficit.
7. Single photon emission computed tomography: A clinical experience
International Nuclear Information System (INIS)
In the past decade, single photon emission computed tomography (SPECT) has evolved from an experimental technique used only in academic settings to a routine clinical examination performed in many community hospitals. Responding to reports of increased diagnostic efficacy, many nuclear medicine physicians have chosen to make SPECT imaging a routine technique for bone, liver, spleen, heart, and brain imaging. However, the enthusiasm for SPECT is not universal. Most nuclear medicine physicians continue to rely primarily on planar imaging, with little or no routine use of SPECT. This milieu has left many physicians asking themselves the following practical questions: Can SPECT be done easily in my hospital? Will not doing SPECT reduce the competitiveness of my nuclear medicine laboratory? The authors' experience at an institution heavily committed to SPECT for over 5 years may be helpful in answering these types of questions. The first rotating gamma camera at the Milwaukee Regional Medical Center was installed in late 1981. At present the authors have eight gamma cameras, of which four routinely perform SPECT examinations. Between 1981 and 1986, over 4,000 SPECT examinations have been performed
8. Brain single photon emission computed tomography in neonates
International Nuclear Information System (INIS)
This study was designed to rate the clinical value of [123I]iodoamphetamine (IMP) or [99mTc] hexamethyl propylene amine oxyme (HM-PAO) brain single photon emission computed tomography (SPECT) in neonates, especially in those likely to develop cerebral palsy. The results showed that SPECT abnormalities were congruent in most cases with structural lesions demonstrated by ultrasonography. However, mild bilateral ventricular dilatation and bilateral subependymal porencephalic cysts diagnosed by ultrasound were not associated with an abnormal SPECT finding. In contrast, some cortical periventricular and sylvian lesions and all the parasagittal lesions well visualized in SPECT studies were not diagnosed by ultrasound scans. In neonates with subependymal and/or intraventricular hemorrhage the existence of a parenchymal abnormality was only diagnosed by SPECT. These results indicate that [123I]IMP or [99mTc]HM-PAO brain SPECT shows a potential clinical value as the neurodevelopmental outcome is clearly related to the site, the extent, and the number of cerebral lesions. Long-term clinical follow-up is, however, mandatory in order to define which SPECT abnormality is associated with neurologic deficit
9. Proceedings of clinical SPECT (single photon emission computed tomography) symposium
Energy Technology Data Exchange (ETDEWEB)
1986-09-01
It has been five years since the last in-depth American College of Nuclear Physicians/Society of Nuclear Medicine Symposium on the subject of single photon emission computed tomography (SPECT) was held. Because this subject was nominated as the single most desired topic we have selected SPECT imaging as the basis for this year's program. The objectives of this symposium are to survey the progress of SPECT clinical applications that have taken place over the last five years and to provide practical and timely guidelines to users of SPECT so that this exciting imaging modality can be fully integrated into the evaluation of pathologic processes. The first half was devoted to a consideration of technical factors important in SPECT acquisition and the second half was devoted to those organ systems about which sufficient clinical SPECT imaging data are available. With respect to the technical aspect of the program we have selected the key areas which demand awareness and attention in order to make SPECT operational in clinical practice. These include selection of equipment, details of uniformity correction, utilization of phantoms for equipment acceptance and quality assurance, the major aspect of algorithms, an understanding of filtered back projection and appropriate choice of filters and an awareness of the most commonly generated artifacts and how to recognize them. With respect to the acquisition and interpretation of organ images, the faculty will present information on the major aspects of hepatic, brain, cardiac, skeletal, and immunologic imaging techniques. Individual papers are processed separately for the data base. (TEM)
10. High-Brightness Beams from a Light Source Injector: The Advanced Photon Source Low-Energy Undulator Test Line Linac
OpenAIRE
Travish, G.; Biedron, S; Borland, M.; Hahne, M.; Harkay, K.; Lewellen, J.W.; Lumpkin, A.; Milton, S.; Sereno, N.
2000-01-01
The use of existing linacs, and in particular light source injectors, for free-electron laser (FEL) experiments is becoming more common due to the desire to test FELs at ever shorter wavelengths. The high-brightness, high-current beams required by high-gain FELs impose technical specifications that most existing linacs were not designed to meet. Moreover, the need for specialized diagnostics, especially shot-to-shot data acquisition, demands substantial modification and upgrade of conventiona...
11. Cavity-Free Scheme for Nondestructive Detection of a Single Optical Photon.
Science.gov (United States)
Xia, Keyu; Johnsson, Mattias; Knight, Peter L; Twamley, Jason
2016-01-15
Detecting a single photon without absorbing it is a long-standing challenge in quantum optics. All experiments demonstrating the nondestructive detection of a photon make use of a high quality cavity. We present a cavity-free scheme for nondestructive single-photon detection. By pumping a nonlinear medium we implement an interfield Rabi oscillation which leads to a ∼π phase shift on a weak probe coherent laser field in the presence of a single signal photon without destroying the signal photon. Our cavity-free scheme operates with a fast intrinsic time scale in comparison with similar cavity-based schemes. We implement a full real-space multimode numerical analysis of the interacting photonic modes and confirm the validity of our nondestructive scheme in the multimode case. PMID:26824538
12. τ-SPAD: a new red sensitive single-photon counting module
Science.gov (United States)
Kell, Gerald; Bülter, Andreas; Wahl, Michael; Erdmann, Rainer
2011-05-01
Single Photon Avalanche Diodes (SPADs) are valuable detectors in numerous photon counting applications in the fields of quantum physics, quantum communication, astronomy, metrology and biomedical analytics. They typically feature a much higher photon detection efficiency than photomultiplier tubes, most importantly in the red to near-infrared range of the spectrum. Very often SPADs are combined with Time-Correlated Single Photon Counting (TCSPC) electronics for time-resolved data acquisition and the temporal resolution ("jitter") of a SPAD is therefore one of the key parameters for selecting a detector. We show technical data and first application results from a new type of red sensitive single photon counting module ("τ-SPAD"), which is targeted at timing applications, most prominently in the area of Single Molecule Spectroscopy (SMS). The τ-SPAD photon counting module combines Laser Components' ultra-low noise VLoK silicon avalanche photodiode with specially developed quenching and readout electronics from PicoQuant. It features an extremely high photon detection efficiency of 75% at 670 nm and can be used to detect single photons over the 400 nm to 1100 nm wavelength range. The timing jitter of the output of the τ-SPAD can be as low as 350 ps, making it suitable for time-resolved fluorescence detection applications. First photon coincidence correlation measurements also show that the typical breakdown flash of SPADs is of comparably low intensity for these new SPADs.
13. Three-dimensional photonic crystals created by single-step multi-directional plasma etching.
Science.gov (United States)
Suzuki, Katsuyoshi; Kitano, Keisuke; Ishizaki, Kenji; Noda, Susumu
2014-07-14
We fabricate 3D photonic nanostructures by simultaneous multi-directional plasma etching. This simple and flexible method is enabled by controlling the ion-sheath in reactive-ion-etching equipment. We realize 3D photonic crystals on single-crystalline silicon wafers and show high reflectance (>95%) and low transmittance (<-15dB) at optical communication wavelengths, suggesting the formation of a complete photonic bandgap. Moreover, our method simply demonstrates Si-based 3D photonic crystals that show the photonic bandgap effect in a shorter wavelength range around 0.6 μm, where further fine structures are required. PMID:25090524
14. Room temperature triggered single-photon source in the near infrared
International Nuclear Information System (INIS)
We report the realization of a solid-state triggered single-photon source with narrow emission in the near infrared at room temperature. It is based on the photoluminescence of a single nickel-nitrogen NE8 colour centre in a chemical vapour deposited diamond nanocrystal. Stable single-photon emission has been observed in the photoluminescence under both continuous-wave and pulsed excitations. The realization of this source represents a step forward in the application of diamond-based single-photon sources to quantum key distribution (QKD) under practical operating conditions
15. Large conditional single-photon cross-phase modulation
CERN Document Server
Beck, Kristin M; Duan, Yiheng; Vuletić, Vladan
2015-01-01
Deterministic optical quantum logic requires a nonlinear quantum process that alters the phase of a quantum optical state by $\\pi$ through interaction with only one photon. Here, we demonstrate a large conditional cross-phase modulation between a signal field, stored inside an atomic quantum memory, and a control photon that traverses a high-finesse optical cavity containing the atomic memory. This approach avoids fundamental limitations associated with multimode effects for traveling optical photons. We measure a conditional cross-phase shift of up to $\\pi/3$ between the retrieved signal and control photons, and confirm deterministic entanglement between the signal and control modes by extracting a positive concurrence. With a moderate improvement in cavity finesse, our system can reach a coherent phase shift of $\\pi$ at low loss, enabling deterministic and universal photonic quantum logic.
16. Performance of a superconducting single photon detector with nano-antenna
Institute of Scientific and Technical Information of China (English)
Zhang Chao; Jiao Rong-Zhen
2012-01-01
The performance of single-photon detectors can be enhanced by using nano-antenna.The characteristics of the superconducting nano-wire single-photon detector with cavity plus anti-reflect coating and specially designed nanoantenna is analysed.The photon collection efficiency of the detector is enhanced without damaging the detector's speed,thus getting rid of the dilemma of speed and efficiency.The characteristics of nano-antenna are discussed,such as the position and the effect of the active area,and the best result is given.The photon collection efficiency is increased by 92 times compared with that of existing detectors.
Science.gov (United States)
Trautmann, N; Alber, G; Agarwal, G S; Leuchs, G
2015-05-01
Readout and retrieval processes are proposed for efficient, high-fidelity quantum state transfer between a matter qubit, encoded in the level structure of a single atom or ion, and a photonic qubit, encoded in a time-reversal-symmetric single-photon wave packet. They are based on controlling spontaneous photon emission and absorption of a matter qubit on demand in free space by stimulated Raman adiabatic passage. As these processes do not involve mode selection by high-finesse cavities or photon transport through optical fibers, they offer interesting perspectives as basic building blocks for free-space quantum-communication protocols. PMID:25978231
18. Optimizing single-nanoparticle two-photon microscopy by in situ adaptive control of femtosecond pulses
Science.gov (United States)
Li, Donghai; Deng, Yongkai; Chu, Saisai; Jiang, Hongbing; Wang, Shufeng; Gong, Qihuang
2016-07-01
Single-nanoparticle two-photon microscopy shows great application potential in super-resolution cell imaging. Here, we report in situ adaptive optimization of single-nanoparticle two-photon luminescence signals by phase and polarization modulations of broadband laser pulses. For polarization-independent quantum dots, phase-only optimization was carried out to compensate the phase dispersion at the focus of the objective. Enhancement of the two-photon excitation fluorescence intensity under dispersion-compensated femtosecond pulses was achieved. For polarization-dependent single gold nanorod, in situ polarization optimization resulted in further enhancement of two-photon photoluminescence intensity than phase-only optimization. The application of in situ adaptive control of femtosecond pulse provides a way for object-oriented optimization of single-nanoparticle two-photon microscopy for its future applications.
19. Wiring up pre-characterized single-photon emitters by laser lithography.
Science.gov (United States)
Shi, Q; Sontheimer, B; Nikolay, N; Schell, A W; Fischer, J; Naber, A; Benson, O; Wegener, M
2016-01-01
Future quantum optical chips will likely be hybrid in nature and include many single-photon emitters, waveguides, filters, as well as single-photon detectors. Here, we introduce a scalable optical localization-selection-lithography procedure for wiring up a large number of single-photon emitters via polymeric photonic wire bonds in three dimensions. First, we localize and characterize nitrogen vacancies in nanodiamonds inside a solid photoresist exhibiting low background fluorescence. Next, without intermediate steps and using the same optical instrument, we perform aligned three-dimensional laser lithography. As a proof of concept, we design, fabricate, and characterize three-dimensional functional waveguide elements on an optical chip. Each element consists of one single-photon emitter centered in a crossed-arc waveguide configuration, allowing for integrated optical excitation and efficient background suppression at the same time. PMID:27507165
20. Wiring up pre-characterized single-photon emitters by laser lithography
Science.gov (United States)
Shi, Q.; Sontheimer, B.; Nikolay, N.; Schell, A. W.; Fischer, J.; Naber, A.; Benson, O.; Wegener, M.
2016-08-01
Future quantum optical chips will likely be hybrid in nature and include many single-photon emitters, waveguides, filters, as well as single-photon detectors. Here, we introduce a scalable optical localization-selection-lithography procedure for wiring up a large number of single-photon emitters via polymeric photonic wire bonds in three dimensions. First, we localize and characterize nitrogen vacancies in nanodiamonds inside a solid photoresist exhibiting low background fluorescence. Next, without intermediate steps and using the same optical instrument, we perform aligned three-dimensional laser lithography. As a proof of concept, we design, fabricate, and characterize three-dimensional functional waveguide elements on an optical chip. Each element consists of one single-photon emitter centered in a crossed-arc waveguide configuration, allowing for integrated optical excitation and efficient background suppression at the same time.
1. Wiring up pre-characterized single-photon emitters by laser lithography
Science.gov (United States)
Shi, Q.; Sontheimer, B.; Nikolay, N.; Schell, A. W.; Fischer, J.; Naber, A.; Benson, O.; Wegener, M.
2016-01-01
Future quantum optical chips will likely be hybrid in nature and include many single-photon emitters, waveguides, filters, as well as single-photon detectors. Here, we introduce a scalable optical localization-selection-lithography procedure for wiring up a large number of single-photon emitters via polymeric photonic wire bonds in three dimensions. First, we localize and characterize nitrogen vacancies in nanodiamonds inside a solid photoresist exhibiting low background fluorescence. Next, without intermediate steps and using the same optical instrument, we perform aligned three-dimensional laser lithography. As a proof of concept, we design, fabricate, and characterize three-dimensional functional waveguide elements on an optical chip. Each element consists of one single-photon emitter centered in a crossed-arc waveguide configuration, allowing for integrated optical excitation and efficient background suppression at the same time. PMID:27507165
2. Single-mode and single-polarization photonics with anchored-membrane waveguides
CERN Document Server
Chiles, Jeff
2016-01-01
An integrated photonic platform with anchored-membrane structures, the T-Guide, is proposed and numerically investigated. These compact air-clad structures have high index contrast and are much more stable than prior membrane-type structures. Their semi-infinite geometry enables single-mode and single-polarization (SMSP) operation over unprecedented bandwidths. Modal simulations quantify this behavior, showing that an SMSP window of 2.75 octaves (1.2 - 8.1 {\\mu}m) is feasible for silicon T-Guides, spanning almost the entire transparency range of silicon. Dispersion engineering for T-Guides yields broad regions of anomalous group velocity dispersion, rendering them a promising platform for nonlinear applications, such as wideband frequency conversion.
3. Radiopharmaceuticals for single-photon emission computed tomography brain imaging.
Science.gov (United States)
Kung, Hank F; Kung, Mei-Ping; Choi, Seok Rye
2003-01-01
In the past 10 years, significant progress on the development of new brain-imaging agents for single-photon emission computed tomography has been made. Most of the new radiopharmaceuticals are designed to bind specific neurotransmitter receptor or transporter sites in the central nervous system. Most of the site-specific brain radiopharmaceuticals are labeled with (123)I. Results from imaging of benzodiazepine (gamma-aminobutyric acid) receptors by [(123)I]iomazenil are useful in identifying epileptic seizure foci and changes of this receptor in psychiatric disorders. Imaging of dopamine D2/D3 receptors ([(123)I]iodobenzamide and [(123)I]epidepride) and transporters [(123)I]CIT (2-beta-carboxymethoxy-3-beta(4-iodophenyl)tropane) and [(123)I]FP-beta-CIT (N-propyl-2-beta-carboxymethoxy-3-beta(4-iodophenyl)-nortropane has proven to be a simple but powerful tool for differential diagnosis of Parkinson's and other neurodegenerative diseases. A (99m)Tc-labeled agent, [(99m)Tc]TRODAT (technetium, 2-[[2-[[[3-(4-chlorophenyl)-8-methyl-8-azabicyclo [3,2,1]oct-2-yl]methyl](2-mercaptoethyl)amino]ethyl]amino] ethanethiolato(3-)]oxo-[1R-(exo-exo)]-), for imaging dopamine transporters in the brain has been successfully applied in the diagnosis of Parkinson's disease. Despite the fact that (123)I radiopharmaceuticals have been widely used in Japan and in Europe, clinical application of (123)I-labeled brain radiopharmaceuticals in the United States is limited because of the difficulties in supplying such agents. Development of (99m)Tc agents will likely extend the application of site-specific brain radiopharmaceuticals for routine applications in aiding the diagnosis and monitoring treatments of various neurologic and psychiatric disorders. PMID:12605353
4. Site-controlled InGaN/GaN single-photon-emitting diode
Science.gov (United States)
Zhang, Lei; Teng, Chu-Hsiang; Ku, Pei-Cheng; Deng, Hui
2016-04-01
We report single-photon emission from electrically driven site-controlled InGaN/GaN quantum dots. The device is fabricated from a planar light-emitting diode structure containing a single InGaN quantum well, using a top-down approach. The location, dimension, and height of each single-photon-emitting diode are controlled lithographically, providing great flexibility for chip-scale integration.
5. Quantum Computing using Single Photons and the Zeno Effect
CERN Document Server
Franson, J D; Pittman, T B
2004-01-01
We show that the quantum Zeno effect can be used to implement a square-root of SWAP quantum logic gate for photonic qubits. The successful operation of these devices depends on the fact that photons can behave in some respects as if they were fermions instead of bosons in the presence of a strong Zeno effect. No actual observations are required and the same results can be obtained by using atoms to record the presence of more than one photon in an optical fiber.
6. Independent telecom-fiber sources of quantum indistinguishable single photons
International Nuclear Information System (INIS)
Quantum-mechanically indistinguishable photons produced by independent (or equivalently, mutually phase incoherent) light sources are essential for distributed quantum information processing applications. We demonstrate heralded generation of such photons in two spatially separate telecom-fiber spools, each driven by pulsed pump waves that are measured to have no mutual phase coherence. Through Hong–Ou–Mandel experiments, we measure the quantum interference visibility of those photons to be 76.4±4.2. Our experimental results are well predicted by a quantum multimode theory we developed for such systems without the need for any fitting parameter
7. EQUIPMENTS TO SINGLE PHOTON REGISTRATION. PART 1. FEATURES AND POSSIBILITIES OF MULTI-CHANNEL PHOTODETECTORS WITH INTRINSIC AMPLIFICATION. (REVIEW
Directory of Open Access Journals (Sweden)
O. V. Dvornikov
2015-04-01
Full Text Available The main types of the modern photo detectors applied to single photon registration are analyzed. It is offered to use silicon photomultipliers for production of multi-channel optoelectronic systems with the single photon resolution.
8. Electrically driven single photon emission from a CdSe/ZnSSe single quantum dot at 200 K
Energy Technology Data Exchange (ETDEWEB)
Quitsch, Wolf; Kümmell, Tilmar; Bacher, Gerd [Werkstoffe der Elektrotechnik and CENIDE, Universität Duisburg-Essen, Bismarckstraße 81, 47057 Duisburg (Germany); Gust, Arne; Kruse, Carsten; Hommel, Detlef [Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28334 Bremen (Germany)
2014-09-01
High temperature operation of an electrically driven single photon emitter based on a single epitaxial quantum dot is reported. CdSe/ZnSSe/MgS quantum dots are embedded into a p-i-n diode architecture providing almost background free excitonic and biexcitonic electroluminescence from individual quantum dots through apertures in the top contacts. Clear antibunching with g{sup 2}(τ = 0) = 0.28 ± 0.20 can be tracked up to T = 200 K, representing the highest temperature for electrically triggered single photon emission from a single quantum dot device.
9. Single Mode Photonic Crystal Vertical Cavity Surface Emitting Lasers
Directory of Open Access Journals (Sweden)
Kent D. Choquette
2012-01-01
Full Text Available We review the design, fabrication, and performance of photonic crystal vertical cavity surface emitting lasers (VCSELs. Using a periodic pattern of etched holes in the top facet of the VCSEL, the optical cavity can be designed to support the fundamental mode only. The electrical confinement is independently defined by proton implantation or oxide confinement. By control of the refractive index and loss created by the photonic crystal, operation in the Gaussian mode can be insured, independent of the lasing wavelength.
10. Large-area single-mode photonic bandgap vcsels
DEFF Research Database (Denmark)
Birkedal, Dan; Gregersen, N.; Bischoff, S.; Madsen, M.; Romstad, F.; Oestergaard, J.
We demonstrate that the photonic bandgap effect can be used to control the modes of large area vertical cavity surface emitting lasers. We obtain more than 20 dB side mode suppression ratios in a 10-micron area device.......We demonstrate that the photonic bandgap effect can be used to control the modes of large area vertical cavity surface emitting lasers. We obtain more than 20 dB side mode suppression ratios in a 10-micron area device....
11. Bright trions in direct-bandgap silicon nanocrystals revealed bylow-temperature single-nanocrystal spectroscopy
Czech Academy of Sciences Publication Activity Database
Kůsová, Kateřina; Pelant, Ivan; Valenta, J.
2015-01-01
Roč. 4, Oct (2015), e336. ISSN 2047-7538 R&D Projects: GA ČR(CZ) GBP108/12/G108; GA ČR GPP204/12/P235 Institutional support: RVO:68378271 Keywords : silicon nanocrystals * single-nanocrystal spectroscopy * luminescing trions Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 14.603, year: 2014
12. Photon Antibunching in the Photoluminescence Spectra of a Single Carbon Nanotube
OpenAIRE
Högele, Alexander; Galland, Christophe; Winger, Martin; Imamoglu, Atac
2007-01-01
We report the first observation of photon antibunching in the photoluminescence from single carbon nanotubes. The emergence of a fast luminescence decay component under strong optical excitation indicates that Auger processes are partially responsible for inhibiting two-photon generation. Additionally, the presence of exciton localization at low temperatures ensures that nanotubes emit photons predominantly one by one. The fact that multiphoton emission probability can be smaller than 5% sugg...
13. Corpuscular model of two-beam interference and double-slit experiments with single photons
CERN Document Server
Jin, Fengping; De Raedt, Hans; Michielsen, Kristel; Miyashita, Seiji
2010-01-01
We introduce an event-based corpuscular simulation model that reproduces the wave mechanical results of single-photon double slit and two-beam interference experiments and (of a one-to-one copy of an experimental realization) of a single-photon interference experiment with a Fresnel biprism. The simulation comprises models that capture the essential features of the apparatuses used in the experiment, including the single-photon detectors recording individual detector clicks. We demonstrate that incorporating in the detector model, simple and minimalistic processes mimicking the memory and threshold behavior of single-photon detectors is sufficient to produce multipath interference patterns. These multipath interference patterns are built up by individual particles taking one single path to the detector where they arrive one-by-one. The particles in our model are not corpuscular in the standard, classical physics sense in that they are information carriers that exchange information with the apparatuses of the ...
14. Elliptical quantum dots as on-demand single photons sources with deterministic polarization states
Energy Technology Data Exchange (ETDEWEB)
Teng, Chu-Hsiang; Demory, Brandon; Ku, Pei-Cheng, E-mail: [email protected] [Department of Electrical Engineering and Computer Science, University of Michigan, 1301 Beal Ave., Ann Arbor, Michigan 48105 (United States); Zhang, Lei; Hill, Tyler A.; Deng, Hui [Department of Mechanical Engineering, University of Michigan, 2350 Hayward St., Ann Arbor, Michigan 48105 (United States)
2015-11-09
In quantum information, control of the single photon's polarization is essential. Here, we demonstrate single photon generation in a pre-programmed and deterministic polarization state, on a chip-scale platform, utilizing site-controlled elliptical quantum dots (QDs) synthesized by a top-down approach. The polarization from the QD emission is found to be linear with a high degree of linear polarization and parallel to the long axis of the ellipse. Single photon emission with orthogonal polarizations is achieved, and the dependence of the degree of linear polarization on the QD geometry is analyzed.
15. Highly efficient coupling of photons from nanoemitters into single-mode optical fibers
CERN Document Server
Fujiwara, Masazumi; Noda, Tetsuya; Zhao, Hong-Quan; Takeuchi, Shigeki; 10.1021/nl2024867
2012-01-01
Highly efficient coupling of photons from nanoemitters into single-mode optical fibers is demonstrated using tapered fibers. 7.4 +/- 1.2 % of the total emitted photons from single CdSe/ZnS nanocrystals were coupled into a 300-nm-diameter tapered fiber. The dependence of the coupling efficiency on the taper diameter was investigated and the coupling efficiency was found to increase exponentially with decreasing diameter. This method is very promising for nanoparticle sensing and single-photon sources.
16. Effective Single Photon Decay Mode of Positronium Decay via Electroweak Interactions
CERN Document Server
Pérez-Ríos, Jesús
2015-01-01
We consider the decay of positronium to a neutrino-antineutrino accompanied by a single photon. Since the neutrino pair go undetected, this appears as a single photon decay of positronium. These decay channel are mediated through the exchange of the massive $W$ and $Z$ vector bosons of the electroweak interaction. After summing over the various neutrino channels, the standard model calculation yields the rate for such a single photon decay process of $\\Gamma_{Ps \\rightarrow \\gamma}$ = 1.72 $\\times 10^{-19}$ s$^{-1}$.
17. Developing a Parametric Downconversion Apparatus for Single-Photon Experiments in Quantum Optics
Science.gov (United States)
Diiorio, Stephen
2015-05-01
We report our progress toward developing a parametric downconversion apparatus for studying single-photon quantum optics in undergraduate laboratory classes, following the model of Galvez et al.. We pump a beta barium borate (BBO) crystal with a 405 nm diode laser to produce correlated pairs of single-photons that we detect using avalanche photodiodes (APD). We can conduct coincidence and anti-coincidence counts and a measurement of the degree of second-order coherence with the apparatus, and we expect to report on single- and bi-photon interferometry experiments.
18. Elliptical quantum dots as on-demand single photons sources with deterministic polarization states
International Nuclear Information System (INIS)
In quantum information, control of the single photon's polarization is essential. Here, we demonstrate single photon generation in a pre-programmed and deterministic polarization state, on a chip-scale platform, utilizing site-controlled elliptical quantum dots (QDs) synthesized by a top-down approach. The polarization from the QD emission is found to be linear with a high degree of linear polarization and parallel to the long axis of the ellipse. Single photon emission with orthogonal polarizations is achieved, and the dependence of the degree of linear polarization on the QD geometry is analyzed
19. Single-photon counting in the 1550-nm wavelength region for quantum cryptography
International Nuclear Information System (INIS)
In this paper, we report the measured performance of an InGaAs avalanche photodiode (APD) Module fabricated for single-photon counting. We measured the dark current noise, the after-pulse noise, and the quantum efficiency of the single- photon detector for different temperatures. We then examined our single-photon source and detection system by measuring the coincident probability. From our measurement, we observed that the after-pulse effect of the APD at temperatures below 105 .deg. C caused cascade noise build-up on the succeeding electrical signals.
20. Photon bremsstrahlung from quark jet via transverse and longitudinal scatterings: single versus multiple scatterings
CERN Document Server
Zhang, Le; Qin, Guang-You
2016-01-01
We study the production of jet-bremsstrahlung photons through the scattering with the constituents of a dense nuclear matter within the framework of deep-inelastic scattering off a large nucleus. Applying a gradient expansion up to the second order for the exchanged three-dimensional momentum between jet and medium, we derive the single photon bremsstrahlung spectrum with the inclusion of the contributions from the transverse broadening as well as the longitudinal drag and diffusion of the hard parton's momentum. We also compare the medium-induced photon radiation spectra for single scattering and from the resummation of multiple scatterings. It is found that the coupling between different scatterings can give additional contribution to medium-induced photon radiation, while for small momentum exchange, the leading contribution from the drag and diffusions to the photon emission spectra remain the same for single and multiple scatterings.
1. Generation of single photons with highly tunable wave shape from a cold atomic quantum memory
CERN Document Server
Farrera, Pau; Albrecht, Boris; Ho, Melvyn; Chávez, Matías; Teo, Colin; Sangouard, Nicolas; de Riedmatten, Hugues
2016-01-01
We report on a single photon source with highly tunable photon shape based on a cold ensemble of Rubidium atoms. We follow the DLCZ scheme to implement an emissive quantum memory, which can be operated as a photon pair source with controllable delay. We find that the temporal wave shape of the emitted read photon can be precisely controlled by changing the shape of the driving read pulse. We generate photons with temporal durations varying over three orders of magnitude up to 10 {\\mu}s without a significant change of the read-out efficiency. We prove the non-classicality of the emitted photons by measuring their antibunching, showing near single photon behavior at low excitation probabilities. We also show that the photons are emitted in a pure state by measuring unconditional autocorrelation functions. Finally, to demonstrate the usability of the source for realistic applications, we create ultra-long single photons with a rising exponential or doubly peaked wave shape which are important for several quantum...
2. Few-photon imaging at 1550 nm using a low-timing-jitter superconducting nanowire single-photon detector
CERN Document Server
Zhou, H; You, L; Chen, S; Zhang, W; Wu, J; Wang, Z; Xie, X
2015-01-01
We demonstrated a laser depth imaging system based on the time-correlated single-photon counting technique, which was incorporated with a low-jitter superconducting nanowire single-photon detector (SNSPD), operated at the wavelength of 1550 nm. A sub-picosecond time-bin width was chosen for photon counting, resulting in a discrete noise of less than one/two counts for each time bin under indoor/outdoor daylight conditions, with a collection time of 50 ms. Because of the low-jitter SNSPD, the target signal histogram was significantly distinguishable, even for a fairly low retro-reflected photon flux. The depth information was determined directly by the highest bin counts, instead of using any data fitting combined with complex algorithms. Millimeter resolution depth imaging of a low-signature object was obtained, and more accurate data than that produced by the traditional Gaussian fitting method was generated. Combined with the intensity of the return photons, three-dimensional reconstruction overlaid with re...
3. Efficient multi-mode to single-mode coupling in a photonic lantern
DEFF Research Database (Denmark)
Noordegraaf, Danny; Skovgaard, Peter M.; Nielsen, Martin D.;
2009-01-01
We demonstrate the fabrication of a high performance multi-mode (MM) to single-mode (SM) splitter or “photonic lantern”, first described by Leon-Saval et al. (2005). Our photonic lantern is a solid all-glass version, and we show experimentally that this device can be used to achieve efficient and...
4. Fluorescence lifetime imaging by time-correlated single-photon counting
NARCIS (Netherlands)
Becker, W.; Bergmann, A.; Hink, M.A.; Konig, K.; Benndorf, K.; Biskup, C.
2004-01-01
We present a time-correlated single photon counting (TCPSC) technique that allows time-resolved multi-wavelength imaging in conjunction with a laser scanning microscope and a pulsed excitation source. The technique is based on a four-dimensional histogramming process that records the photon density
5. Enhancement of Rydberg-mediated single-photon nonlinearities by electrically tuned Förster resonances.
Science.gov (United States)
Gorniaczyk, H; Tresp, C; Bienias, P; Paris-Mandoki, A; Li, W; Mirgorodskiy, I; Büchler, H P; Lesanovsky, I; Hofferberth, S
2016-01-01
Mapping the strong interaction between Rydberg atoms onto single photons via electromagnetically induced transparency enables manipulation of light at the single-photon level and few-photon devices such as all-optical switches and transistors operated by individual photons. Here we demonstrate experimentally that Stark-tuned Förster resonances can substantially increase this effective interaction between individual photons. This technique boosts the gain of a single-photon transistor to over 100, enhances the non-destructive detection of single Rydberg atoms to a fidelity beyond 0.8, and enables high-precision spectroscopy on Rydberg pair states. On top, we achieve a gain larger than 2 with gate photon read-out after the transistor operation. Theory models for Rydberg polariton propagation on Förster resonance and for the projection of the stored spin-wave yield excellent agreement to our data and successfully identify the main decoherence mechanism of the Rydberg transistor, paving the way towards photonic quantum gates. PMID:27515278
6. Experimental realization of highly efficient broadband coupling of single quantum dots to a photonic crystal waveguide
DEFF Research Database (Denmark)
Lund-Hansen, Toke; Stobbe, Søren; Julsgaard, Brian; Nielsen, Henri Thyrrestrup; Sünner, T.; Kamp, M.; Forchel, A.; Lodahl, Peter
2008-01-01
We present time-resolved spontaneous emission measurements of single quantum dots embedded in photonic crystal waveguides. Quantum dots that couple to a photonic crystal waveguide are found to decay up to 27 times faster than uncoupled quantum dots. From these measurements -factors of up to 0.89 ...
7. Microwave single photon counting by using Rydberg atoms and its application for searching invisible axions
International Nuclear Information System (INIS)
A high sensitivity single photon counting method using Rydberg atoms is discussed and shown to be a promissing technique for detecting microwave photons converted from cosmic axions in a strong magnetic field by the Primakov effect. This method could give much better results compared with conventional methods. (author)
8. Single-photon single ionization of W$^{+}$ ions: experiment and theory
CERN Document Server
Müller, A; Hellhund, J; Holste, K; Kilcoyne, A L D; Phaneuf, R A; Ballance, C P; McLaughlin, B M
2015-01-01
Experimental and theoretical results are reported for photoionization of Ta-like (W$^{+}$) tungsten ions. Absolute cross sections were measured in the energy range 16 to 245 eV employing the photon-ion merged-beam setup at the Advanced Light Source in Berkeley. Detailed photon-energy scans at 100 meV bandwidth were performed in the 16 to 108 eV range. In addition, the cross section was scanned at 50 meV resolution in regions where fine resonance structures could be observed. Theoretical results were obtained from a Dirac-Coulomb R-matrix approach. Photoionization cross section calculations were performed for singly ionized atomic tungsten ions in their $5s^2 5p^6 5d^4({^5}D)6s \\; {^6}{\\rm D}_{J}$, $J$=1/2, ground level and the associated excited metastable levels with $J$=3/2, 5/2, 7/2 and 9/2. Since the ion beams used in the experiments must be expected to contain long-lived excited states also from excited configurations, additional cross-section calculations were performed for the second-lowest term, $5d^5... 9. Practical single-photon-assisted remote state preparation with non-maximally entanglement Science.gov (United States) Wang, Dong; Huang, Ai-Jun; Sun, Wen-Yang; Shi, Jia-Dong; Ye, Liu 2016-08-01 Remote state preparation (RSP) and joint remote state preparation (JRSP) protocols for single-photon states are investigated via linear optical elements with partially entangled states. In our scheme, by choosing two-mode instances from a polarizing beam splitter, only the sender in the communication protocol needs to prepare an ancillary single-photon and operate the entanglement preparation process in order to retrieve an arbitrary single-photon state from a photon pair in partially entangled state. In the case of JRSP, i.e., a canonical model of RSP with multi-party, we consider that the information of the desired state is split into many subsets and in prior maintained by spatially separate parties. Specifically, with the assistance of a single-photon state and a three-photon entangled state, it turns out that an arbitrary single-photon state can be jointly and remotely prepared with certain probability, which is characterized by the coefficients of both the employed entangled state and the target state. Remarkably, our protocol is readily to extend to the case for RSP and JRSP of mixed states with the all optical means. Therefore, our protocol is promising for communicating among optics-based multi-node quantum networks. 10. NFAD Arrays for Single Photon Optical Communications at 1.5 um Project Data.gov (United States) National Aeronautics and Space Administration — For this program, we propose to develop large pixel-count single photon counting detector arrays suitable for deployment in spacecraft terminal receivers supporting... 11. Effect of Background Noise on the Photon Statistics of Triggered Single Molecules Institute of Scientific and Technical Information of China (English) XIAO Lian-Tuan; ZHAO Yan-Ting; HUANG Tao; ZHAO Jian-Ming; YIN Wang-Bao; JIA Suo-Tang 2004-01-01 @@ We theoretically derive exact expressions for Mandel's Q parameter of the triggered single molecular source, which is inferred from the probabilities PRS(n) using the recorded of each photon detection event based on Hanbury Brown and Twiss detection. The real triggered source is recognized as an ideal single photon source with a Poissonian statistics background. How to decease the background and to increase the efficiency are discussed. It is established that the sub-Poissonian statistics formation can be determined by comparing the measured QRS of the real single triggered molecular with QC of the Poissonian source containing the same mean photons. By this method, we also give an efficient way to measure signal-to-background ratios of triggered single photons. 12. Quantum Secret Sharing Protocol between Multiparty and Multiparty with Single Photons and Unitary Transformations Institute of Scientific and Technical Information of China (English) YAN Feng-Li; GAO Ting; LI You-Cheng 2008-01-01 @@ We propose a scheme of quantum secret sharing between Alice's group and Bob's group with single photons and unitary transformations. In the protocol, one member in Alice's group prepares a sequence of single photons in one of four different states, while other members directly encode their information on the sequence of single photons via unitary operations; after that, the last member sends the sequence of single photons to Bob's group.Then Bob's, except for the last one, do work similarly. Finally the last member in Bob's group measures the qubits. If the security of the quantum channel is guaranteed by some tests, then the qubit states sent by the last member of Alice's group can be used as key bits for secret sharing. It is shown that this scheme is safe. 13. Single Photon Sensitive HgCdTe Avalanche Photodiode Detector (APD) Project Data.gov (United States) National Aeronautics and Space Administration — Leveraging Phase I SBIR successes, in Phase II, a single photon sensitive LIDAR receiver will be fabricated and delivered to NASA. In Phase I, high-gain,... 14. Tuning the coupling of a single quantum dot to a photonic crystal waveguide OpenAIRE Nielsen, Henri Thyrrestrup; Lodahl, Peter; Lund-Hansen, Toke 2009-01-01 We present time-resolved spontaneous emission measurements of a single quantum dot that is temperature tuned around the band edge of a photonic crystal waveguide. 85% efficient coupling to the slow-light waveguide mode is obtained. 15. Quantum Frequency Conversion of Single-Photon States by Three and Four-Wave Mixing DEFF Research Database (Denmark) Raymer, Michael G.; Reddy, Dileep V.; Andersen, Lasse Mejling; Rottwitt, Karsten 2013-01-01 Three- or four-wave mixing can convert a single-photon wave packet to a new frequency. By tailoring the shapes of the pump(s), one can achieve add/drop functionality for different temporally orthogonal wave packets.... 16. Quantum Secret Sharing Protocol between Multiparty and Multiparty with Single Photons and Unitary Transformations International Nuclear Information System (INIS) We propose a scheme of quantum secret sharing between Alice's group and Bob's group with single photons and unitary transformations. In the protocol, one member in Alice's group prepares a sequence of single photons in one of four different states, while other members directly encode their information on the sequence of single photons via unitary operations; after that, the last member sends the sequence of single photons to Bob's group. Then Bob's, except for the last one, do work similarly. Finally the last member in Bob's group measures the qubits. If the security of the quantum channel is guaranteed by some tests, then the qubit states sent by the last member of Alice's group can be used as key bits for secret sharing. It is shown that this scheme is safe 17. Enhanced single photon emission from positioned InP/GaInP quantum dots coupled to a confined Tamm-plasmon mode International Nuclear Information System (INIS) We report on the enhancement of the spontaneous emission in the visible red spectral range from site-controlled InP/GaInP quantum dots by resonant coupling to Tamm-plasmon modes confined beneath gold disks in a hybrid metal/semiconductor structure. The enhancement of the emission intensity is confirmed by spatially resolved micro-photoluminescence area scans and temperature dependent measurements. Single photon emission from our coupled system is verified via second order autocorrelation measurements. We observe bright single quantum dot emission of up to ∼173 000 detected photons per second at a repetition rate of the excitation source of 82 MHz, and calculate an extraction efficiency of our device as high as 7% 18. Enhanced single photon emission from positioned InP/GaInP quantum dots coupled to a confined Tamm-plasmon mode Energy Technology Data Exchange (ETDEWEB) Braun, T.; Baumann, V.; Iff, O.; Schneider, C.; Kamp, M. [Technische Physik, Physikalisches Institut and Wilhelm Conrad Röntgen-Research Center for Complex Material Systems, Universität Würzburg, Am Hubland, D-97074 Würzburg (Germany); Höfling, S. [Technische Physik, Physikalisches Institut and Wilhelm Conrad Röntgen-Research Center for Complex Material Systems, Universität Würzburg, Am Hubland, D-97074 Würzburg (Germany); SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS (United Kingdom) 2015-01-26 We report on the enhancement of the spontaneous emission in the visible red spectral range from site-controlled InP/GaInP quantum dots by resonant coupling to Tamm-plasmon modes confined beneath gold disks in a hybrid metal/semiconductor structure. The enhancement of the emission intensity is confirmed by spatially resolved micro-photoluminescence area scans and temperature dependent measurements. Single photon emission from our coupled system is verified via second order autocorrelation measurements. We observe bright single quantum dot emission of up to ∼173 000 detected photons per second at a repetition rate of the excitation source of 82 MHz, and calculate an extraction efficiency of our device as high as 7%. 19. Modeling resonant cavities for single-photon waveguide sources International Nuclear Information System (INIS) Spectral correlations between photon pairs generated by spontaneous parametric down conversion (SPDC) in bulk non-linear optical crystals remain a hindrance to the implementation of efficient quantum communication architectures. It has been demonstrated that SPDC within a distributed micro-cavity can result in little or no correlation between photon pairs. We present results on modeling three different cavity configurations based on integrated Bragg gratings. Output from the SPDC process can be tailored by altering the periodicity and geometry of such nanostructures. We will discuss the merits of each cavity configuration from the standpoint of degenerate Type-II SPDC 20. Quantum Computing Using Single Photons and the Zeno Effect CERN Document Server Franson, J D; Pittman, T B 2004-01-01 We show that the quantum Zeno effect can be used to suppress the failure events that would otherwise occur in a linear optics approach to quantum computing. From a practical viewpoint, that would allow the implementation of deterministic logic gates without the need for ancilla photons or high-efficiency detectors. We also show that the photons can behave as if they were fermions instead of bosons in the presence of a strong Zeno effect, which leads to a new paradigm for quantum computation. 1. Quantum Optics with Quantum Dots in Photonic Wires: Basics and Application to “Ultrabright” Single Photon Sources DEFF Research Database (Denmark) Gérard, J. M.; Claudon, J.; Bleuse, J.; 2011-01-01 We review recent experimental and theoretical results, which highlight the strong interest of the photonic wire (PW) geometry for quantum optics experiments with solid-state emitters, and for quantum optoelectronic devices. By studying single InAs QDs embedded within single-mode cylindrical GaAs PW......, we have noticeably observed a very strong (16 fold) inhibition of their spontaneous emission rate in the thin-wire limit, and a nearly perfect funnelling of their spontaneous emission into the guided mode for larger PWs. We present a novel single -photon-source based on the emission of a quantum dot....... Numerical simulations show that an efficiency higher than 0.9 can be obtained for optimized structures, under either optical or electrical pumping.... 2. HIDES spectroscopy of bright detached eclipsing binaries from the$Kepler$field - I. Single-lined objects CERN Document Server Hełminiak, K G; Kambe, E; Kozłowski, S K; Sybilski, P; Ratajczak, M; Maehara, H; Konacki, M 2016-01-01 We present results of our spectroscopic observations of nine detached eclipsing binaries (DEBs), selected from the$Kepler$Eclipsing Binary Catalog, that only show one set of spectral lines. Radial velocities (RVs) were calculated from the high resolution spectra obtained with the HIDES instrument, attached to the 1.88-m telescope at the Okayama Astrophysical Observatory, and from the public APOGEE archive. In our sample we found five single-lined binaries, with one component dominating the spectrum. The orbital and light curve solutions were found for four of them, and compared with isochrones, in order to estimate absolute physical parameters and evolutionary status of the components. For the fifth case we only update the orbital parameters, and estimate the properties of the unseen star. Two other systems show orbital motion with a period known from the eclipse timing variations (ETVs). For these we obtained parameters of outer orbits, by translating the ETVs to RVs of the centre of mass of the eclipsing ... 3. CMOS SPAD-based image sensor for single photon counting and time of flight imaging OpenAIRE Dutton, Neale Arthur William 2016-01-01 The facility to capture the arrival of a single photon, is the fundamental limit to the detection of quantised electromagnetic radiation. An image sensor capable of capturing a picture with this ultimate optical and temporal precision is the pinnacle of photo-sensing. The creation of high spatial resolution, single photon sensitive, and time-resolved image sensors in complementary metal oxide semiconductor (CMOS) technology offers numerous benefits in a wide field of applications.... 4. Exploiting Rydberg Atom Surface Phonon Polariton Coupling for Single Photon Subtraction OpenAIRE Kübler, H.; Booth, D.; Sedlacek, J.; Zabawa, P.; Shaffer, J. P. 2013-01-01 We investigate a hybrid quantum system that consists of a superatom coupled to a surface phonon-polariton. We apply this hybrid quantum system to subtract individual photons from a beam of light. Rydberg atom blockade is used to attain absorption of a single photon by an atomic microtrap. Surface phonon-polariton coupling to the superatom then triggers the transfer of the excitation to a storage state, a single Rydberg atom. The approach utilizes the interaction between a superatom and a Mark... 5. Single-photon quantum nondemolition detectors constructed with linear optics and projective measurements OpenAIRE Kok, Pieter; Lee, Hwang; Dowling, Jonathan P. 2002-01-01 Optical quantum nondemolition devices can provide essential tools for quantum information processing. Here, we describe several optical interferometers that signal the presence of a single photon in a particular input state without destroying it. We discuss both entanglement-assisted and non-entanglement-assisted interferometers, with ideal and realistic detectors. We found that existing detectors with 88% quantum efficiency and single-photon resolution can yield output fidelities of up to 89... 6. Optimal coupling of entangled photons into single-mode optical fibers CERN Document Server Andrews, R; Sarkar, S; Sarkar, Sarben 2004-01-01 We present a consistent multimode theory that describes the coupling of single photons generated by collinear Type-I parametric down-conversion into single-mode optical fibers. We have calculated an analytic expression for the fiber diameter which maximizes the pair photon count rate. For a given focal length and wavelength, a lower limit of the fiber diameter for satisfactory coupling is obtained. 7. Quantum Frequency Conversion of Single-Photon States by Three and Four-Wave Mixing DEFF Research Database (Denmark) Raymer, Michael G.; Reddy, Dileep V.; Andersen, Lasse Mejling; 2013-01-01 Three- or four-wave mixing can convert a single-photon wave packet to a new frequency. By tailoring the shapes of the pump(s), one can achieve add/drop functionality for different temporally orthogonal wave packets.......Three- or four-wave mixing can convert a single-photon wave packet to a new frequency. By tailoring the shapes of the pump(s), one can achieve add/drop functionality for different temporally orthogonal wave packets.... 8. Luminescence-induced noise in single photon sources based on BBO crystals Science.gov (United States) Machulka, Radek; Lemr, Karel; Haderka, Ondřej; Lamperti, Marco; Allevi, Alessia; Bondani, Maria 2014-11-01 Single-photon sources based on the process of spontaneous parametric down-conversion play a key role in various applied disciplines of quantum optics. We characterize the intrinsic luminescence of BBO crystals as a source of non-removable noise in quantum-optics experiments. By analysing its spectral and temporal properties together with its intensity, we evaluate the impact of luminescence on single-photon state preparation using spontaneous parametric down-conversion. 9. Reach of Environmental Influences on the Indistinguishability of Single Photons from Quantum Dots CERN Document Server Huber, Tobias; Föger, Daniel; Solomon, Glenn; Weihs, Gregor 2015-01-01 In this letter, we present a detailed, all optical study of the influence of different excitation schemes on the indistinguishability of single photons from a single InAs quantum dot. For this study, we measure the Hong-Ou-Mandel interference of consecutive photons from the spontaneous emission of an InAs quantum dot state under various excitation schemes and different excitation conditions and give a comparison. 10. Quantum dot resonant tunneling diode single photon detector with aluminum oxide aperture defined tunneling area OpenAIRE Li, H W; Kardynal, Beata; Ellis, D. J. P.; Shields, A.J.; Farrer, I.; Ritchie, D. A. 2008-01-01 Quantum dot resonant tunneling diode single photon detector with independently defined absorption and sensing areas is demonstrated. The device, in which the tunneling is constricted to an aperture in an insulating layer in the emitter, shows electrical characteristics typical of high quality resonant tunneling diodes. A single photon detection efficiency of 2.1%+/- 0.1% at 685 nm was measured corresponding to an internal quantum efficiency of 14%. The devices are simple to fabricate, robust,... 11. A Single-Photon Avalanche Diode Imager for Fluorescence Lifetime Applications OpenAIRE Schwartz, David E.; Charbon, Edoardo; Shepard, Kenneth L. 2007-01-01 A 64-by-64-pixel CMOS single-photon avalanche diode (SPAD) imager for time-resolved fluorescence detection features actively quenched and reset pixels, allowing gated detection to eliminate pile-up nonlinearities common to most time-correlated single-photon counting (TCSPC) approaches. Timing information is collected using an on-chip time-to-digital converter (TDC) based on a counter and a supply-regulated delay-locked loop (DLL). 12. A quantum phase switch between a single solid-state spin and a photon Science.gov (United States) Sun, Shuo; Kim, Hyochul; Solomon, Glenn S.; Waks, Edo 2016-06-01 Interactions between single spins and photons are essential for quantum networks and distributed quantum computation. Achieving spin–photon interactions in a solid-state device could enable compact chip-integrated quantum circuits operating at gigahertz bandwidths. Many theoretical works have suggested using spins embedded in nanophotonic structures to attain this high-speed interface. These proposals implement a quantum switch where the spin flips the state of the photon and a photon flips the spin state. However, such a switch has not yet been realized using a solid-state spin system. Here, we report an experimental realization of a spin–photon quantum switch using a single solid-state spin embedded in a nanophotonic cavity. We show that the spin state strongly modulates the polarization of a reflected photon, and a single reflected photon coherently rotates the spin state. These strong spin–photon interactions open up a promising direction for solid-state implementations of high-speed quantum networks and on-chip quantum information processors using nanophotonic devices. 13. High-fidelity transfer and storage of photon states in a single nuclear spin Science.gov (United States) Yang, Sen; Wang, Ya; Rao, D. D. Bhaktavatsala; Hien Tran, Thai; Momenzadeh, Ali S.; Markham, M.; Twitchen, D. J.; Wang, Ping; Yang, Wen; Stöhr, Rainer; Neumann, Philipp; Kosaka, Hideo; Wrachtrup, Jörg 2016-08-01 Long-distance quantum communication requires photons and quantum nodes that comprise qubits for interaction with light and good memory capabilities, as well as processing qubits for the storage and manipulation of photons. Owing to the unavoidable photon losses, robust quantum communication over lossy transmission channels requires quantum repeater networks. A necessary and highly demanding prerequisite for these networks is the existence of quantum memories with long coherence times to reliably store the incident photon states. Here we demonstrate the high-fidelity (∼98%) coherent transfer of a photon polarization state to a single solid-state nuclear spin that has a coherence time of over 10 s. The storage process is achieved by coherently transferring the polarization state of a photon to an entangled electron–nuclear spin state of a nitrogen–vacancy centre in diamond. The nuclear spin-based optical quantum memory demonstrated here paves the way towards an absorption-based quantum repeater network. 14. A SINGLE PHOTON SOURCE MODEL BASED ON QUANTUM DOT AND MICROCAVITY Directory of Open Access Journals (Sweden) Moez ATTIA 2011-12-01 Full Text Available We report a single photon source model which consists on InAs/GaAs pyramidal quantum dot (QDmodel based on effective mass theory to calculate the emitted photons energies. We study the choice ofgeometrics parameters of QD to obtain emission at 1550 nm. This quantum dot must be embedded on amicrocavity to improve the live time of photon at 1550 nm and inhibit the others photons to increase theprobability to obtain only one emitted photon. We present two kinds of microcavities; the first based ontwo dimensional photonic crystal over GaAs, we study the geometric parameters choice to obtain a heightdensity of mode (DOM at 1550 nm; the second microcavity is based on microdisk structure over GaAswe evaluate the impact of radius variation to obtain whispering-gallery mode at 1550 nm. This study canserve for the conception of new quantum communications protocols. 15. Tailored-waveguide based photonic chip for manipulating an array of single neutral atoms. Science.gov (United States) Ke, Min; Zhou, Feng; Li, Xiao; Wang, Jin; Zhan, Mingsheng 2016-05-01 We propose a tailored-waveguide based photonic chip with the functions of trapping, coherently manipulating, detecting and individually addressing an array of single neutral atoms. Such photonic chip consists of an array of independent functional units spaced by a few micrometers, each of which is comprised of one silica-on-silicon optical waveguide and one phase Fresnel microlens etched in the middle of the output interface of the optical waveguide. We fabricated a number of photonic chips with 7 functional units and measured optical characteristics of these chips. We further propose feasible schemes to realize the functions of such photonic chip. The photonic chip is stable, scalable and can be combined with other integrated devices, such as atom chips, and can be used in the future hybrid quantum system and photonic quantum devices. PMID:27137532 16. Dynamically reconfigurable directionality of plasmon-based single photon sources DEFF Research Database (Denmark) Chen, Yuntian; Lodahl, Peter; Koenderink, A. Femius 2010-01-01 beams can be switched on and off by switching host refractive index. The design method is based on engineering the dispersion relations of plasmon chains and is generally applicable to traveling wave antennas. Controllable photon delivery has potential applications in classical and quantum communication.... 17. A high-fidelity photon gun: intensity-squeezed light from a single molecule CERN Document Server Chu, Xiao-Liu; Sandoghdar, Vahid 2016-01-01 A two-level atom cannot emit more than one photon at a time. As early as the 1980s, this quantum feature was identified as a gateway to "single-photon sources", where a regular excitation sequence would create a stream of light particles with photon number fluctuations below the shot noise. Such an intensity squeezed beam of light would be desirable for a range of applications such as quantum imaging, sensing, enhanced precision measurements and information processing. However, experimental realizations of these sources have been hindered by large losses caused by low photon collection efficiencies and photophysical shortcomings. By using a planar metallo-dielectric antenna applied to an organic molecule, we demonstrate the most regular stream of single photons reported to date. Measured intensity fluctuations reveal 2.2 dB squeezing limited by our detection efficiency, equivalent to 6.2 dB intensity squeezing right after the antenna. 18. Coherent perfect absorption in deeply subwavelength films in the single photon regime CERN Document Server Roger, Thomas; Bolduc, Eliot; Valente, Joao; Heitz, Julius J F; Jeffers, John; Soci, Cesare; Leach, Jonathan; Couteau, Christophe; Zheludev, Nikolay; Faccio, Daniele 2016-01-01 The technologies of heating, photovoltaics, water photocatalysis and artificial photosynthesis depend on the absorption of light and novel approaches such as coherent absorption from a standing wave promise total dissipation of energy. Extending the control of absorption down to very low light levels and eventually to the single photon regime is of great interest yet remains largely unexplored. Here we demonstrate the coherent absorption of single photons in a deeply sub-wavelength 50% absorber. We show that while absorption of photons from a travelling wave is probabilistic, standing wave absorption can be observed deterministically, with nearly unitary probability of coupling a photon into a mode of the material, e.g. a localised plasmon when this is a metamaterial excited at the plasmon resonance. These results bring a better understanding of the coherent absorption process, which is of central importance for light harvesting, detection, sensing and photonic data processing applications. 19. Broad working bandwidth and "endlessly" single-mode guidance within hybrid silicon photonics. Science.gov (United States) Bougot-Robin, K; Hugonin, J-P; Besbes, M; Benisty, H 2015-08-01 The successes of nonlinear photonics and hybrid silicon photonics with a growing variety of functional materials entail ever-enlarging bandwidths. It is best exemplified by parametric comb frequency generation. Such operation challenges the dielectric channel waveguide as the basis for guidance, because of the adverse advent of higher order modes at short wavelengths. Surprisingly, the popular mechanism of endlessly single-mode guidance [Opt. Lett.22, 961 (1997).] operating in photonic crystal fibers has not been transposed within silicon photonics yet. We outline here the strategy and potential of this approach within planar and hybrid silicon photonics, whereby in-plane and vertical confinement are shown to be amenable to near-single-mode behavior in the typical silicon band, i.e., λ=1.1 μm to ∼5 μm. PMID:26258345 20. Super-resolved 3-D imaging of live cells organelles from bright-field photon transmission micrographs CERN Document Server Rychtarikova, Renata; Shi, Kevin; Malakhova, Daria; Machacek, Petr; Smaha, Rebecca; Urban, Jan; Stys, Dalibor 2016-01-01 Current biological and medical research is aimed at obtaining a detailed spatiotemporal map of a live cell's interior to describe and predict cell's physiological state. We present here an algorithm for complete 3-D modelling of cellular structures from a z-stack of images obtained using label-free wide-field bright-field light-transmitted microscopy. The method visualizes 3-D objects with a volume equivalent to the area of a camera pixel multiplied by the z-height. The computation is based on finding pixels of unchanged intensities between two consecutive images of an object spread function. These pixels represent strongly light-diffracting, light-absorbing, or light-emitting objects. To accomplish this, variables derived from R\\'{e}nyi entropy are used to suppress camera noise. Using this algorithm, the detection limit of objects is only limited by the technical specifications of the microscope setup--we achieve the detection of objects of the size of one camera pixel. This method allows us to obtain 3-D re... 1. Single telecom photon heralding by wavelength multiplexing in an optical fiber Science.gov (United States) Lenhard, Andreas; Brito, José; Kucera, Stephan; Bock, Matthias; Eschner, Jürgen; Becher, Christoph 2016-01-01 We demonstrate the multiplexing of a weak coherent and a quantum state of light in a single telecommunication fiber. For this purpose, we make use of spontaneous parametric down conversion and quantum frequency conversion to generate photon pairs at 854 nm and the telecom O-band. The herald photon at 854 nm triggers a telecom C-band laser pulse. The telecom single photon (O-band) and the laser pulse (C-band) are combined and coupled to a standard telecom fiber. Low-background time correlation between the weak coherent and quantum signal behind the fiber shows successful multiplexing. 2. Measurement of the transverse spatial quantum state of light at the single-photon level CERN Document Server Smith, B J; Raymer, M G; Walmsley, I A; Banaszek, K; Smith, Brian J.; Killett, Bryan 2005-01-01 We present an experimental method to measure the transverse spatial quantum state of an optical field in coordinate space at the single-photon level. The continuous-variable measurements are made with a photon-counting, parity-inverting Sagnac interferometer based on all-reflecting optics. The technique provides a large numerical aperture without distorting the shape of the wave front, does not introduce astigmatism, and allows for characterization of fully or partially coherent optical fields at the single-photon level. Measurements of the transverse spatial Wigner functions for highly attenuated coherent beams are presented and compared to theoretical predictions. 3. Single Photon Transport through an Atomic Chain Coupled to a One-dimensional Nanophotonic Waveguide OpenAIRE Liao, Zeyang; Zeng, Xiaodong; Zhu, Shi-Yao; Zubairy, M. Suhail 2015-01-01 We study the dynamics of a single photon pulse travels through a linear atomic chain coupled to a one-dimensional (1D) single mode photonic waveguide. We derive a time-dependent dynamical theory for this collective many-body system which allows us to study the real time evolution of the photon transport and the atomic excitations. Our analytical result is consistent with previous numerical calculations when there is only one atom. For an atomic chain, the collective interaction between the at... 4. Simulation and Characterization of Single Photon Detectors for Fluorescence Lifetime Spectroscopy and Gamma-ray Applications OpenAIRE Benetti, Michele 2012-01-01 Gamma-ray and Fluorescence Lifetime Spectroscopies are driving the development of non-imaging silicon photon sensors and, in this context, Silicon Photo-Multipliers (SiPM)s are leading the starring role. They are 2D array of optical diodes called Single Photon Avalanche Diodes (SPAD)s, and are normally fabricated with a dedicated silicon process. SPADs amplify the charge produced by the single absorbed photon in a way that recalls the avalanche amplification exploited in Photo-Multiplier Tube... 5. Electronic-state-controlled reset operation in quantum dot resonant-tunneling single-photon detectors International Nuclear Information System (INIS) The authors present a systematic study of an introduced reset operation on quantum dot (QD) single photon detectors operating at 77 K. The detectors are based on an AlAs/GaAs/AlAs double-barrier resonant tunneling diode with an adjacent layer of self-assembled InAs QDs. Sensitive single-photon detection in high (dI)/(dV) region with suppressed current fluctuations is achieved. The dynamic detection range is extended up to at least 104 photons/s for sensitive imaging applications by keeping the device far from saturation by employing an appropriate reset frequency 6. Electronic-state-controlled reset operation in quantum dot resonant-tunneling single-photon detectors Energy Technology Data Exchange (ETDEWEB) Weng, Q. C.; Zhu, Z. Q. [Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai 200241 (China); An, Z. H., E-mail: [email protected] [State Key Laboratory of Surface Physics and Institute of Advanced Materials, Fudan University, Shanghai 200433 (China); Song, J. D.; Choi, W. J. [Center for Opto-Electronic Convergence Systems, Institute of Science and Technology, Seoul 130-650 (Korea, Republic of) 2014-02-03 The authors present a systematic study of an introduced reset operation on quantum dot (QD) single photon detectors operating at 77 K. The detectors are based on an AlAs/GaAs/AlAs double-barrier resonant tunneling diode with an adjacent layer of self-assembled InAs QDs. Sensitive single-photon detection in high (dI)/(dV) region with suppressed current fluctuations is achieved. The dynamic detection range is extended up to at least 10{sup 4} photons/s for sensitive imaging applications by keeping the device far from saturation by employing an appropriate reset frequency. 7. Ultrabright single-photon source on diamond with electrical pumping at room and high temperatures Science.gov (United States) Fedyanin, D. Yu; Agio, M. 2016-07-01 The recently demonstrated electroluminescence of color centers in diamond makes them one of the best candidates for room temperature single-photon sources. However, the reported emission rates are far off what can be achieved by state-of-the-art electrically driven epitaxial quantum dots. Since the electroluminescence mechanism has not yet been elucidated, it is not clear to what extent the emission rate can be increased. Here we develop a theoretical framework to study single-photon emission from color centers in diamond under electrical pumping. The proposed model comprises electron and hole trapping and releasing, transitions between the ground and excited states of the color center as well as structural transformations of the center due to carrier trapping. It provides the possibility to predict both the photon emission rate and the wavelength of emitted photons. Self-consistent numerical simulations of the single-photon emitting diode based on the proposed model show that the photon emission rate can be as high as 100 kcounts s‑1 at standard conditions. In contrast to most optoelectronic devices, the emission rate steadily increases with the device temperature achieving of more than 100 Mcount s‑1 at 500 K, which is highly advantageous for practical applications. These results demonstrate the potential of color centers in diamond as electrically driven non-classical light emitters and provide a foundation for the design and development of single-photon sources for optical quantum computation and quantum communication networks operating at room and higher temperatures. 8. Coherent properties of single quantum dot transitions and single photon emission Energy Technology Data Exchange (ETDEWEB) Ester, Patrick 2008-04-23 of the first laser pulse. The relative phase of the QDs exciton can be controlled externally via the bias voltage. This effect is the basis for the observation of RAMSEY-fringes, which are presented in this work. The coherent manipulation of the p-shell is the basis for a novel excitation scheme for single photon emission. In this work it is shown that the first excited state can be coherently manipulated, similar to the ground state. (orig.) 9. Coherent properties of single quantum dot transitions and single photon emission International Nuclear Information System (INIS) of the first laser pulse. The relative phase of the QDs exciton can be controlled externally via the bias voltage. This effect is the basis for the observation of RAMSEY-fringes, which are presented in this work. The coherent manipulation of the p-shell is the basis for a novel excitation scheme for single photon emission. In this work it is shown that the first excited state can be coherently manipulated, similar to the ground state. (orig.) 10. Brightness of synchrotron radiation from undulators and bending magnets International Nuclear Information System (INIS) We consider the maximum of the Wigner distribution (WD) of synchrotron radiation (SR) fields as a possible definition of SR source brightness. Such figure of merit was originally introduced in the SR community by Kim. The brightness defined in this way is always positive and, in the geometrical optics limit, can be interpreted as maximum density of photon flux in phase space. For undulator and bending magnet radiation from a single electron, the WD function can be explicitly calculated. In the case of an electron beam with a finite emittance the brightness is given by the maximum of the convolution of a single electron WD function and the probability distribution of the electrons in phase space. In the particular case when both electron beam size and electron beam divergence dominate over the diffraction size and the diffraction angle, one can use a geometrical optics approach. However, there are intermediate regimes when only the electron beam size or the electron beam divergence dominate. In this asymptotic cases the geometrical optics approach is still applicable, and the brightness definition used here yields back once more the maximum photon flux density in phase space. In these intermediate regimes we find a significant numerical disagreement between exact calculations and the approximation for undulator brightness currently used in literature. We extend the WD formalism to a satisfactory theory for the brightness of a bending magnet. We find that in the intermediate regimes the usually accepted approximation for bending magnet brightness turns out to be inconsistent even parametrically. 11. Generating single-photon catalyzed coherent states with quantum-optical catalysis Science.gov (United States) Xu, Xue-xiang; Yuan, Hong-chun 2016-07-01 We theoretically generate single-photon catalyzed coherent states (SPCCSs) by means of quantum-optical catalysis based on the beam splitter (BS) or the parametric amplifier (PA). These states are obtained in one of the BS (or PA) output channels if a coherent state and a single-photon Fock state are present in two input ports and a single photon is registered in the other output port. The success probabilities of the detection (also the normalization factors) are discussed, which is different for BS and PA catalysis. In addition, we prove that the generated states catalyzed by BS and PA devices are actually the same quantum states after analyzing photon number distribution of the SPCCSs. The quantum properties of the SPCCSs, such as sub-Poissonian distribution, anti-bunching effect, quadrature squeezing effect, and the negativity of the Wigner function are investigated in detail. The results show that the SPCCSs are non-Gaussian states with an abundance of nonclassicality. 12. Heralded single-photon sources for quantum-key-distribution applications Science.gov (United States) Schiavon, Matteo; Vallone, Giuseppe; Ticozzi, Francesco; Villoresi, Paolo 2016-01-01 Single-photon sources (SPSs) are a fundamental building block for optical implementations of quantum information protocols. Among SPSs, multiple crystal heralded single-photon sources seem to give the best compromise between high pair production rate and low multiple photon events. In this work, we study their performance in a practical quantum-key-distribution experiment, by evaluating the achievable key rates. The analysis focuses on the two different schemes, symmetric and asymmetric, proposed for the practical implementation of heralded single-photon sources, with attention on the performance of their composing elements. The analysis is based on the protocol proposed by Bennett and Brassard in 1984 and on its improvement exploiting decoy state technique. Finally, a simple way of exploiting the postselection mechanism for a passive, one decoy state scheme is evaluated. 13. Quantum teleportation between a single-rail single-photon qubit and a coherent-state qubit using hybrid entanglement under decoherence effects Science.gov (United States) Jeong, Hyunseok; Bae, Seunglee; Choi, Seongjeon 2016-02-01 We study quantum teleportation between two different types of optical qubits using hybrid entanglement as a quantum channel under decoherence effects. One type of qubit employs the vacuum and single-photon states for the basis, called a single-rail single-photon qubit, and the other utilizes coherent states of opposite phases. We find that teleportation from a single-rail single-photon qubit to a coherent-state qubit is better than the opposite direction in terms of fidelity and success probability. We compare our results with those using a different type of hybrid entanglement between a polarized single-photon qubit and a coherent state. 14. Single-Photon Avalanche Diodes (SPAD) in CMOS 0.35 μm technology Science.gov (United States) Pellion, D.; Jradi, K.; Brochard, N.; Prêle, D.; Ginhac, D. 2015-07-01 Some decades ago single photon detection used to be the terrain of photomultiplier tube (PMT), thanks to its characteristics of sensitivity and speed. However, PMT has several disadvantages such as low quantum efficiency, overall dimensions, and cost, making them unsuitable for compact design of integrated systems. So, the past decade has seen a dramatic increase in interest in new integrated single-photon detectors called Single-Photon Avalanche Diodes (SPAD) or Geiger-mode APD. SPAD are working in avalanche mode above the breakdown level. When an incident photon is captured, a very fast avalanche is triggered, generating an easily detectable current pulse. This paper discusses SPAD detectors fabricated in a standard CMOS technology featuring both single-photon sensitivity, and excellent timing resolution, while guaranteeing a high integration. In this work, we investigate the design of SPAD detectors using the AMS 0.35 μm CMOS Opto technology. Indeed, such standard CMOS technology allows producing large surface (few mm2) of single photon sensitive detectors. Moreover, SPAD in CMOS technologies could be associated to electronic readout such as active quenching, digital to analog converter, memories and any specific processing required to build efficient calorimeters1 15. Single-photon compressive imaging with some performance benefits over raster scanning International Nuclear Information System (INIS) A single-photon imaging system based on compressed sensing has been developed to image objects under ultra-low illumination. With this system, we have successfully realized imaging at the single-photon level with a single-pixel avalanche photodiode without point-by-point raster scanning. From analysis of the signal-to-noise ratio in the measurement we find that our system has much higher sensitivity than conventional ones based on point-by-point raster scanning, while the measurement time is also reduced. - Highlights: • We design a single photon imaging system with compressed sensing. • A single point avalanche photodiode is used without raster scanning. • The Poisson shot noise in the measurement is analyzed. • The sensitivity of our system is proved to be higher than that of raster scanning 16. Polarization control of single photon quantum orbital angular momentum states OpenAIRE Nagali, E.; Sciarrino, F.; De Martini, F.; Piccirillo, B.; Karimi, E.; Marrucci, L.; Santamato, E. 2009-01-01 The orbital angular momentum of photons, being defined in an infinitely dimensional discrete Hilbert space, offers a promising resource for high-dimensional quantum information protocols in quantum optics. The biggest obstacle to its wider use is presently represented by the limited set of tools available for its control and manipulation. Here, we introduce and test experimentally a series of simple optical schemes for the coherent transfer of quantum information from the polarization to the ... 17. Demonstration of quantum permutation algorithm with a single photon ququart OpenAIRE Feiran Wang; Yunlong Wang; Ruifeng Liu; Dongxu Chen; Pei Zhang; Hong Gao; Fuli Li 2015-01-01 We report an experiment to demonstrate a quantum permutation determining algorithm with linear optical system. By employing photon's polarization and spatial mode, we realize the quantum ququart states and all the essential permutation transformations. The quantum permutation determining algorithm displays the speedup of quantum algorithm by determining the parity of the permutation in only one step of evaluation compared with two for classical algorithm. This experiment is accomplished in si... 18. Quantum Optics with Photonic Nanowires and Photonic Trumpets: Basics and Applications DEFF Research Database (Denmark) Gerard, J.; Claudon, J.; Munsch, M.; Optimizing the coupling between a localized quantum emitter and a single-mode optical channel represents a powerful route to realise bright sources of non-classical light states. Reversibly, the e±cient absorption of a photon impinging on the emitter is key to realise a spin-photon interface, the...... node of future quantum networks. Besides optical microcavities [1], photonic wires have recently demonstrated in this context an appealing potential [2, 3]. For instance, single photon sources (SPS) based on a single quantum dot in a vertical photonic wire with integrated bottom mirror and tapered tip...... solid-state system the unique optical properties of \\one-dimensional atoms".... 19. Generation and efficient measurement of single photons from fixed-frequency superconducting qubits Science.gov (United States) Kindel, William F.; Schroer, M. D.; Lehnert, K. W. 2016-03-01 We demonstrate and evaluate an on-demand source of single itinerant microwave photons. Photons are generated using a highly coherent, fixed-frequency qubit-cavity system, and a protocol where the microwave control field is far detuned from the photon emission frequency. By using a Josephson parametric amplifier (JPA), we perform efficient single-quadrature detection of the state emerging from the cavity. We characterize the imperfections of the photon generation and detection, including detection inefficiency and state infidelity caused by measurement back-action over a range of JPA gains from 17 to 33 dB. We observe that both detection efficiency and undesirable back-action increase with JPA gain. We find that the density matrix has its maximum single-photon component ρ11=0.36 ±0.01 at 29 dB JPA gain. At this gain, back-action of the JPA creates cavity photon number fluctuations that we model as a thermal distribution with an average photon number n ¯=0.041 ±0.003 . 20. Single-Photon-Sensitive HgCdTe Avalanche Photodiode Detector Science.gov (United States) Huntington, Andrew 2013-01-01 The purpose of this program was to develop single-photon-sensitive short-wavelength infrared (SWIR) and mid-wavelength infrared (MWIR) avalanche photodiode (APD) receivers based on linear-mode HgCdTe APDs, for application by NASA in light detection and ranging (lidar) sensors. Linear-mode photon-counting APDs are desired for lidar because they have a shorter pixel dead time than Geiger APDs, and can detect sequential pulse returns from multiple objects that are closely spaced in range. Linear-mode APDs can also measure photon number, which Geiger APDs cannot, adding an extra dimension to lidar scene data for multi-photon returns. High-gain APDs with low multiplication noise are required for efficient linear-mode detection of single photons because of APD gain statistics -- a low-excess-noise APD will generate detectible current pulses from single photon input at a much higher rate of occurrence than will a noisy APD operated at the same average gain. MWIR and LWIR electron-avalanche HgCdTe APDs have been shown to operate in linear mode at high average avalanche gain (M > 1000) without excess multiplication noise (F = 1), and are therefore very good candidates for linear-mode photon counting. However, detectors fashioned from these narrow-bandgap alloys require aggressive cooling to control thermal dark current. Wider-bandgap SWIR HgCdTe APDs were investigated in this program as a strategy to reduce detector cooling requirements. 1. Probabilistically cloning two single-photon states using weak cross-Kerr nonlinearities International Nuclear Information System (INIS) By using quantum nondemolition detectors (QNDs) based on weak cross-Kerr nonlinearities, we propose an experimental scheme for achieving 1→2 probabilistic quantum cloning (PQC) of a single-photon state, secretly choosing from a two-state set. In our scheme, after a QND is performed on the to-be-cloned photon and the assistant photon, a single-photon projection measurement is performed by a polarization beam splitter (PBS) and two single-photon trigger detectors (SPTDs). The measurement is to judge whether the PQC should be continued. If the cloning fails, a cutoff is carried out and some operations are omitted. This makes our scheme economical. If the PQC is continued according to the measurement result, two more QNDs and some unitary operations are performed on the to-be-cloned photon and the cloning photon to achieve the PQC in a nearly deterministic way. Our experimental scheme for PQC is feasible for future technology. Furthermore, the quantum logic network of our PQC scheme is presented. In comparison with similar networks, our PQC network is simpler and more economical. (paper) 2. In-depth study of single photon time resolution for the Philips digital silicon photomultiplier Science.gov (United States) Liu, Z.; Gundacker, S.; Pizzichemi, M.; Ghezzi, A.; Auffray, E.; Lecoq, P.; Paganoni, M. 2016-06-01 The digital silicon photomultiplier (SiPM) has been commercialised by Philips as an innovative technology compared to analog silicon photomultiplier devices. The Philips digital SiPM, has a pair of time to digital converters (TDCs) connected to 12800 single photon avalanche diodes (SPADs). Detailed measurements were performed to understand the low photon time response of the Philips digital SiPM. The single photon time resolution (SPTR) of every single SPAD in a pixel consisting of 3200 SPADs was measured and an average value of 85 ps full width at half maximum (FWHM) was observed. Each SPAD sends the signal to the TDC with different signal propagation time, resulting in a so called trigger network skew. This distribution of the trigger network skew for a pixel (3200 SPADs) has been measured and a variation of 50 ps FWHM was extracted. The SPTR of the whole pixel is the combination of SPAD jitter, trigger network skew, and the SPAD non-uniformity. The SPTR of a complete pixel was 103 ps FWHM at 3.3 V above breakdown voltage. Further, the effect of the crosstalk at a low photon level has been studied, with the two photon time resolution degrading if the events are a combination of detected (true) photons and crosstalk events. Finally, the time response to multiple photons was investigated. 3. Single passband microwave photonic filter with wideband tunability and adjustable bandwidth. Science.gov (United States) Chen, Tong; Yi, Xiaoke; Li, Liwei; Minasian, Robert 2012-11-15 A new and simple structure for a single passband microwave photonic filter is presented. It is based on using an electro-optical phase modulator and a tunable optical filter and only requires a single wavelength source and a single photodetector. Experimental results are presented that demonstrate a single passband, flat-top radio-frequency filter response without free spectral range limitations, along with the capability of tuning the center frequency and filter bandwidth independently. PMID:23164884 4. Coherent propagation of a single photon in a lossless medium:$0\\pi$pulse formation, slow photon, storage and retrieval in multiple temporal modes OpenAIRE Petrosyan, Shushan; Malakyan, Yuri 2013-01-01 Single-photon coherent optics represents a fundamental importance for the investigation of quantum light-matter interactions. While most work has considered the interaction in the steady-state regime, here we demonstrate that a single-photon pulse shorter than any relaxation time in a medium propagates without energy loss and is consistently transformed into a zero-area pulse. A general analytical solution is found for photon passage through a cold ensemble of$\\Lambda$-type atoms confined in... 5. Quantum Transduction of Telecommunications-band Single Photons from a Quantum Dot by Frequency Upconversion CERN Document Server Rakher, Matthew T; Slattery, Oliver; Tang, Xiao; Srinivasan, Kartik 2010-01-01 The ability to transduce non-classical states of light from one wavelength to another is a requirement for integrating disparate quantum systems that take advantage of telecommunications-band photons for optical fiber transmission of quantum information and near-visible, stationary systems for manipulation and storage. In addition, transducing a single-photon source at 1.3 {\\mu}m to visible wavelengths for detection would be integral to linear optical quantum computation due to the challenges of detection in the nearinfrared. Recently, transduction at single-photon power levels has been accomplished through frequency upconversion, but it has yet to be demonstrated for a true single-photon source. Here, we transduce the triggered single-photon emission of a semiconductor quantum dot at 1.3 {\\mu}m to 710 nm with a total detection (internal conversion) efficiency of 21% (75%). We demonstrate that the 710 nm signal maintains the quantum character of the 1.3 {\\mu}m signal, yielding a photon anti-bunched second-ord... 6. Single Photon Counting Detectors for Low Light Level Imaging Applications Science.gov (United States) Kolb, Kimberly 2015-10-01 This dissertation presents the current state-of-the-art of semiconductor-based photon counting detector technologies. HgCdTe linear-mode avalanche photodiodes (LM-APDs), silicon Geiger-mode avalanche photodiodes (GM-APDs), and electron-multiplying CCDs (EMCCDs) are compared via their present and future performance in various astronomy applications. LM-APDs are studied in theory, based on work done at the University of Hawaii. EMCCDs are studied in theory and experimentally, with a device at NASA's Jet Propulsion Lab. The emphasis of the research is on GM-APD imaging arrays, developed at MIT Lincoln Laboratory and tested at the RIT Center for Detectors. The GM-APD research includes a theoretical analysis of SNR and various performance metrics, including dark count rate, afterpulsing, photon detection efficiency, and intrapixel sensitivity. The effects of radiation damage on the GM-APD were also characterized by introducing a cumulative dose of 50 krad(Si) via 60 MeV protons. Extensive development of Monte Carlo simulations and practical observation simulations was completed, including simulated astronomical imaging and adaptive optics wavefront sensing. Based on theoretical models and experimental testing, both the current state-of-the-art performance and projected future performance of each detector are compared for various applications. LM-APD performance is currently not competitive with other photon counting technologies, and are left out of the application-based comparisons. In the current state-of-the-art, EMCCDs in photon counting mode out-perform GM-APDs for long exposure scenarios, though GM-APDs are better for short exposure scenarios (fast readout) due to clock-induced-charge (CIC) in EMCCDs. In the long term, small improvements in GM-APD dark current will make them superior in both long and short exposure scenarios for extremely low flux. The efficiency of GM-APDs will likely always be less than EMCCDs, however, which is particularly disadvantageous for 7. Electro-mechanical engineering of non-classical photon emissions from single quantum dots International Nuclear Information System (INIS) Indistinguishable photons and entangled photon pairs are the key elements for quantum information applications, for example, building a quantum repeater. Self-assembled semiconductor quantum dots (QDs) are promising candidates for the creation of such non-classical photon emissions, and offer the possibility to be integrated into solid state devices. However, due to the random nature of the self-assembled growth process, post-growth treatments are required to engineer the exciton state in the QDs (e.g. energies, exciton lifetimes, and fine structure splittings). In this work, we study the electro-mechanical engineering of the exciton lifetime, emission energy in the QDs, with the aim to produce single photons with higher indistinguishability. Also we present a recent experimental study on the statistical properties of fine structure splittings in the QD ensemble, in order to gain a deeper understanding of how to generate entangled photon pairs using semiconductor QDs. 8. Three-dimensional single gyroid photonic crystals with a mid-infrared bandgap CERN Document Server Peng, Siying; Chen, Valerian H; Khabiboulline, Emil T; Braun, Paul; Atwater, Harry A 2016-01-01 A gyroid structure is a distinct morphology that is triply periodic and consists of minimal isosurfaces containing no straight lines. We have designed and synthesized amorphous silicon (a-Si) mid-infrared gyroid photonic crystals that exhibit a complete bandgap in infrared spectroscopy measurements. Photonic crystals were synthesized by deposition of a-Si/Al2O3 coatings onto a sacrificial polymer scaffold defined by two-photon lithography. We observed a 100% reflectance at 7.5 \\mum for single gyroids with a unit cell size of 4.5 \\mum, in agreement with the photonic bandgap position predicted from full-wave electromagnetic simulations, whereas the observed reflection peak shifted to 8 um for a 5.5 \\mum unit cell size. This approach represents a simulation-fabrication-characterization platform to realize three-dimensional gyroid photonic crystals with well-defined dimensions in real space and tailored properties in momentum space. 9. Atom-Resonant Heralded Single Photons by Interaction-Free Measurement CERN Document Server Wolfgramm, Florian; Beduini, Federica A; Cere, Alessandro; Mitchell, Morgan W; 10.1103/PhysRevLett.106.053602 2011-01-01 We demonstrate the generation of rubidium-resonant heralded single photons for quantum memories. Photon pairs are created by cavity-enhanced down-conversion and narrowed in bandwidth to 7 MHz with a novel atom-based filter operating by "interaction-free measurement" principles. At least 94% of the heralded photons are atom-resonant as demonstrated by a direct absorption measurement with rubidium vapor. A heralded auto-correlation measurement shows$g_c^{(2)}(0)=0.040 \\pm 0.012$, i.e., suppression of multi-photon contributions by a factor of 25 relative to a coherent state. The generated heralded photons can readily be used in quantum memories and quantum networks. 10. Nano-optical observation of cascade switching in a parallel superconducting nanowire single photon detector CERN Document Server Heath, Robert M; Casaburi, Alessandro; Webster, Mark G; Alvarez, Lara San Emeterio; Barber, Zoe H; Warburton, Richard J; Hadfield, Robert H 2014-01-01 The device physics of parallel-wire superconducting nanowire single photon detectors is based on a cascade process. Using nano-optical techniques and a parallel wire device with spatially-separate pixels we explicitly demonstrate the single- and multi-photon triggering regimes. We develop a model for describing efficiency of a detector operating in the arm-trigger regime. We investigate the timing response of the detector when illuminating a single pixel and two pixels. We see a change in the active area of the detector between the two regimes and find the two-pixel trigger regime to have a faster timing response than the one-pixel regime. 11. Exploiting Rydberg Atom Surface Phonon Polariton Coupling for Single Photon Subtraction CERN Document Server Kübler, H; Sedlacek, J; Zabawa, P; Shaffer, J P 2013-01-01 We investigate a hybrid quantum system that consists of a superatom coupled to a surface phonon-polariton. We apply this hybrid quantum system to subtract individual photons from a beam of light. Rydberg atom blockade is used to attain absorption of a single photon by an atomic microtrap. Surface phonon-polariton coupling to the superatom then triggers the transfer of the excitation to a storage state, a single Rydberg atom. The approach utilizes the interaction between a superatom and a Markovian bath that acts as a controlled decoherence mechanism to irreversibly project the superatom state into a single Rydberg atom state that can be read out. 12. Room temperature continuous wave operation of single-mode, edge-emitting photonic crystal Bragg lasers OpenAIRE Zhu, Lin; Sun, Xiankai; DeRose, Guy A.; Scherer, Axel; Yariv, Amnon 2008-01-01 We report the first room temperature CW operation of two dimensional single-mode edge-emitting photonic crystal Bragg lasers. Single-mode lasing with single-lobed, diffraction limited far-fields is obtained for 100μm wide and 550μm long on-chip devices. We also demonstrate the tuning of the lasing wavelength by changing the transverse lattice constant of the photonic crystal. This enables a fine wavelength tuning sensitivity (change of the lasing wavelength/change of the lattice constant) of ... 13. Observation of Entanglement of a Single Photon with a Trapped Atom International Nuclear Information System (INIS) We report the observation of entanglement between a single trapped atom and a single photon at a wavelength suitable for low-loss communication over large distances, thereby achieving a crucial step towards long range quantum networks. To verify the entanglement, we introduce a single atom state analysis. This technique is used for full state tomography of the atom-photon qubit pair. The detection efficiency and the entanglement fidelity are high enough to allow in a next step the generation of entangled atoms at large distances, ready for a final loophole-free Bell experiment 14. Modes of an endlessly single-mode photonic crystal fiber: a finite element investigation NARCIS (Netherlands) Uranus, H.P.; Hoekstra, H.J.W.M.; Groesen, van E. 2004-01-01 Using a finite-element mode solver, the modes of a commercial endlessly single-mode photonic crystal fiber (ESM-PCF) were investigated. Based on the loss discrimination between the dominant and the nearest higher order mode, we set-up a criterion for the single-modeness. Using that measure, we verif 15. Linearly Polarized, Single-Mode Spontaneous Emission in a Photonic Nanowire DEFF Research Database (Denmark) Munsch, Mathieu; Claudon, Julien; Bleuse, Joël; 2012-01-01 We introduce dielectric elliptical photonic nanowires to funnel efficiently the spontaneous emission of an embedded emitter into a single optical mode. Inside a wire with a moderate lateral aspect ratio, the electromagnetic environment is largely dominated by a single guided mode, with a linear... 16. Finite element modeling of plasmon based single-photon sources DEFF Research Database (Denmark) Chen, Yuntian; Gregersen, Niels; Nielsen, Torben Roland; 2011-01-01 A finite element method (FEM) approach of calculating a single emitter coupled to plasmonic waveguides has been developed. The method consists of a 2D model and a 3D model: (I) In the 2D model, we have calculated the spontaneous emission decay rate of a single emitter into guided plasmonic modes by... 17. Conditional preparation of single photons using parametric downconversion: a recipe for purity International Nuclear Information System (INIS) In an experiment reported recently (Mosley et al 2008 Phys. Rev. Lett. 100 133601), we demonstrated that, through group velocity matched parametric downconversion, heralded single photons can be generated in pure quantum states without spectral filtering. The technique relies on factorable photon pair production, initially developed theoretically in the strict collinear regime; focusing-required in any experimental implementation-can ruin this factorability. Here, we present the numerical model used to design our single photon sources and minimize spectral correlations in the light of such experimental considerations. Furthermore, we show that the results of our model are in good agreement with measurements made on the photon pairs and give a detailed description of the exact requirements for constructing this type of source 18. Two-Atom Rydberg Blockade using a Single-Photon Transition CERN Document Server Hankin, A M; Parazzoli, L P; Chou, C W; Armstrong, D J; Landahl, A J; Biedermann, G W 2014-01-01 We explore a single-photon approach to Rydberg state excitation and Rydberg blockade. Using detailed theoretical models, we show the feasibility of direct excitation, predict the effect of background electric fields, and calculate the required interatomic distance to observe Rydberg blockade. We then measure and control the electric field environment to enable coherent control of Rydberg states. With this coherent control, we demonstrate Rydberg blockade of two atoms separated by 6.6(3) {\\mu}m. When compared with the more common two-photon excitation method, this single-photon approach is advantageous because it eliminates channels for decoherence through photon scattering and AC Stark shifts from the intermediate state while moderately increasing Doppler sensitivity. 19. Remote preparation of single-photon "hybrid" entangled and vector-polarization States. Science.gov (United States) Barreiro, Julio T; Wei, Tzu-Chieh; Kwiat, Paul G 2010-07-16 Quantum teleportation faces increasingly demanding requirements for transmitting large or even entangled systems. However, knowledge of the state to be transmitted eases its reconstruction, resulting in a protocol known as remote state preparation. A number of experimental demonstrations to date have been restricted to single-qubit systems. We report the remote preparation of two-qubit "hybrid" entangled states, including a family of vector-polarization beams. Our single-photon states are encoded in the photon spin and orbital angular momentum. We reconstruct the states by spin-orbit state tomography and transverse polarization tomography. The high fidelities achieved for the vector-polarization states opens the door to optimal coupling of down-converted photons to other physical systems, such as an atom, as required for scalable quantum networks, or plasmons in photonic nanostructures. PMID:20867752 20. Development of a high-speed single-photon pixellated detector for visible wavelengths CERN Document Server Mac Raighne, Aaron; Mathot, Serge; McPhate, Jason; Vallerga, John; Jarron, Pierre; Brownlee, Colin; O’Shea, Val 2009-01-01 We present the development of a high-speed, single-photon counting, Hybrid Photo Detector (HPD). The HPD consists of a vacuum tube, containing the detector assembly, sealed with a transparent optical input window. Photons incident on the photocathode eject a photoelectron into a large electric field, which accelerates the incident electron onto a silicon detector. The silicon detector is bump bonded to a Medipix readout chip. This set-up allows for the detection and readout of low incident photon intensities at rates that are otherwise unattainable with current camera technology. Reported is the fabrication of the camera that brings together a range of sophisticated design and fabrication techniques and the expected theoretical imaging performance. Applications to cellular and molecular microscopy are also described in which single-photon-counting abilities at high frame rates are crucial 1. Memory effect in silicon time-gated single-photon avalanche diodes International Nuclear Information System (INIS) We present a comprehensive characterization of the memory effect arising in thin-junction silicon Single-Photon Avalanche Diodes (SPADs) when exposed to strong illumination. This partially unknown afterpulsing-like noise represents the main limiting factor when time-gated acquisitions are exploited to increase the measurement dynamic range of very fast (picosecond scale) and faint (single-photon) optical signals following a strong stray one. We report the dependences of this unwelcome signal-related noise on photon wavelength, detector temperature, and biasing conditions. Our results suggest that this so-called “memory effect” is generated in the deep regions of the detector, well below the depleted region, and its contribution on detector response is visible only when time-gated SPADs are exploited to reject a strong burst of photons 2. Memory effect in silicon time-gated single-photon avalanche diodes Energy Technology Data Exchange (ETDEWEB) Dalla Mora, A.; Contini, D., E-mail: [email protected]; Di Sieno, L. [Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy); Tosi, A.; Boso, G.; Villa, F. [Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy); Pifferi, A. [Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy); CNR, Istituto di Fotonica e Nanotecnologie, Piazza Leonardo da Vinci 32, I-20133 Milano (Italy) 2015-03-21 We present a comprehensive characterization of the memory effect arising in thin-junction silicon Single-Photon Avalanche Diodes (SPADs) when exposed to strong illumination. This partially unknown afterpulsing-like noise represents the main limiting factor when time-gated acquisitions are exploited to increase the measurement dynamic range of very fast (picosecond scale) and faint (single-photon) optical signals following a strong stray one. We report the dependences of this unwelcome signal-related noise on photon wavelength, detector temperature, and biasing conditions. Our results suggest that this so-called “memory effect” is generated in the deep regions of the detector, well below the depleted region, and its contribution on detector response is visible only when time-gated SPADs are exploited to reject a strong burst of photons. 3. A Single Photon Imaging System Based on Wedge and Strip Anodes Institute of Scientific and Technical Information of China (English) MIAO Zhen-Hua; ZHAO Bao-Sheng; ZHANG Xing-Hua; LIU Yong-An 2008-01-01 A new prototype of single photon imaging system based on wedge and strip anodes is developed. The prototype can directly measure the intensity and position information for an ultra-weak radiant source which takes on the character of single photons. The image of the ultra-weak radiant source can be reconstructed with a wedge and strip anodes detector and an electronic readout subsystem by photon counting and photon position sensitive detecting in a period of time. With proper evaluation, the prototype reveals a spatial resolution superior to 150μm, a 66-kHz maximal counting rate and a dark-count below 0.67count/cm2s. 4. Nonclassical correlations between single photons and phonons from a mechanical oscillator CERN Document Server Riedinger, Ralf; Norte, Richard A; Slater, Joshua A; Shang, Juying; Krause, Alexander G; Anant, Vikas; Aspelmeyer, Markus; Gröblacher, S 2015-01-01 Interfacing a single photon with another quantum system is a key capability in modern quantum information science. It allows quantum states of matter, such as spin states of atoms, atomic ensembles or solids, to be prepared and manipulated by photon counting and, in particular, to be distributed over long distances. Such light-matter interfaces have become crucial for fundamental tests of quantum physics as well as for realizations of quantum networks. Here we report nonclassical correlations between single photons and phonons -- the quanta of mechanical motion -- from a nanomechanical resonator. We implement a full quantum protocol involving initialization of the resonator in its quantum ground state of motion and subsequent generation and readout of correlated photon-phonon pairs. The observed violation of a Cauchy-Schwarz inequality is clear evidence for the nonclassical nature of the generated mechanical state. Our results show the availability of on-chip solid-state mechanical resonators as light-matter ... 5. Photon-statistics-based classical ghost imaging with one single detector. Science.gov (United States) Kuhn, Simone; Hartmann, Sébastien; Elsäßer, Wolfgang 2016-06-15 We demonstrate a novel ghost imaging (GI) scheme based on one single-photon-counting detector with subsequent photon statistics analysis. The key idea is that instead of measuring correlations between the object and reference beams such as in standard GI schemes, the light of the two beams is superimposed. The photon statistics analysis of this mixed light allows us to determine the photon number distribution as well as to calculate the central second-order correlation coefficient. The image information is obtained as a function of the spatial resolution of the reference beam. The performance of this photon-statistics-based GI system with one single detector (PS-GI) is investigated in terms of visibility and resolution. Finally, the knowledge of the complete photon statistics allows easy access to higher correlation coefficients such that we are able to perform here third- and fourth-order GI. The PS-GI concept can be seen as a complement to already existing GI technologies thus enabling a broader dissemination of GI as a superior metrology technique, paving the road for new applications in particular with advanced photon counting detectors. PMID:27304308 6. Experimental observation of robust surface states on photonic crystals possessing single and double Weyl points CERN Document Server Chen, Wen-Jie; Chan, C T 2015-01-01 We designed and fabricated a time-reversal invariant Weyl photonic crystal that possesses single Weyl nodes with topological charge of 1 and double Weyl nodes with a higher topological charge of 2. Using numerical simulations and microwave experiment, nontrivial band gaps with nonzero Chern numbers for a fixed kz was demonstrated. The robustness of the surface state between the Weyl photonic crystal and PEC against kz-conserving scattering was experimentally observed. 7. Single and double ionization of helium by high-energy photon impact International Nuclear Information System (INIS) Production of singly and doubly charged helium ions by impact of keV photons is studied. The ratio Rph = σph++/σph+ for photoabsorption is calculated in the photon-energy range 2--18 keV using correlated initial- and final- state wave functions. Extrapolation towards symptotic photon energies yields Rph(ω → ∞) = 1.66% in agreement with previous predictions. Ionization due to Compton scattering, which becomes comparable to photoabsorption above ω ∼ 3 keV, is discussed 8. Generation efficiency of single-photon current pulses in the Geiger mode of silicon avalanche photodiodes International Nuclear Information System (INIS) Statistical fluctuations of the avalanche's multiplication efficiency were studied as applied to the single-photon (Geiger) mode of avalanche photodiodes. The distribution function of partial multiplication factors with an anomalously wide (of the order of the average) dispersion was obtained. Expressions for partial feedback factors were derived in terms of the average gain and the corresponding dependences on the diode's overvoltage were calculated. Final expressions for the photon-electric pulse's conversion were derived by averaging corresponding formulas over the coordinate of initiating photoelectron generation using the functions of optical photon absorption in silicon. 9. Mapping the local density of optical states of a photonic crystal with single quantum dots CERN Document Server Wang, Qin; Lodahl, Peter 2011-01-01 We use single self-assembled InGaAs quantum dots as internal probes to map the local density of optical states of photonic crystal membranes. The employed technique separates contributions from non-radiative recombination and spin-flip processes by properly accounting for the role of the exciton fine structure. We observe inhibition factors as high as 55 and compare our results to local density of optical states calculations available from the literature, thereby establishing a quantitative understanding of photon emission in photonic crystal membranes. 10. Channel analysis for single photon underwater free space quantum key distribution. Science.gov (United States) Shi, Peng; Zhao, Shi-Cheng; Gu, Yong-Jian; Li, Wen-Dong 2015-03-01 We investigate the optical absorption and scattering properties of underwater media pertinent to our underwater free space quantum key distribution (QKD) channel model. With the vector radiative transfer theory and Monte Carlo method, we obtain the attenuation of photons, the fidelity of the scattered photons, the quantum bit error rate, and the sifted key generation rate of underwater quantum communication. It can be observed from our simulations that the most secure single photon underwater free space QKD is feasible in the clearest ocean water. PMID:26366645 11. Atom-Resonant Heralded Single Photons by Interaction-Free Measurement OpenAIRE Wolfgramm, Florian; Astiz, Yannick A. de Icaza; Beduini, Federica A.; Cere, Alessandro; Mitchell, Morgan W. 2011-01-01 We demonstrate the generation of rubidium-resonant heralded single photons for quantum memories. Photon pairs are created by cavity-enhanced down-conversion and narrowed in bandwidth to 7 MHz with a novel atom-based filter operating by "interaction-free measurement" principles. At least 94% of the heralded photons are atom-resonant as demonstrated by a direct absorption measurement with rubidium vapor. A heralded auto-correlation measurement shows$g_c^{(2)}(0)=0.040 \\pm 0.012$, i.e., suppres... 12. A cascade of e ‑ e + pair production by a photon with subsequent annihilation to a single photon in a strong magnetic field Science.gov (United States) Diachenko, M. M.; Novak, O. P.; Kholodov, R. I. 2016-06-01 The process of electron–positron pair production by a photon with subsequent annihilation to a single photon in a strong magnetic field has been studied. The general amplitude has been calculated and the process rates have been found in a low Landau levels approximation (resonant and nonresonant cases). The comparison of resonant and nonresonant cases shows a significant excess of the resonant rate. The polarization of the final photon in a strong magnetic field has also been found. It has been shown that polarizations of the initial and final photons are independent except for the case of normal linear polarization of the initial photon. 13. Quantum Interference Induced Photon Blockade in a Coupled Single Quantum Dot-Cavity System CERN Document Server Tang, Jing; Xu, Xiulai 2015-01-01 We propose an experimental scheme to implement a strong photon blockade with a single quantum dot coupled to a nanocavity. The photon blockade effect can be tremendously enhanced by driving the cavity and the quantum dot simultaneously with two classical laser fields. This enhancement of photon blockade is ascribed to the quantum interference effect to avoid two-photon excitation of the cavity field. Comparing with Jaynes-Cummings model, the second-order correlation function at zero time delay$g^{(2)}(0)\$ in our scheme can be reduced by two orders of magnitude and the system sustains a large intracavity photon number. A red (blue) cavity-light detuning asymmetry for photon quantum statistics with bunching or antibunching characteristics is also observed. The photon blockade effect has a controllable flexibility by tuning the relative phase between the two pumping laser fields and the Rabi coupling strength between the quantum dot and the pumping field. Moreover, the photon blockade scheme based on quantum in...
14. Study on the Single Photons%论单光子研究
Institute of Scientific and Technical Information of China (English)
黄志洵
2009-01-01
In this paper, the historic background of the study on single photons and the recent ad-vances of research are discussed. It must be mentioned that a correct understanding of the photon is on the basis of the classical physics ancl the quantum mechanics. The production and measure-ment of single photons are also discussed. Some aspects of the recent advances during nearly ten years on the single photon experiments and quantum information technology are sketched in the article. For example, because the quantum entanglement, one photon can instantaneously change the properties of another photon, the recently experiment of D. Salart et. al. decribe it how fast "instantaneous" really is. This is a faster-than-light phenomenon.%对单光子研究的历史情况和近年来的新成就作了介绍,指出对光子的正确认识必须以经典物理学及量子力学为基础.简述了单光子的产生与检测技术,讨论了与单光子有关的新实验.例如由于量子纠缠,一个光子可以瞬时地影响另一光子的特性.不久前的D.Salart等人的实验说明了这个"瞬时地"究竟有多快--这是一种超光速现象.
15. High-speed bridge circuit for InGaAs avalanche photodiode single-photon detector
Science.gov (United States)
Hashimoto, Hirofumi; Tomita, Akihisa; Okamoto, Atsushi
2014-02-01
Because of low power consumption and small footprint, avalanche photodiodes (APD) have been commonly applied to photon detection. Recently, high speed quantum communication has been demonstrated for high bit-rate quantum key distribution. For the high speed quantum communication, photon detectors should operate at GHz-clock frequencies. We propose balanced detection circuits for GHz-clock operation of InGaAs-APD photon detectors. The balanced single photon detector operates with sinusoidal wave gating. The sinusoidal wave appearing in the output is removed by the subtraction from APD signal without sharp band-elimination filters. Omission of the sharp filters removes the constraint on the operating frequency of the single photon detector. We present two designs, one works with two identical APDs, the other with one APD and a low-pass filter. The sinusoidal gating enables to eliminate the gating noise even with the simple configuration of the latter design. We demonstrated the balanced single photon detector operating with 1.020GHz clock at 233 K, 193 K, and 186.5 K. The dark count probability was 4.0 x 10-4 counts/pulse with the quantum efficiency of 10% at 233K, and 1.6 x 10-4 counts/pulse at 186.5 K. These results were obtained with easily available APDs (NR8300FP-C.C, RENESASS) originally developed for optical time-domain reflectmeters.
16. Photonics
CERN Document Server
Andrews, David L
2015-01-01
This book covers modern photonics accessibly and discusses the basic physical principles underlying all the applications and technology of photonicsThis volume covers the basic physical principles underlying the technology and all applications of photonics from statistical optics to quantum optics. The topics discussed in this volume are: Photons in perspective; Coherence and Statistical Optics; Complex Light and Singular Optics; Electrodynamics of Dielectric Media; Fast and slow Light; Holography; Multiphoton Processes; Optical Angular Momentum; Optical Forces, Trapping and Manipulation; Pol
17. Photonics
CERN Document Server
Andrews, David L
2015-01-01
Discusses the basic physical principles underlying the technology instrumentation of photonics This volume discusses photonics technology and instrumentation. The topics discussed in this volume are: Communication Networks; Data Buffers; Defense and Security Applications; Detectors; Fiber Optics and Amplifiers; Green Photonics; Instrumentation and Metrology; Interferometers; Light-Harvesting Materials; Logic Devices; Optical Communications; Remote Sensing; Solar Energy; Solid-State Lighting; Wavelength Conversion Comprehensive and accessible coverage of the whole of modern photonics Emphas
18. Photonics
CERN Document Server
Andrews, David L
2015-01-01
Discusses the basic physical principles underlying thescience and technology of nanophotonics, its materials andstructures This volume presents nanophotonic structures and Materials.Nanophotonics is photonic science and technology that utilizeslight/matter interactions on the nanoscale where researchers arediscovering new phenomena and developing techniques that go wellbeyond what is possible with conventional photonics andelectronics.The topics discussed in this volume are: CavityPhotonics; Cold Atoms and Bose-Einstein Condensates; Displays;E-paper; Graphene; Integrated Photonics; Liquid Cry
19. Exploring single-photon ionization on the attosecond time scale
International Nuclear Information System (INIS)
One of the fundamental processes in nature is the photoelectric effect in which an electron is ripped away from its atom via the interaction with a photon. This process was long believed to be instantaneous but with the development of attosecond pulses (1 as 10−18 s) we can finally get an insight into its dynamic. Here we measure a delay in ionization time between two differently bound electrons. The outgoing electrons are created via ionization with a train of attosecond pulses and we probe their relative delay with a synchronized infrared laser. We demonstrate how this probe field influences the measured delays and show that this contribution can be estimated with a universal formula, which allows us to extract field free atomic data.
20. Mini-stop bands in single heterojunction photonic crystal waveguides
KAUST Repository
Shahid, N.
2013-01-01
Spectral characteristics of mini-stop bands (MSB) in line-defect photonic crystal (PhC) waveguides and in heterostructure PhC waveguides having one abrupt interface are investigated. Tunability of the MSB position by air-fill factor heterostructure PhC waveguides is utilized to demonstrate different filter functions, at optical communication wavelengths, ranging from resonance-like to wide band pass filters with high transmission. The narrowest filter realized has a resonance-like transmission peak with a full width at half maximum of 3.4 nm. These devices could be attractive for coarse wavelength selection (pass and drop) and for sensing applications. 2013 Copyright 2013 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License.
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http://blog.geomblog.org/2004/09/voting-and-geometry.html
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## Wednesday, September 08, 2004
### Voting and Geometry
It would be remiss of me (this is the Geomblog, after all) not to remark on the connection between voting and geometry pointed out by a commenter on my earlier post.
Donald Saari has developed an interesting theory of rankings based on mapping rankings to points in simplices. An immediate application of this formulation is the observation that the Kemeny rule determines a ranking minimizes the l1 distance to the original ranking schemes.
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https://docs.opentitan.org/doc/ug/getting_started_dv/
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# Getting Started with an OpenTitan Design Verification
This document aims to enable a contributor to get started with a design verification (DV) effort within the OpenTitan project. While most of the focus is on development of a testbench from scratch, it should also be useful to understand how to contribute to an existing effort. Please refer to the DV methodology document for information on how design verification is done in OpenTitan.
## Stages of DV
The life stages of a design / DV effort within the OpenTitan are described in the Hardware Development Stages document. It separates the life of DV into three broad stages: Initial Work, Under Test and Testing Complete. This document attempts to give guidance on how to get going with the first stage and have a smooth transition into the Under Test stage. They are not hard and fast rules but methods we have seen work well in the project. DV indeed cannot begin until the design has transitioned from Specification to the Development stage first. The design specification, once available, is used as a starting point.
## Getting Started
The very first thing to do in any DV effort is to document the plan detailing the overall effort. This is done in conjunction with developing the initial testbench. It is recommended to use the uvmdvgen tool, which serves both needs.
The uvmdvgen tool provides the ability to generate the outputs in a specific directory. This should be set to the root of the DUT directory where the rtl directory exists. When the tool is run, it creates a dv directory, along with data and doc directories. The dv directory is where the complete testbench along with the collaterals to build and run tests can be found. It puts the documentation sources in doc and data directories respectively (which also exist alongside the rtl directory). It is recommended to grep for ‘TODO’ at this stage in all of these generated files to make some of the required fixes right way. One of these for example, is to create appropriate interfaces for the DUT-specific IOs and have them connected in the testbench (dv/tb/tb.sv).
## Documentation and Initial Review
The skeleton DV plan and the Hjson testplan should be addressed first. The DV plan documentation is not expected to be completed in full detail at this point. However, it is expected to list all the verification components needed and depict the planned testbench as a block diagram. Under the ‘design verification’ directory in the OpenTitan team drive, some sample testbench block diagrams are available in the .svg format, which can be used as a template. The Hjson testplan on the other hand, is required to be completed. Please refer to the testplanner tool documentation for additional details on how to write the Hjson testplan. Once done, these documents are to be reviewed with the designer(s) and other project members for completeness and clarity.
## UVM RAL Model
Before running any test, the UVM RAL model needs to exist (if the design contains CSRs). The DV simulation flow has been updated to generate the RAL model automatically at the start of the simulation. As such, nothing extra needs to be done. A hook for generating it is already provided in the generated dv/Makefile. It can be created manually by simply navigating to the dv directory and invoking the command:
$cd path-to-dv$ make ral
The generated file is placed in the simulation build scratch area instead of being checked in.
## Supported Simulators
The use of advanced verification constructs such as SystemVerilog classes (on which UVM is based on) requires commercial simulators. The DV simulation flow fully supports Synopsys VCS. There is support for Cadence Xcelium as well, which is being slowly ramped up.
## Building and Running Tests
The uvmdvgen tool provides an empty shell sequence at dv/env/seq_lib/<ip>_sanity_vseq.sv for developing the sanity test. The sanity test can be run as-is by invoking make, as a “hello world” step to bring the DUT out of reset.
$cd path-to-dv$ make [SIMULATOR=xcelium] [WAVES=1]
The generated initial testbench is not expected to compile and elaborate successfully right away. There may be additional fixes required, which can be hopefully be identified easily. Once the testbench compiles and elaborates without any errors or warnings, the sanity sequence can be developed further to access a major datapath and test the basic functionality of the DUT.
VCS is used as the default simulator. It can be switched to Xcelium by setting SIMULATOR=xcelium on the command line. The WAVES=1 switch will cause an fsdb dump to be created from the test. The Synopsys Verdi tool can be invoked (separately) to debug the waves. Please refer to the DV simulation flow for additional details.
The uvmdvgen script also provides a CSR suite of tests which can be run right out of the box. The most basic CSR power-on-reset check test can be run by invoking:
$cd path-to-dv$ make TEST_NAME=<dut>_csr_hw_reset [WAVES=1]
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http://adam.chlipala.net/cpdt/repo/rev/cadeb49dc1ef
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Fix typo
author Adam Chlipala Mon, 01 Dec 2008 08:32:20 -0500 a35eaec19781 df289eb8ef76 src/Equality.v 1 files changed, 1 insertions(+), 1 deletions(-) [+]
line wrap: on
line diff
--- a/src/Equality.v Fri Nov 28 14:21:38 2008 -0500
+++ b/src/Equality.v Mon Dec 01 08:32:20 2008 -0500
@@ -25,7 +25,7 @@
(** We have seen many examples so far where proof goals follow "by computation." That is, we apply computational reduction rules to reduce the goal to a normal form, at which point it follows trivially. Exactly when this works and when it does not depends on the details of Coq's %\textit{%#<i>#definitional equality#</i>#%}%. This is an untyped binary relation appearing in the formal metatheory of CIC. CIC contains a typing rule allowing the conclusion $E : T$ from the premise $E : T'$ and a proof that $T$ and $T'$ are definitionally equal.
- The [cbv] tactic will help us illustrate the rules of Coq's definitional equality. We redefine the natural number predecessor function in a somewhat convoluted way and construct a manual proof that it returns [1] when applied to [0]. *)
+ The [cbv] tactic will help us illustrate the rules of Coq's definitional equality. We redefine the natural number predecessor function in a somewhat convoluted way and construct a manual proof that it returns [0] when applied to [1]. *)
Definition pred' (x : nat) :=
match x with
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http://mathhelpforum.com/trigonometry/218199-rhind-papyrus-problem-41-pi.html
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# Math Help - Rhind papyrus problem 41 (pi)
1. ## Rhind papyrus problem 41 (pi)
Okay, i got a little problem. I have to do a research for school about the history of pi. Not that hard you'd think... But then i found that the Egyptians found 3,1605 for pi in 1650 BC. So now i got to find out how he found it out.
he used the formula: Volume of a cylinder = ((1-1/9)d)²h if you calculate it you get 256/81 r² h so he found 256/81 for pi. But i don't get the start. where did that ((1-1/9)d)²h came from? i know it replaces pi r² in our modern formula but that's about it...
I thought it came from the relation between a square and circle, but after looking into that for the last 2 days, i still haven't figured it out.
If someone could help me with this i'd be very grateful.
with regards, danielrowling.
P.S. I hope i posted it in the correct section.
2. ## Re: Rhind papyrus problem 41 (pi)
I am not a specialist in the history of mathematics, but according to the Wikipedia article about Rhind papyrus (sections Volumes and Areas), the idea is as follows.
We take a circle (blue) and its circumscribing square, divide each side of the square in three equal parts and remove the corners. The resulting octagon (red) approximates the circle. If the side of the square is 1, then the area of the octagon is $1 - 4\left(\frac{1}{2}\cdot\frac13\cdot\frac13\right) = 1-\frac29$. So, for a circle of some diameter d, the corresponding octagon's area is $\left(1-\frac29\right)d^2$. However, for some reason the Egyptian mathematicians wanted to express this as $(a d)^2$ for some number $a$. I am guessing that since $\sqrt{1-\frac29}$ is irrational, they decided to approximate it as $1-\frac19$. Indeed, $\left(1-\frac19\right)^2=\left(\frac89\right)^2 =\frac{64}{81}\approx\frac{63}{81} =\frac79=1-\frac29$. That's how they got the formula $((1-1/9)d)^2$ for the area of the circle.
Note that the octagon's approximation of the circle is not too bad because it both adds to and subtracts some areas from the circle. However, according to Wikipedia, "That this octagonal figure, whose area is easily calculated, so accurately approximates the area of the circle is just plain good luck".
If you need a more reliable source than Wikipedia, you should probably look for a book about the history of $\pi$ or ancient Egyptian mathematics.
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http://openstudy.com/updates/55c16e72e4b033255003cc0d
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## anonymous one year ago Find the interval on which the curve of "picture below" is concave up Delete Cancel Submit
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1. anonymous
• one year ago
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##### 1 Attachment
2. anonymous
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@Ashleyisakitty @ganeshie8 @Hero @jim_thompson5910
3. anonymous
• one year ago
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i know i have to find the second derivative im just not sure how
4. anonymous
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$y=\int\limits_{0}^{x}\frac{ dt }{ 1+t+t^2 }=\int\limits_{0}^{x}\frac{ dt }{ t^2+t+\frac{ 1 }{ 4 }-\frac{ 1 }{ 4 }+1 }$ $=\int\limits_{0}^{x}\frac{ dt }{ \left( t+\frac{ 1 }{ 2 } \right)^2+\frac{ 3 }{ 4 } }=\int\limits_{0}^{x}\frac{ dt }{ \left( t+\frac{ 1 }{ 2 } \right)^2+\left( \frac{ \sqrt{3} }{ 2 } \right)^2 }$ $=\frac{ 1 }{ \frac{ \sqrt{3} }{ 2 } }\tan^{-1} \frac{ t+\frac{ 1 }{ 2 } }{ \frac{ \sqrt{3} }{ 2 } }|0\rightarrow x$ $=\frac{ 2 }{ \sqrt{3} }\tan^{-1} \frac{ 2t+1 }{ \sqrt{3} }|0\rightarrow\ x$ $=\frac{ 2 }{ \sqrt{3} }\left\{ \tan^{-1} \left( \frac{ 2x+1 }{ \sqrt{3} }\right)-\tan^{-1}\frac{ 1 }{ \sqrt{3} } \right\}$
5. anonymous
• one year ago
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wow okay give me a second to read that...
6. jim_thompson5910
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@surjithayer there's no need to integrate you just need to find $$\Large \frac{d^2y}{dx^2}$$
7. anonymous
• one year ago
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oh no first derivative is the integrand
8. anonymous
• one year ago
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oh what @jim_thompson5910 said
9. jim_thompson5910
• one year ago
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the first derivative is not too bad because you can use the fundamental theorem of calculus
10. anonymous
• one year ago
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yea thats what im having a problem with , do i just plug in x for every where t is at and then integrate that or do i just plug in x and then that's my first derivative?
11. anonymous
• one year ago
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first derivative replace each $$t$$ in the integrand by an $$x$$ that is all then take the derivative of the result to get the second derivative
12. anonymous
• one year ago
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interval is 0 to x or we can change it to x then diff.
13. anonymous
• one year ago
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i mean derive not integrate
14. anonymous
• one year ago
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yeah plug in x for t
15. anonymous
• one year ago
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then DIFFERENTIATE that , not integrate
16. anonymous
• one year ago
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okay okay one second let me do that
17. anonymous
• one year ago
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i also said differentiate.
18. jim_thompson5910
• one year ago
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Fundamental Theorem of Calculus (one of the 2 parts) If $\Large g(x) = \int_{a}^{x}f(t)dt$ then $\Large g \ '(x) = f(x)$
19. jim_thompson5910
• one year ago
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surjithayer you weren't incorrect. It was just a step in the opposite direction adding unnecessary steps. Then again, doing it that way helps see how the FTC works
20. anonymous
• one year ago
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sorry, i have not used that theorem.
21. anonymous
• one year ago
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thank you for reminding me.
22. anonymous
• one year ago
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okay im getting $\frac{-(2x+1) }{ (x^2+x+1)^2}$
23. anonymous
• one year ago
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looks good to me
24. jim_thompson5910
• one year ago
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agreed
25. anonymous
• one year ago
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i would have written the numerator as $-2x-1$ so that you can solve $-2x-1>0$ rather easily
26. anonymous
• one year ago
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okay out of curiosity whats the second part of the theorem ... it sounds very "fundamental "
27. anonymous
• one year ago
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that is that $$F(b)-F(a)$$ business
28. jim_thompson5910
• one year ago
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Other part of FTC $\Large \int_{a}^{b}f \ '(x) dx = f(b) - f(a)$
29. anonymous
• one year ago
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arh damn i don't know who to give the medal too you were all so helpful
30. jim_thompson5910
• one year ago
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Most books make F ' = f, which is confusing to me because there are 2 different f's to keep track of
31. anonymous
• one year ago
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thats weird every time i see F it means $intf(x)$
32. jim_thompson5910
• one year ago
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F ' = f is equivalent to saying "F is the indefinite integral of f"
33. anonymous
• one year ago
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notation like to be the death of us all nothing worse than having two identical notations for different things
34. anonymous
• one year ago
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ill keep that in mind :D thanks again every one !!
35. jim_thompson5910
• one year ago
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the reason I set up FTC 2 that way was because most calc courses start with derivatives and then teach integrals. So why not set up the integral in terms of a derivative
36. jim_thompson5910
• one year ago
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no problem
37. anonymous
• one year ago
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okay real quick so i should graph that and where its positive is the integral that the original graph is concave up right?!?
38. anonymous
• one year ago
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it is concave up where $-2x-1>0$
39. jim_thompson5910
• one year ago
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Exactly. The denominator is always positive, so you can ignore that portion and focus on where the numerator is positive.
40. anonymous
• one year ago
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so it would be (-infinity , -.5) right?
41. anonymous
• one year ago
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okay ill go ahead and take that as a silent nod
42. jim_thompson5910
• one year ago
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yes when x < -1/2
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http://tex.stackexchange.com/questions/124334/replace-lstlisting-with-verbatim-depending-on-a-boolean
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# Replace lstlisting with verbatim depending on a boolean
I use latex2rtf to convert latex documents to .rtf and thence to MS-word (see this thread). To do this, I set up a custom class and limit which packages are used as latex2rtf only accepts a limited subset of commands (see manual pages). latex2rtf provides a booelan, \iflatextortf, that is set to true if you use latex2rtf as your compiler.
I now need to display code listings and maintain the latex2rtf functionality. That means, I want to define something in the preamble to replace calls to \lstlisting{} with something like \begin{verbatim} ... \end{verbatim} when \iflatextortf is true.
Question: Is it possible to use switch between the lstlisting and verbatim environment depending on the value of \iflatextortf, keeping the content of the environment?
The solution would not require any packages to be installed and should work with the limited subset of commands in latex2rtf (see section 8.6.1). This should help me run compile using latex2rtf. Solutions using the verbatim package won't work unfortunately.
My ideal solution looks like this:
\newif\iflatextortf
\iflatextortf
\documentclass[12pt,letterpaper]{report}
% whatever my replacement for lstlistings is %
\else
\documentclass[10pt,letterpaper]{report}
\usepackage{listings}
% something fancy with listings
\lstnewenvironment{codeenv}[1][]{\lstset{basicstyle=\small\ttfamily}#1}{}
\fi
And I would like something a little more elegant than using find & replace on the raw .tex!
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Best I can tell this is impossible without the verbatim or fancyvrb package, as my ideal solution requires me to use verbatim within another environment. – Andy Clifton Jul 18 '13 at 1:54
My suggestion is to allow loading both listings and verbatim and use a common (new) environment to hold all your code. Under listings, you can define this environment using
\lstnewenvironment{codeenv}[1][]{}{}%
Using verbatim you can define this environment using
\newenvironment{codeenv}[1][]{\verbatim}{\endverbatim}%
Now you're able to condition on whether listings should be loaded using a traditional \@ifundefined{lstlisting}{<undefined>}{<defined>}. Here's a use case:
\documentclass{article}
\usepackage{listings}% http://ctan.org/pkg/listings
\usepackage{verbatim}% http://ctan.org/pkg/verbatim
\makeatletter
\@ifundefined{lstlisting}{% If listings is loaded
\newenvironment{codeenv}[1][]{\verbatim}{\endverbatim}%
}{% listings is not loaded
\lstnewenvironment{codeenv}[1][]{\lstset{basicstyle=\ttfamily,#1}}{}%
}
\makeatother
\begin{document}
\begin{codeenv}[basicstyle=\ttfamily]
This is some verbatim text.
\end{codeenv}
\end{document}
Now all you have to do is wrap the
\usepackage{listings}% http://ctan.org/pkg/listings
in your "boolean switch".
If the verbatim package is not allowed, then some code can be taken from the LaTeX kernel the revolves around the definition of the verbatim environment:
\documentclass{article}
\usepackage{listings}% http://ctan.org/pkg/listings
\makeatletter
\begingroup \catcode |=0 \catcode [= 1
\catcode]=2 \catcode \{=12 \catcode \}=12
\catcode\\=12 |gdef|@xverbatim#1\end{codeenv}[#1|end[codeenv]]
|endgroup
\@ifundefined{lstlisting}{
\newcommand{\codeenv}[1][]{\@verbatim \frenchspacing\@vobeyspaces \@xverbatim}
\def\endcodeenv{\if@newlist \leavevmode\fi\endtrivlist}
}{%
\lstnewenvironment{codeenv}[1][]{\lstset{basicstyle=\ttfamily,#1}}{}%
}
\makeatother
\begin{document}
\begin{codeenv}[basicstyle=\ttfamily]
This is some verbatim text.
\end{codeenv}
\end{document}
A final, fairly elementary approach might be to use the verbatim environment throughout your document for code examples, and redefine this environment to work as a regular listing is listings is loaded:
\documentclass{article}
\usepackage{listings}% http://ctan.org/pkg/listings
\makeatletter
\@ifundefined{lstlisting}{}{%
\let\verbatim\relax%
\lstnewenvironment{verbatim}{\lstset{basicstyle=\ttfamily}}{}%
}
\makeatother
\begin{document}
\begin{verbatim}
This is some verbatim text.
\end{verbatim}
\end{document}
Since listings does not provide \lstrenewenvironment, \letting \verbatim to \relax frees up the verbatim environment for redefinition. For ease-of-use, it's best avoid making verbatim accept optional arguments.
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This would be great except I made a mistake in my post and should have emphasized I meant the verbatim environment, not the package. The version of the listing that I use with latex2rtf should be generated using as few packages as possible (preferably none) to make it compatible with latex2rtf. Unfortunately verbatim is not compatible. – Andy Clifton Jul 17 '13 at 4:29
@LostBrit: I've updated the code to remove the verbatim package requirement. – Werner Jul 17 '13 at 5:07
Apparently \catcode doesn't work with Latex2rtf either (see documentation). Latex2rtf includes the boolean, \iflatextortf. Ideally, I would just define codeenv as you suggest, and replace lstlisting with verbatim if \iflatextortf were true , but AFAIK, you can't use verbatim as the input to an environment. – Andy Clifton Jul 17 '13 at 21:01
@LostBrit: I've dumbed it down even further. See if the last addition works for you. – Werner Jul 18 '13 at 5:24
This works really well. Accepted, thank you! – Andy Clifton Jul 19 '13 at 1:26
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https://cs.stackexchange.com/tags/correctness-proof/hot
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# Tag Info
242
Let me offer one reason and one misconception as an answer to your question. The main reason that it is easier to write (seemingly) correct mathematical proofs is that they are written at a very high level. Suppose that you could write a program like this: function MaximumWindow(A, n, w): using a sliding window, calculate (in O(n)) the sums of all ...
87
A common error I think is to use greedy algorithms, which is not always the correct approach, but might work in most test cases. Example: Coin denominations, $d_1,\dots,d_k$ and a number $n$, express $n$ as a sum of $d_i$:s with as few coins as possible. A naive approach is to use the largest possible coin first, and greedily produce such a sum. For ...
83
(I am probably risking a few downvotes here, as I have no time/interest to make this a proper answer, but I find the text quoted (and the rest of the article cited) below to be quite insightful, also considering they are written by a well-known mathematician. Perhaps I can improve the answer later.) The idea, which I suppose isn't particularly distinct from ...
68
I immediately recalled an example from R. Backhouse (this might have been in one of his books). Apparently, he had assigned a programming assignment where the students had to write a Pascal program to test equality of two strings. One of the programs turned in by a student was the following: issame := (string1.length = string2.length); if issame then for ...
60
Allow me to start by quoting E. W. Dijkstra: "Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians." (from EWD498) Although what Dijkstra meant with `programming' differs quite a bit from the current usage, there is still some merit in this quote. The other ...
52
Lamport provides some ground for disagreement on prevalence of errors in proofs in How to write a proof (pages 8-9): Some twenty years ago, I decided to write a proof of the Schroeder-Bernstein theorem for an introductory mathematics class. The simplest proof I could find was in Kelley’s classic general topology text. Since Kelley was writing for a ...
50
Here is an algorithm for the identity function: Input: $n$ Check if the $n$th binary string encodes a proof of $0 > 1$ in ZFC, and if so, output $n+1$ Otherwise, output $n$ Most people suspect this algorithm computes the identity function, but we don't know, and we can't prove it in the commonly accepted framework for mathematics, ZFC.
41
One big difference is that programs typically are written to operate on inputs, whereas mathematical proofs generally start from a set of axioms and prior-known theorems. Sometimes you have to cover multiple corner cases to get a sufficiently general proof, but the cases and their resolution is explicitly enumerated and the scope of the result is implicitly ...
33
The best example I ever came across is primality testing: input: natural number p, p != 2 output: is p a prime or not? algorithm: compute 2**(p-1) mod p. If result = 1 then p is prime else p is not. This works for (almost) every number, except for a very few counter examples, and one actually needs a machine to find a counterexample in a realistic period ...
32
Ultimately, you'll need a mathematical proof of correctness. I'll get to some proof techniques for that below, but first, before diving into that, let me save you some time: before you look for a proof, try random testing. Random testing As a first step, I recommend you use random testing to test your algorithm. It's amazing how effective this is: in my ...
28
They say the problem with computers is that they do exactly what you tell them. I think this might be one of the many reasons. Notice that, with a computer program, the writer (you) is smart but the reader (CPU) is dumb. But with a mathematical proof, the writer (you) is smart and the reader (reviewer) is also smart. This means you can never afford to get ...
26
Here's one that was thrown at me by google reps at a convention I went to. It was coded in C, but it works in other languages that use references. Sorry for having to code on [cs.se], but it's the only to illustrate it. swap(int& X, int& Y){ X := X ^ Y Y := X ^ Y X := X ^ Y } This algorithm will work for any values given to x and y, ...
24
One issue that I think was not addressed in Yuval's answer, is that it seems you are comparing different animals. Saying "the code is correct" is a semantic statement, you mean to say that the object described by your code satisfies certain properties, e.g. for every input $n$ it computes $n!$. This is indeed a hard task, and to answer it, one has to look ...
23
There are indeed programs like this. To prove this, let's suppose to the contrary that for every machine that doesn't halt, there is a proof it doesn't halt. These proofs are strings of finite length, so we can enumerate all proofs of length less than $s$ for some integer $s$. We can then use this to solve the halting problem as follows: Given a Turing ...
19
There is a whole class of algorithms that is inherently hard to test: pseudo-random number generators. You can not test a single output but have to investigate (many) series of outputs with means of statistics. Depending on what and how you test you may well miss non-random characteristics. One famous case where things went horribly wrong is RANDU. It ...
19
What is so different about writing faultless mathematical proofs and writing faultless computer code that makes it so that the former is so much more tractable than the latter? I believe that the primary reasons are idempotency (gives the same results for the same inputs) and immutability (doesn't change). What if a mathematical proof could give different ...
16
I am rather surprised that you raised this question since the meticulous and enlightening answers you have written to some math questions demonstrate sufficiently that you are capable of rigorous logical deduction. It seems that you became somewhat uncomfortable when you stumbled upon a new and unorthodox way to prove an algorithm is correct. Believe in ...
15
This is not a secure encryption scheme. It is similar to a Hill cipher, and vulnerable to similar attacks. For instance, it is vulnerable to known-plaintext attacks: an attacker who observes a ciphertext E and knows the corresponding message M can recover the secret key and thus decrypt all other messages that were encrypted with the same key. The ...
14
I will use the following simple sorting algorithm as an example: repeat: if there are adjacent items in the wrong order: pick one such pair and swap else break To prove the correctness I use two steps. First I show that the algorithm always terminates. Then I show that the solution where it terminates is the one I want. For the first point,...
13
We are indeed assuming $P(k)$ holds for all $k < n$. This is a generalization of the "From $P(n-1)$, we prove $P(n)$" style of proof you're familiar with. The proof you describe is known as the principle of strong mathematical induction and has the form Suppose that $P(n)$ is a predicate defined on $n\in \{1, 2, \dotsc\}$. If we can show that $... 12 I agree with what Yuval has written. But also have a much simpler answer: In practice softwares engineers typically don't even try to check for correctness of their programs, they simply don't, they typically don't even write down the conditions that define when the program is correct. There are various reasons for it. One is that most software engineers ... 12 There are a lot of good answers already but there are still more reasons math and programming aren't the same. 1 Mathematical proofs tend to be much simpler than computer programs. Consider the first steps of a hypothetical proof: Let a be an integer Let b be an integer Let c = a+b So far the proof is fine. Let's turn that into the first steps of a similar ... 11 2D local maximum input: 2-dimensional$n \times n$array$A$output: a local maximum -- a pair$(i,j)$such that$A[i,j]$has no neighboring cell in the array that contains a strictly larger value. (The neighboring cells are those among$A[i, j+1], A[i, j-1], A[i-1, j], A[i+1, j]$that are present in the array.) So, for example, if$A$is$\$\begin{...
11
No, your algorithm doesn't work. Consider if the array A is A = [1 1 1 1 1 2 2 3 3 3 3 3 3]. Then the array B will be B = [5 5 5 5 5 2 2 6 6 6 6 6 6]. The sum of B will be 65, and the length of B will be 13, so after division, we'll get the number 5. This is equal to the first element of B, so your algorithm will output "Yes". Nonetheless, not all ...
11
I like Yuval's answer, but I wanted to riff off of it for a bit. One reason you might find it easier to write Math proofs might boil down to how platonic Math ontology is. To see what I mean, consider the following: Functions in Math are pure (the entire result of calling a function is completely encapsulated in the return value, which is deterministic and ...
10
Proving that a program is "thread safe" is hard. It is possible, however, to concretely and formally define the term "data race." And it is possible to determine whether an execution trace of a specific run of a program does or does not have a data race in time proportional to the size of the trace. This type of analysis goes back at least to 1988: ...
10
There is no (one) formal definition of "optimal substructure" (or the Bellman optimality criterion) so you can not possibly hope to (formally) prove you have it. You should do the following: Set up your (candidate) dynamic programming recurrence. Prove it correct by induction. Formulate the (iterative, memoizing) algorithm following the recurrence.
10
Cryptosystems which are algebraic in nature are amenable to algebraic cryptanalysis. If you are trying to design a secure cryptosystem for actual use, there is one important maxim that you should keep in mind: Don't design your own cryptosystem! It is easy to design weak cryptosystems. Off-the-shelf cryptosystems have withstood breaking attempts by the ...
10
Most algorithms have not been proven correct in Hoare logic. The main reason is that such correctness proofs are extremely expensive as of Jan 2017, probably by several orders of magnitude in comparison with 'mere' programming. There is a lot of ongoing work to reduce this cost by automation, but it's an uphill struggle. Another reason why an algorithm ...
9
Fisher-Yates-Knuth shuffling algorithm is an (practical) example and one on which one of the the authors of this site has commented about. The algorithm generates a random permutation of a given array as: // To shuffle an array a of n elements (indices 0..n-1): for i from n − 1 downto 1 do j ← random integer with 0 ≤ j ≤ i exchange a[j] ...
Only top voted, non community-wiki answers of a minimum length are eligible
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http://faacets.com/wtf
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Required
### Try these...
CHSH CGMLP Guess Your Neighbor's Input
### Syntax
Faacets supports three notations:
• terms specified using full probabilities, writing P(abc...|xyz...),
• terms in the Collins-Gisin notation, by specifying the parties P_AB(ab|xy),
• correlator terms using the notation < Ax By ... >, with the input and output numbering starting at 1.
Expressions can be entered using rational coefficients before each term. Constant terms, parentheses, operators such as <= or >= are not supported.
|
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http://oscarfalk.com/dc95nd/8e3611-application-of-integration-exercises
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(c) the y-axis If necessary, break the region into sub-regions to determine its entire area. Use both the shell method and the washer method. Answer 7E. A conical tank is 5 m deep with a top radius of 3 m. (This is similar to Example 224.) Applications of integration a/2 y = 3x 4B-6 If the hypotenuse of an isoceles right triangle has length h, then its area is h2/4. 35) $$x=y^2$$ and $$y=x$$ rotated around the line $$y=2$$. 45) [T] Find the surface area of the shape created when rotating the curve in the previous exercise from $$\displaystyle x=1$$ to $$\displaystyle x=2$$ around the x-axis. How much work is performed in stretching the spring? Rotate the line $$y=\left(\frac{1}{m}\right)x$$ around the $$y$$-axis to find the volume between $$y=a$$ and $$y=b$$. 12. Starting from $$\displaystyle 1=¥250$$, when will $$\displaystyle 1=¥1$$? For exercise 48, find the exact arc length for the following problems over the given interval. 28) [T] The force of gravity on a mass $$m$$ is $$F=−((GMm)/x^2)$$ newtons. For exercises 5-6, determine the area of the region between the two curves by integrating over the $$y$$-axis. 27. 100-level Mathematics Revision Exercises Integration Methods. For exercises 20 - 21, find the surface area and volume when the given curves are revolved around the specified axis. If each of the workers, on average, lifted ten 100-lb rocks $$2$$ft/hr, how long did it take to build the pyramid? 5. For a rocket of mass $$m=1000$$ kg, compute the work to lift the rocket from $$x=6400$$ to $$x=6500$$ km. What is the total work done in lifting the box and sand? 13. 46) [T] An anchor drags behind a boat according to the function $$y=24e^{−x/2}−24$$, where $$y$$ represents the depth beneath the boat and $$x$$ is the horizontal distance of the anchor from the back of the boat. Applications of integration 4A. Sebastian M. Saiegh Calculus: Applications and Integration . We will learn how to find area using Integration in this chapter.We will use what we have studied in the last chapter,Chapter 7 Integrationto solve questions.The topics covered in th These revision exercises will help you practise the procedures involved in integrating functions and solving problems involving applications of integration. State in your own words Pascal's Principle. Use first and second derivatives to help justify your answer. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. 46) Yogurt containers can be shaped like frustums. (Hint: Recall trigonometric identities.). −b 0. spring is stretched to $$15$$ in. Note that the half-life of radiocarbon is $$\displaystyle 5730$$ years. Answer 9E. Use Simpson's Rule to approximate the area of the pictured lake whose lengths, in hundreds of feet, are measured in 200-foot increments. Use a calculator to determine the intersection points, if necessary, accurate to three decimal places. For the following exercises, find the derivative $$\displaystyle dy/dx$$. Sebastian M. Saiegh Calculus: Applications and Integration. T/F: The integral formula for computing Arc Length includes a square-root, meaning the integration is probably easy. Stewart Calculus 7e Solutions Chapter 5 Applications of Integration Exercise 5.1. Use the Disk/Washer Method to find the volume of the solid of revolution formed by revolving the region about the y-axis. 38) [T] $$y=\cos(πx),y=\sin(πx),x=\frac{1}{4}$$, and $$x=\frac{5}{4}$$ rotated around the $$y$$-axis. 25) Find the volume of the catenoid $$y=\cosh(x)$$ from $$x=−1$$ to $$x=1$$ that is created by rotating this curve around the $$x$$-axis, as shown here. 4) $$y=\cos θ$$ and $$y=0.5$$, for $$0≤θ≤π$$. area of a triangle or rectangle). 40. Prove that both methods approximate the same volume. The tank is filled with pure water, with a mass density of 1000 kg/m$$^3$$. Solution: $$\displaystyle P'(t)=43e^{0.01604t}$$. Answer 10E. If a man has a mass of 80kg on Earth, will his mass on the moon be bigger, smaller, or the same? Find the total profit generated when selling $$550$$ tickets. 23) You are a crime scene investigator attempting to determine the time of death of a victim. 2. Where is it increasing? 19) A $$1$$-m spring requires $$10$$ J to stretch the spring to $$1.1$$ m. How much work would it take to stretch the spring from $$1$$ m to $$1.2$$ m? A rope of length $$l$$ ft hangs over the edge of tall cliff. If true, prove it. 30) [T] A rectangular dam is $$40$$ ft high and $$60$$ ft wide. (a) How much work is done pulling the entire rope to the top of the building? If $$\displaystyle 1$$ barrel containing $$\displaystyle 10kg$$ of plutonium-239 is sealed, how many years must pass until only $$\displaystyle 10g$$ of plutonium-239 is left? 6. Solution: $$\displaystyle ln(4)−1units^2$$. 10) The populations of New York and Los Angeles are growing at $$\displaystyle 1%$$ and $$\displaystyle 1.4%$$ a year, respectively. 39) [T] $$y=x^2−2x,x=2,$$ and $$x=4$$ rotated around the $$y$$-axis. Worksheets 1 to 15 are topics that are taught in MATH108. Answer 7E. A force of 20 lb stretches a spring from a natural length of 6 in to 8 in. Stewart Calculus 7e Solutions Pdf. 47) [T] Find the arc length of $$\displaystyle y=1/x$$ from $$\displaystyle x=1$$ to $$\displaystyle x=4$$. For exercises 12 - 16, find the mass of the two-dimensional object that is centered at the origin. (b) $$x=1$$ 2. If $$\displaystyle 40%$$ of the population remembers a new product after $$\displaystyle 3$$ days, how long will $$\displaystyle 20%$$remember it? Stewart Calculus 7e Solutions. 44) A light bulb is a sphere with radius $$1/2$$ in. (a) the x-axis The relic is approximately $$\displaystyle 871$$ years old. 12) The effect of advertising decays exponentially. For $$y=x^n$$, as $$n$$ increases, formulate a prediction on the arc length from $$(0,0)$$ to $$(1,1)$$. Start Unit test . (a) Find the work performed in pumping all the water to the top of the tank. Use a calculator to determine intersection points, if necessary, to two decimal places. 4) Find the work done when you push a box along the floor $$2$$ m, when you apply a constant force of $$F=100$$ N. 5) Compute the work done for a force $$F=\dfrac{12}{x^2}$$ N from $$x=1$$ to $$x=2$$ m. 6) What is the work done moving a particle from $$x=0$$ to $$x=1$$ m if the force acting on it is $$F=3x^2$$ N? Answer 7E. A force of $$f$$ N stretches a spring $$d$$ m from its natural length. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. 1) [T] Over the curve of $$y=3x,$$ $$x=0,$$ and $$y=3$$ rotated around the $$y$$-axis. Slices perpendicular to the $$x$$-axis are semicircles. Answer 6E. Each problem has hints coming with it that can help you if you get stuck. 14) $$y=\sin(πx),\quad y=2x,$$ and $$x>0$$, 15) $$y=12−x,\quad y=\sqrt{x},$$ and $$y=1$$, 16) $$y=\sin x$$ and $$y=\cos x$$ over $$x \in [−π,π]$$, 17) $$y=x^3$$ and $$y=x^2−2x$$ over $$x \in [−1,1]$$, 18) $$y=x^2+9$$ and $$y=10+2x$$ over $$x \in [−1,3]$$. What do you notice? Stewart Calculus 7e Solutions Chapter 5 Applications of Integration Exercise 5.4. 13) If $$\displaystyle y=1000$$ at $$\displaystyle t=3$$ and $$\displaystyle y=3000$$ at $$\displaystyle t=4$$, what was $$\displaystyle y_0$$ at $$\displaystyle t=0$$? 52) A telephone line is a catenary described by $$\displaystyle y=acosh(x/a).$$ Find the ratio of the area under the catenary to its arc length. T/F: The integral formula for computing Arc Length was found by first approximating arc length with straight line segments. 48) Rotate the ellipse $$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$$ around the $$y$$-axis to approximate the volume of a football. 20. Stewart Calculus 7e Solutions Chapter 8 Further Applications of Integration Exercise 8.1. 1. 15) The base is the region enclosed by $$y=x^2)$$ and $$y=9.$$ Slices perpendicular to the $$x$$-axis are right isosceles triangles. Revolve the disk (x−b)2 +y2 ≤ a2 around the y axis. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. 24) For the cable in the preceding exercise, how much work is done to lift the cable $$50$$ ft? The solid formed by revolving $$y=2x \text{ on }[0,1]$$ about the x-axis. Rotate about: We use cross-sectional area to compute volume. For exercises 51 - 56, find the volume of the solid described. 29) [T] For the rocket in the preceding exercise, find the work to lift the rocket from $$x=6400$$ to $$x=∞$$. 7. Solution: False; $$\displaystyle k=\frac{ln(2)}{t}$$, For the following exercises, use $$\displaystyle y=y_0e^{kt}.$$. In your own words, describe how to find the total area enclosed by $$y=f(x)\text{ and }y=g(x)$$. Answer 4E. Find the ratio of the area under the catenary to its arc length. The dispensing value at the base is jammed shut, forcing the operator to empty the tank via pumping the gas to a point 1 ft above the top of the tank. If you are unable to determine the intersection points analytically, use a calculator to approximate the intersection points with three decimal places and determine the approximate area of the region. $$f(x) = \sec x\text{ on }[-\pi/4, \pi/4]$$. 21. 57) Prove the expression for $$\displaystyle sinh^{−1}(x).$$ Multiply $$\displaystyle x=sinh(y)=(1/2)(e^y−e^{−y})$$ by $$\displaystyle 2e^y$$ and solve for $$\displaystyle y$$. (b) $$y=1$$ Exercise 3.3 . The triangle with vertices $$(1,1),\,(1,2)\text{ and }(2,1).$$ Chapter 7: Applications of Integration Course 1S3, 2006–07 May 11, 2007 These are just summaries of the lecture notes, and few details are included. Then, use the Pappus theorem to find the volume of the solid generated when revolving around the y-axis. The weight rests on the spring, compressing the spring from a natural length of 1 ft to 6 in. Use the Trapezoidal Rule to approximate the area of the pictured lake whose lengths, in hundreds of feet, are measured in 100-foot increments. Missed the LibreFest? 50) [T] A chain hangs from two posts four meters apart to form a catenary described by the equation $$\displaystyle y=4cosh(x/4)−3.$$ Find the total length of the catenary (arc length). Use a calculator to determine the intersection points, if necessary, accurate to three decimal places. 12) The base is a triangle with vertices $$(0,0),(1,0),$$ and $$(0,1)$$. The answer to each question in every exercise is provided along with complete, step-wise solutions for your better understanding. It takes $$2$$ J to stretch the spring to $$15$$ cm. Find the slope of the catenary at the left fence post. Region bounded by: $$y=\sqrt{x},\,y=0\text{ and }x=1.$$ Answer 2E. For exercises 56 - 57, solve using calculus, then check your answer with geometry. For the following exercises, use a calculator to draw the region enclosed by the curve. If you cannot evaluate the integral exactly, use your calculator to approximate it. Does your expression match the textbook? How much work is performed in stretching the spring from a length of 16 cm to 21 cm? Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. For the following exercises, find the antiderivatives for the given functions. 29) $$y=x^2,$$ $$y=x,$$ rotated around the $$y$$-axis. Does your answer agree with the volume of a cone? In Exercises 5-8, a region of the Cartesian plane is shaded. A water tank has the shape of a truncated cone, with dimensions given below, and is filled with water with a weight density of 62.4 lb/ft$$^3$$. 1. Textbook Authors: Larson, Ron; Edwards, Bruce H. , ISBN-10: 1-28505-709-0, ISBN-13: 978-1-28505-709-5, Publisher: Brooks Cole $$f(x)=-x^3+5x^2+2x+1,\, g(x)=3x^2+x+3$$. 3) Use the slicing method to derive the formula for the volume of a tetrahedron with side length a. The rope has a weight density of $$d$$ lb/ft. Stewart Calculus 7e Solutions Chapter 8 Further Applications of Integration Exercise 8.1. (Hint: Since $$f(x)$$ is one-to-one, there exists an inverse $$f^{−1}(y)$$.). Region bounded by: $$y=2x,\,y=x\text{ and }x=2.$$ Applications of integration E. Solutions to 18.01 Exercises g) Using washers: a π(a 2 − (y2/a)2)dy = π(a 2y− y5/5a 2 ) a= 4πa3/5. In Exercises 3-12, find the fluid force exerted on the given plate, submerged in water with a weight density of 62.4 lb/ft$$^3$$. 32. 4. Rotate about: 15) If a bank offers annual interest of $$\displaystyle 7.5%$$ or continuous interest of $$\displaystyle 7.25%,$$ which has a better annual yield? 6) Take the derivative of the previous expression to find an expression for $$\sinh(2x)$$. Therefore, we let u = x 2 and write the following. 51) The base is the region between $$y=x$$ and $$y=x^2$$. Answer 6E. If you are unable to find intersection points analytically in the following exercises, use a calculator. The first problem is to set up the limits of integration. Rotate about: Answer 2E. For exercises 37 - 44, use technology to graph the region. Is there another way to solve this without using calculus? 9. 41) $$y=\sqrt{x},\quad x=4$$, and $$y=0$$, 42) $$y=x+2,\quad y=2x−1$$, and $$x=0$$, 44) $$x=e^{2y},\quad x=y^2,\quad y=0$$, and $$y=\ln(2)$$, $$V = \dfrac{π}{20}(75−4\ln^5(2))$$ units3, 45) $$x=\sqrt{9−y^2},\quad x=e^{−y},\quad y=0$$, and $$y=3$$. 36) $$\displaystyle ∫^{10}_5\frac{dt}{t}−∫^{10x}_{5x}\frac{dt}{t}$$, 37) $$\displaystyle ∫^{e^π}_1\frac{dx}{x}+∫^{−1}_{−2}\frac{dx}{x}$$, 38) $$\displaystyle \frac{d}{dx}∫^1_x\frac{dt}{t}$$, 39) $$\displaystyle \frac{d}{dx}∫^{x^2}_x\frac{dt}{t}$$, 40) $$\displaystyle \frac{d}{dx}ln(secx+tanx)$$. Region bounded by: $$y=y=x^2-2x+2,\text{ and }y=2x-1.$$ 2) $$y=−\frac{1}{2}x+25$$ from $$x=1$$ to $$x=4$$. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Elasticity of a function Ey/ Ex is given by Ey/ Ex = −7x / (1 − 2x )( 2 + 3x ). 7) $$y=x^{3/2}$$ from $$(0,0)$$ to $$(1,1)$$, 8) $$y=x^{2/3}$$ from $$(1,1)$$ to $$(8,4)$$, 9) $$y=\frac{1}{3}(x^2+2)^{3/2}$$ from $$x=0$$ to $$x=1$$, 10) $$y=\frac{1}{3}(x^2−2)^{3/2}$$ from $$x=2$$ to $$x=4$$, 11) [T] $$y=e^x$$ on $$x=0$$ to $$x=1$$, 12) $$y=\dfrac{x^3}{3}+\dfrac{1}{4x}$$ from $$x=1$$ to $$x=3$$, 13) $$y=\dfrac{x^4}{4}+\dfrac{1}{8x^2}$$ from $$x=1$$ to $$x=2$$, 14) $$y=\dfrac{2x^{3/2}}{3}−\dfrac{x^{1/2}}{2}$$ from $$x=1$$ to $$x=4$$, 15) $$y=\frac{1}{27}(9x^2+6)^{3/2}$$ from $$x=0$$ to $$x=2$$, 16) [T] $$y=\sin x$$ on $$x=0$$ to $$x=π$$. Find the area between the curves from time $$t=0$$ to the first time after one hour when the tortoise and hare are traveling at the same speed. 41) [T] $$y=3x^3−2,y=x$$, and $$x=2$$ rotated around the $$x$$-axis. (Note that $$1$$ kg equates to $$9.8$$ N). 33) [T] How much work is required to pump out a swimming pool if the area of the base is $$800 \, \text{ft}^2$$, the water is $$4$$ ft deep, and the top is $$1$$ ft above the water level? Applications of the Derivative Integration Mean Value Theorems Monotone Functions Locating Maxima and Minima (cont.) 6) If bacteria increase by a factor of $$\displaystyle 10$$ in $$\displaystyle 10$$ hours, how many hours does it take to increase by $$\displaystyle 100$$? Stewart Calculus 7e Solutions Chapter 5 Applications of Integration Exercise 5.1 . 33. (a) $$x=2$$ (c) the x-axis Answer 8E. In Exercises 9-16, a domain D is described by its bounding surfaces, along with a graph. What is the volume of this football approximation, as seen here? 2.Find the area of the region bounded by y^2 = 9x, x=2, x =4 and the x axis in the first quadrant. 1) $$\displaystyle m_1=2$$ at $$\displaystyle x_1=1$$ and $$\displaystyle m_2=4$$ at $$\displaystyle x_2=2$$, 2) $$\displaystyle m_1=1$$ at $$\displaystyle x_1=−1$$ and $$\displaystyle m_2=3$$ at $$\displaystyle x_2=2$$, 3) $$\displaystyle m=3$$ at $$\displaystyle x=0,1,2,6$$, 4) Unit masses at $$\displaystyle (x,y)=(1,0),(0,1),(1,1)$$, Solution: $$\displaystyle (\frac{2}{3},\frac{2}{3})$$, 5) $$\displaystyle m_1=1$$ at $$\displaystyle (1,0)$$ and $$\displaystyle m_2=4$$ at $$\displaystyle (0,1)$$, 6) $$\displaystyle m_1=1$$ at $$\displaystyle (1,0)$$ and $$\displaystyle m_2=3$$ at $$\displaystyle (2,2)$$, Solution: $$\displaystyle (\frac{7}{4},\frac{3}{2})$$. Used Integration formulas with examples, Solutions and exercises y=x^2 \text { }. 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Problems over the given axis ( d\ ) lb/ft ensure your answer agree with the bottom off...
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http://docs.itascacg.com/3dec700/3dec/docproject/source/modeling/problemsolving/rigidvsdeformable.html
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# Rigid vs. Deformable
An important consideration when doing a discontinuum analysis is whether to use rigid or deformable blocks to represent the behavior of intact material. The considerations for rigid versus deformable blocks are discussed in this section. If a deformable block analysis is required, there are several different models available to simulate block deformability; these are discussed in the section Choice of Constitutive Model.
As mentioned in Theory and Background, early distinct element codes assumed that blocks were rigid. However, the importance of including block deformability has become recognized, particularly for stability analyses of underground openings and studies of seismic response of buried structures. One of the most obvious reasons to include block deformability in a distinct element analysis is the requirement to represent the “Poisson’s ratio effect” of a confined rock mass.
Poisson’s Effect
Rock mechanics problems are usually very sensitive to the Poisson’s ratio chosen for a rock mass. This is because joints and intact rock are pressure-sensitive; their failure criteria are functions of the confining stress (e.g., the Mohr-Coulomb criterion). Capturing the true Poisson behavior of a jointed rock mass is critical for meaningful numerical modeling.
The effective Poisson’s ratio of a rock mass comprises two parts: a component due to the jointing; and a component due to the elastic properties of the intact rock. Except at shallow depths or low confining stress levels, the compressibility of the intact rock makes a large contribution to the compressibility of a rock mass as a whole. Thus, the Poisson’s ratio of the intact rock has a significant effect on the Poisson’s ratio of a jointed rock mass.
Strictly speaking, a single Poisson’s ratio, $$\nu$$, is defined only for isotropic elastic materials. However, there are only a few jointing patterns that lead to isotropic elastic properties for a rock mass. Therefore, it is convenient to define a “Poisson effect” that can be used for discussion of anisotropic materials.
Note
The following discussion assumes 2D plain strain conditions with $$y$$ as the vertical direction.
The Poisson effect will be defined as the ratio of horizontal-to-vertical stress when a load is applied in the vertical direction and no strain is allowed in the horizontal direction; plane-strain conditions are assumed. As an example, the Poisson effect for an isotropic elastic material is
(1)$\frac{\sigma_{xx}}{\sigma_{yy}} = \frac{\nu}{1-\nu}$
Consider the Poisson effect produced by the vertical jointing pattern shown in the figure below. If this jointing were modeled with rigid blocks, applying a vertical stress would produce no horizontal stress at all. This is clearly unrealistic, because the horizontal stress produced by the Poisson’s ratio of the intact rock is ignored.
The joints and intact rock act in series. In other words, the stresses acting on the joints and on the rock are identical. The total strain of the jointed rock mass is the sum of the strain due to the jointing and the strain due to the compressibility of the rock. The elastic properties of the rock mass as a whole can be derived by adding the compliances of the jointing and the intact rock:
(2)$\begin{split}\begin{bmatrix}\epsilon_{xx}\\\epsilon_{yy}\end{bmatrix} = \biggl(C^{\mathrm{rock}}+ C^{\mathrm{jointing}}\biggr)\begin{bmatrix}\sigma_{xx}\\\sigma_{yy}\end{bmatrix}\end{split}$
If the intact rock were modeled as an isotropic elastic material, its compliance matrix would be
(3)$\begin{split}C^{\mathrm{rock}} = \frac{1+\nu}{E}\begin{bmatrix}1-\nu & -\nu\\-\nu & 1-\nu\end{bmatrix}\end{split}$
The compliance matrix due to the jointing is
(4)$\begin{split}C^{\mathrm{jointing}} = \begin{bmatrix}\frac{1}{Sk_n}&0\\0&\frac{1}{Sk_n}\end{bmatrix}\end{split}$
where $$S$$ is the joint spacing, and $$k_n$$ is the normal stiffness of the joints.
If $$\epsilon_{xx}$$ = 0 in Equation (2) then
(5)$\frac{\sigma_{xx}}{\sigma_{yy}}=-\frac{C^{(total)}_{12}}{C^{(total)}_{11}}$
where $$C^{(total)} = C^{(rock)} + C^{(jointing)}$$.
Thus, the Poisson effect for the rock mass as a whole is
(6)$\frac{\sigma_{xx}}{\sigma_{yy}}=\frac{\nu(1+\nu)}{E/(Sk_n)+(1+\nu)(1-\nu)}$
Equation (6) is graphed as a function of the ratio $$E/(Sk_n)$$ in the next figure. Also graphed are the results of several two-dimensional UDEC simulations run to verify the formula. The ratio $$E/(Sk_n)$$ is a measure of the stiffness of the intact rock in relation to the stiffness of the joints. For low values of $$E/(Sk_n)$$, the Poisson effect for the rock mass is dominated by the elastic properties of the intact rock. For high values of $$E/(Sk_n)$$, the Poisson effect is dominated by the jointing.
Now consider the Poisson effect produced by joints dipping at various angles. The Poisson effect is a function of the orientation and elastic properties of the joints. Consider the special case shown in Figure 3. A rock mass contains two sets of equally spaced joints dipping at an angle, $$θ$$, from the horizontal. The elastic properties of the joints consist of a normal stiffness, $$k_n$$, and a shear stiffness, $$k_s$$. The blocks of intact rock are assumed to be completely rigid.
where $$S$$ is the joint spacing, and $$k_n$$ is the normal stiffness of the joints.
The Poisson effect for this jointing pattern is
(7)$\frac{\sigma_{xx}}{\sigma_{yy}}=\frac{\cos^2\theta[(k_n\, / \,k_s)-1]}{\sin^2\theta+cos^2\theta(k_n\, / \,k_s)}$
This formula is illustrated graphically for several values of $$θ$$ in the next figure. Also shown are the results of numerical simulations using UDEC. The UDEC simulations agree closely with Equation (7).
Equation (7) demonstrates the importance of using realistic values for joint shear stiffness in numerical models. The ratio of shear stiffness to normal stiffness dramatically affects the Poisson response of a rock mass. If shear stiffness is equal to normal stiffness, the Poisson effect is zero. For more reasonable values of $$k_n/k_s$$ , from 2.0 to 10.0, the Poisson effect is quite high, up to 0.9.
Next, the contribution of the elastic properties of the intact rock will be examined for the case of θ = 45º. Following the analysis for the vertical jointing case, the intact rock will be treated as an isotropic elastic material. The elastic properties of the rock mass as a whole will be derived by adding the compliances of the jointing and the intact rock.
The compliance matrix due to the two equally spaced sets of joints dipping at 45º is
(8)$\begin{split}C^{(jointing)}=\frac{1}{2S\:k_nk_s}\begin{bmatrix}k_s+k_n&k_s-k_n\\k_s-k_n&k_s+k_n\end{bmatrix}\end{split}$
Thus, the Poisson effect for the rock mass as a whole is
(9)$\frac{\sigma_{xx}}{\sigma_{yy}}=\frac{\nu(1+\nu)\,/E+(k_n-k_s)\,/\,(2S\,k_nk_s)}{[(1+\nu)(1_-\nu)]\,/E+\,(k_n+k_s)\,/\,(2S\,k_nk_s)}$
Equation (9) is graphed for several values of the ratio $$E/(Sk_n)$$ for the case of $$ν$$ = 0.2 (see the next figure). Also plotted are the results of UDEC simulations. For low values of $$E/(Sk_n)$$, the Poisson effect of a rock mass is dominated by the elastic properties of the intact rock. For high values of $$E/(Sk_n)$$, the Poisson effect is dominated by the jointing.
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http://nbviewer.jupyter.org/github/amplab/datascience-sp14/blob/master/lab4/joins.ipynb
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# Joining DataFrames in Pandas¶
In previous labs, we've explored the power tables as a data management abstraction, in particular with the Pandas DataFrame object. Tables let us select rows and columns of interest, group data, and measure aggregates.
But what happens when we have more than one table? Traditional relational databases usually contain many tables. Moreover, when integrating multiple data sets, we necessarily need tools to combine them.
In this lab, we will use Panda's take on the database join operation to see how tables can be linked together. Specifically, we're going to perform a "fuzzy join" based on string edit-distance as another approach to finding duplicate records.
Remember to fill out the response form at http://goo.gl/ZgfzAN at the end !
## Setup¶
### Data¶
Today we'll be using a small data set of restaurants. Download the data from here. Put the data file, "restaurants.csv", in the same directory as this notebook.
### Edit Distance¶
We're going to be using a string-similarity python library to compute "edit distance". Install it on your VM by running the following:
sudo apt-get install python-levenshtein
NOTE: You may also need to run sudo apt-get update.
To test that it works, the following should run OK:
In [ ]:
import Levenshtein as L
## Joins¶
A join is a way to connect rows in two different data tables based on some criteria. Suppose the university has a database for student records with two tables in it: Students and Grades.
In [ ]:
import pandas as pd
Students = pd.DataFrame({'student_id': [1, 2], 'name': ['Alice', 'Bob']})
Students
In [ ]:
Grades = pd.DataFrame({'student_id': [1, 1, 2, 2], 'class_id': [1, 2, 1, 3], 'grade': ['A', 'C', 'B', 'B']})
Let's say we want to know all of Bob's grades. Then, we can look up Bob's student ID in the Students table, and with the ID, look up his grades in the Grades table. Joins naturally express this process: when two tables share a common type of column (student ID in this case), we can join the tables together to get a complete view.
In Pandas, we can use the merge method to perform a join. Pass the two tables to join as the first arguments, then the "on" parameter is set to the join column name.
In [ ]:
pd.merge(Students, Grades, on='student_id')
### DIY¶
1. Use merge to join Grades with the Classes table below, and find out what class Alice got an A in.
In [ ]:
Classes = pd.DataFrame({'class_id': [1, 2, 3], 'title': ['Math', 'English', 'Spanish']})
# Joining the Restaurant Data¶
Now let's load the restaurant data that we will be analyzing:
In [ ]:
resto = pd.read_csv('restaurants.csv')
resto.info()
In [ ]:
resto[:10]
The restaurant data has four columns. id is a unique ID field (unique for each row), name is the name of the restaurant, and city is where it is located. The fourth column, cluster, is a "gold standard" column. If two records have the same cluster, that means they are both about the same restaurant.
The type of join we made above between Students and Grades, where we link records with equal values in a common column, is called an equijoin. Equijoins may join on more than one column, too (both value have to match).
Let's use an equijoin to find pairs of duplicate restaurant records. We join the data to itself, on the cluster column.
Note: a join between a table and itself is called a self-join.
The result ("clusters" below) has a lot of extra records in it. For example, since we're joining a table to itself, every record matches itself. We can filter on IDs to get rid of these extra join results. Note that when Pandas joins two tables that have columns with the same name, it appends "_x" and "_y" to the names to distinguish them.
In [ ]:
clusters = pd.merge(resto, resto, on='cluster')
clusters = clusters[clusters.id_x != clusters.id_y]
clusters[:10]
### DIY¶
1. There are still extra records in clusters, above. If records A and B match each other, then we will get both (A, B) and (B, A) in the output. Filter clusters so that we only keep one instance of each matching pair (HINT: use the IDs again).
## Fuzzy Joins¶
Sometimes an equijoin isn't good enough.
Say you want to match up records that are almost equal in a column. Or where a function of a columns is equal. Or maybe you don't care about equality: maybe "less than" or "greater than or equal to" is what you want. These cases call for a more general join than equijoin.
We are going to make one of these joins between the restaurants data and itself. Specifically, we want to match up pairs of records whose restaurant names are almost the same. We call this a fuzzy join.
To do a fuzzy join in Pandas we need to go about it in a few steps:
1. Join every record in the first table with every record in the second table. This is called the Cartesian product of the tables, and it's simply a list of all possible pairs of records.
2. Add a column to the Cartesian product that measures how "similar" each pair of records is. This is our join criterion.
3. Filter the Cartesian product based on when the join criterion is "similar enough."
SQL Aside: In SQL, all of joins are supported in about the same way as equijoins are. Essentially, you write a boolean expression on columns from the join-tables, and whenever that expression is true, you join the records together. This is very similar to writing an if statement in python or Java.
Let's do an example to get the hang of it.
#### 1. Join every record in the first table with every record in the second table.¶
We use a "dummy" column to compute the Cartesian product of the data with itself. dummy takes the same value for every record, so we can do an equijoin and get back all pairs.
In [ ]:
resto['dummy'] = 0
prod = pd.merge(resto, resto, on='dummy')
# Clean up
del prod['dummy']
del resto['dummy']
# Show that prod is the size of "resto" squared:
print len(prod), len(resto)**2
In [ ]:
prod[:10]
### DIY¶
• Like we did with clusters remove "extra" record pairs, e.g., ones with the same ID.
#### 2. Add a column to the Cartesian product that measures how "similar" each pair of records is.¶
In the homework assignment, we used a string similarity metric called cosine similarity which measured how many "tokens" two strings shared in common. Now, we're going to use an alternative measure of string similarity called edit-distance. Edit-distance counts the number of simple changes you have to make to a string to turn it into another string.
Import the edit distance library:
In [ ]:
import Levenshtein as L
L.distance('Hello, World!', 'Hallo, World!')
Next, we add a computed column, named distance, that measures the edit distance between the names of two restaurants:
In [ ]:
# This takes a minute or two to run
prod['distance'] = prod.apply(lambda r: L.distance(r['name_x'], r['name_y']), axis=1)
#### 3. Filter the Cartesian product based on when the join criterion is "similar enough."¶
Now we complete the join by filtering out pairs or records that aren't equal enough for our liking. As in the first homework assignment, we can only figure out how similar is "similar enough" by trying out some different options. Let's try maximum edit-distance from 0 to 10 and compute precision and recall.
In [ ]:
%matplotlib inline
import pylab
def accuracy(max_distance):
similar = prod[prod.distance < max_distance]
correct = float(sum(similar.cluster_x == similar.cluster_y))
precision = correct / len(similar)
recall = correct / len(clusters)
return (precision, recall)
thresholds = range(1, 11)
p = []
r = []
for t in thresholds:
acc = accuracy(t)
p.append(acc[0])
r.append(acc[1])
pylab.plot(thresholds, p)
pylab.plot(thresholds, r)
pylab.legend(['precision', 'recall'], loc=2)
### DIY¶
1. Another common way to visualize the tradeoff between precision and recall is to plot them directly against each other. Create a scatterplot with precision on one axis and recall on the other. Where are "good" points on the plot, and where are "bad" ones.
1. The python Levenshtein library provides another metric of string similarity called "ratio" (use L.ratio(s1, s1)). ratio gives a similarity score between 0 and 1, with higher meaning more similar. Add a column to "prod" with the ratio similarities of the name columns, and redo the precision/recall tradeoff analysis with the new metric. (Note: you will have to alter the accuracy method and the threshold range.) On this data, does Levenshtein.ratio do better than Levenshtein.distance?
Finally, remember to fill out the response form at http://goo.gl/ZgfzAN !
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# Which of the following equations represents a line that is perpendicul
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Which of the following equations represents a line that is perpendicul [#permalink]
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29 Nov 2015, 10:47
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Which of the following equations represents a line that is perpendicular to y=1/2*x+2?
A. y−2x=8
B. 2x+4y=10
C. 3y+6x=12
D. 4y−8x=16
E. 5x−10y=20
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Re: Which of the following equations represents a line that is perpendicul [#permalink]
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29 Nov 2015, 11:02
For two lines to be perpendicular, the product of slopes should be equal to -1.
Slope of line 1 = 1/2
Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2
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Re: Which of the following equations represents a line that is perpendicul [#permalink]
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30 Nov 2015, 15:12
Hi All,
This question asks for a line that is perpendicular to the line Y = (1/2)(X) + 2.
When graphing lines, it's often easiest for most Test Takers to put the line in slope-intercept 'format' (the same format as the one used in the given equation above). Perpendicular lines have slopes that are 'opposite inverse' (sometimes called 'negative reciprocal'), so we're looking for a line that has a slope of -2 (since the opposite of a positive is a negative and the inverse of 1/2 is 2).
Rather than convert all 5 answer choices to slope-intercept format, we can use some patterns to our advantage. To start, the slope will have to be NEGATIVE. Eliminate Answers A and D (their slopes will be positive). With the remaining 3 answers, we have:
B: Y = (1/2)X + 5/2
C: Y = -2X + 4
E: Y = (-1/2)X -2
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Re: Which of the following equations represents a line that is perpendicul [#permalink]
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01 Jan 2018, 11:49
Bunuel wrote:
Which of the following equations represents a line that is perpendicular to y=1/2*x+2?
A. y−2x=8
B. 2x+4y=10
C. 3y+6x=12
D. 4y−8x=16
E. 5x−10y=20
VERITAS PREP OFFICIAL SOLUTION:
In order for two lines to be perpendicular, the slopes need to be negative reciprocals of each other. Since the given slope is 1/2, you're looking for a slope of −2.
To find the slope, you need to put the equations in point-slope form, y = mx + b, where m is the slope. Checking the answer choices quickly:
Choices A, D, and E will each give x a positive coefficient, as your first step is to get y on the opposite side of the equation from x.
Only choice C simplifies to a coefficient of −2:
3y + 6x = 12
3y = −6x + 12
y = −2x + 4
So C is the correct answer.
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Re: Which of the following equations represents a line that is perpendicul [#permalink]
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23 Apr 2018, 05:44
Bunuel wrote:
Which of the following equations represents a line that is perpendicular to y=1/2*x+2?
A. y−2x=8
B. 2x+4y=10
C. 3y+6x=12
D. 4y−8x=16
E. 5x−10y=20
Two lines are perpendicular when their slopes are negative reciprocal of each other.
Slope of given line =$$\frac{1}{2}$$
Required slope = $$-2$$
Only equation of line $$3y+6x=12$$ satisfies
$$y = -2x + 12$$
(C)
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Re: Which of the following equations represents a line that is perpendicul [#permalink] 23 Apr 2018, 05:44
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https://email.esm.psu.edu/pipermail/macosx-tex/2006-March/020949.html
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# [OS X TeX] increased memory allocation
Herbert Schulz herbs at wideopenwest.com
Sat Mar 4 13:35:37 EST 2006
On Mar 4, 2006, at 11:55 AM, Miriam Belmaker wrote:
> Hi,
>
> I can run the pdflatex with no problem and then when I try to
> bibtex the aux file , I see nothing (this happens when I run it
> indivually or using the Macro in TexShop).... I can then open the
> bbl file which has the bibliography up to the c's about 80 refs of
> 416.. without the \end {bibliography}. If I rerun pdflatex I get
> the file with all ? instead of the ref (after the c's ofcourse)..
> As I mentioned before, it ran fine on FINK, so there is no problem
> in my bib file (I also tried this on my computer on a copy with no
> accents etc.. and it still wouldn't work).. If I break up my file
> into smaller files.. it will compile the small files up to 80 kb..
> it is not a single c ref because I can rearrange the smaller parts
> and it will always compile the first two.
>
> The log does not recognize any of the uncompiled refs.. is there
> any thing specific to look for in the log that may help?
> When I entered usr/local/teTeX/share/texmf/web2c/texmf.cnf to
> edit and recreate the formats as i was suggested it requested
> permission (???).
>
>
> Miriam
>
Howdy,
What does TeXShop's Console output look like when you run bibtex?
Does bibtex complain at all? (Others on the list are better at
diagnosing bibtex problems.)
Will the .bib file open correctly in BibDesk? Maybe making a change
there, saving the change and then changing back and saving will help.
Grasping at straws here.
Good Luck,
Herb Schulz
(herbs at wideopenwest.com)
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https://mathematica.stackexchange.com/questions/139520/labelling-points-on-a-numberlineplot
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# Labelling points on a NumberLinePlot
I have a list of points plotted using the command:
NumberLinePlot[{1, 1.5, 2}, PlotStyle -> {{Thick, Red, PointSize[Large]}, {Thick, Darker[Green],
PointSize[Large]}, {Thick, Blue, PointSize[Large]}},
PlotTheme -> "Scientific"]
The output is of the form:
How can I label each point in the graph. Say, for instance, the red term is the first term in a sequence, the green term is the second term in the sequence etc. How can I label the plot such that this labelling, as $x_1, x_2$ is reflected in the graph. It'd be great if someone could suggest a way where I can introduce these labels directly on the graph, and not in the legend, so I don't necessarily have to color the points differently.
labels={"label1","label2","label3"};
i=1;
NumberLinePlot[{1,1.5, 2}, PlotStyle-> {{Thick, Red, PointSize[Large]},
{Thick, Darker[Green], PointSize[Large]}, {Thick, Blue, PointSize[Large]}},
ImagePadding -> 20] /. Point[x_]->{Point[x], Text[labels[[i++]], {0,1} + x]}
Update: Stealing @Mr.Wizard's idea of using Tooltips with an alternative way to post-process
nlp = NumberLinePlot[Tooltip@@@Transpose[{{1,1.5, 2}, labels}],
PlotStyle -> {{Thick, Red, PointSize[Large]}, {Thick, Darker[Green],
PointSize[Large]}, {Thick, Blue, PointSize[Large]}}];
Show[nlp /. Tooltip[x_, y_] :> {x, Text[y, {0,1} + x[[1,1]]]}, ImagePadding -> 20]
Update 2: Neither of the methods above work in version 11.3. The following modification of the first method works:
labels = {"label1", "label2", "label3"};
i = 1;
NumberLinePlot[List /@ {1, 1.5, 2},
PlotStyle -> ({{Thick, Red, PointSize[Large]},
{Thick, Darker[Green], PointSize[Large]}, {Thick, Blue,
PointSize[Large]}}),
ImagePadding -> 20, Spacings -> {1/4, 0, 0}] /.
Point[x_] :> {Point[x], Text[labels[[i++]], {0, 1/4} + x]}
• I was about to note the example in the ListPlot documentation, but you got there first. Nov 16, 2018 at 16:24
Tooltip gives you hover-over labels:
dat = {Tooltip[1, "x1"], Tooltip[1.5, "x2"], Tooltip[2, "x3"]};
p1 = NumberLinePlot[dat,
PlotStyle -> {{Thick, Red, PointSize[Large]}, {Thick, Darker[Green],
PointSize[Large]}, {Thick, Blue, PointSize[Large]}}, PlotTheme -> "Scientific"]
I am working on always-visible labels now.
I could not quickly trace the handling of Labeled in NumberLinePlot but it seems it is not supported. We could extract points and re-plot them with a function that does support Labeled, ListPlot:
pts = Cases[p1, Tooltip[{_[pt_]}, lbl_] :> Labeled[pt, lbl], -3];
Show[p1, ListPlot[pts, PlotStyle -> None], PlotRange -> All]
• Oh. But if I want to embed the graph in a PDF? For that, ideally, I was hoping there's a way I could label the points on the numberline and make that labelling apparent. Mar 8, 2017 at 3:39
• @JunaidAftab Yes, I understand. Please see my updated answer. This uses the automatically positioned labeling of ListPlot in an overlay of the NumberLinePlot. Mar 8, 2017 at 4:08
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http://math.stackexchange.com/questions/204892/how-to-solve-this-summation-polynomial
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# How to solve this summation/polynomial?
Is there a simple/fast way to find $y$ for the equation:
$$120,000=8000\sum_{t=1}^{4}\frac{1}{(1+y)^t}+\frac{100,000}{(1+y)^4}$$
?
I am trying to calculate the yield to maturity of a bond, and the answer is 2.66% or 2.67% (depending on your rounding off). I know some other method (some sort of trail and run method), but its rather long in my opinion.
The question was:
A bond has an annual coupon (interest) rate of 8%, with nominal value of 100,000 that has maturity in 4 years time. If the bond sells at 120,000, what is the yield to maturity?
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Multiply through by $(1+y)^4$. You get a quartic in $1+y$ (even in $y$ if you masochistically expand). There is a formula for the roots of a quartic, initially due to Cardano and Ferrari, with variants by a bunch of people. None of these is useful for your purposes. Use a numerical method, like Newton-Raphson. A couple of iterations are enough. – André Nicolas Sep 30 '12 at 15:24
Hint: use $1+a+a^2+..+a^k = \displaystyle\frac{a^{k+1}-1}{a-1}$ for $b:=\displaystyle\frac1{1+y}$
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Remember that $$\sum_{k=0}^{n+1}x^k=\frac{1-x^n}{1-x}$$ So: \begin{align*}120 =& 8\sum_{t=1}^{4}\frac{1}{(1+y)^t}+\frac{100}{(1+y)^4}=8\left(\frac{1-\frac{1}{(1+y)^5}}{1-\frac{1}{1+y}}-1\right)+\frac{100}{(1+y)^4}\\ =&8\frac{(1+y)^5-1-(1+y)^5+(1+y)^4}{(1+y)^5-(1+y)^4}+\frac{100}{(1+y)^4}\\ =&\frac{8(1+y)^4-8+100(1+y-1)}{(1+y)^4(1+y-1)}=\frac{8(1+y)^4-8+100y}{(1+y)^4y}\end{align*} Multiplying and both sides by $y(1+y)^4$, dividing by $4$ and rearranging, we get: $$(30y-2)(1+y)^4-25y+2=0$$
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Either let $z=1+y$ and multiply through by $z^4$, or let $z=\frac{1}{1+y}$ and do nothing. Your equation is a quartic equation in $z$.
There is a closed form formula for the roots of the quartic, obtained initially by Cardano and Ferrari in the sixteenth century. Variants were found by several mathematicians, including Descartes, Newton, and Lagrange. All the formulas are very complicated, and not suitable for your purposes. The link above is meant only to show you how complicated the Cardano-Ferrari formula is.
It is best to use a numerical method, such as the Newton-Raphson method. Special algorithms have also been developed for equations that arise from interest rate calculations. In your case, you will be able to supply a good initial estimate $z_0$ of $z$, so Newton-Raphson will converge very rapidly. A couple of iterations will suffice for an answer that is accurate enough for all practical purposes.
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http://physics.stackexchange.com/questions/41124/bouncing-ball-pattern
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# Bouncing Ball Pattern
If a ball is simply dropped, each time a ball bounces, it's height decreases in what appears to be an exponential rate.
Let's suppose that the ball is thrown horizontally instead of being simply dropped. How does the horizontal distance travelled change after each bounce?
Context behind question: I read a question involving a ball that travels horizontally 1m during the first bounce, 0.5m during the second bounce, 0.25 during the third bounce etc. I was wondering if this model is physically valid?
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It is very similiar to my question. Look at that physics.stackexchange.com/questions/28863/… – Mathlover Oct 19 '12 at 12:34
If a bounce has a maximum height $h$ then the time taken for the ball to leave the ground, reach $h$ and fall back is simply $t = 2\sqrt{2h/g}$ so if the horizontal speed is constant at $v$ the horizontal distance travelled in the bounce is $s = 2v\sqrt{2h/g}$.
In your example the distance travelled appears to halve with each bounce i.e. $s_{n+1}/s_n = 1/2$. Since $s \propto \sqrt{h}$ we get:
$$\frac{s_{n+1}}{s_n} = \sqrt{\frac{h_{n+1}}{h_n}} = \frac{1}{2}$$
so $h_{n+1}/h_n = 1/4$. This seems physically reasonable and it is an exponential decay of bounce height.
NB this all assumes the horizontal velocity doesn't change at the bounce.
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The geometric sum of horizontal distance after infinite bounces would be finite (e.g if each bounce is halved, the sum is 2m in total after infinite bounces). But you assume horizontal velocity doesn't change. Will the ball travel forever or just 2m? – Mew Oct 18 '12 at 14:48
Good question: that's Zeno's paradox isn't it? Assuming the exponential relation holds exactly, the ball will start bouncing infinitely quickly as the horizontal distance approaches whatever 1 + 1/4 + 1/16 + etc is. It will therefore lose energy infinitely quickly and stop bouncing. beyond this point the ball will roll without bouncing. – John Rennie Oct 18 '12 at 15:01
Thanks, nice explanation. – Mew Oct 18 '12 at 15:03
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http://physics.stackexchange.com/questions/22390/would-one-actually-find-their-doppelg%c3%a4nger-in-a-googolplex-universe?answertab=oldest
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# Would one actually find their doppelgänger in a “Googolplex Universe”?
I've recently become a fan of Numberphile, and today I happened to watch their video regarding Googol and Googolplex. In the video, I found a rather confusing claim that I'm hoping someone here can help me sort out.
It's first stated in the introduction, and then explained in more detail at around 4:10. The claim can be summed up as this:
In a universe which is "a Googolplex meters across", if you would travel far enough, you would expect to eventually begin finding duplicates of yourself.
Getting deeper into the detail of this, Tony Padilla explains that this is because there is a finite number of possible quantum states which can represent the volume of space in which your body resides. That volume is given as roughly one cubic meter, and the number of possible states for that volume is estimated at $10^{10^{70}}$. This is obviously much less than the number of cubic meters within a "Googolplex Universe", and so the idea does make some sense.
But I believe the idea relies on a false premise. That premise would be that the universe as a whole is entirely comprised of random bits of matter. We can easily see that this is not true. The vast majority of our observed universe is occupied by the near-vacuum of space, and those volumes which are not empty are occupied by some fairly organized objects which all interact according to certain laws and patterns.
So, I'm curious to know two things:
1. Who originally proposed this idea? Is it something that perhaps Tony just came up with to include in the video, or is there a noted physicist or mathematician who actually wrote about this at some point?
2. Given the possibility that a universe similar to ours could exist and be one Googolplex across, would this actually be probable? Or, would the natural order and organization of the universe prevent this from being as likely as it might be in a more random universe?
A note regarding the size of the universe, in respect to this question. In the linked video, the following constraints are mentioned:
• The number of particles in the universe is $10^{80}$
• Stated at 1:38 in the video.
• The number of the grains of sand that could fit within the universe is $10^{90}$.
• Stated at 1:55 in the video.
• The number of Planck volumes in the universe is $10^{183}$
• Stated at 2:22 in the video.
• The size of the universe is $(10^{26}m.)^{3}$
• Stated at 6:36 in the video.
A few times in the video, Tony does qualify his statements by referring specifically to the observable universe. However, sometimes it's not quite so clear.
So, to simplify the problem for the purposes of this question, let's assume:
• Our universe is finite, and much less than a Googolplex in diameter.
• The "Googolplex Universe" suggested in the video, and in question here, is also finite.
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Regarding the source of claims such as those, I believe they are due to Max Tegmark, likely from this article. He has curious ideas, though discerning whether they are correct, useful or at least in the realm of possibility is far beyond my capacity. He is a strong proponent of the idea of a mathematical Universe. If I recall correctly, he goes to the point of stating that anything exists at all merely because mathematics/logic exists, and everything we perceive as reality is logical statements playing out in a marvelously complex fashion very far down the line. Why does it happen? Because it can, basically.
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I think this assertion would be more correct if it was something like:
There are more 1 cubic-meters of matter units in a googolplex-meter-wide universe than there are possible quantum states of 1 cubic-meters of matter units, so at least one of those quantum states of 1 cubic-meters of matter occurs in more than one 1 cubic-meters of matter somewhere.
In fact there are at least as many duplicates of some kind, to make up the difference between the number of possible states, and the number of total volumes.
But, this does not imply that any particular configuration is duplicated. Heaven forbid there be more of me out there. Maybe a rather simple configuration accounts for 99.99% of all the duplications.
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Exactly, he's implicitly assuming all configurations are equally probably. There is no reason to believe that. – Tobias Brandt Aug 1 '14 at 21:41
If you mass 120 kg (264 lbs) and the average atomic weight in your substance is, we'll be generous, 25, then you contain $(120,000/25) \times (6.022 \times 10^{23})$ atoms or $2.9x10^{27}$ atoms. They can be arranged in $(2.9x10^{27})!$ ways.
\begin{align} n! &\approx \sqrt{2\pi n}(n/e)^n = (10^{14})(10^{27})^{27} \end{align}
is a big number, dwarfing string theory's $10^{500}$ acceptable vacua.
How much time are you given to look? Then QM intrudes (Heisenberg compensators?).
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Well, the universe has evidently produced you at least once, so we can certainly say the probability of producing you is nonzero.
Of course, you're the end result of a very long chain of events, encompassing all sorts of cultural, biological, planetary, astrophysical, and cosmological processes. Ultimately (well, to the extent of our cosmological knowledge) your existence traces back to certain random quantum fluctuations during the inflationary era of the Big Bang, which acted as the seeds for galaxies to form, and so on.
If we imagine that the universe extends far beyond the part we can see (the observable universe), at least $10^{10^{100}}$ meters in each direction, but has evolved from similar initial conditions everywhere, then it isn't too difficult to imagine that somewhere in that immensity, some inflation fluctuations occurred that were sufficiently similar to ours, to generate a galaxy sufficiently similar to the Milky Way, to generate a planet sufficiently similar to Earth, to be inhabited by beings sufficiently similar to us, that one of them is very similar to you.
All of this would be done by exactly the same physical processes that produced you. It doesn't require that the universe be filled with a random distribution of all possible physical states; it only requires that whatever random processes contributed to your existence will randomly occur again, which they certainly will in a big enough universe. I won't attempt to quantify it, but if a googolplex meters is not enough, just make it bigger. :)
As for the history of this idea, it seems quite similar to the notion of Poincaré recurrence, which dates back to 1890. That idea concerns repetition of states over time, due to arbitrarily-unlikely fluctuations occurring if you wait long enough, but it's straightforward to think also of repetition in space due to arbitrarily-unlikely fluctuations occurring if you have enough space for them to occur in.
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Another such argument was made by Jaume Garriga and Alexander Vilenkin, see here:
A generic prediction of inflation is that the thermalized region we inhabit is spatially infinite. Thus, it contains an infinite number of regions of the same size as our observable universe, which we shall denote as O-regions. We argue that the number of possible histories which may take place inside of an O-region, from the time of recombination up to the present time, is finite. Hence, there are an infinite number of O-regions with identical histories up to the present, but which need not be identical in the future. Moreover, all histories which are not forbidden by conservation laws will occur in a finite fraction of all O-regions. The ensemble of O-regions is reminiscent of the ensemble of universes in the many-world picture of quantum mechanics. An important difference, however, is that other O-regions are unquestionably real.
But you can just consider all the useful information stored in your brain that you are aware of. Even if there exists someone who is not an exact physical copy, it can still be identical to you if whatever algorithm his/her brain is executing is the same as the one your brain is executing. This means that the local environment only needs to be approximately the same. A copy of me doesn't have to have the exact same number of hairs growing in his head, because I have never counted the exact number. The Earth's radius can be several meters more or less. The copy of the Milky Way galaxy does not need to contain the exact same number of stars. Only what I am aware of must be the same, and it's only the awareness that counts not if it is actually true, although the two things will be strongly correlated.
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So, what you're saying is, there will be some exact copies and some near-exact copies who won't even be able to realize that they aren't exact copies. – Iszi Sep 25 '15 at 20:32
@Iszi, that's indeed what I'm saying. Also, I believe (but have to admit that it's just my belief), that it's essential to think of ourselves as ensembles of nearly identical states instead of a sharply defined state. If you think of yourself as a machine in some well defined state, you get into philosophical problems that can be addressed better if you replace the machine by a set of machines in slightly different states. This makes the algorithm executed by the machines well defined, at the expense of not knowing exactly what state it is in which it couldn't know anyway. – Count Iblis Sep 25 '15 at 20:42
## protected by Community♦Dec 11 '14 at 15:23
Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site.
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https://doc.cgal.org/4.14/Polygon_mesh_processing/group__PkgPolygonMeshProcessingRef.html
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CGAL 4.14 - Polygon Mesh Processing
Polygon Mesh Processing Reference
Sébastien Loriot, Jane Tournois, Ilker O. Yaz
This package provides a collection of methods and classes for polygon mesh processing, ranging from basic operations on simplices, to complex geometry processing algorithms.
Introduced in: CGAL 4.7
Depends on: documented for each function; CGAL and Solvers
BibTeX: cgal:lty-pmp-19a
Windows Demo: Polyhedron demo
Common Demo Dlls: dlls
## Parameters
Optional parameters of the functions of this package are implemented as Named Parameters. The page Named Parameters describes their usage and provides a list of the parameters that are used in this package.
## Hole Filling Functions
• CGAL::Polygon_mesh_processing::triangulate_hole()
• CGAL::Polygon_mesh_processing::triangulate_and_refine_hole()
• CGAL::Polygon_mesh_processing::triangulate_refine_and_fair_hole()
• CGAL::Polygon_mesh_processing::triangulate_hole_polyline()
## Predicate Functions
• CGAL::Polygon_mesh_processing::does_self_intersect()
• CGAL::Polygon_mesh_processing::self_intersections()
• CGAL::Polygon_mesh_processing::do_intersect()
• CGAL::Polygon_mesh_processing::intersecting_meshes()
• CGAL::Polygon_mesh_processing::is_degenerate_edge()
• CGAL::Polygon_mesh_processing::degenerate_edges()
• CGAL::Polygon_mesh_processing::is_degenerate_triangle_face()
• CGAL::Polygon_mesh_processing::degenerate_faces()
• CGAL::Polygon_mesh_processing::is_needle_triangle_face()
• CGAL::Polygon_mesh_processing::is_cap_triangle_face()
## Orientation Functions
• CGAL::Polygon_mesh_processing::orient_polygon_soup()
• CGAL::Polygon_mesh_processing::orient()
• CGAL::Polygon_mesh_processing::orient_to_bound_a_volume()
• CGAL::Polygon_mesh_processing::is_outward_oriented()
• CGAL::Polygon_mesh_processing::reverse_face_orientations()
## Combinatorial Repairing Functions
• CGAL::Polygon_mesh_processing::merge_duplicate_points_in_polygon_soup()
• CGAL::Polygon_mesh_processing::merge_duplicate_polygons_in_polygon_soup()
• CGAL::Polygon_mesh_processing::remove_isolated_points_in_polygon_soup()
• CGAL::Polygon_mesh_processing::repair_polygon_soup()
• CGAL::Polygon_mesh_processing::stitch_borders()
• CGAL::Polygon_mesh_processing::is_polygon_soup_a_polygon_mesh()
• CGAL::Polygon_mesh_processing::polygon_soup_to_polygon_mesh()
• CGAL::Polygon_mesh_processing::remove_isolated_vertices()
• CGAL::Polygon_mesh_processing::is_non_manifold_vertex()
• CGAL::Polygon_mesh_processing::duplicate_non_manifold_vertices()
• CGAL::Polygon_mesh_processing::merge_duplicated_vertices_in_boundary_cycle()
• CGAL::Polygon_mesh_processing::merge_duplicated_vertices_in_boundary_cycles()
## Normal Computation Functions
• CGAL::Polygon_mesh_processing::compute_face_normal()
• CGAL::Polygon_mesh_processing::compute_face_normals()
• CGAL::Polygon_mesh_processing::compute_vertex_normal()
• CGAL::Polygon_mesh_processing::compute_vertex_normals()
• CGAL::Polygon_mesh_processing::compute_normals()
## Corefinement and Boolean Operation Functions
• CGAL::Polygon_mesh_processing::corefine_and_compute_union()
• CGAL::Polygon_mesh_processing::corefine_and_compute_difference()
• CGAL::Polygon_mesh_processing::corefine_and_compute_intersection()
• CGAL::Polygon_mesh_processing::corefine_and_compute_boolean_operations()
• CGAL::Polygon_mesh_processing::corefine()
• CGAL::Polygon_mesh_processing::surface_intersection()
• CGAL::Polygon_mesh_processing::clip()
• CGAL::Polygon_mesh_processing::does_bound_a_volume()
## Distance Functions
• CGAL::Polygon_mesh_processing::approximate_Hausdorff_distance()
• CGAL::Polygon_mesh_processing::approximate_symmetric_Hausdorff_distance()
• CGAL::Polygon_mesh_processing::approximate_max_distance_to_point_set()
• CGAL::Polygon_mesh_processing::max_distance_to_triangle_mesh()
• CGAL::Polygon_mesh_processing::sample_triangle_mesh()
## Feature Detection Functions
• CGAL::Polygon_mesh_processing::sharp_edges_segmentation()
• CGAL::Polygon_mesh_processing::detect_sharp_edges()
• CGAL::Polygon_mesh_processing::detect_vertex_incident_patches()
## Collision Detection
• CGAL::Rigid_triangle_mesh_collision_detection
## Miscellaneous
• CGAL::Polygon_mesh_slicer
• CGAL::Side_of_triangle_mesh
• CGAL::Polygon_mesh_processing::bbox()
• CGAL::Polygon_mesh_processing::vertex_bbox()
• CGAL::Polygon_mesh_processing::edge_bbox()
• CGAL::Polygon_mesh_processing::face_bbox()
• CGAL::Polygon_mesh_processing::border_halfedges()
• CGAL::Polygon_mesh_processing::extract_boundary_cycles()
• CGAL::Polygon_mesh_processing::transform()
## Modules
Named Parameters for Polygon Mesh Processing
In this package, all functions optional parameters are implemented as BGL optional named parameters (see Named Parameters for more information on how to use them).
Concepts
Connected Components
Two faces are in the same connected component if there is a path of adjacent faces such that all edges between two consecutive faces of the path are not marked as constrained.
Hole Filling
Functions to fill holes given as a range of halfedges or as range of points.
Meshing
Functions to triangulate faces, and to refine and fair regions of a polygon mesh.
Normal Computation
Functions to compute unit normals for individual/all vertices or faces.
Geometric Measure Functions
Functions to compute lengths of edges and borders, areas of faces and patches, as well as volumes of closed meshes.
Orientation Functions
Functions to compute or change the orientation of faces and surfaces.
Intersection Functions
Functions to test if there are self intersections, and to report faces that do intersect.
Combinatorial Repairing
Functions to repair polygon soups and polygon meshes.
Distance Functions
Functions to compute the distance between meshes, between a mesh and a point set and between a point set and a mesh.
Corefinement and Boolean Operations
Functions to corefine triangulated surface meshes and compute triangulated surface meshes of the union, difference and intersection of the bounded volumes.
Feature Detection Functions
Functions to detect sharp edges and surface patches of polygon meshes.
Intersection Detection Functions
Functions to detect intersections.
## Files
file polygon_mesh_processing.h
Convenience header file including the headers for all the free functions of this package.
## Classes
class CGAL::Polygon_mesh_slicer< TriangleMesh, Traits, VertexPointMap, AABBTree, UseParallelPlaneOptimization >
Function object that computes the intersection of a plane with a triangulated surface mesh. More...
class CGAL::Side_of_triangle_mesh< TriangleMesh, GeomTraits, VertexPointMap >
This class provides an efficient point location functionality with respect to a domain bounded by one or several disjoint closed triangle meshes. More...
## Functions
template<typename PolygonMesh , typename CGAL_PMP_NP_TEMPLATE_PARAMETERS >
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::bbox (const PolygonMesh &pmesh, const CGAL_PMP_NP_CLASS &np)
computes a bounding box of a polygon mesh. More...
template<typename PolygonMesh , typename NamedParameters >
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::vertex_bbox (typename boost::graph_traits< PolygonMesh >::vertex_descriptor vd, const PolygonMesh &pmesh, const NamedParameters &np)
computes a bounding box of a vertex of a polygon mesh. More...
template<typename PolygonMesh , typename NamedParameters >
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::edge_bbox (typename boost::graph_traits< PolygonMesh >::edge_descriptor ed, const PolygonMesh &pmesh, const NamedParameters &np)
computes a bounding box of an edge of a polygon mesh. More...
template<typename PolygonMesh , typename NamedParameters >
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::face_bbox (typename boost::graph_traits< PolygonMesh >::face_descriptor fd, const PolygonMesh &pmesh, const NamedParameters &np)
computes a bounding box of a face of a polygon mesh. More...
template<typename PolygonMesh , typename CGAL_PMP_NP_TEMPLATE_PARAMETERS >
CGAL_DEPRECATED CGAL::Bbox_3 CGAL::Polygon_mesh_processing::bbox_3 (const PolygonMesh &pmesh, const CGAL_PMP_NP_CLASS &np)
template<typename PolygonMesh , typename FaceRange , typename HalfedgeOutputIterator , typename NamedParameters >
HalfedgeOutputIterator CGAL::Polygon_mesh_processing::border_halfedges (const FaceRange &faces, const PolygonMesh &pmesh, HalfedgeOutputIterator out, const NamedParameters &np)
collects the border halfedges of a surface patch defined as a face range. More...
template<typename PolygonMesh , typename OutputIterator >
OutputIterator CGAL::Polygon_mesh_processing::extract_boundary_cycles (PolygonMesh &pm, OutputIterator out)
extracts boundary cycles as a list of halfedges, with one halfedge per border. More...
template<class Transformation , class PolygonMesh , class NamedParameters >
void CGAL::Polygon_mesh_processing::transform (const Transformation &transformation, PolygonMesh &mesh, const NamedParameters &np)
applies a transformation to every vertex of a PolygonMesh. More...
## ◆ bbox()
template<typename PolygonMesh , typename CGAL_PMP_NP_TEMPLATE_PARAMETERS >
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::bbox ( const PolygonMesh & pmesh, const CGAL_PMP_NP_CLASS & np )
#include <CGAL/Polygon_mesh_processing/bbox.h>
computes a bounding box of a polygon mesh.
Template Parameters
PolygonMesh a model of HalfedgeListGraph NamedParameters a sequence of Named Parameters
Parameters
pmesh a polygon mesh np optional sequence of Named Parameters among the ones listed below
Named Parameters
vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh geom_traits an instance of a geometric traits class, providing the functor Construct_bbox_3 and the function Construct_bbox_3 construct_bbox_3_object(). Construct_bbox_3 must provide BBox_3 operator()(Point_3) where Point_3 is the value type of the vertex point map.
Returns
a bounding box of pmesh
## ◆ bbox_3()
template<typename PolygonMesh , typename CGAL_PMP_NP_TEMPLATE_PARAMETERS >
CGAL_DEPRECATED CGAL::Bbox_3 CGAL::Polygon_mesh_processing::bbox_3 ( const PolygonMesh & pmesh, const CGAL_PMP_NP_CLASS & np )
#include <CGAL/Polygon_mesh_processing/bbox.h>
Deprecated:
This function is deprecated since CGAL 4.10, CGAL::Polygon_mesh_processing::bbox() should be used instead.
## ◆ border_halfedges()
template<typename PolygonMesh , typename FaceRange , typename HalfedgeOutputIterator , typename NamedParameters >
HalfedgeOutputIterator CGAL::Polygon_mesh_processing::border_halfedges ( const FaceRange & faces, const PolygonMesh & pmesh, HalfedgeOutputIterator out, const NamedParameters & np )
#include <CGAL/Polygon_mesh_processing/border.h>
collects the border halfedges of a surface patch defined as a face range.
For each returned halfedge h, opposite(h, pmesh) belongs to a face of the patch, but face(h, pmesh) does not belong to the patch.
Template Parameters
PolygonMesh model of HalfedgeGraph. If PolygonMesh has an internal property map for CGAL::face_index_t and no face_index_map is given as a named parameter, then the internal one must be initialized FaceRange range of boost::graph_traits::face_descriptor, model of Range. Its iterator type is InputIterator. HalfedgeOutputIterator model of OutputIterator holding boost::graph_traits::halfedge_descriptor for patch border NamedParameters a sequence of Named Parameters
Parameters
pmesh the polygon mesh to which faces belong faces the range of faces defining the patch whose border halfedges are collected out the output iterator that collects the border halfedges of the patch, seen from outside. np optional sequence of Named Parameters among the ones listed below
Named Parameters
face_index_map a property map containing the index of each face of pmesh
Returns
out
Examples:
Polygon_mesh_processing/isotropic_remeshing_example.cpp.
## ◆ edge_bbox()
template<typename PolygonMesh , typename NamedParameters >
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::edge_bbox ( typename boost::graph_traits< PolygonMesh >::edge_descriptor ed, const PolygonMesh & pmesh, const NamedParameters & np )
#include <CGAL/Polygon_mesh_processing/bbox.h>
computes a bounding box of an edge of a polygon mesh.
Template Parameters
PolygonMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
ed a descriptor of an edge in pmesh pmesh a polygon mesh np optional sequence of Named Parameters among the ones listed below
Named Parameters
vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh geom_traits an instance of a geometric traits class, providing the functor Construct_bbox_3 and the function Construct_bbox_3 construct_bbox_3_object(). Construct_bbox_3 must provide BBox_3 operator()(Point_3) where Point_3 is the value type of the vertex point map.
Returns
a bounding box of pmesh
## ◆ extract_boundary_cycles()
template<typename PolygonMesh , typename OutputIterator >
OutputIterator CGAL::Polygon_mesh_processing::extract_boundary_cycles ( PolygonMesh & pm, OutputIterator out )
#include <CGAL/Polygon_mesh_processing/border.h>
extracts boundary cycles as a list of halfedges, with one halfedge per border.
Template Parameters
PolygonMesh a model of HalfedgeListGraph OutputIterator a model of OutputIterator holding objects of type boost::graph_traits::halfedge_descriptor
Parameters
pm a polygon mesh out an output iterator where the border halfedges will be put
## ◆ face_bbox()
template<typename PolygonMesh , typename NamedParameters >
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::face_bbox ( typename boost::graph_traits< PolygonMesh >::face_descriptor fd, const PolygonMesh & pmesh, const NamedParameters & np )
#include <CGAL/Polygon_mesh_processing/bbox.h>
computes a bounding box of a face of a polygon mesh.
Template Parameters
PolygonMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
fd a descriptor of a face in pmesh pmesh a polygon mesh np optional sequence of Named Parameters among the ones listed below
Named Parameters
vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh geom_traits an instance of a geometric traits class, providing the functor Construct_bbox_3 and the function Construct_bbox_3 construct_bbox_3_object(). Construct_bbox_3 must provide BBox_3 operator()(Point_3) where Point_3 is the value type of the vertex point map.
Returns
a bounding box of pmesh
## ◆ transform()
template<class Transformation , class PolygonMesh , class NamedParameters >
void CGAL::Polygon_mesh_processing::transform ( const Transformation & transformation, PolygonMesh & mesh, const NamedParameters & np )
#include <CGAL/Polygon_mesh_processing/transform.h>
applies a transformation to every vertex of a PolygonMesh.
Template Parameters
Transformation a functor that has an operator()(Point_3), with Point_3 the value_type of vertex_point_map (see below). Such a functor can be CGAL::Aff_transformation_3 for example. PolygonMesh a model of VertexListGraph NamedParameters a sequence of Named Parameters
Parameters
transformation the transformation functor to apply to the points of mesh. mesh the PolygonMesh to transform. np optional sequence of Named Parameters for Polygon Mesh Processing for mesh, among the ones listed below
• Named Parameters
vertex_point_map the property map with the points associated to the vertices of mesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh
## ◆ vertex_bbox()
template<typename PolygonMesh , typename NamedParameters >
CGAL::Bbox_3 CGAL::Polygon_mesh_processing::vertex_bbox ( typename boost::graph_traits< PolygonMesh >::vertex_descriptor vd, const PolygonMesh & pmesh, const NamedParameters & np )
#include <CGAL/Polygon_mesh_processing/bbox.h>
computes a bounding box of a vertex of a polygon mesh.
Template Parameters
PolygonMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
vd a descriptor of a vertex in pmesh pmesh a polygon mesh np optional sequence of Named Parameters among the ones listed below
Named Parameters
vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh geom_traits an instance of a geometric traits class, providing the functor Construct_bbox_3 and the function Construct_bbox_3 construct_bbox_3_object(). Construct_bbox_3 must provide BBox_3 operator()(Point_3) where Point_3 is the value type of the vertex point map.
Returns
a bounding box of pmesh
|
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http://clay6.com/qa/18774/if-a-b-c-are-the-angles-of-a-delta-le-then-the-value-of-the-determinant-beg
|
Browse Questions
If $A,B,C$ are the angles of a $\Delta$le then the value of the determinant $\small\begin{vmatrix}-1+\cos B&\cos C+\cos B&\cos B\\\cos C+\cos A&-1+\cos A&\cos A\\-1+\cos B&-1+\cos B&-1\end{vmatrix}$ is
$(a)\;0\qquad(b)\;1\qquad(c)\;-1\qquad(d)\;2$
We have
$\begin{vmatrix}-1+\cos B&\cos C+\cos B&\cos B\\\cos C+\cos A&-1+\cos A&\cos A\\-1+\cos B&-1+\cos B&-1\end{vmatrix}$
Apply $C_1\Rightarrow C_1-C_3$ and $C_2\rightarrow C_2-C_3$
$\begin{vmatrix}-1&\cos C&\cos B\\cos C&-1&\cos A\\\cos B&\cos A&-1\end{vmatrix}$
Multiply and divide by a in column 1
Apply $C_1\rightarrow C_1+bC_2+cC_3$
$\large\frac{1}{a}$$\begin{vmatrix}-a&\cos C&\cos B\\a\cos C&-1&\cos A\\acos B&\cos A&-1\end{vmatrix} \Rightarrow \large\frac{1}{a}$$\begin{vmatrix}0&\cos C&\cos B\\0&-1&\cos A\\0&\cos A&-1\end{vmatrix}$
$\Rightarrow 0$
Hence (a) is the correct answer.
edited Mar 20, 2014
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http://openturns.github.io/openturns/latest/user_manual/_generated/openturns.Field.html
|
Field¶
class Field(*args)
Base class for Fields.
Available constructors:
Field(mesh, dim)
Field(mesh, values)
Parameters: mesh : Mesh Each vertice of the mesh is in a domain of . dim : int Dimension of the values. values : 2-d sequence of float of dimension The values associated to the vertices of the mesh. The size of values is equal to the number of vertices in the associated mesh. So we must have the equality between values.getSize() and mesh.getVerticesNumber().
Notes
A field is an association between vertices and values:
where the are the vertices of a mesh of the domain and are the associated values.
Mathematically speaking, is an element where is the number of vertices of the mesh of the domain .
Examples
Create a field:
>>> import openturns as ot
>>> myVertices = [[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [1.5, 1.0], [2.0, 1.5], [0.5, 1.5]]
>>> mySimplicies = [[0,1,2], [1,2,3], [2,3,4], [2,4,5], [0,2,5]]
>>> myMesh = ot.Mesh(myVertices, mySimplicies)
>>> myValues = [[2.0],[2.5],[4.0], [4.5], [6.0], [7.0]]
>>> myField = ot.Field(myMesh, myValues)
Draw the field:
>>> myGraph = myField.draw()
Methods
asDeformedMesh(*args) Get the mesh deformed according to the values of the field. draw() Draw the first marginal of the field if the input dimension is less than 2. drawMarginal([index, interpolate]) Draw one marginal field if the input dimension is less than 2. exportToVTKFile(fileName) Create the VTK format file of the field. getClassName() Accessor to the object’s name. getDescription() Get the description of the field values. getId() Accessor to the object’s id. getImplementation(*args) Accessor to the underlying implementation. getInputDimension() Get the dimension of the domain . getInputMean() Get the input weighted mean of the values of the field. getMarginal(*args) Marginal accessor. getMesh() Get the mesh on which the field is defined. getName() Accessor to the object’s name. getOutputDimension() Get the dimension of the values. getSize() Get the number of values inside the field. getTimeGrid() Get the mesh as a time grid if it is 1D and regular. getValueAtIndex(index) Get the value of the field at the vertex of the given index. getValues() Get the values of the field. setDescription(description) Set the description of the vertices and values of the field. setName(name) Accessor to the object’s name. setValueAtIndex(index, val) Assign the value of the field to the vertex at the given index. setValues(values) Assign values to a field.
__init__(*args)
Initialize self. See help(type(self)) for accurate signature.
asDeformedMesh(*args)
Get the mesh deformed according to the values of the field.
Parameters: verticesPadding : sequence of int The positions at which the coordinates of vertices are set to zero when extending the vertices dimension. By default the sequence is empty. valuesPadding : sequence of int The positions at which the components of values are set to zero when extending the values dimension. By default the sequence is empty. deformedMesh : Mesh The initial mesh is deformed as follows: each vertex of the mesh is translated by the value of the field at this vertex. Only works when the input dimension : is equal to the dimension of the field after extension.
draw()
Draw the first marginal of the field if the input dimension is less than 2.
Returns: graph : Graph Calls drawMarginal(0, False).
drawMarginal(index=0, interpolate=True)
Draw one marginal field if the input dimension is less than 2.
Parameters: index : int The selected marginal. interpolate : bool Indicates whether the values at the vertices are linearly interpolated. graph : Graph If the dimension of the mesh is and interpolate=True: it draws the graph of the piecewise linear function based on the selected marginal values of the field and the vertices coordinates (in ). If the dimension of the mesh is and interpolate=False: it draws the cloud of points which coordinates are (vertex, value of the marginal index). If the dimension of the mesh is and interpolate=True: it draws several iso-values curves of the selected marginal, based on a piecewise linear interpolation within the simplices (triangles) of the mesh. You get an empty graph if the vertices are not connected through simplicies. If the dimension of the mesh is and interpolate=False: if the vertices are connected through simplicies, each simplex is drawn with a color defined by the mean of the values of the vertices of the simplex. In the other case, it draws each vertex colored by its value.
exportToVTKFile(fileName)
Create the VTK format file of the field.
Parameters: myVTKFile : str Name of the output file. No extension is append to the filename.
Notes
Creates the VTK format file that contains the mesh and the associated values that can be visualised with the open source software Paraview .
getClassName()
Accessor to the object’s name.
Returns: class_name : str The object class name (object.__class__.__name__).
getDescription()
Get the description of the field values.
Returns: description : Description Description of the vertices and values of the field, size .
getId()
Accessor to the object’s id.
Returns: id : int Internal unique identifier.
getImplementation(*args)
Accessor to the underlying implementation.
Returns: impl : Implementation The implementation class.
getInputDimension()
Get the dimension of the domain .
Returns: n : int Dimension of the domain : .
getInputMean()
Get the input weighted mean of the values of the field.
Returns: inputMean : Point Weighted mean of the values of the field, weighted by the volume of each simplex.
Notes
The input mean of the field is defined by:
where is the simplex of index of the mesh, its volume and the values of the field associated to the vertices of , and .
getMarginal(*args)
Marginal accessor.
Parameters: i : int or sequence of int Index of the marginal. value : Marginal field.
getMesh()
Get the mesh on which the field is defined.
Returns: mesh : Mesh Mesh over which the domain is discretized.
getName()
Accessor to the object’s name.
Returns: name : str The name of the object.
getOutputDimension()
Get the dimension of the values.
Returns: d : int Dimension of the field values: .
getSize()
Get the number of values inside the field.
Returns: size : int Number of vertices in the mesh.
getTimeGrid()
Get the mesh as a time grid if it is 1D and regular.
Returns: timeGrid : RegularGrid Mesh of the field when it can be interpreted as a RegularGrid. We check if the vertices of the mesh are scalar and are regularly spaced in but we don’t check if the connectivity of the mesh is conform to the one of a regular grid (without any hole and composed of ordered instants).
getValueAtIndex(index)
Get the value of the field at the vertex of the given index.
Parameters: index : int Vertex of the mesh of index index. value : Point The value of the field associated to the selected vertex, in .
getValues()
Get the values of the field.
Returns: values : Sample Values associated to the mesh. The size of the sample is the number of vertices of the mesh and the dimension is the dimension of the values (). Identical to getSample().
setDescription(description)
Set the description of the vertices and values of the field.
Parameters: myDescription : Description Description of the field values. Must be of size and give the description of the vertices and the values.
setName(name)
Accessor to the object’s name.
Parameters: name : str The name of the object.
setValueAtIndex(index, val)
Assign the value of the field to the vertex at the given index.
Parameters: index : int Index that characterizes one vertex of the mesh. value : New value assigned to the selected vertex.
setValues(values)
Assign values to a field.
Parameters: values : 2-d sequence of float Values assigned to the mesh. The size of the values is the number of vertices of the mesh and the dimension is .
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https://arxiv.org/abs/1502.06720
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gr-qc
(what is this?)
# Title: Charged isotropic non-Abelian dyonic black branes
Abstract: We construct black holes with a Ricci flat horizon in Einstein--Yang-Mills theory with a negative cosmological constant, which approach asymptotically an AdS$_d$ spacetime background (with $d\geq 4$). These solutions are isotropic, $i.e.$ all space directions in a hypersurface of constant radial and time coordinates are equivalent, and possess both electric and magnetic fields. We find that the basic properties of the non-Abelian solutions are similar to those of the dyonic isotropic branes in Einstein-Maxwell theory (which, however, exist in even spacetime dimensions only). These black branes possess a nonzero magnetic field strength on the flat boundary metric, which leads to a divergent mass of these solutions, as defined in the usual way. However, a different picture is found for odd spacetime dimensions, where a non-Abelian Chern-Simons term can be incorporated in the action. This allows for black brane solutions with a magnetic field which vanishes asymptotically.
Comments: 14 pages, 4 figures Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th) DOI: 10.1016/j.physletb.2015.04.029 Cite as: arXiv:1502.06720 [gr-qc] (or arXiv:1502.06720v1 [gr-qc] for this version)
## Submission history
From: Brihaye Yves [view email]
[v1] Tue, 24 Feb 2015 09:15:07 GMT (33kb)
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|
https://farside.ph.utexas.edu/teaching/336L/Fluidhtml/node14.html
|
Next: Equations of Incompressible Fluid Up: Mathematical Models of Fluid Previous: Navier-Stokes Equation
# Energy Conservation
Consider a fixed volume surrounded by a surface . The total energy content of the fluid contained within is
(1.59)
where the first and second terms on the right-hand side are the net internal and kinetic energies, respectively. Here, is the internal (i.e., thermal) energy per unit mass of the fluid. The energy flux across , and out of , is [cf., Equation (1.29)]
(1.60)
where use has been made of the tensor divergence theorem. According to the first law of thermodynamics, the rate of increase of the energy contained within , plus the net energy flux out of , is equal to the net rate of work done on the fluid within , minus the net heat flux out of : that is,
(1.61)
where is the net rate of work, and the net heat flux. It can be seen that is the effective energy generation rate within [cf., Equation (1.31)].
The net rate at which volume and surface forces do work on the fluid within is
(1.62)
where use has been made of the tensor divergence theorem.
Generally speaking, heat flow in fluids is driven by temperature gradients. Let the be the Cartesian components of the heat flux density at position and time . It follows that the heat flux across a surface element , located at point , is . Let be the temperature of the fluid at position and time . Thus, a general temperature gradient takes the form . Let us assume that there is a linear relationship between the components of the local heat flux density and the local temperature gradient: that is,
(1.63)
where the are the components of a second-rank tensor (which can be functions of position and time). In an isotropic fluid we would expect to be an isotropic tensor. (See Section B.5.) However, the most general second-order isotropic tensor is simply a multiple of . Hence, we can write
(1.64)
where is termed the thermal conductivity of the fluid. It follows that the most general expression for the heat flux density in an isotropic fluid is
(1.65)
or, equivalently,
(1.66)
Moreover, it is a matter of experience that heat flows down temperature gradients: that is, . We conclude that the net heat flux out of volume is
(1.67)
where use has been made of the tensor divergence theorem.
Equations (1.59)-(1.62) and (1.67) can be combined to give the following energy conservation equation:
(1.68)
However, this result is valid irrespective of the size, shape, or location of volume , which is only possible if
(1.69)
everywhere inside the fluid. Expanding some of the derivatives, and rearranging, we obtain
(1.70)
where use has been made of the continuity equation, (1.40). The scalar product of with the fluid equation of motion, (1.53), yields
(1.71)
Combining the previous two equations, we get
(1.72)
Finally, making use of Equation (1.26), we deduce that the energy conservation equation for an isotropic Newtonian fluid takes the general form
(1.73)
Here,
(1.74)
is the rate of heat generation per unit volume due to viscosity. When written in vector form, Equation (1.73) becomes
(1.75)
According to the previous equation, the internal energy per unit mass of a co-moving fluid element evolves in time as a consequence of work done on the element by pressure as its volume changes, viscous heat generation due to flow shear, and heat conduction.
Next: Equations of Incompressible Fluid Up: Mathematical Models of Fluid Previous: Navier-Stokes Equation
Richard Fitzpatrick 2016-03-31
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http://export.arxiv.org/list/gr-qc/1806?skip=100&show=25
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# General Relativity and Quantum Cosmology
## Authors and titles for Jun 2018, skipping first 100
[ total of 418 entries: 1-25 | 26-50 | 51-75 | 76-100 | 101-125 | 126-150 | 151-175 | 176-200 | ... | 401-418 ]
[ showing 25 entries per page: fewer | more | all ]
[101]
Title: Inflation in an effective gravitational model & asymptotic safety
Journal-ref: Phys. Rev. D 98, 043505 (2018)
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
[102]
Title: Lensing observables: Massless dyonic vis-à-vis Ellis wormhole
Journal-ref: Phys. Rev. D 97, 124027 (2018)
Subjects: General Relativity and Quantum Cosmology (gr-qc)
[103]
Title: Unequal binary configurations of interacting Kerr black holes
Journal-ref: Phys. Lett. B 786: 466-471 (2018)
Subjects: General Relativity and Quantum Cosmology (gr-qc)
[104]
Title: Lagrangian theory of structure formation in relativistic cosmology. V. Irrotational fluids
Comments: 28 pages, 7 captioned figures, matches published version in PRD
Journal-ref: Phys. Rev. D 98, 043507 (2018)
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO)
[105]
Title: Gedanken Tests for Correlated Michelson Interferometers (One- interferometer tests and two-interferometer tests: the role of cosmologically-implemented models including Poincaré particles)
Comments: 4 pages, two figures; ICEEA2018 invited contribution paper for TPC Chair - AEEA2018- AMMSA2018; Atlantis Press on Advances in Intelligent Systems Research
Subjects: General Relativity and Quantum Cosmology (gr-qc)
[106]
Title: Abbott-Deser-Tekin like conserved quantities in Lanczos-Lovelock gravity: beyond Killing diffeomorphisms
Comments: A little change in the title, a little bit modification in the presentation, results are unchanged, to appear in the Classical and Quantum Gravity
Journal-ref: Class. Quantum Grav. 36 (2019) no.6, 065009
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
[107]
Title: Scattering of co-current surface waves on an analogue black hole
Journal-ref: Phys. Rev. Lett. 124, 141101 (2020)
Subjects: General Relativity and Quantum Cosmology (gr-qc); Fluid Dynamics (physics.flu-dyn)
[108]
Title: Weak-field limit and regular solutions in polynomial higher-derivative gravities
Comments: 37 pages. References added, some misprints corrected; matches the version published in EPJC
Journal-ref: Eur. Phys. J. C 79, 217 (2019)
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
[109]
Title: Waveforms of compact binary inspiral gravitational radiation in screened modified gravity
Comments: 21 pages, to appear in PRD
Journal-ref: Phys. Rev. D 98, 083023 (2018)
Subjects: General Relativity and Quantum Cosmology (gr-qc)
[110]
Title: Structure of Polytropic Stars in General Relativity
Comments: This is a replacement and major revision of arXiv:1605.08650
Subjects: General Relativity and Quantum Cosmology (gr-qc); Solar and Stellar Astrophysics (astro-ph.SR)
[111]
Title: Thermodynamics of regular black holes with cosmic strings
Comments: Accepted for publication in EPJ Plus, 6 pages
Journal-ref: Eur. Phys. J. Plus (2018) 133: 377
Subjects: General Relativity and Quantum Cosmology (gr-qc)
[112]
Title: Effective dynamics of the Schwarzschild black hole interior with inverse triad corrections
Comments: 24 pages, 7 figures; v2: title, abstract and conclusion modified and some comments added for more clarity
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[113]
Title: Universal electromagnetic fields
Journal-ref: Class. Quantum Grav. 35 (2018) 175017
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
[114]
Title: Noether Current, Black Hole Entropy and Spacetime Torsion
Journal-ref: Phys. Lett. B 786, 432 (2018)
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
[115]
Title: Symmetries of Differential Equations in Cosmology
Comments: 44 pages, review article to appear in Symmetry
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[116]
Title: The geometry and entanglement entropy of surfaces in loop quantum gravity
Journal-ref: Phys. Rev. D 98, 066009 (2018)
Subjects: General Relativity and Quantum Cosmology (gr-qc)
[117]
Title: Horizon Quantum Mechanics of collapsing shells
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
[118]
Title: Rotation of Polarization Vector, in Case of Non-Inertial Rotational Frame
Subjects: General Relativity and Quantum Cosmology (gr-qc)
[119]
Title: Iron Line Spectroscopy of Black Holes in Vector-Tensor Galileons Modified Gravity
Comments: 11 pages, 6 figures. v2: fixed a few typos
Journal-ref: Phys. Rev. D 98, 044024 (2018)
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Astrophysical Phenomena (astro-ph.HE)
[120]
Title: From parabolic to loxodromic BMS transformations
Comments: 16 pages, 1 figure. In the final version, a missing symbol in Eq. (1.1) has been restored
Journal-ref: Gen. Relativ. Gravit. 50 (11), 141 (2018)
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
[121]
Journal-ref: Phys. Rev. D 98, 064008 (2018)
Subjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics of Galaxies (astro-ph.GA); High Energy Physics - Phenomenology (hep-ph)
[122]
Title: Kinematic model-independent reconstruction of Palatini $f(R)$ cosmology
Comments: 10 pages, 6 figures. Accepted for publication in Gen. Rel. Grav
Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
[123]
Title: Weak gravitational lensing by Kerr-MOG Black Hole and Gauss-Bonnet theorem
Comments: 9 pages, 3 Figures. Accepted for publication in Annals of Physics
Journal-ref: Annals of Physics 411 (2019) 167978
Subjects: General Relativity and Quantum Cosmology (gr-qc)
[124]
Title: Stealth Chaos due to Frame Dragging
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http://git.0pointer.net/dbus.git/tree/dbus/dbus-desktop-file.h?id=a0e8a279802aa9f26a3ccf3f8ee27110a1509d19
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summaryrefslogtreecommitdiffstats log msg author committer range
path: root/dbus/dbus-desktop-file.h
blob: 812d82f362018685e14d43fc4b6bfcaae0ca8228 (plain)
```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 ``` ``````/* -*- mode: C; c-file-style: "gnu"; indent-tabs-mode: nil; -*- */ /* desktop-file.h .desktop file parser * * Copyright (C) 2003 CodeFactory AB * * Licensed under the Academic Free License version 2.1 * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA * */ #ifndef BUS_DESKTOP_FILE_H #define BUS_DESKTOP_FILE_H #include #include #define DBUS_DESKTOP_PARSE_ERROR_INVALID_SYNTAX "org.freedesktop.DBus.DesktopParseError.InvalidSyntax" #define DBUS_DESKTOP_PARSE_ERROR_INVALID_ESCAPES "org.freedesktop.DBus.DesktopParseError.InvalidEscapes" #define DBUS_DESKTOP_PARSE_ERROR_INVALID_CHARS "org.freedesktop.DBus.DesktopParseError.InvalidChars" typedef struct DBusDesktopFile DBusDesktopFile; DBusDesktopFile *_dbus_desktop_file_load (DBusString *filename, DBusError *error); void _dbus_desktop_file_free (DBusDesktopFile *file); dbus_bool_t _dbus_desktop_file_get_raw (DBusDesktopFile *desktop_file, const char *section_name, const char *keyname, const char **val); dbus_bool_t _dbus_desktop_file_get_string (DBusDesktopFile *desktop_file, const char *section, const char *keyname, char **val, DBusError *error); #endif /* BUS_DESKTOP_FILE_H */ ``````
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http://www.emis.de/classics/Erdos/cit/79605050.htm
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## Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 796.05050
Autor: Erdös, Paul; Faudree, Ralph J.; Rousseau, C.C.; Schelp, R.H.
Title: A local density condition for triangles. (In English)
Source: Discrete Math. 127, No.1-3, 153-161 (1994).
Review: Authors' abstract: Let G be a graph on n vertices and let \alpha and \beta be real numbers, 0 < \alpha, \beta < 1. Further, let G satisfy the condition that each \lfloor \alpha n \rfloor subset of its vertex set spans at least \beta n2 edges. The following question is considered. For a fixed \alpha what is the smallest value of \beta such that G contains a triangle.
Reviewer: S.Stahl (Lawrence)
Classif.: * 05C35 Extremal problems (graph theory)
Keywords: local density condition; triangle
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag
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http://cs.stackexchange.com/questions/9987/tasks-in-which-recursion-is-either-the-fastest-or-only-way-to-produce-a-result
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# Tasks in which recursion is either the fastest or only way to produce a result [duplicate]
I've just finished studying recursion at university. One thing that stood out for me however was that in both the lectures and in the practical we completed, all the tasks we were asked to do could be performed faster, and in less code, using iterative means.
This was something the lecturer confirmed.
Could somebody please give me some examples of situations when recursion is a better solution than iterative techniques? Additionally, are there any situations in which recursion is the only way to sole a problem?
-
## marked as duplicate by Juho, vonbrand, Luke Mathieson, AJed, KavehFeb 23 '13 at 7:30
@DaveClarke: You're a star Dave - should I delete this topic then? – Andrew Martin Feb 20 '13 at 20:37
If you think it overlaps too much, then yes. – Dave Clarke Feb 20 '13 at 21:11
There are no questions which can only be solved with recursion. This is because they can be solved with Turing machines, which don't use recursion.
The set of problems which can be solved with a TM are exactly the same as the ones which can be solved with recursion (or its formal model, the Lambda Calculus).
In particular, if you want to simulate recursion iteratively, the way to do this is to use a data structure called a stack (which simulates the call stack for functions).
As for algorithms that can be solved better using recursion, there are tons. I'm surprised that your recursive versions were longer, as recursion usually leads to less code. This is one of the reasons haskell is gaining popularity.
Consider the algorithm quicksort, for sorting lists. In rough pseudocode, it's as follows:
function quicksort(list)
if length(list) <= 1
return list
pivot = first element of list
lessList = []
equalList = []
greaterList = []
for each element in list:
if element < pivot, add to lessList
if element == pivot, add to equalList
if element > pivot, add to greater list
sortedLess = quicksort(lessList)
sortedGreater = quicksort(greaterList)
return sortedLess ++ equalList ++ sortedGreater
where ++ means concatenation.
The code isn't purely functional, but by dividing the list into different parts, and sorting each sublist recursively, we get a very short $O(n\log n)$ sort.
Recursion is also very useful for recursive data structures. Often times you'll have a traversal on trees, of the following form:
function traverseTree(tree)
if (tree is a single node)
do something to that node
else, for each child of tree:
traverseTree(child)
-
Thanks for this. We used recursion for things like Fibonnaci and Triangle numbers, where iterative means were much faster. These are fascinating. – Andrew Martin Feb 20 '13 at 22:41
You'll come across some problems where recursion isn't any slower, because the only non-recursive way to solve them is basically to build your own function call stack. Also, in languages like Lisp or Prolog, which support tail recursion, certain types of recursion can be made as efficient as iterative methods (because a new stack frame doesn't need to be created). – jmite Feb 20 '13 at 22:43
Easier answer: Your CPU is purely sequential, yet C (and Java, and Scheme, even latest FORTRAN) allow recursion. – vonbrand Feb 20 '13 at 23:03
@AndrewMartin, as it turns out, computing Fibonacci numbers using the recurrence directly as written (two function calls) is terrible, but you don't have to do it that way. And as the answer says, there are many, many situations in which a recursive algorithm is simply the only understandable way to express a computation. – vonbrand Feb 20 '13 at 23:09
@AndrewMartin, recursion is an important tool in the programmer's arsenal. Not required every day, but indispensable when you need it. Get familiar with the idea of recursion. – vonbrand Feb 21 '13 at 3:25
Anything that can be implemented through recursion can be implemented through iteration, and vice versa. So there is no task which it is impossible to accomplish without recursion (assuming a programming language that has the usual iterative constructs).
The cost of transforming a recursive program into an equivalent interative one is up to polylogarithmic time in most settings, and close to constant time (depending on the size of the code, but not on the size of the data) in practice. This is because the gist of the transformation from a recursive program to an iterative program is to push a record on a global stack every time a function is called, and pop that record when the function returns. This doesn't make any significant change to running time, other than memory management for the additional stack. So where a recursive program exists, an equally fast equivalent iterative program exists (for reasonable values of “equally”).
For some recursive programs, a transformation to an iterative program can significantly increase the complexity in terms of code maintenance. All that stack management can amount to significant amounts of code, especially to ensure that you have captured the right data in stack records.
A typical example where recursion is natural and avoiding it is cumbersome is tree traversal. Consider a program that manipulates binary trees and must often traverse them. A recursive traversal goes like this:
def traverse(tree):
if tree.left_child != None: traverse(tree.left_child)
if tree.right_child != None: traverse(tree.right_child)
An iterative traversal requires explicit stack maintenance — and this is a simplified example which doesn't maintain local data as it traverses the tree:
def traverse(tree):
stack = new_empty_stack()
stack.push(tree)
while not stack.is_empty():
node = stack.pop()
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https://plainmath.net/16117/find-vectors-given-point-equal-less-then-frac-more-than-point-less-then-frac
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# Find the vectors T, N, and B at the given point. r(t) =<t^2, \frac{2}{3}t^3 , t> and point <4,-\frac{16}{3},-2>
Find the vectors T, N, and B at the given point.
$r\left(t\right)=<{t}^{2},\frac{2}{3}{t}^{3},t>$ and point $<4,-\frac{16}{3},-2>$
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Jeffrey Jordon
Given $R\left(t\right)=<{t}^{2},\frac{2}{3}{t}^{3},t>$ and point $<4,-\frac{16}{3},-2>$
The point $<4,-\frac{16}{3},-2>$ occursat t=-2
Find the derivative of the vector,
${R}^{\prime }\left(t\right)=<2t,2{t}^{2},1>$
$|{R}^{\prime }\left(t\right)|=\sqrt{\left(2t{\right)}^{2}+\left(2{t}^{2}{\right)}^{2}+{1}^{2}}$
$=\sqrt{4{t}^{2}+4{t}^{4}+1}$
$=\sqrt{\left(2{t}^{2}+1{\right)}^{2}}$
$=2{t}^{2}+1$
Tangent vectors:
$T\left(t\right)=\frac{{R}^{\prime }\left(t\right)}{|{R}^{\prime }\left(t\right)|}$
$=\frac{1}{2{t}^{2}+1}<2t,2{t}^{2},1>$
$T\left(-2\right)=\frac{1}{2\left(-2{\right)}^{2}+1}<2\left(-2\right),2\left(-2{\right)}^{2},1>$
$T\left(-2\right)=\frac{1}{2\left(-2{\right)}^{2}+1}<2\left(-2\right),2\left(-2{\right)}^{2},1>$
$=<-\frac{4}{9},\frac{8}{9},\frac{1}{9}>$
${T}^{\prime }\left(t\right)=<\frac{\left(2{t}^{2}+1\right)2-2t\left(4t\right)}{\left(2{t}^{2}+1{\right)}^{2}},\frac{\left(2{t}^{2}+1\right)4t-\left(2{t}^{2}\right)\left(4t\right)}{\left(2{t}^{2}+1{\right)}^{2}},-\frac{4t}{\left(2{t}^{2}+1{\right)}^{2}}>$
$=<\frac{4{t}^{2}+2-8{t}^{2}}{\left(2{t}^{2}+1{\right)}^{2}},\frac{8{t}^{3}+4t-8{t}^{3}}{\left(2{t}^{2}+1{\right)}^{2}},-\frac{4t}{\left(2{t}^{2}+1{\right)}^{2}\right)}>$
$=<\frac{2-4{t}^{2}}{\left(2{t}^{2}+1{\right)}^{2}},\frac{4t}{\left(2{t}^{2}+1{\right)}^{2}},-\frac{4t}{\left(2{t}^{2}+1{\right)}^{2}}>$
$|{T}^{\prime }\left(t\right)|=\sqrt{\frac{\left(2-4{t}^{2}{\right)}^{2}+\left(4t{\right)}^{2}+\left(-4t{\right)}^{2}}{\left(2{t}^{2}+1{\right)}^{4}}}$
$=\frac{1}{\left(2{t}^{2}+1{\right)}^{2}}\sqrt{4-16{t}^{2}+16{t}^{4}+16{t}^{2}+16{t}^{2}}$
$=\frac{1}{\left(2{t}^{2}+1{\right)}^{2}}\sqrt{16{t}^{4}+16{t}^{2}+4}$
$=\frac{2\left(2{t}^{2}+1\right)}{\left(2{t}^{2}+1{\right)}^{2}}$
$=\frac{2}{2{t}^{2}+1}$
The normal vectors.
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http://crypto.stackexchange.com/users/4028/bob?tab=activity&sort=all&page=4
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bob
Reputation
1,067
Top tag
Next privilege 1,250 Rep.
Create tag synonyms
Oct24 revised A discrete-log-like problem, with matrices: given $A^k x$, find $k$ required for matrix operations Oct24 revised Hash function from narrower block cipher operated in CBC-encryption mode? simple formating Oct24 suggested approved edit on A discrete-log-like problem, with matrices: given $A^k x$, find $k$ Oct23 revised Because the algorithm is known, it is no longer a trade secret fixed typos Oct23 awarded Custodian Oct23 reviewed Reviewed Finding the LFSR and connection polynomial for binary sequence. Oct23 reviewed Reviewed Because the algorithm is known, it is no longer a trade secret Oct23 suggested approved edit on Because the algorithm is known, it is no longer a trade secret Oct23 comment One time pad key exchange Well, I construe one time pad as a pad that you use one time. Please also note that the distinction you're trying to make is already part of the answer: sequences thus genereated are "only" pseudo-random. Also, you'll have a hard time defining what a perfectly random string is in practice: anything that you'll use to generate it has some bias... Oct22 revised Traditional DES scheme in Unix crypt function E does not expand the key, but rather the half state Oct22 comment Could the Enigma algorithm be classified as a Feistel network? @JohnDeters: I'd be interested in your definition of a stream cipher and a block cipher then. (You might have noted the caveat in my previous comment that the view I have of a stream cipher might not be universally recognized; but at least I gave one.) Oct22 revised Hash function from narrower block cipher operated in CBC-encryption mode? added 43 characters in body Oct22 revised Hash function from narrower block cipher operated in CBC-encryption mode? added 4 characters in body Oct22 comment Hash function from narrower block cipher operated in CBC-encryption mode? @fgrieu: you are correct that the case $n>1$ cannot be attacked since the key after first round was the same for both messages and due to the bijectivity of the block cipher, a collision could not occur. I updated the last paragraph accordingly. As I write, I'm concerned about the small "bandwidth", and there is probably a lot to do, but would require some more time. Oct22 revised Hash function from narrower block cipher operated in CBC-encryption mode? update for the case $n>1$ Oct21 awarded Revival Oct21 revised Hash function from narrower block cipher operated in CBC-encryption mode? added 66 characters in body Oct20 comment Shamir Secret Sharing - Threshold decryption implementation The polynomial $f$ underlying Shamir's $(t,n)$ secret scheme is such that it has degree $t-1$ and $f(0)$ is the key (or secret) to be shared. The share given to participant $i$ is $f(i)$. You can compute $f$ using Lagrange interpolation from $f(j)$, $j=0,...,t$. See also section 2.1 of the paper linked in the answer above. Oct19 awarded Analytical Oct19 revised Using pairings to verify an extended euclidean relation without leaking the values? improved the description of the problem
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https://philpapers.org/rec/MACMHC
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# Martin Heidegger: Critical Assessments
Routledge (1992)
Abstract Martin Heidegger (1899-1976), born in Baden, Germany, is one of the most important philosophers of the twentieth century. The one-time assistant of Edmund Husserl, the founder of the phenomenological movement, Heidegger established himself as an independent and original thinker with the publication of his major work Being and Time in 1927. This collection of papers is the most comprehensive and international examination of Heidegger's work available. It contains established classic articles, some appearing in English for the first time, and many original pieces provided especially for this collection. The cross-cultural and political aspects of Heidegger's thought are examined, including his relationship to the Nazi party. The purpose of this collection is to provide a critical examination of Heidegger's work which evaluates its limits as well as its strengths, and to assess the prospects for the future development of his thought. Since many of the leading themes of contemporary philosophy such as hermeneutics, phenomenology, existentialism, postmodernism and deconstructivism trace their intellectual heritage back to Heidegger, this collection will be an indispensable guide to the issues which are currently being disputed in the field of philosophy. Keywords Heidegger, Martin Categories (categorize this paper) Buy this book $407.30 used (73% off)$880.00 new (41% off) Amazon page Call number B3279.H49.M2854 1992 ISBN(s) 0415049822 9780415049825 0415049822 Options Mark as duplicate Export citation Request removal from index
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Chapters BETA
## References found in this work BETA
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## Citations of this work BETA
The Ambiguity of Being.Andrew Haas - 2015 - In Paul J. Ennis & Tziovanis Georgakis (eds.), Heidegger in the Twenty-First Century. Springer Verlag.
A besta desamarrada..Róbson Ramos dos Reis - 1999 - Natureza Humana 1 (2):265-282.
Colloquium 4: Plato’s Question of Truth.Francisco Gonzalez - 2008 - Proceedings of the Boston Area Colloquium of Ancient Philosophy 23 (1):83-119.
## Similar books and articles
Pathmarks.Martin Heidegger (ed.) - 1998 - Cambridge University Press.
Heidegger: A Very Short Introduction.Michael Inwood - 2000 - Oxford University Press.
Speaking Out of Turn: Martin Heidegger and Die Kehre.Laurence Paul Hemming - 1998 - International Journal of Philosophical Studies 6 (3):393 – 423.
Off the Beaten Track.Martin Heidegger - 2002 - Cambridge University Press.
Heidegger for Beginners.Eric LeMay - 1994 - For Beginners Llc.
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48 ( #238,022 of 2,519,863 )
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http://doingbayesiandataanalysis.blogspot.co.uk/2013/
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## Saturday, December 28, 2013
### Icons for the essence of Bayesian and frequentist data analysis
Goal: Simple graphical icons that capture the essence of Bayesian data analysis and frequentist data analysis. Why? Visual icons serve as mnemonic cognitive packaging that facilitate initial understanding and subsequent remembering. In this post, I propose simple icons that attempt to portray the essence of Bayesian data analysis and frequentist data analysis.
[Feb. 14, 2014: See follow-up post, with new icons, HERE.]
(The prod that got me thinking about this was a light-hearted blog post by Rasmus Baath regarding a "mascot" for Bayesian data analysis. My comment on that post is the beginning of this post. Please note that the icons presented here are not intended as advocacy or cheer leading or as mascots. Instead, I would like the icons to capture succinctly key ideas.)
What is "the essence" of Bayesian data analysis? And what is "the essence" of frequentist data analysis? Any answer will surely provoke disagreement, but that is not my goal. The questions are earnest and often asked by beginners and by experienced practitioners alike. As an educator, I think that the questions deserve earnest answers, with the explicit caveat that they will be incomplete and subject to discussion and improvement. So, here goes.
The essence of Bayesian data analysis is inferring the uncertainty (i.e., relative credibility) of parameters in a model space, given the data. Therefore, an icon should represent the data, the form of the model space, and the credible parameters.
The simplest example I can think of is linear regression: Many people are familiar with x-y scatter plots as diagrams of data, and many people are familiar with lines as a model form. The credible parameters can then be suggested by a smattering of lines sampled from the posterior distribution, like this (Fig. 1):
Figure 1. An icon for Bayesian data analysis.
The icon in Figure 1 represents the data as black dots. The icon represents the model form by the obvious linearity of every trend line. The icon represents uncertainty, or relative credibility, by the obvious range of slopes and intercepts, with greater density in the middle of the quiver of lines. I like Figure 1 as a succinct representation of Bayesian analysis because the figure makes it visually obvious that there is a particular model space being considered, and that there is a range of credible possibilities in that space, given the data.
Are there infelicities in Figure 1? Of course. For example, the shape and scale of the noise distribution are not represented. But many ancillary details must be suppressed in any icon.
Perhaps a more important infelicity in Figure 1 is that the prior distribution is not represented, other than the form of the model space. That is, the lines indicate that the prior distribution puts zero probability on quadratic or sinusoidal or other curved trends, but the lines do not indicate the form of the prior distribution on the allowed parameters.
Some people may feel that this lack of representing the prior is a failure to capture an essential part of Bayesian data analysis. Perhaps, therefore, a better icon would include a representation of the prior -- maybe as a smattering of grey lines set behind the data and the blue posterior lines. For the vague prior used in this example, the prior would be a background of randomly criss-crossing grey lines, which might be confusing (and ugly).
Now, an analogous icon for frequentist data analysis.
The essence of frequentist data analysis is inferring the extremity of a data property in the space of possibilities sampled a specified way from a given hypothesis. (That is, inferring a p value.) Note that the data property is often defined with respect to a model family, such as the best fitting slope and intercept in linear regression. Therefore, an icon should represent the data, the data property, and space of possibilities sampled from the hypothesis (with the extremity of the data property revealed by its visual relation to the space of possibilities).
Keeping with the linear regression scenario, an icon for frequentist analysis might look like this (Fig. 2):
Figure 2. An icon for frequentist data analysis.
As before, the data are represented by black dots. The data property is represented by the single blue line, which shows the least-squares fit to the data. The space of possibilities is represented by the smattering of red lines, which were created as least-squares fits to randomly resampled x and y values (with replacement, using fixed sample size equal to the data sample size). In other words, the hypothesis here is a "null" hypothesis that there is no systematic covariation between the x and y values. I like Figure 2 as a succinct representation of frequentist data analysis, especially when juxtaposed with Figure 1, because Figure 2 shows that there is a point estimate to describe the data (i.e., the single blue line) and a sample of hypothetical descriptions unrelated to the data.
Are there infelicities in Figure 2? Of course. Perhaps the most obvious is that there is no representation of a confidence interval. In my opinion, to properly represent a confidence interval in the format of Figure 2, there would need to be two additional figures, one for each limit of the confidence interval. One additional figure would show a quiver of red lines generated from the lower limit of the confidence interval, which would show the single blue line among the 2.5% steepest red lines. The second additional figure would show a quiver of red lines generated from the upper limit of confidence interval, which would show the single blue line among the 2.5% shallowest red lines. The key is that there would be a single unchanged blue line in all three figures; what changes across figures is the quiver of red lines sampled from the changing hypothesis.
Well, there you have it. I should have been spending this Saturday morning on a thousand other pressing obligations (my apologies to colleagues who know what I'm referring to!). Hopefully it will have taken you less time to have read this far than it took me to have written this far.
Appended 12:30pm, 28 Dec 2013: My wife suggested that the red lines of the frequentist sampling distribution ought to be more distinct from the data, and from the best fitting line. So here are modified versions that might be better:
Description of data is the single blue line. Red lines show the sampling distribution from the null hypothesis.
Blue lines show the distribution of credible descriptions from the posterior.
## Monday, November 4, 2013
### Optional stopping in data collection: p values, Bayes factors, credible intervals, precision
This post argues that data collection should stop when a desired degree of precision is achieved (as measured by a Bayesian credible interval), not when a critical p value is achieved, not when a critical Bayes factor is achieved, and not even when a Bayesian highest density interval (HDI) excludes a region of practical equivalence (ROPE) to the null value.
Update: For expanded follow-up talk, from March 14, 2014 at U.C. Irvine, see:
It is a well-known fact of null-hypothesis significance testing (NHST) that when there is "optional stopping" of data collection with testing at every new datum (a procedure also called "sequential testing" or "data peeking"), then the null hypothesis will eventually be rejected even when it is true. With enough random sampling from the null hypothesis, eventually there will be some accidental coincidence of outlying values so that p < .05 (conditionalizing on the current sample size). Anscombe (1954) called this phenomenon, "sampling to reach a foregone conclusion."
Bayesian methods do not suffer from this problem, at least not to the same extent. Using either Bayesian HDI with ROPE, or a Bayes factor, the false alarm rate asymptotes at a level far less than 100% (e.g., 20-25%). In other words, using Bayesian methods, the null hypothesis is accepted when it is true, even with sequential testing of every datum, perhaps 75-80% of the time.
But not all is well with the Bayesian methods.Within the two Bayesian methods, the Bayes-factor method is far too eager to accept the null when it is not true. And both Bayesian methods, like the p-value method, give biased estimates of the parameter value when the null is not true, because they stop when extreme values are (randomly) obtained.
The proposed solution to the problem of biased estimates is to stop when a desired degree of precision is achieved, regardless of what it implies about the null hypothesis. This is standard procedure in political polling, in which sampling is designed to achieve a desired confidence bound on the estimate (e.g., "plus or minus 3 percentage points"), not to argue for one extreme or the other. I previously mentioned this proposal in a video (at 6:45 minutes) and alluded to it in an article (pp. 579-580) and in the book (Doing Bayesian Data Analysis; goals for power analysis, e.g., pp. 320-321), but surely I am not the first to suggest this; please let me know of precursors.
What follows is a series of examples of sequential testing of coin flips, using four different stopping criteria. The underlying bias of the coin is denoted θ (theta). Here are the four stopping rules:
• NHST: For every new flip of the coin, stop and reject the null hypothesis, that θ=0.50, if p < .05 (two-tailed, conditionalizing on the current N), otherwise flip again.
• Bayes factor (BF): For every flip of the coin, conduct a Bayesian model comparison of the null hypothesis that θ=0.50 against the alternative hypothesis that there is a uniform prior on θ. If BF > 3, accept null and stop. If BF < 1/3 reject null and stop. Otherwise flip again.
• Bayesian HDI with ROPE: For every flip of the coin, compute the 95% HDI on θ. If the HDI is completely contained in a ROPE from 0.45 to 0.55, stop and accept the null. If the HDI falls completely outside the ROPE stop and reject the null. Otherwise flip again.
• Precision: For every flip of the coin, compute the 95% HDI on θ. If its width is less than 0.08 (.8*width of ROPE) then stop, otherwise flip again. Once stopped, check whether null can be accepted or rejected according to HDI with ROPE criteria.
The diagrams below show the results for when the null hypothesis is true, and for three cases in which the null hypothesis is not true. The panels show the results for Monte Carlo simulation of flipping (or spinning) a coin that has bias θ. In each case, there were 1,000 simulated experiments, and for each experiment the sample size was allowed to grow up to 1,500 flips. The upper panels in each figure show the proportion of the 1,000 experiments that decided to accept the null, reject the null, or remain undecided, as a function of the sample size. The light blue curve shows the proportion of decisions to accept the null, the dark blue curve shows the proportion of decisions to reject the null, and the grey curve shows the remaining undecided proportion.
The lower panels in each figure show a histogram of the 1,000 sample proportions of heads when the sequence was stopped. The solid triangle marks the true underlying theta value, and the outline triangle marks the mean of the 1,000 sample proportions when the sequence was stopped. If the sample proportion at stopping is unbiased, then the outline triangle would be superimposed on the solid triangle.
Figure 1
Figure 1, above, shows the case of θ=0.50, that is, when the null hypothesis is true. The left column shows the behavior of the p-value stopping rule. As the sample size increases (notice that N is plotted on a logarithmic scale), the proportion of sequences that have rejected the null continues to rise -- in fact linearly with the logarithm of N. The lower left panel shows the distribution of sample proportions when the sequence stopped, that is, when the sequence had successfully rejected the null.
The second column of Figure 1 shows the results from using the Bayes-factor (BF) stopping rule. When the null hypothesis is true, it shows similar behavior to the HDI-with-ROPE stopping rule, but with smaller sample sizes. In fact, it can make decisions with very small sample sizes that yield very uncertain estimates of theta.
The third column of Figure 1 shows the results from using the HDI-with-ROPE stopping rule. You can see that there is some false rejection of the null for small sample sizes, but the false alarms soon asymptote. When the sample size gets big enough so the HDI is narrow enough to fit in the ROPE, the remaining sequences all eventually accept the null.
The fourth column of Figure 1 shows the results of using the precision stopping rule. Because the desired precision is a width of 0.08, a fairly large sample is needed. Once the desired HDI width is attained, it is compared with the ROPE to make a decision. The curves extend (misleadingly) farther right over larger N even though data collection has stopped.
Figure 2
Figure 2 shows the results when the true bias is θ=0.60 (not 0.50). The left column shows that decision by p-value always rejects the null, but sooner that when θ=0.50. The second column shows that the BF still accepts the null hypothesis more than 50% of the time! The third column shows that the HDI-with-ROPE method always gets the right answer (in terms of rejecting the null) but can take a lot of data for the HDI to exclude the ROPE. The real news is in the lower row of Figure 2, which shows that the sample proportion, at the point of decision, over estimates the true value of θ, for all methods except stopping at desired precision. (Actually, there is a slight bias even in the latter case because of ceiling and floor effects for this type of parameter; but it's very slight.)
Figure 3
The same remarks apply when θ=0.65 as in Figure 3. Notice that the BF still accepts the null almost 40% of the time! Only the stop-at-critical-precision method does not overestimate θ.
Figure 4
The same remarks apply when θ=0.70 as in Figure 4. Notice that the BF still accepts the null about 20% of the time! Only the stop-at-critical-precision method does not overestimate θ.
Discussion:
"Gosh, I see that the stop-at-critical-precision method does not bias the estimate of the parameter, which is nice, but it can take a ton of data to achieve the desired precision. Yuck!" Oh well, that is an inconvenient truth about noisy data -- it can take a lot of data to cancel out the noise. If you want to collect less data, then reduce the noise in your measurement process.
"Can't the method be gamed? Suppose the data collector actually collects until the HDI excludes the ROPE, notes the precision at that point, and then claims that the data were collected until the precision reached that level. (Or, the data collector rounds down a little to a plausibly pre-planned HDI width and collects a few more data values until reaching that width, repeating until the HDI still excludes the ROPE.)" Yup, that's true. But the slipperiness of the sampling intention is the fundamental complaint against all frequentist p values, which change when the sampling or testing intentions change. The proportions being plotted by the curves in these figures are p values -- just p values for different stopping intentions.
"Can't I measure precision with a frequentist confidence interval instead of a Bayesian posterior HDI?" No, because a frequentist confidence interval depends on the stopping and testing intention. Change, say, the testing intention --e.g., there's a second coin you're testing-- and the confidence interval changes. But not the Bayesian HDI.
The key point: If the sampling procedure, such as the stopping rule, biases the data in the sample, then the estimation can be biased, whether it's Bayesian estimation or not. A stopping rule based on getting extreme values will automatically bias the sample toward extreme estimates, because once some extreme values show up by chance, sampling stops. A stopping rule based on precision will not bias the sample unless the measure of precision depends on the value of the parameter (which actually is the case here, just not very noticeably for parameter values that aren't very extreme).
## Thursday, October 31, 2013
### Diagrams for hierarchical models: New drawing tools
Two new drawing tools for making hierarchical diagrams have been recently developed. One tool is a set of distribution and connector templates in LibreOffice Draw and R, created by Rasmus Bååth. Another tool is scripts for making the drawings in LaTeX via TikZ, created by Tinu Schneider. Here is an example of a diagram made by Tinu Schneider, using TikZ/LaTeX with Rasmus Bååth's distribution icons:
The drawing language TikZ is very powerful and can create very elaborate illustrations. Here is a variation in which the distribution nodes have boxes around them:
The distribution icons above are images created in R with a program by Rasmus Bååth. The program generates a catalog of icons with the same visual formatting. The icons can then be used in TikZ/LaTeX as shown in Tinu Schneider's drawings above ...
... or they can be used with freehand drawing in LibreOffice Draw. Rasmus has created a screencast that shows how do use the icons in LibreOffice Draw:
If you use LaTeX and you want precise positioning of nodes, ability to show wavy arrows and double-line arrows, and math fonts in the diagram that exactly match the math fonts in the text, then the TikZ/LaTeX tools are for you. If you want WYSIWYG editing, then LibreOffice is for you.
Rasmus Bååth's blog post about his system is here. In particular, the LibreOffice template is here, and the R code for generating the distributions is at his Github folder. You can download LibreOffice here. (You might recall that Rasmus also created the in-browser app for "Bayesian estimation supersedes the t test" (BEST) available here.)
Tinu Schneider's description of his TikZ/LaTeX examples are in this README document at his Github folder. Info about the TikZ package is here, and it can be downloaded here. (You might recall that Tinu also created the dynamic visualization of the Metropolis algorithm with rejected proposals at this blog post.)
Big THANKS to Rasmus and Tinu for creating these terrific tools!
## Wednesday, October 9, 2013
### Diagrams for hierarchical models - we need your opinion
When trying to understand a hierarchical model, I find it helpful to make a diagram of the dependencies between variables. But I have found the traditional directed acyclic graphs (DAGs) to be incomplete at best and downright confusing at worst. Therefore I created differently styled diagrams for Doing Bayesian Data Analysis (DBDA). I have found them to be very useful for explaining models, inventing models, and programming models. But my idiosyncratic impression might be only that, and I would like your insights about the pros and cons of the two styles of diagrams.
To make the contrast concrete, let's consider the classic "rats" example from BUGS. I will start with a textual explanation of the model (using modified phrasing and variable names), and then provide two diagrams of the model, one in DAG style and one in DBDA style. Here is the text:
The data come from 30 young rats whose weights were measured weekly starting at birth for five weeks, with the goal being to assess how their weights changed as a function of age. The variable yj|i denotes the weight of the ith rat measured at days since birth xj|i. The weights are assumed to be distributed normally around the predicted value ωj|i (omega):
yj|i ~ normal( ωj|i , λ )
The parameter λ (lambda) represents the precision (i.e., 1/variance) of the normal distribution. The predicted weight of the ith rat is modeled as a linear function of days since birth:
ωj|i = φi + ξi xj|i
The individual intercepts φi (phi) and slopes ξi (xi) are assumed to come from group-level normal distributions,
φi ~ normal( κ , δ ) and ξi ~ normal( ζ , γ )
where κ (kappa) and ζ (zeta) are the means of the group-level distributions. The priors on the group-level means are set as vague normal distributions,
κ ~ normal( M , H ) and ζ ~ normal( M , H )
where the mean M is approximately central on the scale of the data and the precision H is very small. The precision parameters, λ (lambda), δ (delta), and γ (gamma), are given vague gamma priors,
λ ~ gamma( K , I ) and δ ~ gamma( K , I ) and γ ~ gamma( K , I )
where the shape K and rate I parameters are set to very small values.
Below are two different diagrams of the model. The first is a DAG. Because there are a variety of style conventions in the literature for DAGs, I used my own hybrid explained in the caption. But I think it is a good and useful hybrid, one that I would want to use if I used DAGs. Take a look at the DAG:
Squares denote constants, circles denote variables. Solid arrows denote stochastic dependency, heavy dotted arrows denote deterministic dependency. Rounded-corner rectangles denote "plates" for indices.
For DAG users, does the style above capture what you think is needed in a DAG? Does the DAG above help you understand the model? How? Does the DAG confuse you? Why? Would the DAG help you program the model in BUGS / JAGS / Stan? Or not?
Below is a DBDA-style diagram for the model:
Arrows marked by "~" denote stochastic dependency, arrows marked by "=" denote deterministic dependency. Ellipses on arrows denote indices over which the dependency applies.
Does the DBDA-style diagarm above help you understand the model? How? Does the DBDA-style confuse you? Why? Would the DBDA-style help you program the model in BUGS / JAGS / Stan? Or not?
## Monday, September 16, 2013
### Visualizing a normal distribution as outcomes from a spinner
Mike Meredith has a new blog post showing an animation that converts a spinner to a normal distribution. It shows hows segments of the spinner map to regions under the normal distribution. Give it a look!
(Mike Meredith is also the fellow who created the BEST package for R. See this previous post about that!)
## Sunday, September 15, 2013
### JAGS users: runjags has been updated
Image credit: http://www.potracksgalore.com/ accessories/hanging-chains/premierpotrackchains.cfm
The package runjags by Matt Denwood has been recently updated. The runjags package has many nice facilities for running JAGS, especially a seamless interface for running parallel chains on multi-core computers and thereby greatly reducing the time needed to achieve a desired MCMC sample size from JAGS. Give it a look!
## Thursday, September 12, 2013
### Visualization of Metropolis with rejected proposals
In response to a previous post, Tinu Schneider has embellished the Metropolis visualization of Maxwell Joseph so it includes explicit plotting of rejected proposals (shown as grey segments). Here are the animated gif and R code. Many thanks to Tinu for sending this! (The gif, below, may take a few moments to load.)
#
# Animating the Metropolis Algorithm
# -------------------------------------------
# source:
# http://mbjoseph.github.io/blog/2013/09/08/metropolis/
# Prepare
----------------------------------------
require(sm) # needs 'rpanel'
dir.create("metropolis_ex")
# Setup
# --------------------------------------
# population level parameters
mu <- 6
sigma <- 3
# data-values
n <- 50
# metropolis
iter <- 10000
chains <- 3
sigmaJump <- 0.2
# plotting
seq1 <- seq( 1, 200, by= 5)
seq2 <- seq(200, 450, by= 10)
seq3 <- seq(450, 750, by= 50)
seq4 <- seq(750, iter, by=150)
xlims <- c(4, 8)
ylims <- c(1, 5)
zlims <- c(0, 0.7)
widthPNG <- 1200
heightPNG <- 750
# Helpers
# --------------------------------------
# collect some data (e.g. a sample of heights)
gendata <- function(n, mu, sigma) {
rnorm(n, mu, sigma)
}
# log-likelihood function
ll <- function(x, muhat, sigmahat){
sum(dnorm(x, muhat, sigmahat, log=TRUE))
}
# prior densities
pmu <- function(mu){
dnorm(mu, 0, 100, log=TRUE)
}
psigma <- function(sigma){
dunif(sigma, 0, 10, log=TRUE)
}
# posterior density function (log scale)
post <- function(x, mu, sigma){
ll(x, mu, sigma) + pmu(mu) + psigma(sigma)
}
geninits <- function(){
list(mu = runif(1, 4, 10),
sigma = runif(1, 2, 6))
}
jump <- function(x, dist = 0.1){ # must be symmetric
x + rnorm(1, 0, dist)
}
# compute
# ----------------------------------------
# init
proposed <- array(dim = c(chains, 2, iter))
posterior <- array(dim = c(chains, 2, iter))
accepted <- array(dim = c(chains, iter-1))
# the data
x <- gendata(n, mu, sigma)
for (c in 1:chains){
props <- array(dim=c(2, iter))
theta.post <- array(dim=c(2, iter))
inits <- geninits()
theta.post[1, 1] <- inits$mu theta.post[2, 1] <- inits$sigma
for (t in 2:iter){
# theta_star = proposed next values for parameters
jumpMu <- jump(theta.post[1, t-1], sigmaJump)
jumpSigma <- jump(theta.post[2, t-1], sigmaJump)
theta_star <- c(jumpMu, jumpSigma)
pstar <- post(x, mu = theta_star[1], sigma = theta_star[2])
pprev <- post(x, mu = theta.post[1, t-1], sigma = theta.post[2, t-1])
lr <- pstar - pprev
r <- exp(lr)
# theta_star is accepted if posterior density is higher w/ theta_star
# if posterior density is not higher, it is accepted with probability r
# else theta does not change from time t-1 to t
accept <- rbinom(1, 1, prob = min(r, 1))
accepted[c, t - 1] <- accept
if (accept == 1){
theta.post[, t] <- theta_star
} else {
theta.post[, t] <- theta.post[, t-1]
}
props[, t] <- theta_star
}
proposed[c, , ] <- props
posterior[c, , ] <- theta.post
}
# Plot
# ----------------------------------------------
oldPath <- getwd()
setwd("metropolis_ex")
sequence <- c(seq1, seq2, seq3, seq4)
cols <- c("blue", "purple", "red")
png(file = "metrop%03d.png", width=widthPNG, height=heightPNG)
for (i in sequence){
par(font.main=1, cex.main=1.2)
layout(matrix(1:2, nrow=1), widths=c(1.0, 1.5))
# prepare empty plot
plot(0, type="n",
xlim=xlims, ylim=ylims,
xlab="mu", ylab="sigma", main="Markov chains")
for (j in 1:chains) { # first all the gray lines
lines(proposed[j, 1, 1:i], proposed[j, 2, 1:i], col="gray")
}
for (j in 1:chains) { # now the accepteds
lines(posterior[j, 1, 1:i], posterior[j, 2, 1:i], col=cols[j])
}
text(x=6, y=1.0, paste("Iteration ", i), cex=1.2)
sm.density(x=cbind(c(posterior[, 1, 1:i]), c(posterior[, 2, 1:i])),
xlab="mu", ylab="sigma", zlab="",
xlim=xlims, ylim=ylims, zlim=zlims,
col="white")
title(main="Posterior density")
}
dev.off()
# combine .png's into one .gif
# system('convert2gif.bat') # had to write a .bat-file
# system('convert -delay 20 *.png "metropolis.gif"') # doesent work
#file.remove(list.files(pattern=".png"))
setwd(oldPath)
#
Created by Pretty R at inside-R.org
## Tuesday, September 10, 2013
### Cool visualization of Metropolis sampling
A cool visualization of Metropolis sampling has been posted by Maxwell Joseph here. I've pasted in his animated gif below, as a teaser for you to check his post (and I figured it would be okay because his work focuses on "parasitic biodiversity" ;-). Thanks to Joseph Young for pointing me to this.
From Maxwell Joseph's post.
What would also be cool is an animation of Metropolis that shows the proposals at every step, even if rejected.
## Friday, September 6, 2013
### Bayesian methods article wins best paper award in Organizational Research Methods
The article, "The Time Has Come: Bayesian Methods for Data Analysis in the Organizational Sciences," won the 2012 Best Paper Award for the journal, Organizational Research Methods. The publisher has made the article freely available. You can see the announcement and find a link to the article here. The accompanying programs can be found here . If you find that article interesting, you would probably also like the article, "Bayesian estimation supersedes the t test," described here.
## Thursday, August 8, 2013
### How much of a Bayesian posterior distribution falls inside a region of practical equivalence (ROPE)
The posterior distribution of a parameter shows explicitly the relative credibility of the parameter values, given the data. But sometimes people want to make a yes/no decision about whether a particular parameter value is credible, such as the "null" values of 0.0 difference or 0.50 chance probability. For making decisions about null values, I advocate using a region of practical equivalence (ROPE) along with a posterior highest density interval (HDI). The null value is declared to be rejected if the (95%, say) HDI falls completely outside the ROPE, and the null value is declared to be accepted (for practical purposes) if the 95% HDI falls completely inside the ROPE. This decision rule accepts the null value only when the posterior estimate is precise enough to fall within a ROPE. The decision rule rejects the null only when the posterior exceeds the buffer provided by the ROPE, which protects against hyper-inflated false alarms in sequential testing. And the decision rule is intuitive: You can graph the posterior, its HDI, its ROPE, and literally see what it all means in terms of the meaningful parameter being estimated. (For more details about the decision rule, its predecessors in the literature, and alternative approaches, see the article on this linked web page.)
But how do we set the limits of the ROPE? How big is "practically equivalent to the null value"? There is typically no uniquely correct answer to this question, because it depends on the particular domain of application and the current practice in that domain. But the rule does not need a uniquely correct ROPE, it merely needs a reasonable ROPE that is justifiable to the audience of the analysis. As a field matures, the limits of practical equivalence may change, and therefore what may be most useful to an audience is a description of how much of the posterior falls inside or outside the ROPE as a function of the width of the ROPE. The purpose of this blog post is to provide some examples and an R program for doing that.
Consider a situation in which we want to estimate an effect size parameter, which I'll call δ. Suppose we collect a lot of data so that we have a very precise estimate, and the posterior distribution shows that the effect size is very nearly zero, as plotted in the left panel below:
We see that zero is among the 95% most credible values of the effect size, but we can ask whether we should decide to "accept" the value zero (for practical purposes). If we establish a ROPE around zero, from -0.1 to +0.1 as shown above, then we see that the 95% HDI falls entirely within the ROPE and we accept zero. What if we think a different ROPE is appropriate, either now or in the future? Simply display how much of the posterior distribution falls inside the ROPE, as a function of the ROPE size, as shown in the right panel above. The curve plots how much of the posterior distribution falls inside a ROPE centered at the null value, as a function of the radius (i.e., half width) of the ROPE. As a landmark, the plot shows dashed lines at the 95% HDI limit farthest from the null value. From the plot, readers can decide for themselves.
Here is another example. Suppose we are spinning a coin (or doing something more interesting that has dichotomous outcomes) and we want to estimate its underlying probability of heads, denoted θ. Suppose we collect a lot of data so that we have a precise estimate, as shown in the left panel below.
We see that the chance value of 0.50 is among the 95% most credible values of the underlying probability of heads, but we can ask whether we should decide to "accept" the value 0.50. If we establish a ROPE around zero, from 0.49 to 0.51 as shown above, we can see that the 95% HDI falls entirely within the ROPE and we would decide to accept 0.50. But we can provide more information by displaying the amount of the posterior distribution inside a ROPE centered on the null value as a function of the width of the ROPE. The right panel, above, allows the readers to decide for themselves.
The plots can be used for cases of rejecting the null, too. Suppose we spin a coin and the estimate shows a value apparently not at chance, as shown in the left panel below.
Should we reject the null value? The 95% HDI falls entirely outside the ROPE from 0.49 to 0.51, which means that the 95% most credible values are all not practically equivalent to 0.5. But what if we used a different ROPE? The posterior distribution, along with the explicit marking of the 95% HDI limits, is all we really need to see what the biggest ROPE could be and still let us reject the null. If we want more detailed information, the panel on the right, above, reveals the answer --- although we need to mentally subtract from 1.0 to get the posterior area not in the ROPE (on either side).
Here is the R script I used for creating the graphs above. Notice that it defines a function for plotting the area in the ROPE.
#------------------------------------------------------------------------------
# From http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/Programs/ get
# openGraphSaveGraph.R, plotPost.R, and HDIofMCMC.R. Put them in the working
# directory of this script, or specify the path in the next lines' source()
# commands:
source("./openGraphSaveGraph.R")
source("./plotPost.R")
source("./HDIofMCMC.R")
# Define function for computing area in ROPE and plotting it:
plotAreaInROPE = function( mcmcChain , maxROPEradius , compVal=0.0 ,
HDImass=0.95 , ... ) {
ropeRadVec = seq( 0 , maxROPEradius , length=201 ) # arbitrary comb
areaInRope = rep( NA , length(ropeRadVec) )
for ( rIdx in 1:length(ropeRadVec) ) {
areaInRope[rIdx] = ( sum( mcmcChain > (compVal-ropeRadVec[rIdx])
/ length(mcmcChain) )
}
xlab=bquote("Radius of ROPE around "*.(compVal)) ,
ylab="Posterior in ROPE" ,
type="l" , lwd=4 , col="darkred" , cex.lab=1.5 , ... )
# From http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/Programs/
# get HDIofMCMC.R. Put it in the working directory of this script, or specify
# the path in the next line's source() command:
# source("./HDIofMCMC.R")
HDIlim = HDIofMCMC( mcmcChain , credMass=HDImass )
farHDIlim = HDIlim[which.max(abs(HDIlim-compVal))]
areaInFarHDIlim = ( sum( mcmcChain > (compVal-ropeRadHDI)
/ length(mcmcChain) )
lty="dashed" , col="darkred" )
bquote( atop( .(100*HDImass)*"% HDI limit" ,
"farthest from "*.(compVal) ) ) , adj=c(0.5,0) )
lty="dashed" , col="darkred" )
text( 0 , areaInFarHDIlim , bquote(.(signif(areaInFarHDIlim,3))) ,
}
#------------------------------------------------------------------------------
# Generate a fictitious MCMC posterior:
m = 0.03
s = (0.1-m)/3
paramMCMCsample = rnorm(50000,m,s)
# Specify the desired comparison value, ROPE radius, and HDI mass:
compVal = 0.0
HDImass = .95
# Open graphics window and specify layout:
openGraph(width=7.5,height=3.5)
par(mar=c(3.5,3.5,2,1),mgp=c(2,0.7,0))
layout( matrix( c(1,2) , nrow=1 , byrow=FALSE ) )
# Plot the posterior with HDI and ROPE:
postInfo = plotPost( paramMCMCsample , compVal=compVal ,
credMass=HDImass , xlab=expression(delta*" (parameter)") )
# Plot the area in ROPE:
ropeInfo = plotAreaInROPE( mcmcChain=paramMCMCsample , maxROPEradius=0.15 ,
compVal=compVal , HDImass=HDImass )
#------------------------------------------------------------------------------
## Friday, August 2, 2013
### Near Paris? Snap a shot of the book with Laplace. Or pose it with other Bayesians.
The book previously has been posed at Bayes' tomb, Fisher's remains, and Jacob Bernoulli's grave (in an attempt to be amusing and informative; hopefully not inadvertently being offensive). Conspicuously absent from that list is Pierre-Simon Lapace, who was the foundational developer of Bayesian methods. If you are in or near Paris, and would have fun posing the book at Laplace's grave, please do so and send me a photo! If you're among the first responders, I'll post the photo, with attribution to you, on the blog. Information about the location of Laplace's grave can be found here, with a map here.
If you pose the book with other famous Bayesians, or pre-Bayesians, or anti-Bayesians, either dead or not-quite-yet dead, please send me those photos too! (Again, the goal is to be amusing and informative, not offensive.) Thanks, and have fun!
## Saturday, July 20, 2013
### Decisions from posterior distributions: Tail probability or highest density interval?
How should we decide whether a parameter's posterior distribution "rejects" a particular value such as zero? Should we consider the percentage of the distribution above/below the value? Should we consider the relation of the highest density interval (HDI) to the value? Here are some examples to explain why I think it makes more sense to use the HDI.
Here are the two decision rules being compared. First, the tail-probability decision rule: If there is less than 2.5% of the distribution on either side of the value, then reject the value. This is tantamount to using a 95% equal-tailed credibility interval: Values outside the 95% equal-tailed credibility interval are "rejected." Second, the HDI decision rule: Values outside the 95% HDI are "rejected." (Of course, I like to enhance the decision rule with a ROPE, to allow acceptance decisions and to provide a buffer against false alarms -- but that's a separate discusssion.)
The two histograms below represent the MCMC results for two hypothetical parameters.
The upper panel shows a posterior distribution for which the parameter value of zero falls will within the 95% HDI, but 2.0% (<2.5%) of the distribution falls below the value zero. Do we "reject" zero or not? I think it would be wrong to reject zero, because the probability density (i.e., credibility) of zero is high. Zero is clearly among the most credible values of the parameter, even though less than 2.5% of the distribution falls below zero.
The lower panel shows a posterior distribution for which the parameter value of zero falls well outside the 95% HDI (thus, even with of a modest ROPE, e.g. from -1 to +1, zero would still fall outside the 95% HDI), but a full 3.0% (>2.5%) of the distribution falls below zero. Do we "reject" zero or not? If we use a tail-probability decision rule, we do not reject zero. But clearly zero is not among the most credible values of the parameter, in that zero has low probability density.
Proponents of using equal-tailed credibility intervals will argue that percentiles of distributions are invariant under transformations of the parameter, but HDIs are not. True enough, but I think that most parameters are specifically scaled to be meaningful, and we want to know about credibility (probability density) on the meaningful scale, not on a meaningless transformed scale. But I am not saying that one decision rule is "correct" and the other is "wrong." The decision rules are merely rules with differing interpretations and characteristics; I am showing examples that convince me that a more useful, intuitive rule is using the HDI not the equal-tailed interval.
Then why do the plots in DBDA (like those above) bother to display the percentage of the distribution below/above the comparison value? Primarily merely as an additional descriptive statistic, but also to inform those who wish to think about tail probabilities for a decision rule that I eschew.
For another example, see this previous post.
## Wednesday, June 26, 2013
### Doing Bayesian Data Analysis at Jacob Bernoulli's grave
The book visited the grave of Jacob Bernoulli (1655-1705) in Basel, Switzerland, as shown in these photos taken by Dr. Benjamin Scheibehenne. Jacob Bernoulli pre-dated Bayes (1701-1761), of course, but Bernoulli established foundational concepts and theorems of probability.
The cutie admiring the book in the first photo is Benjamin's daughter. Many thanks to Benjamin and family for venturing out to take these photos. Thanks also to Benjamin and colleagues for hosting my visit to Basel for a day back in June, during which we unfortunately did not have time to visit Jacob Bernoulli's grave.
If you find this amusing, you might also like the book at Bayes' tomb and the book at R. A. Fisher's remains.
## Sunday, June 16, 2013
### Bayesian robust regression for Anscombe quartet
In 1973, Anscombe presented four data sets that have become a classic illustration for the importance of graphing the data, not merely relying on summary statistics. The four data sets are now known as "Anscombe's quartet." Here I present a Bayesian approach to modeling the data. The Anscombe quartet is used here as merely another illustration of two frequently made points in Bayesian analysis: JAGS/BUGS is a very flexible language for expressing a variety of models (e.g., robust non-linear regression), and it is important to conduct a posterior predictive check of the descriptive adequacy of the model.
(I first messed around with analyzing Anscombe's quartet back in October 2010, for personal interest. A conversation I had last week in Basel, Switzerland, suggested that this analysis might interest a larger audience. Hence this blog post.)
Below are the four data sets, shown as black circles. They are modeled with typical linear regression that assumes normality:
y ~ dnorm( b0+b1*x , sigma )
with vague priors on the intercept b0, the slope b1, and the standard deviation sigma.
Actually, for easy consistency with the subsequent analysis, I used a t distribution with the normality (df) parameter given a prior that insists it is very large, near 500, which is essentially normal. Thus, the model is
y ~ dt( b0+b1*x , sigma , nu )
with vague priors on b0, b1, and sigma, and the prior on normality being
nu ~ dnorm( 500 , sd=0.1 )
The figures below show the data in the left panels, with a smattering of credible regression lines superimposed, and veritical bars that indicate the 95% HDI of posterior predicted y values at selected x values:
Notice that the marginal parameter estimates are the same for all four data sets (up to MCMC sampling error), which is exactly the point that Anscombe wanted to emphasize for least-squares regression. Here we see that it is also true for Bayesian estimation, and this is no surprise when we remember from formal Bayesian analysis of linear regression (with normally distributed noise) that the "sufficient statistics" of the data determine the posterior distribution, and the sufficient statistics are identical for the four data sets.
One of the beauties of the flexibility of JAGS/BUGS is that it is easy to implement other models. In particular, it is easy to implement regression that is robust to outliers, using the t distribution. I used the same model as above,
y ~ dt( b0+b1*x , sigma , nu )
with vague priors on b0, b1, and sigma, but I put a vague prior on the normality of the t distribution:
nu <- nuMinusOne + 1
nuMinusOne ~ dexp( 1/29 )
This is the same prior on nu as is used in the "BEST" model for robust comparison of two groups. The resulting posteriors look like this:
The normality parameter (nu) is not much different from its prior for Types 1, 2, and 4, resulting in slightly smaller estimates of sigma than when forcing nu to be 500. Most notably, however, for Type 3, the model detects that the data fall on a line and have a single outlier, indicated by the SD (sigma) estimated as an extremely small value, and the normality (nu) hugging 1.0, which is its smallest possible.
Analogously, we could easily do a robust quadratic trend analysis, and thereby detect the non-linear trend in Type 2. See this previous blog post for how to extend a JAGS/BUGS linear regression to include a quadratic trend.
To reiterate and conclude, the Anscombe quartet not only makes its original point, that we should look at the posterior predictions to make sure that the model is a reasonable description of the data, but it also highlights that for Bayesian analysis using JAGS/BUGS, it is easy to try other models that may be better descriptions of the data.
ADDED 18 JUNE 2013: Rasmus Baath, after reading the above post, has actually implemented the extensions that I merely suggested above. Please continue reading his very interesting follow up.
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|
http://hackage.haskell.org/package/fftwRaw
|
# fftwRaw: Low level bindings to FFTW.
[ bsd3, library, math ] [ Propose Tags ]
Yet another set of Haskell bindings to FFTW, the Fastest Fourier Transform in the West.
These are low level bindings with some type safety for a small subset of FFTW's functionality. Raise an Issue on Github if you need something I haven't implemented.
Unlike the fft package, this package provides low level manipulation of FFTW plans (such as fftw_plan_dft_1d).
Unlike the vector-fftw package, this package is based on pointers instead of the Vector datatype and it avoids copying the input arrays by assuming that the pointers are aligned as FFTW expects.
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https://www.physicsforums.com/threads/walkie-talkies.9533/
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# Walkie-talkies
1. Nov 24, 2003
### Junior Ivan
Anyone know anything about that rule that says you have to have an FCC license to use walkie talkies?
2. Nov 24, 2003
### Guybrush Threepwood
I'm sure there must be some unlicensed bands you can use....
3. Nov 24, 2003
I don't know any of the details, but it relates to power levels and what part of the freq spectrum you're using. Eg. very low power walkie talkies, sold in toy stores, are below the power levels required for licensing. Any ham radio operator could give you details regarding frequencies and power output.
4. Nov 25, 2003
### Junior Ivan
its says something about certain channels like FMRS or GMS
When i look it up in the manual, pretty much all the good long distance channels are the ones i cant use, and i heard that they can trace you if you dont have a callsign or something like that.
5. Nov 27, 2003
### kleinphi
It is like this: There are essentially two types of walkie-talkies you are allowed to use without any specific kind of license: CB, which has been around for several decades. These frequencies are around 29 MHz, so theoretically you could under certain not too infrequent conditions use them to communicate over great distances, but the FCC explicitly prohibits such activities: You are not ALLOWED to use CB to communicate over a distance of more than 150 miles. Since there is also a restriction on the power any CB radio is allowed to put out, in most cases it will be physically impossible to use CB over a distance of more than 50 or 100 miles.
The other type of "license-free" walkie talkies are the newer UHF ones called FRS or something like that. I don't know the exact acronyms, but I believe it stands for Family Radio Services or General something... If I am not mistaken, these use frequencies around 455 MHz and no more than 0.5 watts, which limits their range to no more than a couple of miles under virtually all conditions.
GMRS is General Mobile Radio Service, and as far as I know it requires an FCC license, which is about $75, but no test. I think they use certain frequencies around 460 MHz. Marine VHF radios also require an FCC license, but no test. Then there is Ham Radio, also called Amateur Radio. For these radios you need an FCC license, which is free, but you have to take a little multiple choice test, and I believe the test costs$12 or \$14. Depending on what class of amateur license you go for (if you are a physics major you should have no difficulty getting the highest class, called Amateur Extra in the US), you are allowed to use certain (quite large) frequency ranges all over the spectrum. I believe there are some long wave bands, there are definitely the 160 meter, 80m, 40m, 30m, 20m, 18m, 15m, 12m, 10m, 6m, 2m, 1.25m, 70cm, 33cm, and 23cm bands, plus a lot of available space if you want to go even higher. For those frequencies, you will probably have to build your own equipment, which by the way you are allowed to if you hold any class amateur license.
Anyway, if you want a radio that goes farther than a few miles, you either have to pay for some sort of a commercial license or become a ham. But of course, ham radio may not be used for commercial purposes, I believe the rule says you are not allowed to have any financial interest in any communication carried out over ham radio (with certain reasonable exceptions).
Last edited: Nov 27, 2003
6. Nov 29, 2003
### Junior Ivan
So they'd bust you even if its just casual conversation?
7. Nov 29, 2003
### Integral
Staff Emeritus
I don't think they are much concerned with the content, it is the simple fact that you are broadcasting that matters.
8. Nov 29, 2003
### Zantra
corrrect me if I'm wrong, but I believe 5 watts is the maximum power rating allow for a handheld.
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|
https://math.stackexchange.com/questions/2108844/how-to-prove-that-these-two-quotients-are-isomorphic-as-rings-circle-and-hyperb?noredirect=1
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# How to prove that these two quotients are isomorphic as rings (circle and hyperbola)?
Let $k$ be an algebraically closed field. Consider the polynomial ring $A=k[x,y]$. Consider the ideal $I=\langle x^2+y^2-1\rangle$ (which is just the vanishing set of the circle) and $J=\langle y^2-x^2-1\rangle$ (the vanishing set of the hyperbola). How to prove that $$A/I\cong A/J.$$
Consider $K=\langle y-x^2\rangle$. How to prove that $$A/K\ncong A/I.$$
• If $k=\mathbb C$, then you can do a linear change of coordinates sending $x^2+y^2$ to $y^2-x^2$. I think maybe $u=x+iy$ and $v=x-iy$ works. – hwong557 Jan 22 '17 at 15:52
• I asked math.stackexchange.com/questions/1984063/… some time ago :-) – Alphonse Jan 22 '17 at 15:54
• I have another idea (but its validity depends on proving that $I=\langle x^2+y^2-1\rangle$ is prime in $\mathbb{C}[x,y]$). Correct me if I am wrong. If $I$ is prime, then $R/I$ is integral domain. Then the ideal $L=\langle I+x, I+y\rangle$ is not principal in $R/I$. – random_guy Jan 22 '17 at 20:52
• In $A/I$, $\langle x,y\rangle = \langle 1\rangle$. – user14972 Jan 22 '17 at 21:48
• The first comment solves the first question (which is pretty simple), and the second question is settled here: math.stackexchange.com/questions/1463572/… – user26857 Jan 22 '17 at 22:15
Geometrically, over an algebraically closed field, the line, circle, hyperbola, and parabola are all isomorphic projective varieties.
Up to isomorphism, the only difference between these rings, then, is which points at infinity they are missing. Your circle and hyperbola are each missing two points ($(1 : \pm i : 0)$ and $(1 : \pm 1 : 0)$ respectively), and the parabola is missing one point: $(0:1:0)$.
With one point removed, the coordinate ring of each of these curves is isomorphic to $k[t]$. Removing a second point corresponds to inverting the appropriate linear function. By a suitable change of variable, we can insist that the result is isomorphic to $k[t, t^{-1}]$.
For the parabola, the correspondence is $(x,y) = (t, t^2)$. For the hyperbola, one such correspondence comes from $t = x+y$ (and $t^{-1} = y-x$). For the circle, $t = x+iy$ (and $t^{-1} = x-iy$) works.
So, the remainder of the problem is to show that $k[t]$ and $k[t, t^{-1}]$ are not isomorphic as rings. There are probably lots of ways to do this (including some geometric argument using the count of missing points I described above); however, a simple method is to compute the unit group.
• In the similar posts I've seen so far it's asked to prove that $k[t,t^{-1}]\not\simeq k[z]$ (I wouldn't write $k[t]$) as rings, not as $k$-algebras. Moreover, all the proofs assume (by contradiction) the isomorphism is of unitary rings. It would be interesting to find out a proof without this assumption (which means to find other properties of the two rings not involving units). – user26857 Jan 22 '17 at 23:27
• To prove my point see here: math.stackexchange.com/questions/1050291/… – user26857 Jan 22 '17 at 23:30
• @user26857: A ring that is also a $k$-algebra (i.e. a ring with a specified homomorphism to it from $k$, or a ring extension of $k$ or other equivalent formulation) is certainly what's intended by the question, but I did intend to edit my first draft to switch over to just plain rings, and apparently missed an occurrence; I've corrected. – user14972 Jan 22 '17 at 23:33
• I can understand this, but the question has been posted for few times and all the OPs have looked for a non-isomorphism as rings. Most likely the question is an exercise in a textbook (I think could be Vakil notes), and I suppose this was the requirement there. – user26857 Jan 22 '17 at 23:38
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|
http://mathhelpforum.com/pre-calculus/106498-integrating-get-velocity-notation.html
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# Math Help - Integrating to get velocity. (notation)
1. ## Integrating to get velocity. (notation)
I'm stuck on how to get the proper notation for this problem.
In physics, we know that Force= Mass x acceleration, or F=ma
In this case, the force is equal to $(A)/c * cos(theta)$
So i'm looking at $((A)/c * cos(theta))/m = a$
BUT, I need to velocity as a function of time, v(t).
Basically, what would a formula for $v(t)=$ look like?
2. Originally Posted by elninio
I'm stuck on how to get the proper notation for this problem.
In physics, we know that Force= Mass x acceleration, or F=ma
In this case, the force is equal to $(A)/c * cos(theta)$
So i'm looking at $((A)/c * cos(theta))/m = a$
BUT, I need to velocity as a function of time, v(t).
Basically, what would a formula for $v(t)=$ look like?
You could start by saying $a = \frac {dv}{dt}$ (rate of change of velocity with time) and so:
$(A)/c * cos(theta) = \frac {dv}{dt}$
If the expression on the left has no time dependency, i.e. is constant w.r.t. time, you can just write:
$t (A)/c * cos(theta) = v + v_0$
where $v_0$ is some arbitrary constant velocity that will be determined by applying some boundary condition or initial value or whatever.
3. So, If I wanted to find the Kinetic Energy, which equals 1/2mv^2, would that give me:
$KE=.5m(A(dt)/cm)^2$?
I hope you can follow my notation. (also, lets ignore cos theta)
4. Oh okay then ...
For a start I HATE that $.5 m$ - I much prefer $m/2$ at this stage, because after you've integrated with respect to $t$ your complicated expression with all that $ A$ in it (haven't a clue what it means BTW) you may find the 2 cancels out with something else.
Okay, so yes you get your velocity by integrating your LHS, then square it, and times it by $m/2$.
There's obviously something in the problem you're doing that you're not telling us ... we may be able to enlighten you better if you post the whole thing you're trying to solve.
5. Ok, here's the entire question. Its a high level astrophysics problem but I just needed a hand with the calculus part:
Consider a spacecraft of mass m whose engine is a perfectly absorbing laser sail that is initially at rest in space. No gravity is being exerted on it. We aim a laser at the sail and cause it to accelerate into deep space.
Derive a formula for its kinetic energy, as a function of its mass and the total amount of energy Ei that it absorbs from the laser beam during some time interval t. Assume that the spacecrafts velocity remains NON-relativistic.
I.E. You're firing radiation and using the pressure of light to accelerate it.
6. You'd need to explain what S, A, c and theta are (although I guess c is the velocity of light). And what's the $$ notation? I'm a bit of a pure mathematician, physics notation I've never got on with, it tends to confuse me.
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https://earthscience.stackexchange.com/tags/minerals/hot
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Tag Info
19
That is the multimillion dollar question! "looking for surface formations" is indeed one way, and it was the main method of exploration in the past. This does not necessarily mean that you directly see the ore deposit in front of your eyes. Many ore-forming systems are accompanied by different kinds of alteration (for example potassic or argillic alteration) ...
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I'll take the form of the question given by another person here and attempt to provide a different answer. So what you are asking is: "How did gold become so concentrated in certain parts of the world?" So yes, gold is all around but the concentration is too low to make extraction of it worthwhile. You need some process to take small amounts of gold from a ...
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In addition to the above, what happens is that people look for commonalities between known deposits. So, for example, if you have a lot of gold veins in one area, and lots in another area, then you look at what is needed for these veins to form. Once you have a reasonable idea of possible ways to form your ore, then you have something that you can look for. ...
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The hardness of minerals is diagnostic because the hardness is determined by the strength of bonds and the structure of the mineral lattice. Hardness is basically the stress required to create and grow extended lattice defects such as micro-fractures, stress twins, and dislocations. Diamond, quartz, and framework silicates, such as feldspar, are hard ...
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I've been looking for these things over a few decades and along with other geologists doing this we have seen how we find things change somewhat. Many methods used a century ago are still in use, but with the addition of refinements. So looking at how large and small deposits were found will change over time. (Simple example of that would be that Romans and ...
10
Double-terminated crystals can from by crystallizing from a melt. The crystallization nucleus has to float freely in the magma chamber. As long as no other crystals obstruct the growth the crystal will grow in its own characteristic form (euhedral). This happens for example with feldspar crystals. (Example: http://www.erdwissen.ch/wp-content/uploads/2010/12/...
9
The lifetime of a fluorescence excited state is on the nanosecond to microsecond time scale. So once the excitation source light is removed, the emission of light will stop within microseconds. Note that fluorescence is distinct from phosphoresence, and phosphorescence can involve longer lifetime excited states. Spectroscopic Characterization of the ...
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Ivigtut Cryolite deposit, Ivittuut (Ivigtut), Arsuk Fjord, Sermersooq, Greenland deposit is the first and largest occurrence of Cryolite but it is not the only location to report Cryolite. Some of these other locations listed below have produced collectible specimens but cryolite does not occur in large enough quantities to be mined. Other important ...
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Soil color is highly dependant on the oxides and other minerals in the composition. Purplish tones appear to be possible by inclusion of manganese oxide compounds. There are locations in China that have markedly violet soils. If you broaden your search to sands as well as soils, there are plenty of examples of garnet-based sands that can appear markedly ...
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Calcite and hematite may not be the the answer to my question Hematite is not the answer, but calcite is. The inclusions are not cubic, they are rhombohedral. This is precisely how calcite looks like. but why they stand out from the rest of the stone is beyond me. Because calcite is a translucent mineral, and pectolite is not. You can drop some ...
7
I am not a minerals expert, and can't claim expertise on these particular materials. However, from a general physics / materials point of view I'm pretty sure the answer will be that, There is more than enough UV in sunlight to make the minerals fluoresce, but... The amount of visible light from the fluorescence is low enough to be undetectable by eye on ...
7
It mostly has to do with the fact many minerals are partially translucent. Trace impurities or even crystal structure can dominate the color of a translucent material but when ground in to a fine powder (streak) they can no longe do so and you can see the true color. In other minerals surface oxidation can mask the true color.
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Your mineral specimen is most likely goethite after pyrite, a common pseudomorph found in many different geological environments. A quick google search revealed pyrite and goethite can be found in Normandy. Mindat - Goethite (map before from Mindat) Soumont-Saint-Quentin mine, Calvados, Normandy, France
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Remember that you are concerned about stability fields. The lines on your stability diagram are the places where two minerals are in equilibrium. One one side one mineral will be more stable, on the other side the other one will be. Let's talk about $\ce{Ca}$ first. The reactions all have the same $\ce{Ca}$ so it's activity isn't a factor in their relative ...
6
It's biotite. Not muscovite. That's why you have the pleochroic halos in it. I don't understand why you are saying that the interference colours are like muscovite. First of all, the lack of cleavage suggests you are looking down (or close to) the x axis, so this means the interference colours you see are going to be very low. Let's say 1st order white or ...
6
It is a quartz crystal artificially coated in thin layer of metal called aura quartz or rainbow quartz. They come in various colours and often can be found in new age shops. More information on the topic can be found on wiki: https://en.wikipedia.org/wiki/Metal-coated_crystal
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Start with my answer to this very highly related question here: https://earthscience.stackexchange.com/a/2742/725 The melting point of minerals in isolation, or a pure substance is higher than mixtures of minerals. For example - a (well-mixed) mixture of quartz and pyroxene will melt at a lower temperature than pure quartz or pure pyroxene. The exact ...
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Minerals are defined by chemical composition and crystallography. Dana classification scheme or new Dana classification scheme divides known mineral species in eight broad groups based on primary chemical properties and crystal form. Organic vs inorganic Silicates vs non-silicates Subdivided silicates into smaller groups by crystalline structures ...
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I assume by "mineral excavation" you mean mineral collecting. I've collected minerals for years. In general the biggest danger is naivete not the minerals themselves. You need proper safety equipment, proper tools, and proper planning. If you're breaking rocking with a hammer, then the hammer should be a soft steel. Hardened steel can splinter. Since ...
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I'd like to add to Gordon's answer. A phase change in this context does not only refer to the change in the state of matter (e.g. liquid to solid) but a change in different solid states as well. Olivine, $\ce{(Mg,Fe)2SiO4}$, is the stable magnesian silicate in pressures down to those prevailing at a depth of ~410 km below the surface of the Earth. As the ...
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The first step I did was divide each wt% by their molecular weights to get a molecular proportion: Actually that's not what you did. What you did is how much moles of each oxide you have assuming 100 grams of mineral. But that's less important now. You are mostly correct in your steps. Eventually you have 0.972 Fe, 0.375 Ti, and 0.972 + 2×0.375 = 1.722 O. ...
5
Gold has primary origin in hydrothermal veins and contact metamorphic deposits and pegmatites. Also occurs in placer deposits of secondary origin. It is more easily found in veins that is related to igneous rocks rich in silica. The main sources of gold are in hydrothermal quartz veins with pyrite and other sulfides. Gold is mechanically mixed with ...
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I'm pretty sure a more rigorous answer deserves to come along, but I can give a simple overview of some of the important factors. Cleavage planes have to do with bond strength and bond geometry. If there isn't a plane of bonds that can be cut through, then you won't get cleavage. When a mineral is fractured, the fracture "wants" to take the path where the ...
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There are some subtleties that I'd like to add, in addition to Mark's answer. When talking about the hardness of a mineral, the nature of the chemical bonds in the crystal structure (e.g. covalent vs ionic) are not the only important thing. Crystal morphology is also important. For example, Si-O-Si and Al-O-Al bonds usually cause minerals to be hard, such ...
5
You have a specimen of gypsum, CaSO4 · 2H2O. Reference
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Yes, there are. Here are some examples from Southern Israel: Another exceptional example is the "rainbow mountain" in Peru: The cause of these colours is the usually trace oxide amount in the soil. The soil is usually composed mostly of silt-sized quartz. This quartz is coated with with various oxides. Differing proportions of these oxides will change the ...
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The color of a mineral can be caused by a variety of mechanisms. This is also true of amethyst, which is a variety of quartz ($\ce{SiO2}$), and can be found in many colors. The major factors responsible for the production of color in minerals fall into five categories: The presence of an element essential to the mineral composition The presence of a minor ...
Only top voted, non community-wiki answers of a minimum length are eligible
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https://brilliant.org/problems/if-only-you-could-flip-it/
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If only you could flip it...
Calculus Level 2
This integral is equal to $$A-B\ln C,$$ where $$A,$$ $$B,$$ and $$C$$ are positive integers and $$C$$ is prime. What is $$A+B+C\text{?}$$ $\int_0^3\dfrac{2x^3}{x^2+9}\text{ }dx$
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https://brilliant.org/problems/2002-osk-number-7/
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# 2002 Math OSK, Number 7
Algebra Level pending
For every real number $$x, y$$ applies $$xy\quad =\quad xy\quad -\quad x\quad +\quad y$$ then $$(x+y)(x-y)$$ equals to...
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https://aubinhoudetcaseneuve.com/cipher-codes-bpza/list-of-perfect-cubes-pdf-88768e
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8, 27, 64, 125, 216, 343, … are perfect cube My students can never remember how! Mathematics (Geometry) Algebraic curves Rational curves. 5 and (25)(25) equal 25.So, 25 has two square roots, 5 and 25.A radical sign, Ïw, is the symbol used to indicate the positive square root of a number.So, Ï25w 5 5. Open Microsoft Excel. Similarly, a perfect cube is an integer that can be expressed as the product of three equal integers. Lists of shapes cover different types of geometric shape and related topics. Perfect Cubes are whole numbers with an exponent of _____. what are perfect cubes and how to calculate the cube root of a perfect cube, Evaluate Square Roots of Perfect Squares and Cube Roots of Perfect Cubes, How to simplify radicals with negative radicands and odd indexes, Grade 8 math, with video lessons, examples and step-by-step solutions. This activity is meant as the follow-up to perfect squares and extends the conceptual understanding already established with squares into cubes and also cube roots. If, anyone has objection(copy righted) then kindly mail [email protected] to request removal of the link. Send This Result Download PDF Result About Cube Numbers List . Finding Out Cube Roots of Perfect Cubes Using Vedic mathematics. Download, Technology & Computer Awareness Important Points All Exams, Ankur Yadav GK One Liner Hand written Notes PDF Download, World of Geography Raj Holkar Handwritten Notes Hindi PDF Square Cube Sq. In mathematics, a cube number, also called a perfect cube, or sometimes just cubed number, is an integer that is the cube of an integer. By the end of this unit I should be able to: ü Determine the square of a number. These are codes which are perfect in the sense that for fixed numbei"s r and µ every word is within Hamming distance r from exactly p. codewords. 4 Best Images of Printable Number Cube - Paper Cube Template, Perfect Cube Numbers List and ... 1275 x 1650 png 65kB. 1. stream A cube root of a number x is a number a such that a 3 = x. Send This Result Download PDF Result ... list of first n (up to 1000) cube numbers. 1. Square Cube Sq. Apply Use square tiles. Perfect Cubes 10 Terms. Solution : Prime factorisation of 1728 is 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 Since all prime factors can be grouped in triplets. If a variable with an exponent has an exponent which is divisible by 3 then it is a perfect cube. Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. A list of perfect squares under 100 includes 1, 4, 9, 16, 25, 36, 49, 64 and 81. You might also like: Squares, Cubes, and Roots Cheat Sheets For more math, ELA, and Special Education Resources; visit: Adventures In Inclusion Visit me on: Facebook Pinterest Instagram Visit my blog! From shop NarwhalSupplies. In dieser Rangliste sehen Sie als Kunde unsere absolute Top-Auswahl von Perfect ice cubes, bei denen die oberste Position unseren TOP-Favorit darstellt. The numbers such as 1, 8, 27, 64, etc. We are providing the squares and cubes of numbers from 1 to 50 below. = = = = How do you find the cube root of a non-perfect cube? I printed these on a full sheet of sticker paper and then cut the Because cubing and finding a number’s cube root are opposite operations, they cancel each other out. Trends that follow this type of curve include female literacy, vaccination rates, and refrigeration. Send This Result Download PDF Result ... list of first n (up to 1000) cube numbers. 췓��ԝ����V��ȶ�ЏH�=����B����p}k /���V���ӯ���N�S���g}��WR���ԭKlU�h �O?�]��*I��}D�9�8�5$e� u�/����mM���O�q��bk�/(�P��pGe�2��c�,$+�����'nx���ۦY5�j�v��V��?aZ��zc�������P���Z���ޣ=���8m0a�C������gl��T��#�?xh�eVvgx�F�M�皆e�5��c�Ve��.��p��Ƅ�Z����Z(r�d�YM�rMj߷Zq(�T,����WR����[gyP���k�i/�W? Section 3.2 Perfect squares, Perfect Cubes, and Their Roots notes.notebook 3 December 15, 2011 Dec 145:05 PM Page 146 #6 Use factoring to determine whether each number is a perfect square, a perfect cube, or neither. Download, SSC All Previous Year Asked One Word Substitution Till SSC CGL Know that √2 is irrational. Download, {***Maths Capsule***} for Competitive Exams PDF Download, NEO IAS Current Affairs September 2018 PDF Download, Reasoning Seating Arrangement Notes pdf Download, Rakesh Yadav Class Notes of Maths in Hindi PDF Download, Sagir Ahmad Maths Book PDF in Hindi Download, Mathematics SSC CGL TIER-II 2016 Solved Paper Download PDF, Statements & Assumptions Notes for Competitive Exams PDF It is called "Cubes", because this operation is similar to calculation of cube volume. Learning Intention. Therefore, 1728 is a perfect cube. We give a short analysis of the o To find the square root, find the number when multiplied by itself that’s equal to the number under the radical symbol. 5 2 = 125. 11deledani . lmlumpkin. Some problems require students to identify the GCF (greatest common factor), numerical and/or variable, before using the. 337 x 400 jpeg 30kB. Example 22 : Check whether 1728 is a perfect cube by using prime factorisation. Each of them is obtained when a number is multiplied by taking it three times. 27, 64, 1000 are some of the perfect cubes. After completing the perfect squares activity using the square tiles to model values squared visually, completing this perfect cubes activity should run much more smoothly. The seventh paper is about so-called perfect multiple coverings (PMC's). 3 2. For example, 27 is a cube number, since it can be written as 3 × 3 × 3. 2. Root Reciprocal No. ). Vocab Unit 6 20 Terms. o A square root is the _____ (opposite) of a perfect square. Squares - Cubes - Square Root Chart number s q u n are n 2 cube s q n 3 uare root number s q u n are n cube s q n uare root n n 81 6561 531441 9.0000 121 14641 1771561 11.0000 82 6724 551368 9.0554 122 14884 1815848 11.0454 83 6889 571787 9.1104 123 15129 1860867 11.0905 %PDF-1.5 endobj For example, 27 27 2 7 is a perfect cube because it is equal to 3 × 3 × 3. When a cube is broken or cut, total volume still remains the same. The smallest perfect cube is 1. phsoccer94. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Can you say why they are named so? This is a list of Squares and Cubes from 1-50. 3 × 3 × 3. 4 2 = 64. Here is a list of Perfect cubes from 1 to 1000. x���]o�6�� �?��Q�o PDF (1.2 MB) With this ... Includes a review of perfect cube numbers, example problems, and practice problems. They include mathematics topics and other lists of shapes such as shapes used by drawing or teaching tools. 8, 27, 64, 125, 216, 343, … are perfect cube Root Reciprocal No. Perfect ice cubes - Nehmen Sie dem Favoriten. 3 × 3 × 3. <> If a variable with an exponent has an exponent which is divisible by 3 then it is a perfect cube. Cubes and Cube Roots Worksheet Name Date Period What does it mean to “cube” a number? Making a Chart of Perfect Squares Through Perfect Fifths With Microsoft Excel Mr. Clausen Algebra II STEP 1 Set up the spreadsheet WHAT TO DO: Set up your Excel spreadsheet to make a chart of perfect squares, perfect cubes, perfect fourths, and perfect fifths. en: square cube root numbers ; Sponsored Links . Refer this free online list of perfect squares for first 100 numbers chart to make your calculations simple and save your time. Hence, we can observe that to construct a cube of edge length ‘2a’ with cubes of edge length ‘a’ we need to have 8 cubes of edge length a. For example,√3125 = 5 because 53= 125. This enables us to find the cheapest cost of producing any given level of output. 3\times 3 \times 3. Root Reciprocal No. 3. The perfect cube is the cube of any whole number. Squares, Cubes and Roots - Numbers - squares, cubes, square roots and cube roots ; Trigonometric Functions - Sine, Cosine and Tangent - Natural Trigonometric Functions; Two Equations with Two Unknowns - Online calculator for two equations with two unknowns; Tag Search . Cubes and Cube Roots CHAPTER7 Hardy – Ramanujan Number 1729 is the smallest Hardy– Ramanujan Number. What are the cube numbers? These are called perfect cubes or cube numbers. 4 0 obj Root Cu. 3\times 3 \times 3. Disclaimer: sscnotes.com neither created these files nor uploaded, we shared link is which is already available on the Internet. Square Cube Sq. These types of curves are low and flat at Level 1, rise sharply at Level 2, and flatten off at Levels 3 and 4. ���^�{�x��`�v�X�ߡD}��ј a. 1 3 = 1 2 3 = 8 3 3 = 27 4 3 = 64 5 3 = 125 6 3 = 216 7 3 = 343 8 3 = 512 9 3 = 729 10 3 = 1000. ü List the perfect squares between 1 and 144. ü Show that a number is a perfect square using symbols, diagram, prime factorization or by listing factors. ( Evaluate square roots of small perfect squares and cube roots of small perfect cubes. 22 3. Root Cu. Perfect cube is a number whose cube root is an integer Example : 23, 33, 43, 53, 63, 73 , … are perfect cube i.e. demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us. An example of a perfect square is 144. The other two special factoring formulas you'll need to memorize are very similar to one another; they're the formulas for factoring the sums and the differences of cubes. www.dummies.com. number system notes for ssc cgl pdf, number system questions pdf, number system tricks for ssc, number system in maths for competitive exams pdf, Download PDF of Squares & Cubes. The following is a list of perfect Cubes. Root Reciprocal No. There are an infinitely many such numbers. {David Hilbert, Address to the International Congress of Mathematicians, 1900 Our Euclidean intuition, probably, inherited from ancient primates, might have grown out of the rst seeds of space in the motor control systems of early animals who were brought … Example: √ 9 = 3 Where: 3 is the original integer. Perfect squares are infinite in number because they are found by multiplying a number by itself, meaning that the possibilities are endless. The principles in these tutorials are taken from various systems like Indian Vedic Mathematics and the German Trachtenberg System. 5 out of 5 stars (385) 385 reviews $0.95. In the Formula Bar, highlight the number 2 as shown below in black. Know that √2 is irrational. Lead a short two minute review of the work completed on day one using any pictures taken of student models and a quick review of the answers to the table using a student paper and the document camera . In mathematics, a cube number, also called a perfect cube, or sometimes just cubed number, is an integer that is the cube of an integer. �N�� This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), physics, engineering, economics, medicine, biology, psychology, ecology, etc. Mini Clear Ice Cubes - Perfect For Slime, Jewelry, Crafts, etc. Start studying First 10 Perfect Cubes. The following is a list of common perfect squares: 02 = 0. Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. www.youtube.com. Download, Top 100 General Knowledge Questions & Answers Capsule PDF Root Cu. Squares, Cubes, Perfect Fourths & Perfect Fifths. lmlumpkin. The goal is to complete the rest of the Perfect Cubes activity including any parts of the extension activity you choose to use. Although there are many square numbers, perfect squares are unique and very easy to calculate since whole numbers are involved. Remember these values make the calculation faster and accurate. List of Perfect Cubes for 101 - 200 numbers. Dynamic Table of Squares, Cubes, Perfect Fourths & Fifths and so on. For example x 9 is a perfect cube, its cube root is x 3. x 11 is not a perfect cube. Sämtliche in dieser Rangliste gelisteten Perfect ice cubes sind 24 Stunden am Tag auf amazon.de verfügbar und dank der schnellen Lieferzeiten in weniger als 2 Tagen bei Ihnen zuhause. Three equal integers is obtained when a cube number, since it be... Before using the cell A1, Type your Last Name, first and. Being a perfect cube by using prime factorisation a number a such that a 3 = x we if! Earn ; Discussion Forum ; Results ; Contact ; Student Login ; Institute Login ; Toggle navigation easy to since! Date Period What does it mean to “ cube ” a number is cube! N ( up to 1000 ) cube numbers, example problems, and practice problems the GCF ( common. Level of output cubes activity including any parts of the perfect cubes are., which we get if µ = 1 the list of mathematical shapes list. Cube number just by looking at the number seventh Paper is about perfect... Squares are infinite in number because they are found by multiplying a number by,.: square cube root of a number is multiplied by taking it three times cube is an integer can... Oberste Position unseren TOP-Favorit darstellt What does it mean to “ cube ” a number and 25 are few! By looking at the number are opposite operations, they cancel each other.! 'S ) expressed as the product of three equal integers principles in these tutorials are from! Goal is to complete the rest of the same poster to remind students about method... Vedic mathematics and the method of its calculation, and RECIPROCALS No Fourths! Which is divisible by 3 then it is equal to 3 × 3 × 3, and/or... Use to factor perfect cubes is nothing but the Result of squaring the same integer Student... These tutorials are taken from various systems like Indian Vedic mathematics and the method of its calculation taken... Roots, and RECIPROCALS No of two-dimensional geometric shapes table of squares and cubes for 101 200! 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https://socratic.org/questions/how-do-you-solve-10x-2-27x-18
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Algebra
Topics
# How do you solve 10x^2 - 27x + 18?
Jun 21, 2015
Use the quadratic formula to find zeros $x = \frac{3}{2}$ or $x = \frac{6}{5}$
$10 {x}^{2} - 27 x + 18 = \left(2 x - 3\right) \left(5 x - 6\right)$
#### Explanation:
$f \left(x\right) = 10 {x}^{2} - 27 x + 18$ is of the form $a {x}^{2} + b x + c$, with $a = 10$, $b = - 27$ and $x = 18$.
The discriminant $\Delta$ is given by the formula:
$\Delta = {b}^{2} - 4 a c = {27}^{2} - \left(4 \times 10 \times 18\right) = 729 - 720$
$= 9 = {3}^{2}$
Being a positive perfect square, $f \left(x\right) = 0$ has two distinct rational roots, given by the quadratic formula:
$x = \frac{- b \pm \sqrt{\Delta}}{2 a} = \frac{27 \pm 3}{20}$
That is:
$x = \frac{30}{20} = \frac{3}{2}$ and $x = \frac{24}{20} = \frac{6}{5}$
Hence $f \left(x\right) = \left(2 x - 3\right) \left(5 x - 6\right)$
graph{10x^2-27x+18 [-0.25, 2.25, -0.28, 0.97]}
Jun 21, 2015
color(red)(x= 6/5 , x =3/2
#### Explanation:
$10 {x}^{2} - 27 x + 18 = 0$
We can first factorise the above expression and thereby find the solution.
Factorising by splitting the middle term
$10 {x}^{2} - 15 x - 12 x + 18 = 0$
$5 x \left(2 x - 3\right) - 6 \left(2 x - 3\right) = 0$
$\textcolor{red}{\left(5 x - 6\right) \left(2 x - 3\right)} = 0$
Equating each of the two terms with zero we obtain solutions as follows:
color(red)(x= 6/5 , x =3/2
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https://chemistry.stackexchange.com/questions/24358/why-do-internal-combustion-engines-only-burn-to-carbon-monoxide-not-dioxide
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# Why do internal combustion engines only burn to carbon monoxide, not dioxide?
Why don't diesel and regular car engines burn all the way to $\ce{CO2}$?
## migrated from physics.stackexchange.comJan 29 '15 at 21:52
This question came from our site for active researchers, academics and students of physics.
• Most of the carbon-oxygen stuff coming out is CO2. Some isn't, because of detailed balance of the chemistry, inhomogeneous conditions in the piston, etc. – Jon Custer Jan 29 '15 at 20:42
• Seems like another question easily answered with very minor googling. – Carl Witthoft Jan 30 '15 at 2:00
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https://www.physicsforums.com/threads/just-a-simple-question-on-dot-products.180465/
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# Just a simple question on dot products
1. Aug 14, 2007
### mohdhm
1. The problem statement, all variables and given/known data
Ok so i ran into trouble in the momentum section because i do not understand dot products as well as i thought. I tried going back and revising my notes but nothing new comes to mind. Your help is highly appreciated.
ok so let me just state that m1=m2
the problem consists of 2 billiard balls, one is at rest and the other strikes it and sends it towards the corner pocket, they both share the same mass. the purpose is to find theta, but that is not what i'm trying to find out here.
We write the kinetic formula which gets reduced to v1i^2 = v1f^2 + v2f^2
then the momentum formula also gets reduced, this time it gets reduced to : v1i = v1f + v2f.
what i can't figure out, is that the example tells me to to square both sides (of the previous formula) and find the dot product.
then i get v1i^2 = (v1f + v2f)(v1f+v2f)... which gets expanded.. and so on
[the formula makes sense from a logical point of view]
The point is, how is the equation above, the DOT PRODUCT. I don't get that. i thought the dot product formula is AB = ABCOS(THETA)
any explanations?
2. Aug 14, 2007
### Mindscrape
Dot product? I have absolutely no idea. The equation is simply a product. You can't just take dot products for no reason, like your book seems to have done to suddenly get an angle. Are you sure your book didn't make momentum vectors?
My advice is to do what makes sense to you. If your book uses some clever way to find the angle that the balls go off at, but you have a way that simply does it by looking at conservation of momentum in the x and y directions then you should do it your way.
Could you write out exactly what your book has done, or is this it? Dot products, in case you are confused, are merely a way to multiply two vectors. You can either multiply the like components, (i.e. A1x + A2y + A3z dot B1x + B2Y + B3Z = A1B1x + A2B2y + A3B3z), or you can use the formula you listed which is A dot B = ABcosØ.
3. Aug 14, 2007
### mohdhm
i guess your right, this example in the book isnt even useful anyway, it is only used to determine the angle, and we can do that by this formula Phi + theta = 90 degrees. (only when the collision [k is conserved] is elastic and we have m1=m2)
4. Aug 14, 2007
### Hurkyl
Staff Emeritus
The dot product satisfies some properties. For example, it is distributive (just like ordinary multiplication)...
5. Aug 14, 2007
### Dick
I think the point is that the formula "Phi + theta=90 degrees" can be derived by taking the dot product of the vector equation v1i=v1f+v2f with itself and applying energy conservation, the distributive law of which Hurkyl spoke and your A.B=|A||B|cos(phi).
6. Aug 15, 2007
### Mindscrape
Yes, I imagine it was really doing something similar to using vectors and the dot product for proving law of cosines. Still, with what the poster wrote it isn't exactly a dot product. Given the velocity vectors, which I actually made a mistake earlier on thinking he was writing out the components in the i(hat) direction (I was tired), it should go more like:
$$\mathbf{v_1_0} = \mathbf{v_1_f} + \mathbf{v_2_f}$$
then square both sides of the formula
$$\mathbf{v_1_0}^2 = (\mathbf{v_1_f} + \mathbf{v_2_f})^2$$
which would be the vectors dotted with themselves
$$v{_1_0}^2 = (\mathbf{v_1_f} + \mathbf{v_2_f}) \cdot (\mathbf{v_1_f} + \mathbf{v_2_f})$$
then use the cosine distribution and dot products
$$v{_1_0}^2 = |v_1_f|^2+|v_2_f|^2 + 2*v_1_f*v_2_f*cos \theta$$
Still, it's obviously not something the book explained well, nor something I would expect an introductory physics course to go over and expect the students to use.
7. Aug 15, 2007
### mohdhm
8. Aug 15, 2007
### Dick
Maybe not explained well, but it works. Either the incoming ball stops dead or the ricochet angle is 90 degrees. It's an interesting use of the dot product.
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http://math.stackexchange.com/questions/356186/richardson-extrapolation
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# Richardson Extrapolation
Suppose that $$L=\lim_{h\rightarrow 0}f(h)$$ and that $$L-f(h)=c_{6}h^{6}+c_{9}h^{9}+\cdots$$ What combination of f(h) and f(h/2) should be the best estimate of L ?
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@Amzoti That's why I came here and try to find someone who can understands this question more. It is from the book directly. – CatSensei Apr 9 '13 at 18:26
@CatSensei, what book are you referring to? And where in it can the problem be found? – leeabarnett Apr 9 '13 at 18:27
$L-f(h)=ah^6+bh^9$
$L-f(h/2)=a(h/2)^6+b(h/2)^9$
Now cancel the $a$ term between the two
$[L-f(h)]-64[L-f(h/2)]=bh^9-64b(h/2)^9$
$64f(h/2)-f(h)-63L=7b/8h^9$
$L=(64f(h/2)-f(h))/63-b/72h^9$
Hence
the best approximation for $L$ from this step of Richardson is $(64f(h/2)-f(h))/63$.
You can see that if the first exponent is $n$ (in place of $6$) then $\displaystyle L\approx {2^nf(h/2)-f(h) \over 2^n-1}$
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I added explanation. – Maesumi Apr 9 '13 at 19:35
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https://infoscience.epfl.ch/record/224275
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Infoscience
Report
# Computing the equivalent number of parameters of fixed-interval smoothers
The problem of reconstructing an unknown signal from $n$ noisy samples can be addressed by means of nonparametric estimation techniques such as Tikhonov regularization, Bayesian regression and state-space fixed-interval smoothing. The practical use of these approaches calls for the tuning of a regularization parameter that controls the amount of smoothing they introduce. The leading tuning criteria, including Generalized Cross Validation and Maximum Likelihood, involve the repeated computation of the so-called equivalent number of parameters, a normalized measure of the flexibility of the nonparametric estimator. The paper develops new state-space formulas for the computation of the equivalent number of parameters in $O(n)$ operations. The results are specialized to the case of uniform sampling yielding closed-form expressions of the equivalent number of parameters for both linear splines and first-order deconvolution.
#### Reference
• EPFL-REPORT-224275
Record created on 2017-01-10, modified on 2017-05-10
### Fulltext
• There is no available fulltext. Please contact the lab or the authors.
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http://dsp.stackexchange.com/questions/6230/zeroing-bins-before-ifft
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# Zeroing bins before IFFT
Endolith's recent question on zeroing FFT bins got me thinking about a possible error in my workflow and I'd like to double check.
Consider a signal $x_i[m],\ m\in\{1,\ldots,M\}$, i.e. $M$ samples sampled at $f_s$ and the subscript denotes the $i^{th}$ such signal segment. I then filter this with a bandpass filter to between $0.1 f_s$ and $0.3f_s$ (at this stage, I was careful to not do a zero-the-bins kind of filtering) and Fourier transform it with an $N>2M$ long FFT. Let $X_i[k],\ k\in\{0,\ldots,N-1\}$ denote the Fourier coefficients and the filtered portion (including the roll-off frequencies on both ends) be the indices $0< k_l,...,k_u< N-1$.
My application now involves applying some function, $g$ to the Fourier coefficients $X_i[k_l],\ldots,X_i[k_u]$, averaging across the different segments ($i$) and inverse Fourier transforming the resulting vector. In math, I compute
$$X_{avg}[k]=\left\langle g(X_i[k])\right\rangle_i,\ k\in\{k_l,\ldots,k_u\}$$
where $\langle\cdot\rangle_i$ denotes averaging over the different segments. So far, so good.
Now, I didn't know what to do with the remaining Fourier coefficients $X_i[k'],\ k'\in\{0,\ldots,N-1\}\backslash \{k_l,\ldots,k_u\}$ before taking the IFFT. These coefficients are theoretically insignificant, since I've already filtered out content in them. So I went ahead and set $X_{avg}[k']=0$ and then computed the IFFT of $X_{avg}$. The results were along the lines of what I expected, but I didn't think of the aforementioned filtering issue, although I was aware of it (this is the same situation, with a bit of twists at places).
My question then is: Is it still a problem in this case i.e., when the bins that I "zeroed out" were technically low/insignificant? If so, how should I have handled it?
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Filtering a signal by modifying the Fourier coefficients and then inverse Fourier-transforming it is a filter design method known as the "frequency-sampling" method.
Many research works on source separation for instance consider such filters because they are convenient (working on spectral characteristics to separate the signals - e.g. the fact that the frequency support of 2 sources is different) easy to implement and still lead to very convincing results (even the infamous "binary masks" :D).
You could compare this method to others, for instance FIR filter design by the window method : compute the ideal IIR impulse response and crop it or window it with a Hann/Hamming/your-preferred-window function. The window method corresponds to multiplying your impulse response by a window, in the time domain. It therefore results in a convolution between the involved Fourier transforms, leading to the well-known Gibbs effect.
For the frequency sampling method, you don't need to find the impulse response, but this comes at the cost that you do not control much of what is happening /between/ the frequency bins: in your example, that would correspond to the frequencies $\frac{\nu}{N} f_s$ where $\nu \notin \{0,1, 2,..., N-1\}$. The actual frequency response of such a filtering process is then an interpolation between the sampled points of the desired frequency response. This issue is not often discussed in the literature, but could lead to big cripples in the resulting frequency response.
There are other methods for designing filters, for instance for designing low/high pass or band-pass filters, but I have less practical experience there. I guess those are anyway not what you are looking for. I mentioned the window method only as a way of comparing what's happening: with the window method, you have trouble with the Gibbs effect, and with the frequency sampling method, you don't really know what's happening between the sampled frequency bins.
This said, for your practical problem, from my own experience, zeroing frequency bins is usually fine. Assuming the way you decide how to enhance this or that frequency bin makes sense (avoiding too many "jumps" in the frequency response, for instance), the result should not exhibit too many artifacts from that process. Note that setting the low values to zeros, instead of keeping the original ones, may however deteriorate what is happening in the frequency region of interest. In source separation as I have experience it, we usually try to minimize some criterion (e.g. mean squared estimation errors), and that can provide us with an optimal way of setting all the values of the Fourier transform. I would argue that this is a better way of dealing with the matter, instead of trying all sort of values for the "missing" ones until the result is acceptable (a method which is most likely to depend on the test signal, hence poorly generalizing to other signals).
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The FFT operation is linear. Thus any FFT bin that is in the noise floor relative to the sum magnitude of the spectrum of your signal of interest in the frequency domain will likely still be in the noise floor in the time domain, and thus so will the "noise" generated by zeroing that bin.
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https://electronics.stackexchange.com/questions/506432/jtag-voltage-compatibility
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# JTAG Voltage compatibility
I am having this microcontroller - S32K142 64 pins 5V core voltage.
I am using the this J LINK 20 pin JTAG Debugger. Using JLINK Flash Lite software tool in Windows PC to program the microcontroller by connected the debugger through USB port of the PC
JTAG User Manual
I just want to verify, theorectically, the the Vih,Vil,Voh & Voh levels between the Microcontroller JTAG pins and the JTAG debugger output and input pins.
Can someone tell me how to proceed with the calculation. USB 2.0 Type A to type B cable is used to interface the PC to the debugger.
Please tell me how to evaluate the voltage levels in this scenario where the PC sends data to the debugger in differential format and the debugger gives the single ended data to the JTAG debugger pins. What would be the voltage levels and their tolerances in the debugger to the JTAG Microcontroller lines ?
• USB has nothing to do with it at all (beyond probably meaning a common ground) that Segger device is its own little computer with entirely distinct I/O drivers for the JTAG. Given what they charge for it, it presumably has a target Vcc input and adjusts its I/O voltages accordingly, but you'd have to check the Segger user manual - for the actual probe model you want to use, not the generic connector description you linked. Jun 19 '20 at 16:16
• Yes, I understand that USB might not have something to do. I have checked the user manual too. There is no mention of the Voltage levels in the user manual too. How to check for the voltage compatibility between the JTAG and the microcontroller JTAG pins? Jun 19 '20 at 16:20
• It would seem you are not looking in the manual or technical specification of the actual unspecified probe you want to use. Again, what you linked was a generic connector pinout, not a manual. Jun 19 '20 at 16:33
• @ChrisStratton - segger.com/downloads/jlink/UM08001_JLink.pdf - This is the user manual. I tried to find it in here, but I couldn't find Jun 20 '20 at 3:54
• No, again, that is not the manual for the physical debug adapter. What you are linking is a manual for the software. You've still failed to even specify which specific debug adapter you are using! Look at the part number on the physical tool, and look up the specifications of that. It's still unclear if you are using a full featured version with target voltage level translation, a simple version without, or a knockoff of unknown specification. Jun 21 '20 at 16:12
From a general perspective, to do these checks you need to locate the hardware specifications for the programmer you are using. This information is usually available from the manufacturer in the form of a specifications page or a datasheet. If no such page exists, either contact the manufacturer directly, or don't buy it (same goes for any electronic component!).
You can the find the corresponding data for the microcontroller itself in the datasheet available from chip manufacturer (in your case NXP). The IC datasheet will again tell you the IO voltage for the microcontroller.
Beware that the numbers for both programmer and MCU may be stated in terms of %age of VDD or VDDIO or some such similar. This means you will need to know what voltage your microcontroller is running at, and additionally how the voltage of the programmer is set.
A further point to node is that many, but by no means all, programmers have a target voltage reference pin which is an input to the programmer that you drive from the supply voltage of the target in order to allow the programmer to level shift its signals to match the target. This pin if present must be connected otherwise comms will fail.
Once you know the specifications for both in terms of a voltage level, you simply then need to compare the numbers and ensure that $$\V_{OH} \ge V_{IH}\$$ and $$\V_{OL} \le V_{IL}\$$ in both directions (MCU->Programmer and Programmer->MCU) to make sure the programmer and target can talk to each other.
As a final note, some microcontrollers with built in flash memory may support running and communication at lower VDD voltages, but are unable to be programmed below a certain level (certain ATTiny MCUs do this for example), so make sure that your target is running at a voltage at which it supports programming.
On to your specific case. You haven't specified in the question which specific model of J-Link you are using. Furthermore the manual you have linked to is a user guide, not the specifications of the programming adapter.
Looking on the manufacturers website, we can see there is a comparison table of all of the different J-Link programmers, which shows the key specs of each of the models. The following is an extract from the table where we can see the supported target voltage ranges of each.
From this table we can see that all of the except for the J-Link EDU Mini support any voltage within the range of 1.2V to 5V. The voltage of this interface is set by connecting the supply voltage of the target to the reference voltage pin on the 20-way interface.
Further details are then available on the detailed specification pages of each of the individual programmers - clicking on one of the programmer names in the title row of the table linked above takes you to the page for that programmer.
For example, if I click on the first programmer in that table, we get the full specs of the programmer with relation to the input voltage specifications. The following is the voltage specifications for the J-Link EDU programmer:
• Thank you for the answer. Jun 22 '20 at 5:18
• But what about the Vol and Voh values? The above values are mentioned with a condition of a load of 10k ohms? Which value should I consider for Voh and Vol? Jun 22 '20 at 5:23
• @Newbie with no load the voltage will be closer to 0%/100%. Jun 22 '20 at 8:21
• Thank you. In this case, does the load mean, the internal pull-up resistors inside the microcontroller? Jun 22 '20 at 8:43
• @Newbie a pull-up resistor would count as a load, yes. Jun 22 '20 at 9:11
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http://math.stackexchange.com/questions/60014/langs-proof-of-the-fact-that-a-finitely-generated-p-module-is-the-direct-sum
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# Lang's proof of the fact that a finitely generated $p$-module is the direct sum of cyclic $p$-modules
The question refers to a proof of the theorem that a finitely generated $p$-module is the direct sum of cyclic $p$-modules. In particular, refer to Lang's "Algebra" p. 151, right above Theorem 7.7. I can not understand what he is inducting on, even though i see that $dim\bar{E}_p < dimE_p$. I can't see how we obtain that $E$ is generated by an independent set.
Alternatively, could we not construct a proof by induction on the cardinality of a minimal generating set of $E$, instead of resorting to the vector space $E_p$ induced by $E$?
Thank you :-)
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Dear Manos: What is a $p$-module? – Pierre-Yves Gaillard Aug 27 '11 at 4:30
Hi Piere: a $p$-module is a torsion module for which each element has period a power of $p$. ($p$ is a prime element of the underlying principal ideal domain). – Manos Aug 27 '11 at 14:00
Thanks! I think Lang is almost the only one to use this terminology, but never mind. - Is it the existence or the uniqueness part of the proof that you don’t understand? - I looked at various proofs of this theorem. I reproduced the one I find the simplest here. (See Theorem 3.) - I got the notification, but it’s safer I think if you use an @Pierre. – Pierre-Yves Gaillard Aug 27 '11 at 14:46
The excerpt in question can be viewed here.
George Bergman writes here:
P. 151, statement of Theorem III.7.7: Note where Lang above the display refers to the $R/(q_i)$ as nonzero, this is equivalent to saying that the $q_i$ are nonunits.
P. 151, next-to-last line of text: After "i = 1, ... , l" add, ", with some of these rows 'padded' with zeros on the left, if necessary, so that they all have the same length r as the longest row".
Here is the link to George Bergman's A Companion to Lang's Algebra.
And here is a statement of the main results.
Let $A$ be a principal ideal domain and $T$ a finitely generated torsion module. Then there is a unique sequence of nonzero ideals $I_1\subset I_2\subset\cdots$ such that $T\simeq A/I_1\oplus A/I_2\oplus\cdots$ (Of course we have $I_j=A$ for $j$ large enough.)
The proper ideals appearing in this sequence are called the invariant factors of $T$.
Let $P_1,\dots,P_n$ be the distinct prime ideals of $A$ which contain $I_1$, and for $1\le i\le n$ let $T_i$ be the submodule of $T$ formed by the elements annihilated by a high enough power of $P_i$. Then $T=T_1\oplus\cdots\oplus T_n$, and the sequence of invariant factors of $T_i$ has the form $$P_i^{r(i,1)}\subset P_i^{r(i,2)}\subset\cdots$$ with $r(i,1)\ge r(i,2)\ge\cdots\ge0$. (Of course we have $r(i,j)=0$ for $j$ large enough.)
The $P_i^{r(i,j)}$ called the elementary divisors of $T$.
We clearly have $I_j=P_1^{r(1,j)}\cdots P_n^{r(n,j)}$.
Let $M$ be a finitely generated $A$-module and $T$ its torsion submodule. Then there a unique nonnegative integer $r$ satisfying $M\simeq T\oplus A^r$.
The simplest proof of these statements I know is in this answer (which I wrote without any claim of originality).
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Thank you very much. Regarding Bergman's companion to Lang's algebra, how do i open the files? Can they be found in a pdf form? Regarding the terminology, Steven Roman in "Advanced Linear Algebra" refers to these modules as $p$-primary modules as well. Lang skips the "primary". I find it convenient because it refers to the same concept as the terminology "$p$-group". Regarding the theorem, my question actually refers to theorem 7.5 and part of its proof on the upper half on page 151. More precisely, i can not see what he is inducting upon... – Manos Aug 30 '11 at 13:29
...In particular, it is claimed that if $E \neq 0$, then there exist elements $\bar{x}_2, \cdots, \bar{x}_s$ that are independent, and then he invokes Lemma 7.6. I can see that by using the lemma, $x_1, x_2, \cdots, x_s$ are independent. What i can't see is why independent elements $\bar{x}_2, \cdots, \bar{x}_s$ exist and also what we are inducting on to prove the decomposition. – Manos Aug 30 '11 at 13:34
@Manos: You're welcome. Here is what I think: He is inducting on $\dim E_p$. Since $\dim\overline E_p < \dim E_p$, the elements $\overline{x}_2, \cdots, \overline{x}_s$ exist by induction assumption. – Pierre-Yves Gaillard Aug 30 '11 at 14:30
@Manos: Sorry I forgot about Bergman's files. I only found them in ps format. My browser (Safari) can read this format. You may try to write to Bergman. I don't what kind of computer you're using, but I think you should be able to find free software capable of reading ps. (If you study Lang's book, Bergman's Companion can be very helpful.) – Pierre-Yves Gaillard Aug 30 '11 at 15:32
On unux/linux, the "ps2pdf" utility will convert Postscript to PDF. The downloadable freeware "TeXShop" for Mac OS X includes ps2pdf, also. – paul garrett Nov 22 '11 at 17:55
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http://cool.conservation-us.org/byauth/lynn/glossary/term1-5.html
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[Document Tree]
The Original Document
1.1 Medium
1.2 Format
1.3 Periodicity
1.4 Properties
1.5 Condition
1.6 Content
1.5. Document Condition
Condition refers to the physical state of the document compared with its state when originally published. The following presents only those characteristics of the physical state of a document that are pertinent to the main thrust of this Glossary, that is, to the paper milieu.
1.5.1. Archival
A document that can be expected to be kept permanently as closely as possible to its original form. An archival document medium is one that can be "expected" to retain permanently its original characteristics (such expectations may or may not prove to be realized in actual practice). A document published in such a medium is of archival quality and can be expected to resist deterioration.
Permanent paper is manufactured to resist chemical action so as to retard the effects of aging as determined by precise technical specifications. Durability refers to certain lasting qualities with respect to folding and tear resistance.
1.5.2. Non-Archival
A document that is not intended or cannot be expected to be kept permanently, and that may therefore be created or published on a medium (1.1) that cannot be expected to retain its original characteristics and resist deterioration.
1.5.3. Acidic
A condition in which the concentration of hydrogen ions in an aqueous solution exceeds that of the hydroxyl ions. In paper, the strength of the acid denotes the state of deterioration that, if not chemically reversed (3.1.2), will result in embrittlement (1.5.4). Discoloration of the paper (for example, yellowing) may be an early sign of deterioration in paper.
1.5.4. Brittle
That property of a material that causes it to break or crack when depressed by bending. In paper, evidence of deterioration usually is exhibited by the paper's inability to withstand one or two (different standards are used) double corner folds. A corner fold is characterized by bending the corner of a page completely over on itself, and a double corner fold consists of repeating the action twice.
1.5.5. Other
There are many other conditions that characterize the condition of a document. Bindings of books, for example, may have deteriorated for a variety of conditions. Non-paper documents may exhibit a variety of conditions (see, for example, 3.3.5 for a discussion of the concept of "Useful Life"). However, with the focus on paper original documents and on media conversion technologies for preservation, a full analysis of document condition would be beyond the scope of this Glossary.
[Document Tree]
URL: http://cool.conservation-us.org/byauth/lynn/glossary/term1-5.html
Timestamp: Sunday, 23-Nov-2008 15:20:17 PST
Retrieved: Tuesday, 16-Oct-2018 21:36:48 GMT
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https://www.physicsforums.com/threads/financial-diffeq-question.257704/
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# Financial DiffEq question
1. Sep 19, 2008
### jaejoon89
I am having trouble understanding conceptually the following DiffEq problem:
"Suppose you can afford no more than $500 per month of payment on a mortgage. The interest rate is 8% and the mortgage term is 20 yrs. If the interest is compounded continuously and payments are made continuously, what is the max. amount you can borrow and the total interest paid during the mortgage term?" 1) dA/dt = r*A 2) A(t)=A_0*e^rt dA/dt is the rate of change of the value of the investment... would that just be the 500/month, and use that to find the original investment? I'm not sure I understand... From the 2nd equation A'(t) = A_0*r*e^rt, but 500/month would be fixed so doesn't resemble A'(t)... 2. Sep 20, 2008 ### chaoseverlasting What does it mean that "the Interest is compounded continuously"? 3. Sep 20, 2008 ### bdforbes A(t) is the amount you owe at time t. It increases continuously due to interest, and decreases continuously due to repayments. I think you need the variable r to encompass both these effects. 4. Sep 20, 2008 ### bdforbes I've been thinking about this problem I feel like it's not being asked properly... it seems like they want you to calculate the principle A_0 which would grow to$120 000 after 20 years of continuous compounding at 8%, ignoring repayments.
The fact that it says "continuous repayments" is also troubling. If we make payments continuously at a rate of $500 / month, but the amount continuously grows at a rate 0.08*A, the only way to ever reduce A to zero would be if the initial rate of growth is$500 / month. Otherwise A could only increase.
EDIT: I just read what I wrote and realized that I pretty much answered the question for you :P. Here's the trick:
$$\frac{dA}{dt}=r*A - 6000$$
Ie, the rate of change of the amount includes a fixed continuous rate of \$6000 / year.
5. Sep 20, 2008
### jaejoon89
Thanks.
Last edited: Sep 20, 2008
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https://www.physicsforums.com/threads/analytic-function-definiton.523890/
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# Analytic function definiton
1. Aug 24, 2011
### JamesGoh
From my lecture notes I was given, the definiton of an analytic function was as follows:
A function f is analytic at xo if there exists a radius of convergence bigger than 0 such that f has a power series representation in x-xo which converges absolutely for [x-xo]<R
What I undestand is that for all x values, |x-xo| must be less than R (radius of convergence) in order for f to be analytic at xo.
Convergence in a general sense is when the sequence of partial sums in a series approaches a limit
Is my understanding of convergence and analytic functions correct ?
2. Aug 24, 2011
### Fredrik
Staff Emeritus
What you're saying here would imply that the truth value ("true" or "false") of the statement "f is analytic at x0" depends on the value of some variable x. It certainly doesn't. It depends only on f and x0. (What you said is actually that if |x-x0|≥R, then f is not analytic at x0).
I'm a bit surprised that your definition says "converges absolutely". I don't think the word "absolutely" is supposed to be there. But then, in $\mathbb C$, a series is convergent if and only if it's absolutely convergent. So if you're talking about functions from $\mathbb C$ into $\mathbb C$, then it makes no difference if the word "absolutely" is included or not.
What the definition is saying is that there needs to exist a real number R>0 such that for all x with |x-x0|<R, there's a series $$\sum_{n=0}^\infty a_n \left( x-x_0 \right)^n$$ that's convergent and =f(x).
I like Wikipedia's definitions by the way. Link.
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https://www.physicsforums.com/threads/zwiebach-page-210.193837/
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# Zwiebach page 210
1. Oct 25, 2007
### ehrenfest
1. The problem statement, all variables and given/known data
equation 12.28 is only true if $$\dot{X'^j}$$ is equal to 0, right? Why is that true?
2. Relevant equations
3. The attempt at a solution
2. Oct 25, 2007
### nrqed
No. It follows from 12.27 which does not require anything like that
3. Oct 25, 2007
### ehrenfest
but isn't the only way that
$$\frac{d}{d\sigma} (X^I \dot{X^J}-\dot{X}^J X^I) = X^I' \dot{X^J}-\dot{X}^J X^I'$$
if \dot{X^J}' equal 0
?
4. Oct 25, 2007
### nrqed
No. I am not sure why you conclude this. Notice that for I not equal to J, the expression in parenthesis is zero even before taking a derivative.
5. Oct 25, 2007
### ehrenfest
I think I see now. It should really be
$$\frac{d}{d\sigma} (X^I (\tau, \sigma) \dot{X^J}(\tau, \sigma')-\dot{X}^J(\tau, \sigma') X^I(\tau, \sigma))$$
and the sigma derivative of a function of sigma prime is 0.
6. Oct 25, 2007
### nrqed
I am sorry, maybe I am too slow tonight (after 8 hours of marking) but I don't quite see what you mean. The expression in parenthesis is zero whenever I is not equal to J. Those X's are operators. And they commute when I is not equal to J. when I = J, they don't commute but give a delta function of sigma - sigma'.
7. Oct 25, 2007
### Jimmy Snyder
Note that $\sigma$ and $\sigma'$ are independent variables in this equation.
8. Oct 25, 2007
### ehrenfest
I think maybe you are missing the dot on top of the x^J. That represents a tau derivative.
9. Oct 25, 2007
### nrqed
You are right, I forgot to say that it's the conmmutator of X with dot X. But my point is the same: X^I and (dot X)^J commute whenever I is not equal to J. So the derivative is zero trivially because the expression in parenthesis is zero before even taking thee derivative and not because there is no sigma dependence (well, there is sigma dependence trivially because it's zero!)
10. Oct 25, 2007
### ehrenfest
$$X^I (\tau, \sigma) \dot{X^J}(\tau, \sigma')-\dot{X}^J(\tau, \sigma') X^I(\tau, \sigma) = 2 \pi \alpha' \eta^{IJ} \delta(\sigma - \sigma ')$$
is equation 12.27 expanded
$$\frac{d}{d\sigma} (X'^I (\tau, \sigma) \dot{X^J}(\tau, \sigma')-\dot{X}^J(\tau, \sigma') X'^I(\tau, \sigma)) = 2 \pi \alpha' \eta^{IJ} \frac{d}{d \sigma}\delta(\sigma - \sigma ')$$
is equation 12.28 expanded
12.28 follows from 12.27 only if $$\frac{d}{d\sigma}(\dot{X}^J(\tau, \sigma')) = 0$$ which is true only because the sigma argument has a prime but the sigma in the derivative operator has no prime.
Last edited: Oct 25, 2007
11. Oct 25, 2007
### nrqed
There si no d/dsigma on the left side
Ok, I see what your question was. yes, of course, $\frac{d}{d \sigma} f(\sigma') = 0$. Sorry, I did not understand your question because this was implicit for me.
Similar Discussions: Zwiebach page 210
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https://rank1neet.com/unit-5-states-of-matter-summary/
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# Unit 5 – States Of Matter – Summary
Intermolecular forces operate between the particles of matter. These forces differ from pure electrostatic forces that exist between two oppositely charged ions.
Also, these do not include forces that hold atoms of a covalent molecule together through covalent bond.
Competition between thermal energy and intermolecular interactions determines the state of matter.
“Bulk” properties of matter such as behaviour of gases, characteristics of solids and liquids and change of state depend upon energy of constituent particles and the type of interaction between them.
Chemical properties of a substance do not change with change of state, but the reactivity depends upon the physical state.
Avogadro law states that equal volumes of all gases under same conditions of temperature and pressure contain equal number of molecules.
Dalton’s law of partial pressure states that total pressure exerted by a mixture of non-reacting gases is equal to the sum of partial pressures exerted by them. Thus p = p1+p2+p3+ ... .
Relationship between pressure, volume, temperature and number of moles of a gas describes its state and is called equation of state of the gas.
Equation of state for ideal gas is pV=nRT, where R is a gas constant and its value depends upon units chosen for pressure, volume and temperature.
At high pressure and low temperature intermolecular forces start operating strongly between the molecules of gases because they come close to each other.
Under suitable temperature and pressure conditions gases can be liquified.
Liquids may be considered as continuation of gas phase into a region of small volume and very strong molecular attractions.
Some properties of liquids e.g., surface tension and viscosity are due to strong intermolecular attractive forces.
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http://math.stackexchange.com/questions/24660/condition-for-existence-of-lagrange-multiplier
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# Condition for existence of Lagrange-multiplier
Using the implicit function theorem one can prove the following:
Let $X,Y$ be Banach-spaces, $U\subset X$ open, $f\colon U\to \mathbf{R}$, $g\colon U\to Y$ continuously differentiable function. If $f|_{g^{-1}(0)}$ has a local extremum at $x$, and $g'(x)\in L(X;Y)$ has a right inverse in $L(Y;X)$, then there is a unique $\lambda\in Y^*$, such that $f'(x)=\lambda\circ g'(x)$.
One can also give some second order necessary and sufficient conditions. This generalizes the case where $Y$ is finite dimensional, and $g'(x)$ is surjective. However I have seen some texts that claimed that only surjectivity is sufficient even in the infinite dimensional case.
My question is does that hold true? If it does what is the method of the proof, because I cannot figure how the implicit function theorem could be used. If the proof is complicated I would appreciate even just some good references.
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Yes, surjectivity of dg(x) is sufficient.
The proof is not very complicated, but takes some work. The reference cited by Planetmath is: Eberhard Zeidler. Applied functional analysis: main principles and their applications. Springer-Verlag, 1995. Take a look at page 268 and following.
The key ingredient is a weaker formulation of the implicit function theorem: Suppose $F: X \times Y \to Z$ is $C^1$ in a neighbourhood of $0$, with $F(0,0) = 0$ and $D_Y F(0,0) : Y \to Z$ is surjective. Then,
(1) For each $r > 0$, there exists $\rho > 0$ so for every $|| u || < \rho$, there exists $v = v(u)$ with $F(u, v(u) ) = 0$ and $|| v || < r$.
(2) There exists $d > 0$ so that $|| v(u) || \le d || D_Y F(0,0) v(u) ||$.
The proof of this is a bit more delicate than the standard implicit function theorem, but you use the closed range theorem to construct a surrogate for the inverse, and then use this to construct your iteration.
You then prove the Lagrange multiplier theorem from this, essentially following the standard proof (presumably the one you had in mind above).
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http://arxiv-export-lb.library.cornell.edu/abs/1911.05766?context=physics
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physics
(what is this?)
# Title: Generalized and multiplexed $q$-plates with radial and azimuthal dependence
Abstract: In this paper we generalize the concept of the $q$-plate allowing arbitrary functions of both the radial and the azimuthal variables, and simulate their effect on uniformly polarized beams in the far-field regime. This gives a tool for achieving beams with hybrid states of polarization (SoPs), and alternative phase and intensity distributions. We propose an experimental device based on a liquid crystal on silicon (LCoS) display for emulating these generalized $q$-plates and show a new application that takes advantage of the pixelated nature of this kind of devices for representing discontinuous elements resulting from the random combination of two different $q$-plates, i.e. multiplexed $q$-plates.
Comments: arXiv admin note: text overlap with arXiv:1812.08202 Subjects: Optics (physics.optics) Cite as: arXiv:1911.05766 [physics.optics] (or arXiv:1911.05766v1 [physics.optics] for this version)
## Submission history
From: Martin Vergara [view email]
[v1] Wed, 13 Nov 2019 19:14:39 GMT (6390kb,D)
Link back to: arXiv, form interface, contact.
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https://kb.osu.edu/dspace/handle/1811/15755
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A NEW HYDRIDE SPECTRUM NEAR 7666{\AA}.
Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/15755
Files Size Format View
1969-L-07.jpg 105.1Kb JPEG image
Title: A NEW HYDRIDE SPECTRUM NEAR 7666{\AA}. Creators: Johns, J. W. C. Issue Date: 1969 Abstract: Whilst searching for emission spectra of $AlH^{+}$ an aluminum hollow cathode lamp was run with a mixture of deuterium and argon. The lamp was found to emit a simple band with wide rotational structure near $7666{\AA}$. The band has P, Q and R branches which are clearly resolved into doublets; the magnitude of the doubling is approximately independent of the rotational quantum number. A similar band was also observed when the lamp was run with hydrogen and argon but the lines were broad and consequently no doublet splitting was resolved. Preliminary rotational analysis gives B values which seem to be too large for $AlH^{+}$ or $AlD^{+}$. The identity of the emitter will be discussed. URI: http://hdl.handle.net/1811/15755 Other Identifiers: 1969-L-7
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https://blackhole12.blogspot.nl/2012_05_01_archive.html
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May 29, 2012
When I was growing up and trying to figure out what was going on in this crazy planet I was born on, there were several important questions I asked that took many, many years to find answers to. What was frustrating is that almost every single answer was usually extremely obvious once I could just find someone who actually knew what they were talking about. So here are the answers to several simple life questions that always bugged me as a kid, based on my own life experiences. Many people will probably disagree with one or two things here, which is fine, because I don't care.
1. What is the purpose of Math?
Math is simply repeated abstraction and generalization. All of it. Every single formula and rule in mathematics is derived by generalizing a simpler concept, all the way down to the axioms of set theory. It was invented to make our lives easier by abstracting away annoying things. Why count from 2 to 6 when you can simply add 4? Adding is simply repeated counting, after all. But then, if you can add 4 to 2 and get 6, you should be able to generalize it so you can add 4 to 2.5 and get 6.5, and what about adding 2 to 4 over and over and over? Well that's just multiplication. What about multiplying 2 over and over and over? Well that's just exponentiation. What's that funky Gamma Function I see every now and then? That's simply the factorial ($5! = 5\cdot 4\cdot 3\cdot 2\cdot 1$) generalized to real and complex numbers, so it can evaluate 5.5!, its just written Γ(5.5 - 1) = Γ(4.5). Math is generalization.
Usually smart people figured all the generalizations out for you, so in some cases you can simply memorize a formula or look it up, but its much easier to simply remember the rules that the smart people figured out for you so you can rederive everything you need without having to memorize it. When you understand the rules (which are all carefully constructed to be consistent with each other), you can then use Mathematics as a language to express problems in. By abstracting the problem into mathematics, the answer becomes much easier to obtain. The only thing math does is make thing easier to do by abstracting them. That's all.
2. Why does college think high grades in math correspond to programming ability?
This is because programming is math. Programming is all about abstracting a problem to automate it. Think of it as a lingual descendant of Math. The problem is that in high school they teach you calculus and programming at the same time and try to tell you that they are related. They aren't. Calculus doesn't have anything to do with programming. Set Theory does. The mathematical constructs of logic are what programming derives from, not calculus. Naturally, they don't teach you any of that. Even though you can consider programming a sub-discipline of mathematics, ones programming ability is not connected to your test-taking abilities.
3. How do you compose music?
First, you come up with a melody. The best way to do this is to find a song you like, and figure out its melody. Knowing basic music theory will help, because then you know what a chord progression is, so you can find that too. Simply rip off all the common chord progressions you like - you'll come up with your own later. Rhythm is important too, so take note of that - be careful to focus on notes that seem to carry the beat.
Great, that was the easy part. But how do you make techno music? How do you record things? How does it get on a computer? All I have is this stupid electric piano I can record things off of, there has to be a better way! The answer is DAWs and VSTi, or Digital Audio Workstations and their virtual instrument plugins. A great DAW to start with is FL Studio, and there are a lot of free VSTi plugins floating around. VSTi plugins are simply synths or effects or other tools that you drop into your DAW and use to play notes or modify the sound. If you want natural sounding instruments, use samples. Soundfonts are widely supported, have an extension .sf2 and there are gigabytes upon gigabytes of free samples everywhere. You should try to hunt down an independent artist whose music you like, they'll often be willing to give on advice on how they create their style.
But now I've made a song, where do I post it? Soundcloud, newgrounds, last.fm, and bandcamp lets you sell it for moneys. Don't worry if you're terrible, just keep doing it over and over and over and paying attention to advice and constructive criticism.
4. How do you draw clean art?
Clean digital art is commonly done using vectorization and gradients. There are multiple photoshop techniques that can be combined with tablets to create very nice looking lines by doing fake-tapering and line adjustments, but more commonly the tablet is simply pressure sensitive. There are many different techniques for doing various styles, so its more appropriate to ask the artist themselves.
I say instinct but no one really knows yet (only 90% of humans kiss). Provided you are in a culture that does kiss, you'll grow up to be around 16-17 and suddenly you'll feel this inexplicable urge to kiss whomever you've fallen in love with for no apparent reason. It's theorized to have arisen due to needing to evaluate certain proteins in a potential partner, which requires physical contact, along with various other things. I say instinct because I always thought it wasn't instinct and I wouldn't fall for it and then why am I fantasizing about kissing girls CRAP.
6. Why do adults fall in love in the first place?
Instinct. By the time you are 20, if you haven't yet found an intimate partner, you will feel crushing loneliness regardless of how many friends you have. Do not underestimate just how badly Nature wants you to have babies. This is why people get desperate - the desire to be in an intimate, loving relationship can be extremely powerful. It also leaves a giant hole that often explains various other bizarre things adults do in apparent attempts to kill themselves in the most amusing way possible.
7. Why don't popular people respond to fan mail very often?
This usually only comes up if you are using a bad medium. Artists often want to talk to their non-retarded fans, but the majority of people are incredibly stupid (see below), and thus in certain cases the signal-to-noise ratio is so high they simply can't justify spending the time to find you in a sea of insane idiocy when they have better things to do, like be awesome. Some artists simply don't want to be bothered, and this is usually the result of being disillusioned with how utterly stupid most people are, so it's hard to blame them, but unfortunate. Usually there will be a way to at least throw a meaningful thank you to the artist, possibly by e-mail or twitter if you look hard enough, and they will always appreciate it if they can just find your message. Never assume an artist is too stuck up and full of themselves to answer you. They just can't find you. Although quite a few of them actually are assholes.
8. Why is everything I do always wrong?
Because people are idiots and have no idea what they're talking about. Only ever listen to someone telling you that you are doing something wrong if you know they have extensive experience in exactly what you are trying to do. Otherwise, take the advice with a mountain-sized lump of salt, because people in specialized professions almost always take advice out of context and inappropriately simplify it to the point of it actually being completely wrong. There is always a catch. This is taken up to eleven in programming - I once had someone who did networking tell me my choice of language for my graphics engine was completely wrong and insisted I was so bad at programming I should just stop, because it would make the world a better place. He is an asshole, and he is completely wrong. Don't listen to those people, ever.
9. Why does everyone call everyone else an idiot?
BECAUSE EVERYONE IS AN IDIOT. Trying to comprehend just how unbelievably stupid people can be is one of the most difficult things to learn while growing up. It's far too easy to disregard someone as evil when in fact they really are that dumb. "Never attribute to malice that which is adequately explained by stupidity" - Hanlon's Razor. The best you can hope to do is dedicate your life to not being an idiot in your choice of profession and don't think it makes you qualified to give advice on vaguely related fields (see networking programmer above).
Because they are 10-year-olds that have to pay taxes, and nobody really knows how to pay taxes properly. They don't know what they're doing. Common sense is not common, people are not rational, and people are idiots. They don't care if they're wrong, and they don't care if you're right. They just don't care, because life sucks, and life isn't fair, and they didn't get the memo until after they wasted their youth either being too drunk to remember anything, or studying in a library all day to get a useless scrap of paper.
Do something that matters to you, and know this: Life isn't fair, so you have to make it fair. You have to do things the hard way. You have to fail miserably hundreds of times and keep on trying because you aren't going to let life win. You have to do what matters to you, no matter what anyone else thinks. You have to fight for it, and you have from now until you die to win. Go.
Cheat Codes
1. If you don't know how to properly socialize with someone, ask them about themselves. There is nothing people love more than talking about themselves.
2. If you like programming, bury yourself in it. It is, by far, the most useful skill you can have right now.
4. Bunnies make everything better =:3
May 26, 2012
"We are what and where we are because we have first imagined it." - Donald Curtis
The wisdom of antiquity suggests that we must first imagine what we want to achieve if we are ever to succeed, but science has other ideas. A study demonstrated that visualizing yourself reaching a goal tricks your brain into thinking you actually did it, causing a relaxation response, which in turn robs you of ambition and energy.
This is a troubling counter-argument to age-old wisdom, but perhaps both sides can be right? I have been relentlessly pursuing the same goal for many years, and from my experience, it matters what you visualize just as much as if. In particular, one should imagine what you are actually trying to create, rather than what you would do with all your riches.
By coupling your imagination to your problem solving skills, you can draw a line between where you are now and what you need to do to make your vision come to life. This both solidifies your goals, highlights potential problem areas and outlines a clear plan of action, which helps prevent procrastination caused by not knowing what to do. Simply imagining that we are living the high life after hitting the big time, however, merely drains us of ambition by creating a false sense of accomplishment. You must visualize your finished creation, not the act of finishing it.
There is a marvelous, unspeakably beautiful thing that wanders around in my subconscious. Every now and then I am given another glimpse, or shown another spark of inspiration of this indescribable vision that seems so real and yet could not possibly be written about, because nothing like it has ever existed. It's like looking into a future that could arrive tomorrow if only I could bring it to life. Sometimes I wonder if I'm losing my way, only for something else to trigger another magnificent concept. It shows me why I can never give up, even it if takes me an eternity to craft my thoughts into a new reality.
Your imagination is a tool, and like any other, it can be used or abused. Wield it wisely.
May 23, 2012
A couple years ago, when I first started designing a game engine to unify Box2D and my graphics engine, I thought this was a superb opportunity to join all the cool kids and multithread it. I mean all the other game developers were talking about having a thread for graphics, a thread for physics, a thread for audio, etc. etc. etc. So I spent a lot of time teaching myself various lockless threading techniques and building quite a few iterations of various multithreading structures. Almost all of them failed spectacularly for various reasons, but in the end they were all too complicated.
I eventually settled on a single worker thread that was sent off to start working on the physics at the beginning of a frame render. Then at the beginning of each subsequent frame I would check to see if the physics were done, and if so sync the physics and graphics and start up another physics render iteration. It was a very clean solution, but fundamentally flawed. For one, it introduces an inescapable frame of input lag.
Single Thread Low Load FRAME 1 +----+ | | . Input1 -> | | |[__]| Physics |[__]| Render . FRAME 2 +----+ INPUT 1 ON BACKBUFFER . Input2 -> | | . Process ->| | |[__]| Physics . Input3 -> |[__]| Render . FRAME 3 +----+ INPUT 2 ON BACKBUFFER, INPUT 1 VISIBLE . | | . | | . Process ->|[__]| Physics |[__]| Render FRAME 4 +----+ INPUT 3 ON BACKBUFFER, INPUT 2 VISIBLE Multi Thread Low Load FRAME 1 +----+ | | | | . Input1 -> | | . |[__]| Render/Physics START . FRAME 2 +----+ . Input2 -> |____| Physics END . | | . | | . Input3 -> |[__]| Render/Physics START . FRAME 3 +----+ INPUT 1 ON BACKBUFFER . |____| . | | PHYSICS END . | | |____| Render/Physics START FRAME 4 +----+ INPUT 2 ON BACKBUFFER, INPUT 1 VISIBLE
The multithreading, by definition, results in any given physics update only being reflected in the next rendered frame, because the entire point of multithreading is to immediately start rendering the current frame as soon as you start calculating physics. This causes a number of latency issues, but in addition it requires that one introduce a separated "physics update" function to be executed only during the physics/graphics sync. As I soon found out, this is a massive architectural complication, especially when you try to put in scripting or let other languages use your engine.
There is another, more subtle problem with dedicated threads for graphics/physics/audio/AI/anything. It doesn't scale. Let's say you have a platformer - AI will be contained inside the game logic, and the absolute vast majority of your CPU time will either be spent in graphics or physics, or possibly both. That means your game effectively only has two threads that are doing any meaningful amount of work. Modern processors have 8 logical cores1, and the best one currently available has 12. You're using two of them. You introduced all this complexity and input lag just so you could use 16.6% of the processor instead of 8.3%.
1 The processors actually only have 4 or 6 physical cores, but use hyperthreading techniques so that 8 or 12 logical cores are presented to the operating system. From a software point of view, however, this is immaterial.
IP Law Makes You an Asshole
I haven't had a very good relationship with IP law. My 2 favorite childhood game franchises - Descent and Freespace, were thrown into IP limbo after Interplay shot itself in the foot too many times and finally fell over. As a result, I have come to utterly despise the common practice of publishers simply taking the IP of the developers for themselves, and in a more broad sense, forcing artists to give up their ownership on everything they make for a company. This becomes especially painful when they aren't just making silly UI art, but creating a universe filled with lore and character and spirit, only to watch corporate meddling turn their idea into a wretched, free-to-play money-grubbing disaster.
What can the artist do? Exactly nothing. Under current IP law, the company usually owns all rights to everything the artist does for them, no matter what. If it doesn't, it's because the company screwed up its legal contracts, which is dangerous for both you and the company. There is essentially no middle ground. That means an artist can't sue the company for screwing up their idea, because it isn't their idea anymore. They can't take it to another studio or even work on their own idea without permission from the company. It makes about as much sense as a company saying they own the rights to your startup idea because you came up with it at work one day and wrote a prototype during break. That isn't just hypothetical, either, it's a disturbingly common problem.
This is not beneficial to companies, either. Artists are increasingly aware of how little control they have over their own work. A paranoid artist who gets a great idea will be unwilling to tell anyone at the company about it until after they've been working on it in secret, distracting them from what they're supposed to be working on and making them uncomfortable and stressed. They'll worry about what will happen if they try to take the idea somewhere else and no one likes it. They could lose their only job. But if they tell anyone about the idea inside their current company, they risk losing all rights to it and then having the company decide it doesn't like the idea and burying it forever, killing the artists brainchild without any hope of resuscitation. What's worse is that an artist is just about as far from a lawyer as you can get - they have absolutely no idea how any of this stuff works and what they can or cannot do, so they tend to either screw up immediately and lose all rights to their idea or tell no one about it, ever. Your company will essentially lose an employee for months as they succumb to stress, and you might never even know about their idea because they're too paranoid about you stealing it.
So what would good handling of IP be? A more fair agreement would give the company nonexclusive rights to use ideas the artist comes up with. The company only maintains nonexclusive rights to partially or completed work the artist created while employed at the company if the artist decides to quit, not the idea itself. It can even attempt to finish partially completed work, but the artist still retains the right to take his idea elsewhere. This is a compromise between ensuring a company can use everything an artist makes for them while employed without restriction, and ensuring that the artist can still walk out with his idea and bring it to life on his own or at another company. For game development companies, there would clearly need to be a clause protecting the companies right to finish a project if the lead designer leaves.
It seems reasonable to approximate this by assigning permanent nonexclusive rights to the company instead of exclusive rights, but things get complicated very quickly. If you don't own all the rights to a copyrighted material, you can get sued if you modify the original even if you have permission to use it. It's possible such situations could also occur with IP assignments, especially when you are specifically allocating certain nonexclusive rights in certain circumstances but not in others, or revoking certain rights upon termination. If an artist leaves a company in the middle of making a game, they shouldn't be able to sue the resulting game because it used their old art, or even created new art based off their old art. Likewise, a company shouldn't be able to sue an artist if they leave and create a game on their own using their idea even if the company had already released a game based on it. How one would achieve this, I have no idea. It gets even murkier when an idea is the collaborative effort of multiple people. Who owns what part? If one person leaves, the company must still retain the right to use his ideas and ideas based off his ideas, and he should only retain the right to use his own ideas, but not everyone else's ideas or ideas based off everyone else's ideas. What happens when they live in another country?
Because of the vast complexity of this issue, most companies say "fuck it" and simply assign all rights to themselves. This is standard advice from lawyers. The mentality is that you don't have time to worry about silly little legal issues with artists. The problem is that it erodes artists' rights, which are already disturbingly emancipated. This is unacceptable.
I'm not a lawyer. I don't know how to fix this. I don't know if it can be fixed. I don't even know how to properly assign IP to my own company or write a contract. All I know is that artists are getting screwed over because IP law makes everyone an asshole.
Obligatory legal crap: The information provided in this blog is not intended as legal advice.
May 13, 2012
Stop Following The Rules
The fact that math, for most people, is about a set of rules, exemplifies how terrible our attempts at teaching it are. A disturbing amount of programming education is also spent hammering proper coding guidelines into students' heads. Describing someone as a cowboy programmer is often derisive, and wars between standards, rules and languages rage like everlasting fires. It is into these fires we throw the burnt-out husks that were once our imaginations. We have taken our holy texts and turned them into weapons to crush any remnants of creativity that might have survived our childhood's educational incarceration.
Math and programming are not sets of rules to be followed. Math is a language - an incredibly dense, powerful way of conveying ideas about abstraction and generalization taken to truly astonishing levels. Each theorem is another note added to a chord, and as the chords play one after another, they build on each other, across instruments, to form a grand symphony. Math, in the right hands, is the language of problem solving. Most people know enough math to get by. It's like knowing enough French to say hello, order food, and call a taxi. You don't really know the language, you're just repeating phrases to accomplish basic tasks. Only when you have mastered a certain amount of fluency can you construct your own epigraphs, and taste the feeling of putting thoughts into words.
With the proper background, Math becomes a box of legos. Sometimes you use the legos to solve problems. Other times you just start playing around and see what you can come up with. Like any language, Math can do simple things, like talk about the weather. Or, you can write a beautiful novel with words that soar through the reader's imagination. There are many ways to say things in Math. Perhaps you want to derive the formula for the volume of a sphere? You can use geometry, or perhaps calculus, or maybe it would be easier with spherical coordinates. Math even has dialects, there being many ways of writing a derivative, or even a partial derivative (one of my professors once managed to use three in a single lecture). As our mathematical vocabulary grows, we can construct more and more elegant sentences and paragraphs, refining the overall structure of our abstract essay.
Programming too, is just a language, one of concurrency, functions and flow-control. Programming could be considered a lingual descendant of Math. Just as English is Latin-based, so is programming a Math-based language. We can use it to express many arcane designs in an efficient manner. Each problem has many different solutions in many different dialects. There's functional programming and procedural programming and object-oriented programming. But the programming community is obsessed with solving boring problems and writing proper code. Too overly concerned about maintainability, naming conventions and source control. What constitutes "common sense" varies wildly depending on your chosen venue, and then everyone starts arguing about semicolons.
Creativity finds little support in modern programming. Anything not adhering to strict protocols is considered useless at best, and potentially damaging at worst. Programming education is infused with corporate policy, designed to teach students how to behave and not get into trouble. Even then, its terribly inconsistent, with multiple factions warring with each other over whose corporate policies are superior. Programming languages are treated more like religions than tools.
The issue is that solving new problems, by definition, requires creative thinking. Corporate policy designed to stamp out anything not adhering to "best practices" is shooting itself in the foot, because it is incapable of solving new classes of problems that didn't exist 5 years ago. Companies that finally succeed in beating the last drop of creativity out of their employees suddenly need to hire college graduates to solve new problems they don't know how to deal with, and the cycle starts again. We become so obsessed with enforcing proper code etiquette that we forget how to play with the language. We think we're doing ourselves a favor by ruthlessly enforcing strict coding guidelines, only to realize our code has already become irrelevant.
We need to separate our mathematical language from the proof. Just as there is more to English than writing technical specifications, there is more to Math than formal research papers, and more to programming than writing mission-critical production code. Rules and standards are part of a healthy programming diet, but we must remember to take everything in moderation. We can't be so obsessed with writing standardized code that we forget to teach students all the wonderful obscurities of the language. We can't be telling people to never use a feature of a programming language because they'll never use it properly. Of course they won't use it properly if they can't even try! We should not only be teaching programmers the importance of formality, but where it's important, and where it's not. We should encourage less stringent rules on non-critical code and small side projects.
In mathematics, one never writes a proof from beginning to finish. Often you will work backwards, or take shortcuts, until you finally refine it to a point where you can write out the formal specification. When messy code is put into production, it's not the programmer's fault for being creative, it's the idiot who didn't refactor it first. Solving this by removing all creativity from the entire pipeline is like banning cars to lower the accident rate.
Corporate policy is for corporate code, not experimental features. Don't let your creativity die. Stop following the rules.
May 7, 2012
The Standards Problem
When people leave the software industry citing all the horrors of programming, it confuses me when they blame software development itself as the cause of the problems. Programming is very similar to architecture - both an art and a science. The comparison, however, falls apart when you complain about architecture and buildings having all these well-established best practices. The art of making buildings hasn't really changed all that much in the past 50 years. Programming didn't exist 50 years ago.
The fact is, we've been building buildings for thousands of years. We've been writing programs for around 40, and in that period we have gone from computers the size of rooms to computers the size of watches. The instant we establish any sort of good practice, it's bulldozed by new technology. Many modern functional programming languages had to be updated to elegantly handle concurrency at all, and we've only just barely established the concept of worker threads for efficiently utilizing 4-8 cores as we step into the realm of CPU/GPU collision and the advent of massively parallel processing on a large scale, which once again renders standard concepts of programming obsolete. The fact that software runs at all is, quite simply, astonishing. Windows still has old DOS code dating back to the 1980s having repercussions in Windows 7 (You can't name a folder "con" because it was a reserved device name in DOS). If they were to completely rewrite the operating system now, it'll be completely obsolete in 20 years anyway and we'd be complaining about NT's lingering 32-bit compatibility issues and old functions not being threadsafe on a 128 core processor and problems I can't even predict.
Standards can't exist if we can't agree on the right way to do things, and in software development, we can't agree on the right way to do things because nobody knows (and if someone tells you they know, they're lying). Just as we all begin to start settling down on good practices, new technology changes the rules again. This further complicates things because we often forget exactly which parts of the technology are changing. There's a reason you write a kernel in C and not F#. Our processor architecture is the same fundamental concept it was almost 30 years ago. Ideally we would have moved away from complex instruction sets now that nobody uses them anymore, but we haven't even done that. Language fanboys forget this and insist that everything should be written in whatever their favorite language is, without having any idea what they're talking about. This results in a giant mess, with literally everyone telling everyone else they're doing it wrong.
That's the software industry today. It's where everyone says everyone else is wrong, because we have no goddamn idea what software development should be, because what software development should be keeps changing, and its changing so rapidly we can barely keep up, let alone actually settle on a bunch of standards. Instead, individual groups standardize themselves and you get a bunch of competing ecosystems each insisting they are right, without observing that they are all right at the same time - each standard is built to match the demands of not only where, but when it is being used.
Luckily, I don't program because I want to write programs all day. I program because I want to build something magnificent. If you make a living programming for a bunch of clients that try to tell you what to do and always say it should be faster and cheaper, well, welcome to being an artist.
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https://www.physicsforums.com/threads/faraday-rotation-and-permittivity-tensor.783814/
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# Faraday rotation and permittivity tensor
Tags:
1. Nov 24, 2014
### Hassan2
Dear all,
In text books about optics in magneto-optic materials, we often come across a Hermitian permittivity tensor with off-diagonal imaginary components. These components are relevant to the Faraday rotation of plane of polarization of light through the material.
Now my question is: Is the knowledge of the tensor enough to solve the wave equation and calculate the wave propagation ( including rotation)?
I ask this because they usually talk about breaking the incident linearly polarized light into left and right circularly polarized lights, where the refractive index is different for each. if the knowledge of permittivity tensor is enough for the calculations, why would we need such a non-easy-to-understand trick?
2. Nov 24, 2014
### DrDu
The point is that the wave equation with the permittivity being a tensor depending on wavenumber has two solutions (for given direction of the k vector and frequency) which turn out to correspond to left and right circularly polarized waves. Basically, you have to find a basis where the permittivity tensor is diagonal. This is a matrix eigenvalue problem which you can solve with the usual methods.
3. Nov 25, 2014
### Hassan2
Very clear.Thanks.
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https://kb.osu.edu/dspace/handle/1811/19961
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# ANALYSIS OF SELF-BROADENED SPECTRA IN THE $\nu_{5}$ AND $\nu_{6}$ FUNDAMENTAL BANDS OF $^{12}CH_{3}D$
Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/19961
Files Size Format View
2000-WG-11.jpg 153.4Kb JPEG image
Title: ANALYSIS OF SELF-BROADENED SPECTRA IN THE $\nu_{5}$ AND $\nu_{6}$ FUNDAMENTAL BANDS OF $^{12}CH_{3}D$ Creators: Brown, L. R.; Devi, V. Malathy; Benner, D. Chris; Smith, M. A. H.; Rinsland, C. P.; Sams, Robert L. Issue Date: 2000 Publisher: Ohio State University Abstract: A multispectrum nonlinear least-squares fitting $technique^{a}$ has been applied to determine accurate line center positions, absolute line intensities, Lorentz self-broadening coefficients and self-induced pressure-shift coefficients for a large number of transitions in the two perpendicular fundamental bands of $^{12}CH_{3}D$ near 1160 and $1470 cm^{-1}$. We analyzed together high-resolution room temperature absorption spectra recorded with two Fourier transform spectrometers (FTS). Three spectra were recorded using the Bruker IFS 120 HR at PNNL at $0.002 cm^{-1}$ resolution, and fourteen spectra were obtained with the McMath-Pierce FTS $(0.006 cm^{-1}$ resolution) at the National Solar Observatory on Kitt Peak. Self-broadening coefficients for over 1000 transitions and self-shift coefficients for more than 800 transitions were determined. The measurements include transitions with rotational quantum numbers over $J^{\prime\prime} = 15$ and $K^{\prime\prime} = 15$ and some forbidden transitions. Measurements were made in all sub-bands $(^{P}P, ^{P}Q, ^{P}R, ^{R}P, ^{R}Q$ and $^{R}R$). The measured broadening coefficients vary from 0.040 to $0.096 cm^{-1}$ at $m^{-1}$ 296K. Self-shift coefficients vary from about -0.014 to $+0.004 cm^{-1} atm^{-1}$. Less than 5% of the measured shift coefficients are positive, and majority of these positive shifts are associated with the $J^{\prime\prime} = K^{\prime\prime}$ transitions in the $^{P}Q$ sub-bands. The values for the two perpendicular bands are compared and discussed. Description: Author Institution: Jet Propulsion Laboratory, California Institute of Technology; Department of Physics, The College of William and Mary; Atmospheric Sciences, NASA Langley Research Center. Mail Stop 401A; Atmospheric Sciences, Pacific Northwest National Laboratory (PNNL) URI: http://hdl.handle.net/1811/19961 Other Identifiers: 2000-WG-11
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http://mathhelpforum.com/calculus/116481-integrals-2-a.html
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# Math Help - Integrals : 2
1. ## Integrals : 2
Calculate integral for the function :
$
\begin{array}{l}
\ln (\sin (x)) \\
\ln (\cos (x)) \\
\end{array}$
2. Originally Posted by dhiab
Calculate integral for the function :
$
\begin{array}{l}
\ln (\sin (x)) \\
\ln (\cos (x)) \\
\end{array}$
Mathematica got a nasty result for $\int \ln(\sin(x))dx$ involving i and non-elementary functions, so I don't know if I am misunderstanding what you are asked to do. If you meant a fraction, Mathematica can't solve it.
3. Originally Posted by dhiab
Calculate integral for the function :
$
\begin{array}{l}
\ln (\sin (x)) \\
\ln (\cos (x)) \\
\end{array}$
Originally Posted by Jameson
Mathematica got a nasty result for $\int \ln(\sin(x))dx$ involving i and non-elementary functions, so I don't know if I am misunderstanding what you are asked to do. If you meant a fraction, Mathematica can't solve it.
Did the OP perhaps mean $\int\frac{\ln(\sin(x))}{\ln(\cos(x))}dx$?
4. Originally Posted by Drexel28
Did the OP perhaps mean $\int\frac{\ln(\sin(x))}{\ln(\cos(x))}dx$?
I plugged that in as well and Mathematica couldn't find a solution. I haven't tried to work it out myself.
5. Originally Posted by Jameson
I plugged that in as well and Mathematica couldn't find a solution. I haven't tried to work it out myself.
Maybe we can make that a tad more apparent? Let $x=\arcsin(z)\implies dx=\frac{dz}{\sqrt{1-z^2}}$ so our integral becomes $\int\frac{\ln(z)}{\sqrt{1-z^2}\ln\left(\sqrt{1-z^2}\right)}$. Let $\sqrt{1-z^2}=\tau\implies \frac{-\tau}{\sqrt{1-\tau^2}}d\tau=dz$. So then our integral becomes $\frac{-1}{2}\int\frac{\ln\left(1-\tau^2\right)}{\sqrt{1-\tau^2}\ln\left(\tau\right)}d\tau$. That looks almost doable. I am not feeling it right now. Maybe the OP can continue.
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http://pillars.che.pitt.edu/student/slide.cgi?course_id=12&slide_id=87.0
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# McCabe-Thiele Analysis
McCabe-Thiele analysis for (almost) arbitrary reflux ratios is similar to total reflux, if slightly harder.
In this case the two operating equations (lines), an equilibrium expression (line) using the relative volatility, and a feed expression (line) do not simplify, and thus must be used in their normal forms:
EQUILIBRIUM LINE: $y=\frac{\alpha_{AB}x}{1+(\alpha_{AB}-1)x}$
RECTIFYING LINE: y = xL/V + xD(1-L/V)
STRIPPING LINE: y = xL'/V' - xB(L'/V'-1)
FEED LINE: y = xq/(q-1) - z/(q-1)
We first plot the equilibrium line on an x-y diagram. We then plot the rectifying and stripping operating lines -- using the xD and xB points on the y=x line as our first points and the slopes L/V and L'/V', respectively.
##### NOTE
The feed line will start at the xF composition on the y=x line and go to the intersection of the two operating lines. It is possible that we might need to use this info rather than the distillate and bottoms compositions and slopes. One option would be to set the feed equation equal to one of the other operating equations to analytically find the intersection point.
The steps in this case still go horizontally (left) for equilibrium, but now when we go vertically (down) for our material balance, we go to the rectifying operating line (prior to the intersection point) and down to the stripping operating line (after the intersection point):
##### NOTE
It is possible that we will not match our distillate and bottoms compositions both exactly. In this case, we say we need 2.9 stages, for example. In reality we obviously can only have an integer number of stages (but would achieve a better separation than expected).
If we think about it, we can see that there is a limit to how small our reflux ratio (L/D) can be. As L/D decreases, we also decrease our slope L/V (prove this to yourself with an overall material balance on the rectifying section). In this case, we might obtain a graph like the following:
Clearly we cannot operate the column in this way, as we would need to move horizontally beyond the equilibrium point, which is physically impossible. Instead there is a minimum value of the reflux ratio that can be determined by finding the conditions under which the intersection point just "pinches" the equilibrium line:
##### DEFINITION:
The minimum reflux ratio is the ratio of L/D that leads to the intersection of the rectifying and stripping operating lines falling on the equilibrium curve (rather than inside it).
This condition, however, would require an infinite number of stages (can you see why?).
##### NOTE
In reality, each stage will not quite achieve the equilibrium compositions (due to poor mixing, or finite contact times), therefore our predictions from a McCabe-Thiele analysis will be slightly low relative to the actual number of stages required.
##### OUTCOMES:
Determine the number of stages required to achieve a separation at minimum or higher reflux ratios using the McCabe-Thiele method
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http://docs.astropy.org/en/stable/api/astropy.nddata.UnknownUncertainty.html
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# UnknownUncertainty¶
class astropy.nddata.UnknownUncertainty(array=None, copy=True, unit=None)[source] [edit on github]
This class implements any unknown uncertainty type.
The main purpose of having an unknown uncertainty class is to prevent uncertainty propagation.
Parameters: args, kwargs :
Attributes Summary
supports_correlated False : Uncertainty propagation is not possible for this class. uncertainty_type "unknown" : UnknownUncertainty implements any unknown uncertainty type.
Attributes Documentation
supports_correlated
False : Uncertainty propagation is not possible for this class.
uncertainty_type
"unknown" : UnknownUncertainty implements any unknown uncertainty type.
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https://www.maplesoft.com/Applications/Detail.aspx?id=154362
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Fibonacci Numbers - Maple Application Center
Application Center Applications Fibonacci Numbers
## Fibonacci Numbers
Author
: Dr. Jürgen Gerhard
This Application runs in Maple. Don't have Maple? No problem!
Many programming language tutorials have an example about computing Fibonacci numbers to illustrate recursion. Usually, however, these simple examples exhibit an abysmal runtime behaviour, namely, exponential in the index.
In this presentation, several more efficient ways of computing Fibonacci numbers, using Maple, are discussed. The best algorithm presented is based on doubling formulae for the Fibonacci numbers, which we also prove using Maple.
#### Application Details
Publish Date: November 21, 2017
Created In: Maple 2017
Language: English
#### Share
This app is not in any Collections
#### Tags
algorithm number-theory
2
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http://jdh.hamkins.org/tag/hugh-woodin/
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# A conference in honor of W. Hugh Woodin’s 60th birthday, March 2015
I am pleased to announce the upcoming conference at Harvard celebrating the 60th birthday of W. Hugh Woodin. See the conference web site for more information. Click on the image below for a large-format poster.
# The ground axiom is consistent with $V\ne{\rm HOD}$
• J. D. Hamkins, J. Reitz, and W. Woodin, “The ground axiom is consistent with $V\ne{\rm HOD}$,” Proc.~Amer.~Math.~Soc., vol. 136, iss. 8, pp. 2943-2949, 2008.
@ARTICLE{HamkinsReitzWoodin2008:TheGroundAxiomAndVequalsHOD,
AUTHOR = {Hamkins, Joel David and Reitz, Jonas and Woodin, W.~Hugh},
TITLE = {The ground axiom is consistent with {$V\ne{\rm HOD}$}},
JOURNAL = {Proc.~Amer.~Math.~Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {136},
YEAR = {2008},
NUMBER = {8},
PAGES = {2943--2949},
ISSN = {0002-9939},
CODEN = {PAMYAR},
MRCLASS = {03E35 (03E45 03E55)},
MRNUMBER = {2399062 (2009b:03137)},
MRREVIEWER = {P{\'e}ter Komj{\'a}th},
DOI = {10.1090/S0002-9939-08-09285-X},
URL = {http://dx.doi.org/10.1090/S0002-9939-08-09285-X},
file = F
}
Abstract. The Ground Axiom asserts that the universe is not a nontrivial set-forcing extension of any inner model. Despite the apparent second-order nature of this assertion, it is first-order expressible in set theory. The previously known models of the Ground Axiom all satisfy strong forms of $V=\text{HOD}$. In this article, we show that the Ground Axiom is relatively consistent with $V\neq\text{HOD}$. In fact, every model of ZFC has a class-forcing extension that is a model of $\text{ZFC}+\text{GA}+V\neq\text{HOD}$. The method accommodates large cardinals: every model of ZFC with a supercompact cardinal, for example, has a class-forcing extension with $\text{ZFC}+\text{GA}+V\neq\text{HOD}$ in which this supercompact cardinal is preserved.
# The necessary maximality principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal
• W. Hamkins Joel D.~and Woodin, “The necessary maximality principle for c.c.c.\ forcing is equiconsistent with a weakly compact cardinal,” MLQ Math.~Log.~Q., vol. 51, iss. 5, pp. 493-498, 2005.
@ARTICLE{HamkinsWoodin2005:NMPccc,
AUTHOR = {Hamkins, Joel D.~and Woodin, W.~Hugh},
TITLE = {The necessary maximality principle for c.c.c.\ forcing is equiconsistent with a weakly compact cardinal},
JOURNAL = {MLQ Math.~Log.~Q.},
FJOURNAL = {MLQ.~Mathematical Logic Quarterly},
VOLUME = {51},
YEAR = {2005},
NUMBER = {5},
PAGES = {493--498},
ISSN = {0942-5616},
MRCLASS = {03E65 (03E55)},
MRNUMBER = {2163760 (2006f:03082)},
MRREVIEWER = {Tetsuya Ishiu},
DOI = {10.1002/malq.200410045},
URL = {http://dx.doi.org/10.1002/malq.200410045},
eprint = {math/0403165},
archivePrefix = {arXiv},
primaryClass = {math.LO},
file = F,
}
The Necessary Maximality Principle for c.c.c. forcing asserts that any statement about a real in a c.c.c. extension that could become true in a further c.c.c. extension and remain true in all subsequent c.c.c. extensions, is already true in the minimal extension containing the real. We show that this principle is equiconsistent with the existence of a weakly compact cardinal.
See related article on the Maximality Principle
# Small forcing creates neither strong nor Woodin cardinals
• J. D. Hamkins and W. Woodin, “Small forcing creates neither strong nor Woodin cardinals,” Proc.~Amer.~Math.~Soc., vol. 128, iss. 10, pp. 3025-3029, 2000.
@article {HamkinsWoodin2000:SmallForcing,
AUTHOR = {Hamkins, Joel David and Woodin, W.~Hugh},
TITLE = {Small forcing creates neither strong nor {W}oodin cardinals},
JOURNAL = {Proc.~Amer.~Math.~Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {128},
YEAR = {2000},
NUMBER = {10},
PAGES = {3025--3029},
ISSN = {0002-9939},
CODEN = {PAMYAR},
MRCLASS = {03E35 (03E55)},
MRNUMBER = {1664390 (2000m:03121)},
MRREVIEWER = {Carlos A.~Di Prisco},
DOI = {10.1090/S0002-9939-00-05347-8},
URL = {http://dx.doi.org/10.1090/S0002-9939-00-05347-8},
eprint = {math/9808124},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}
After small forcing, almost every strongness embedding is the lift of a strongness embedding in the ground model. Consequently, small forcing creates neither strong nor Woodin cardinals.
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https://docs.mfem.org/html/classmfem_1_1ESDIRK33Solver.html
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MFEM v4.4.0 Finite element discretization library
mfem::ESDIRK33Solver Class Reference
#include <ode.hpp>
Inheritance diagram for mfem::ESDIRK33Solver:
[legend]
Collaboration diagram for mfem::ESDIRK33Solver:
[legend]
## Public Member Functions
virtual void Init (TimeDependentOperator &f_)
Associate a TimeDependentOperator with the ODE solver. More...
virtual void Step (Vector &x, double &t, double &dt)
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in]. More...
Public Member Functions inherited from mfem::ODESolver
ODESolver ()
virtual void Run (Vector &x, double &t, double &dt, double tf)
Perform time integration from time t [in] to time tf [in]. More...
virtual int GetMaxStateSize ()
Function for getting and setting the state vectors. More...
virtual int GetStateSize ()
virtual const VectorGetStateVector (int i)
virtual void GetStateVector (int i, Vector &state)
virtual void SetStateVector (int i, Vector &state)
virtual ~ODESolver ()
## Protected Attributes
Vector k
Vector y
Vector z
Protected Attributes inherited from mfem::ODESolver
TimeDependentOperatorf
Pointer to the associated TimeDependentOperator. More...
MemoryType mem_type
## Detailed Description
Three stage, explicit singly diagonal implicit Runge-Kutta (ESDIRK) method of order 3. A-stable.
Definition at line 495 of file ode.hpp.
## Member Function Documentation
void mfem::ESDIRK33Solver::Init ( TimeDependentOperator & f_ )
virtual
Associate a TimeDependentOperator with the ODE solver.
This method has to be called:
Reimplemented from mfem::ODESolver.
Definition at line 747 of file ode.cpp.
void mfem::ESDIRK33Solver::Step ( Vector & x, double & t, double & dt )
virtual
Perform a time step from time t [in] to time t [out] based on the requested step size dt [in].
Parameters
[in,out] x Approximate solution. [in,out] t Time associated with the approximate solution x. [in,out] dt Time step size.
The following rules describe the common behavior of the method:
• The input x [in] is the approximate solution for the input time t [in].
• The input dt [in] is the desired time step size, defining the desired target time: t [target] = t [in] + dt [in].
• The output x [out] is the approximate solution for the output time t [out].
• The output dt [out] is the last time step taken by the method which may be smaller or larger than the input dt [in] value, e.g. because of time step control.
• The method may perform more than one time step internally; in this case dt [out] is the last internal time step size.
• The output value of t [out] may be smaller or larger than t [target], however, it is not smaller than t [in] + dt [out], if at least one internal time step was performed.
• The value x [out] may be obtained by interpolation using internally stored data.
• In some cases, the contents of x [in] may not be used, e.g. when x [out] from a previous Step() call was obtained by interpolation.
• In consecutive calls to this method, the output t [out] of one Step() call has to be the same as the input t [in] to the next Step() call.
• If the previous rule has to be broken, e.g. to restart a time stepping sequence, then the ODE solver must be re-initialized by calling Init() between the two Step() calls.
Implements mfem::ODESolver.
Definition at line 755 of file ode.cpp.
## Member Data Documentation
Vector mfem::ESDIRK33Solver::k
protected
Definition at line 498 of file ode.hpp.
Vector mfem::ESDIRK33Solver::y
protected
Definition at line 498 of file ode.hpp.
Vector mfem::ESDIRK33Solver::z
protected
Definition at line 498 of file ode.hpp.
The documentation for this class was generated from the following files:
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https://cs.stackexchange.com/questions/91538/why-is-adding-log-probabilities-considered-numerically-stable/91546
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# Why is adding log probabilities considered "numerically stable"?
Every once in a while, I come across the term numerical stability, which I don't really understand. In particular, I have seen a description of the practice of "adding logs rather than multiplying numbers" as "numerically stable." I would like to know why this is considered numerically stable.
By "adding logs rather than multiplying numbers" I mean that if you have several numbers, for example 0.01, 0.001, 0.0001, and you want to get their product, you can instead add the logs of each term. In this case assuming log base 10, the result would be -2 -3 -4 = -9. This doesn't give you the same output as multiplying, but it's a good way to get something like the product so that you don't experience numerical underflow.
My question is that I'm a bit confused because the definitions of numerical stability I've found on the Internet don't seem to apply to this case. The definitions of "numerical stability" I've found are that it occurs when a "malformed input" doesn't affect the performance of an algorithm, see for example here. In this case I don't really see how we would consider the numbers 0.01 etc "malformed," they are what they are. It would be more accurate to say that the algorithm (of multiplying them) is bad in this context since the computer can't handle it, so we choose a better algorithm. So why do people say this is "numerically stable"?
• Investigate how non-integers are represented in most computers (IEEE floats), the limitations of that format, and relevant error-estimating techniques.
– Raphael
May 6 '18 at 7:14
• I suspect you meant "the definition" (not "definitions"). I've never seen a definition that uses "malformed" or anything like it. That MathWorld "definition" is nonsensical precisely because "malformed" is a bizarre word to use. Presumably, "malformed" was just meant to mean "is (slightly) inaccurate", but even this isn't correct. Numerical stability is relevant even if the input is exactly represented. May 7 '18 at 14:29
A "numerically stable" method calculates a result in a way that will not produce excessive rounding errors.
Given a small number x, let's say x = 0.00079, it is possible to calculate log (1 + x) with much higher precision than 1 + x. (Of course calculating log (1 + x) avoids adding 1 + x). In both cases the relative error will be small and about equal size, but since the logarithm is very small, it's absolute error is much smaller.
So if you want to calculate the product of values $1 + x_i$ for many small i, then you use a clever method to calculate $log (1 + x_i)$, add those values, and calculate the exponential. With probabilities, it is possible that you have say 1,000,000 events each with small probability $p_i$, and the probability that none of the events happens is the product of $1 - p_i$, and calculating that probability is more precisely done by adding logarithms (you would also keep the rounding errors down by always adding the two smallest values).
In other situations, using logarithms can be less precise. For multiplication, the relative error is independent of the size of the numbers. But if you add logarithms, and say their sum is around 100, then each addition loses precision because 7 bits of the mantissa are used to store the 100. The precision of your result will be much less. So it's quite the opposite of numerically stable.
Start with x = 1, y = 0. Then for i = 1 to 100, multiply x by i, and add log i to y. Then for i = 1 to 100, divide x by i, and subtract log i from y. Except for rounding errors, you should end up with x = 1 and y = 0. Check how much the difference is.
PS. How do we calculate log (1 + x) without calculating 1 + x? There is the power series around 1, $ln (x) = (x-1) / 1 - (x-1)^2 / 2 + (x-1)^3 / 3 ...$. If we substitute 1 + x, then $ln(1 + x) = x / 1 - x^2 / 2 + x^3 / 3 ...$, which is obviously calculated without ever calculating 1 + x.
That's an important lesson: Given a problem that suggests an obvious sequence of steps to solve it, you will very often find a better and less obvious solution. To calculate log (1+x), the obvious sequence of steps is to calculate y = 1+x, z = log (y), but there is a much better solution that completely avoids the first step.
• In your last paragraph I think you mean "divide x by i" right? May 6 '18 at 16:57
• I like your definition of "numerically stable" in your first paragraph, and I think I see overall what you're getting at. May 6 '18 at 17:04
• But your second paragraph doesn't make much sense to me: "it is possible to calculate log (1 + x) with much higher precision than 1 + x" but we can calculate 1 + x perfectly, it is just 1.00079, whereas log(1.00079) can only be imperfectly represented since its mantissa never ends. "Of course calculating log (1 + x) avoids adding 1 + x" but of course we have to calculate 1 + x before we can take the log of that. May 6 '18 at 17:04
• "In both cases the relative error will be small and about equal size, but since the logarithm is very small, it's absolute error is much smaller." again I don't see any error in just 1.00079, it's an exact number. Only the logarithm has an error. But I'm not very familiar with the discussion of numerical errors, so I'm probably missing something fundamental. May 6 '18 at 17:06
• @Stephen: 0.00079 is a bit above 1/2048. Adding 1, the exponent increases by 11, eleven mantissa bits will be lost, so if you had a typical 53 bit mantissa, only 42 bits of the 0.00079 are left in the result 1 + x. The error has just increased by a factor 2048. Using binary floating point, 1.00079 is absolutely not an exact number. May 6 '18 at 17:39
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http://latex.org/forum/viewtopic.php?f=12&p=98823&sid=8175ba24244ada79c12c6b0f4f095bc4
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## LaTeX forum ⇒ TeX Live and MacTeX ⇒ mactex paths texlive acmart
Information and discussion about TeX Live distribution for all platforms (Windows, Linux, Mac OS X) and the related MacTeX: installing, updating, configuring
David Epstein
Posts: 2
Joined: Fri Mar 03, 2017 11:11 am
### mactex paths texlive acmart
I have just joined Latex Community, and I am not familiar with it, so I hope I haven't missed the answer to my questions below.
I have searched but I have not been able to find answers.
I have just installed MacTeX. I'm using command line
`latexmk -pdf filename.tex`
to compile. The first line of my file is
`\documentclass[format=acmsmall]{acmart}`
which provokes the error message
`LaTeX Error: File `acmart.cls' not found.`
That file is found on my system at
/usr/local/texlive/2016/texmf-dist/tex/latex/acmart/acmart.cls
How can I persuade latex to find this file? Or do I need to copy it to somewhere else?
Where do I find the paths along which this distribution of tex searches?
Should I set these path, or take some other action?
Are the paths set by MacTeX or by texlive?
Also what path will be used to look for my .bib files (called by \bibliography).
Thanks
Tags:
Stefan Kottwitz
Site Admin
Posts: 8077
Joined: Mon Mar 10, 2008 9:44 pm
Location: Hamburg, Germany
Contact:
Hi David,
welcome to the forum!
Try the `kpsewhich` tool at the command prompt, it shows the paths. Regarding bib files, take a look here: viewtopic.php?f=50&t=29206
Stefan
Site admin
David Epstein
Posts: 2
Joined: Fri Mar 03, 2017 11:11 am
Thanks. The reply from Stefan Kottwitz is helpful in pointing to the reason for my problems, because I did in fact try kpsewhich but got null response.
However, my system's response to
`which kpsewhich`
is
`/usr/local/texlive/2014/bin/universal-darwin/kpsewhich`
.
Since the file I was searching for is in texlive/2016, kpsewhich didn't find it.
I had thought that installing MacTex would automatically change my path. I use tcsh. So now I'm assuming that the path needs to be changed manually. Here is the response to
`echo \$path`
:
`/opt/local/bin /opt/local/sbin /Library/Frameworks/Python.framework/Versions/2.7/bin /opt/local/bin /opt/local/sbin /Users/dbae/bin/qepcad-B.1.65.MacOSX/qesource/bin /usr/local/texlive/2014/bin/universal-darwin /usr/local/texlive/2014/bin/x86_64-darwin /Users/dbae/bin /opt/local/bin /opt/local/sbin /usr/bin /bin /usr/sbin /sbin /usr/local/bin /opt/X11/bin /Library/TeX/texbin`
What should be added to pick up commands defined in my recent installation of MacTex?
Stefan Kottwitz
Site Admin
Posts: 8077
Joined: Mon Mar 10, 2008 9:44 pm
Location: Hamburg, Germany
Contact:
On my Macbook it's simply:
`% echo \$path/usr/bin /bin /usr/sbin /sbin /usr/local/bin /opt/X11/bin /usr/texbin`
Better remove the old 2014 entries from the path. Perhaps look into ~/.tcshrc or ~/.profile or what your shell uses to add path entries.
Check the folder `/etc/paths.d`. On my system, there's a `TeX` file containing just the line `/usr/texbin`. The contents of the files in that folder is added to the path. Perhaps you haven an older file there.
Stefan
Site admin
Return to “TeX Live and MacTeX”
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https://computergraphics.stackexchange.com/questions/5140/does-smooth-lighting-work-with-gouraud-shading-on-single-triangles
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# Does smooth lighting work with Gouraud shading on single triangles?
I'm currently working on a project where a 3D model gets computed through an isosurface algorithm. This algorithm outputs single triangles with vertices and normals, but without indices. So therefore I have a lot of duplicates which can't be avoided, because of a software restriction.
I was asked to write smooth lighting for this model, by sending the proper normals to the visualisation software, which uses OpenGL and runs under Windows. What I tried was to set the normals for duplicated vertices to the same direction but this also results in unsmoothed lighting
as visible here:
Is it possible to have smooth Gouraud shading on a 3D Model which consists of many single unconnected triangles?
• As long as all duplicates of a vertex have the same normal, you should get smooth shading. Check that (i) the duplicated normals are indeed identical, and (b) the shader is actually doing Gouraud shading and not, say, flat shading (incorrect setting of glShadeModel or interpolation qualifier). – Rahul May 23 '17 at 2:06
• If you just want to know whether this is possible, this seems ready to answer, and @Rahul's comment contains a good start on such an answer. If you want to know why your specific code isn't working, we'd need to see it in order to investigate it. – trichoplax May 23 '17 at 10:17
• @Rahul Thank you for your hints. I check the normals and the glShadeModel and both are set correctly. I also wrote the model into an Wavefront obj file and this also results in strange lightning. Here is an image of the model imgur.com/a/JjLxp. – Tim Rolff May 23 '17 at 12:11
• Oh..could it be that you are seeing "Mach band-ish" related" artefacts that appear when you get a discontinuity in the 1st derivative of the shading? Basically, the human visual system amplifies these discontinuities (probably to save our ancestors being eaten by lions). – Simon F May 23 '17 at 16:12
• Going by your image, it looks like you have Gouraud shading working perfectly well. The problem is a combination of skinny triangles and poorly estimated normals, making it look like the shading is not smooth when really it is just varying rapidly over a narrow region. – Rahul May 24 '17 at 5:06
After thinking about it for some days I came up with a proof sketch (which is hopefully correct) that it is possible to use Gouraud shading on disconnected triangles, if they share an edge with the same normals as in the picture. The simple idea of this proof is to check that there is no discontinuity between the intensity of the triangles by approaching from each side to the edge. So given two triangles $T_1: (P_1,P_2,P_3)$ and $T_2: (P_1', P_2', P_3')$ which share an edge and let's assume w.l.o.g. that this edges are constructed by $(P_2,P_3)$ and $(P_2', P_3')$. Because Gouraud shading only computes the light intensity at the vertex positions and interpolate in between them, it's save to assume that the intensity at $P_2$ is the same as on $P_2'$, same goes for $P_3$ and $P_3'$. Because it's also save to assume that the values inside the triangles are getting computed correctly so it's only necessary to show that there is no discontinuity between the triangles. To interpolate inside the triangle it's rational to use Barycentric coordinates so that the intensity at any point inside the triangle is given by \begin{align*} I &= aI_2 + bI_3 + (1 - (a+b)) I_1\\ I' &= a'I_2' + b'I_3' + (1 - (a'+b')) I_1' \end{align*} By now going from $I_1$ respectively $I_1'$ to the edge, a sequence can be constructed to archive this, by setting $a_n = \frac{c}{n+1}, b_n=\frac{d}{n+1}, c + d = 1$ and analogously for $a_n', b_n'$. Then the intensity is \begin{align*} I_n &= \frac{c}{n+1} I_2 + \frac{d}{n+1} I_3 + (1 - \frac{c+d}{n+1}) I_1\\ I_n' &= \frac{c'}{n+1}I_2' + \frac{d'}{n+1}I_3' + (1 - \frac{c'+d'}{n+1}) I_1' \end{align*} If one now approaches the edge with: \begin{align*} &\lim\limits_{n\rightarrow 0^+} I_n = cI_2 + dI_3\\ &\lim\limits_{n\rightarrow 0^+} I_n' = c'I_2 + d'I_3' \end{align*} and using the requirement that $I_n$ and $I_n'$ share the same position $P_n$ if they are on an edge, which can be constructed by \begin{align*} P_n &= \frac{c}{n+1} P_2 + \frac{d}{n+1} P_3 + (1 - \frac{c+d}{n+1}) P_1\\ P_n &= \frac{c'}{n+1}P_2' + \frac{d'}{n+1}P_3' + (1 - \frac{c'+d'}{n+1}) P_1' \end{align*} with the fact that $P_2 =P_2'$ and $P_3 = P_3'$ it follows: \begin{align*} &\lim\limits_{n\rightarrow 0^+} P_n = cP_2 + dP_3\\ &\lim\limits_{n\rightarrow 0^+} P_n' = c'P_2 + d'P_3 \end{align*} and $d = 1 - c$ \begin{align*} &\lim\limits_{n\rightarrow 0^+} P_n = cP_2 + (1-c)P_3\\ &\lim\limits_{n\rightarrow 0^+} P_n' = c'P_2 + (1-c')P_3 \end{align*} this results in $c = c'$ and therefore this gives the final result: \begin{align*} \lim\limits_{n\rightarrow 0^+} I_n = cI_2 + (1-c)I_3 = c'I_2' + (1-c')I_3' = \lim\limits_{n\rightarrow 0^+}I_n' \end{align*} Thereby is possible to use Gouraud shading over disconnected triangles as in my case, because the intensity on the edge is the same on both triangles.
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http://mathhelpforum.com/business-math/108430-paying-advance.html
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The premiums on an insurance policy are $60 every 3 months, payable at the beginning of each three-month period. If the policy holder wishes to pay 1 year’s premiums in advance, how much should be paid provided that the interest rate is 4.3% compounded quarterly? What formula would I use for this? The Present value annutiy formula is what i believe it should be... 2. Originally Posted by lil_cookie The premiums on an insurance policy are$60 every 3 months, payable at the beginning of each three-month period. If the policy holder wishes to pay 1 year’s premiums in advance, how much should be paid provided that the interest rate is 4.3% compounded quarterly?
The question is worded poorly, normally you'd expect premium payments to stay stable so it would be $240. However, if you mean the premiums go up 4.3% a quarter then use the compound interest formula:$\displaystyle A(t) = A_0(1+x)^t$3. Look at it this way to "unconfuse(!)" yourself: assume that the insured left$180 at beginning (after paying 1st $60) in an account that pays 4.3% compounded quarterly? He then withdraws 60 every 3 months to pay next 3 quarterly premiums. Calculate the interest he will receive in that account. That interest is the amount by which the$240 would be reduced.
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https://ask.libreoffice.org/en/question/47249/solved-is-there-a-macro-wizard-out-there/
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# [solved] is there a macro-wizard out there? [closed] edit
Hello,
I wrote this simple macro. I'm not a macro-expert so maybe I'm doing something wrong here.
What the macro should do is reset the revision number (EditingCycles) and the total editing time (EditingDuration) of a document.
By setting EditingCycles to 0 before saving the document, the amount of EditingCycles when saving the document will be raised with 1. Therefore the revision number will be 1. This works great. However, I can't find the right way to set EditingDuration (the total editing time) to 0 (00:00:00). When I manually execute the macro and then look at the document properties, the total editing time is indeed reset to 0 (yahooo!). However when I save the document, the original editing time re-appears while it still should be 0 (boooo!).
Does anyone with macro expertism know what I'm doing wrong? Any help would be very very welcome. Here is the macro:
Sub ResetMetadata
Dim DocumentProperties As Object
DocumentProperties = ThisComponent.getDocumentProperties()
DocumentProperties.EditingCycles = 0
DocumentProperties.EditingDuration = 0
End Sub
edit retag reopen merge delete
### Closed for the following reason the question is answered, right answer was accepted by Alex Kemp close date 2020-08-16 22:16:27.781851
What about store document immediately after setting EditingDuration to zero? And why do you want to do this? The surest way that I see right now is to open the saved file, change the line in meta.hml PTххHххMххS and meta:editing-cycles=хх and save again.
( 2015-03-06 12:15:47 +0200 )edit
1
I NAILED IT! IT WORKS
Haha! JohnSUN, you said I needed to add "ThisComponent.Store(True)" but this didn't solve it. Thinking over the explanation of Lupp, I thought to myself what if I save the file twice? So the first time it resets and the second time the editing duration will be zero. And ... it works! So the trick was to add this line "ThisComponent.Store(True)" twice and now it seems to work like a charm. WOW ... thanks guys! :-)
( 2015-03-06 14:52:40 +0200 )edit
Sort by » oldest newest most voted
Not from profound knowledge; "reversely engineered".
LibreOffice will keep an editing duration for any session and any document opened. It will only add it to the duration kept in the document properties event driven on one or some events from this set: "Save document", "Document has been saved" or "Document is closing". During a continued session the 'Total editing time' never gets updated. Resetting it "by force" will only afflict the 'Total editing time' of past sessions.
I cannot confirm "... the original editing time re-appears ...". What appeared in my experiments was the editing duration of the last session.
But: Even if the 'Total editing time' was reset to 0 via the properties dialogue with 'Apply user data' off, the 'Session editing time' will be saved if 'Apply user data' was meanwhile switched on again.
You may find a specification, explore this thoroughly and shift to calling the proper 'Reset' method for the preliminary 'Session editing time'. I cannot help you that far. Maybe @Regina can.
Editing with respect to comments: Completely switching off 'Apply uer data' in the properties dialogue will also suppress accumulating the editing time and counting the revisions. I don't know exactly what it will change in addition because I'm not interested in these document properties, anyway.
more
"What appeared in my experiments was the editing duration of the last session."
Yes, that is indeed what it is. When I save the document, I see the editing duration of the last session. Your explanation sounds solid. The "build up" editing duration resets, but the editing duration of the current session is added to it (where "it" is zero), so the last session's editing time is shown. I don't want this. If I send a document to someone I don't want to give an indication of the time I spent on it.
( 2015-03-06 14:42:17 +0200 )edit
You will have to open the saved document again, reset editing time again reset revision number again (within about 0 seconds) and save the document a second time. Another way may require a deep dive into the workings of the LibreOffice framework outside the documents where the accounting seems to take place.
I cannot help with this, however.
( 2015-03-06 15:33:21 +0200 )edit
Read my comment above (underneath my question). I fixed it with your help and the help of JohnSUN. Works great now! :)
( 2015-03-06 16:19:47 +0200 )edit
@JohnSUN
I tried that, but unfortunately that doesn't work (feel free to try yourself) unless I'm doing something wrong that I'm not aware of. For example, I could run the macro right now. When I check document properties the editing time is 00:00:00. Then when I save the document right after, the editing time all of a sudden is (for example) around 2 minutes. What am I doing wrong here?
more
I meant to add ThisComponent.Store(True) as a last line of your macro
( 2015-03-06 12:30:15 +0200 )edit
Thanks, but this still doesn't solve the problem. I want the total editing duration (including the editing duration of the current session) to be reset to zero. Is there a way to reset the editing duration of the current session maybe?
( 2015-03-06 14:44:30 +0200 )edit
## Stats
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https://www.jiskha.com/users?name=Randy
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# Randy
Popular questions and responses by Randy
1. ## Math
sec 7pi/4 without a calculator Find the exact answer
2. ## Chemistry
A selenium atom (Se) would form its most stable ion by the 1. loss of 2 electrons. 2. gain of 1 electron. 3. loss of 1 electron. 4. loss of 7 electrons. 5. gain of 2 electrons. Help please and tell me how you got the answer. Thanks!
3. ## Statistics
A box contains five numbered balls (1,2,2,3 and 4). We will randomly select two balls from the box (without replacement). (a) The outcome of interest is the number on each of the two balls we select. List the complete sample space of outcomes. (b) What is
4. ## math
the absolute value of an integer is always greater than the integer. True or False?
5. ## Physics
Two horizontal forces, F1-> and F2-> , are acting on a box, but only F1->is shown in the drawing. F2-> can point either to the right or to the left. The box moves only along the x axis. There is no friction between the box and the surface. Suppose that
6. ## ALGEBRA
What are the odds in favor of drawing face card from an ordinary deck of cards? to
7. ## ALGEBRA
The product of two consecutive positive even numbers is 528. What are the numbers? (Enter solutions from smallest to largest.) and
8. ## geometry
The altitude of an equilateral triangle is 7 square root 3 units long. The length of one side of the triangle is ____ units. 7 14 14 square root 3 7 square root 3 over 2
9. ## chemistry
Isotonic saline is 0.89% NaCl (w/v). Suppose you wanted to make 1.0 L of isotonic solution of NH4Cl. What mass of NH4Cl would you need? Question 23 options: 1.6 g 8.1 g 8.9 g 54 g
10. ## Trig / Calc
What angle (in degrees) corresponds to 18.96 rotations around the unit circle? Enter the exact decimal answer.
11. ## geometry
Ray OX bisects angle AOC and angle AOX =42 degrees, angle AOC is: 42 degrees 84 degrees 21 degrees 68 degrees
12. ## Chemistry
What is the percent by mass of C in methyl acetate (C3H6O2)? The molecular weight of carbon is 12.0107 g/mol, of hydrogen 1.00794 g/mol, and of oxygen 15.9994 g/mol. Answer in units of %. Please work it out for me so I totally understand it. Thanks!
13. ## Word Problem
Assume that the mathematical model C(x) = 16x + 130 represents the cost C, in hundreds of dollars, for a certain manufacturer to produce x items. How many items x can be manufactured while keeping costs between $525,000 and$781,000? Thanks in advance!
14. ## Statistics/Probability
So I tried solving the first one and apparently failed miserably, attempted both twice and got it wrong each time and I have one submission attempt left, so any help is definitely appreciated! 1. Hotels R Us has kept the following recordes concerning the
15. ## physics
A golfer hits a shot to a green that is elevated 3.0 m above the point where the ball is struck. The ball leaves the club at a speed of 16.8 m/s at an angle of 30.0¢ª above the horizontal. It rises to its maximum height and then falls down to the green.
16. ## Physics
To move a large crate across a rough floor, you push on it with a force at an angle of 21 below the horizontal, as shown in the figure. Find the acceleration of the crate if the applied force is 400 , the mass of the crate is 32 and the coefficient of
17. ## chemistry
The solubility of Na3(PO4) is 0.025 M. What is the Ksp of sodium phosphate?
18. ## math
order the numbers from least to greatest. _ 1 4/5, 1.78, 1 5/6, 7/4, 1.7, 1 8/11 I am confused on going back and forth between decimals and fractions.
19. ## Chemistry
Help with lab report Need Help finishing my lab report.KNOWN VALUES ARE V OF HCL=50ML,M=2.188.V OF NAOH=55.3ML,M=2.088.INTIAL TEMP FOR HCL=22.5C,NAOH IS 23C.this is for part A: Mass of final NACL solution assuming that the density of a 1 M Nacl solution is
20. ## Statistics
How do frequency tables, relative frequencies, and histograms showing relative frequencies help us understand sampling distributions? A. They help us to measure or estimate of the likelihood of a certain statistic falling within the class bounds. B. They
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consider a pair of planets that find the distance between them is decreased by a factoer of 5. Show that the force between them becomes 25 times as strong?
22. ## Chemistry
What mass of oxygen is consumed when 1.73L of carbon dioxide (STP) are produced in the following equation. C4H8 + 6 O2 > 4 CO2 + 4 H2O please help and show your work. My answer for this problem is 11.12g/O2. I have no confidence in my answer.
23. ## Chemistry
What volume of carbon monoxide gas (at STP) is needed when 1.35 Moles of oxygen gas react completely in the following equation. 2CO + O2 > 2CO2 please show your work I'm having trouble with Gas Stoichiometry.
24. ## ALGEBRA
Select all statements that are true. (log_b$$A$$)/(log_b$$B$$)=log_b$$A-B$$ (If ) log_1.5$$8$$=x, text( then ) x**(1.5) =8. log$$500$$ text( is the exponent on ) 10 text( that gives ) 500. text (In )log_b$$N$$, text( the exponent is )N. text( If )
25. ## math
Ray OX bisects angle AOC and angle AOX =42 degrees, angle AOC is: 42 degrees 84 degrees 21 degrees 68 degrees
26. ## statistics
A USU today survey found that of the gun owners surveyed 275 favor stricter gun laws. Test the claim that the majority (more than 50%) of gun owners favor stricter gun laws. Use a .05 significance level.
27. ## chemistry
How many moles of Cu are needed to react with 3.50 moles of AgNO3?
28. ## Geometry
How do you find the coordinates of the image of J (-7,-3) after the translation (x,y) (x-4,y+6)
29. ## Pre-Calculous (Trig)
The Singapore Flyer, currently the world's largest Ferris wheel, completes one rotation every 37 minutes.1 Measuring 150 m in diameter, the Flyer is set atop a terminal building, with a total height of 165 m from the ground to the top of the wheel. When
30. ## chemistry
While in Europe, if you drive 105km per day, how much money would you spend on gas in one week if gas costs 1.10 euros per liter and your car's gas mileage is 22.0mi/gal? Assume that 1euro = 1.26 dollars.
62. ## chemistry
how many grams of NaOH would be needed to make 896mL of a 139 M solution
63. ## chemistry
calculate the molarity of an acetic acid solution if 39.96 mL of the solution is needed to neutralize 136mL of 1.41 M sodium hydroxide. the equation for the reaction is HC2H3O2(aq) + NaOH(aq) > Na+(aq) + C2H3O2(aq) +H2O(aq)
64. ## chemistry
calculate the molarity of an acetic acid solution if 39.96 mL of the solution is needed to neutralize 136mL of 1.41 M sodium hydroxide. the equation for the reaction is HC2H3O2(aq) + NaOH(aq) > Na+(aq) + C2H3O2(aq) +H2O(aq)
65. ## Chemistry
the heat of fusion water is 335J/g,the heat of vaporization of water is 2.26kJ/g, the specific heat of water is 4.184J/deg/g. how many grams of ice at 0 degrees could be converted to steam at 100 degrees C by 9,574J
66. ## ALGEBRA
Graph the equation. x = -6
67. ## ALGEBRA
Use the definition of logarithm to simplify each expression. text((a) )log_(3b) $$3b$$ text((b) )log_(4b) $$(4b)^6$$ text((c) )log_(7b) $$(7b)^(-11)$$
68. ## chemistry
the heat of fusion water is335 J/g. The heat of evaporization of water is 2.26 kJ/g, the specific heat of ice is 2.05 J/Deg/g, the specific heat of steam is 2.08 J/deg/g and the specific heat of liquid water is 4.184 J/deg/g. How much heat would be needed
69. ## chemistry
the heat of vaporization of water is 2.26kJ/g. how much heat is needed to change 2.55 g of water to steam?
70. ## Chemistry
what volume of ammonia gas will be produced when 8.01 L of hydrogen react completely in the following equation. N2 + 3H2 > 2NH3 this stuff is so confusing because one little word seems to change the entire process for solving.
71. ## Chemistry
what volume of ammonia gas will be produced when 1.26L of nitrogen react completely in the following equation? N2 + 3H2 > 2NH3 Please if someone can just give me the order of operation it will be much appreciated because chemistry is just not my forte.
72. ## ALGEBRA
3x2 = 17x + 6
73. ## ALGEBRA
Consider the following expression. 3(x - 2) - 9(x**2 + 7 x + 4) - 5(x + 8) (a) Simplify the expression.
74. ## ALGEBRA
The Greek God Zeus ordered his blacksmith Hephaestus to create a perpetual water-making machine to fill Zeus' mighty chalice. The volume of Zeus' chalice was reported to hold about one hundred and fifty sextillion gallons (that is a fifteen followed by
75. ## ALGEBRA
Evaluate the given expressions (to two decimal places). (a) ) log((23.0) (b) ) log_(2) $$128$$ (c) ) log_(9) $$1$$
76. ## ALGEBRA
Use the definition of logarithm to simplify each expression. (a) )log_(3b) $$3b$$ ((b) )log_(8b) $$(8b)^6$$ (c) )log_(10b) $$(10b)^(-13)$$
77. ## ALGEBRA
Evaluate the given expressions (to two decimal places). (a) log((23.0) ((b) log_(2) $$128$$ text((c) ) log_(9) $$1$$
78. ## ALGEBRA
Find a simplified value for x by inspection. Do not use a calculator. (a) log5(25) = x (b) log2(16) = x
79. ## ALGEBRA
Contract the expressions. That is, use the properties of logarithms to write each expression as a single logarithm with a coefficient of 1. text ((a) ) ln$$3$$-2ln$$4$$+ln$$8$$ ((b) ln$$3$$-2ln$$4+8$$ (c) )ln$$3$$-2(ln$$4$$+ln$$8$$)
80. ## ALGEBRA
Solve the equations by finding the exact solution. ln$$x$$ - ln$$9$$ = 3
81. ## ALGEBRA
ln$$e$$ = ln$$sqrt(2)/x$$ -ln$$e$$
82. ## ALGEBRA
(1)/(2) log$$x$$ - log$$10000$$ = 4
83. ## ALGEBRA
Solve the equations by finding the exact solution. ln$$x$$ - ln$$9$$ = 3
84. ## ALGEBRA
A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.4 multiplied by 102 µm. Find this earthquake's magnitude on the Richter scale. (Round your answer to the nearest tenth.)
85. ## ALGEBRA
Find the number of decibels for the power of the sound. Round to the nearest decibel. A rock concert, 5.21 multiplied by 10-6 watts/cm2
86. ## Algebra II
if y varies directly as x, if y=80 when x=32, find x if y=100
87. ## geometry
The altitude of an equilateral triangle is 7 square root 3 units long. The length of one side of the triangle is ____ units. 7 14 14 square root 3 7 square root 3 over 2
88. ## math
1. find the lateral area of a right prism whose altitude measures 20 cm and whose base is a square with a width 7 cm long. 2. the volume of a rectangular solid is 5376 cubic meters, and the base is 24 meters by 16 meters. find the height of the solid. 3. a
89. ## physics
A jetliner can fly 5.57 hours on a full load of fuel. Without any wind it flies at a speed of 2.43 x 102 m/s. The plane is to make a round-trip by heading due west for a certain distance, turning around, and then heading due east for the return trip.
90. ## physics
Relative to the ground, a car has a velocity of 14.4 m/s, directed due north. Relative to this car, a truck has a velocity of 24.8 m/s, directed 52.0° north of east. What is the magnitude of the truck's velocity relative to the ground?
91. ## physics
A ball is thrown upward at a speed v0 at an angle of 59.0¢ª above the horizontal. It reaches a maximum height of 8.7 m. How high would this ball go if it were thrown straight upward at speed v0?
92. ## physics
A speedboat starts from rest and accelerates at +1.68 m/s2 for 5.43 s. At the end of this time, the boat continues for an additional 8.16 s with an acceleration of +0.475 m/s2. Following this, the boat accelerates at -0.866 m/s2 for 7.54 s. (a) What is the
93. ## algebra
what is the slope of line that passes through (-3,-8) and (0,6)
94. ## physics
Driving in your car with a constant speed of 12 m/s, you encounter a bump in the road that has a circular cross-section. If the radius of curvature of the bump is 35 m, find the apparent weight of a 63-kg person in your car as you pass over the top of the
95. ## Math
What is the surface area of a right circular cylinder with base circle of radius of 5m and height of the cylinder 10m?
96. ## statistics
Find z such that 20.3% of the standard normal curve lies to the right of z. 0.831 0.533 -0.533 -0.257 0.257
97. ## statistics
Assume that about 45% of all U.S. adults try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 110 insurance claims to be processed in the next few days. What is the
99. ## Pre-cal
Please determine the following limit if they exist. If the limit doe not exist put DNE. lim 2x^3 / x^2 + 10x - 12 x->infinity. Thanks.
|
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https://www.zappos.com/women-ankle-boots-and-booties/CK_XARCz1wEYxuwBegLZBIIBAooYwAEB4gIFAQIDGA8.zso?s=isNew/desc/goLiveDate/desc/recentSalesStyle/desc/&si=4854271,4826467,4854080,4858081,4782232,5004551,4863216,4889721,4891568,4953830,4977618,4854267,5014479,4878913,4805845&sy=1
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# Women Ankle Boots and Booties
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http://math.stackexchange.com/tags/multilinear-algebra/hot
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# Tag Info
5
The symmetrizer $S: \bigotimes^k V \to \bigotimes^k V$ is idempotent. Hence, $\ker(S) = \mathrm{im}(\mathrm{id}-S)$. This is generated by elements of the form $\alpha-{}^\sigma \alpha$, where $\sigma$ is some permutation.
2
Remember: for finite dimensional spaces, two vectors spaces (over the same field) are isomorphic if and only if they have the same dimension. So, for all these, it suffices to simply find a basis, and therefore conclude the dimension. In particular, we have $$\dim(\mathcal L(V,W)) = \dim(V \otimes W) = \dim(V) \dim(W)$$ When $V$ and $W$ are finite ...
2
SECTION A : The linearly independent elements of a Totally Symmetric Tensor $\;T_{i_{1}i_{2}\cdots i_{p-1}i_{p}}\;$(important for the interpretation of Quark Theory of Baryons in Particle Physics) \begin{equation*} \bbox[#FFFF88,8px] {\boldsymbol{3}\boldsymbol{\otimes}\boldsymbol{3}\boldsymbol{\otimes}\boldsymbol{3}= ...
1
Multiply by $g^{\sigma\tau}$ and use that $$g^{ab}g_{bc} = \delta^a_c,$$ so the right-hand side becomes $d^{\sigma}$, which is what you want. I'll leave the left-hand side to you, since you don't say if you mind raising the index on $A_{\mu\nu\tau}$.
1
$0$-tensors are just scalars, so the tensor product in this case is just scalar multiplication.
1
Symbolically, it is an $n\times n$ matrix. Don't expand the $\vec{e}_i$ into coordinates. Just take the determinant according to however you normally do so, and whenever multiplication involves the scalars from below, multiply accordingly, and when it involves a scalar times one of these vectors from the top row, multiply the scalar times the vector ...
1
I assume that by transoposition you mean dual mapping $T^*$. That is if $T:V\rightarrow V$ then $T^*:V^*\rightarrow V^*$ in following manner $$\left[T^*\alpha\right](v):=\alpha(T(v)).$$ Let $\alpha_1,\dots,\alpha_n\in V^*.$ Fix arbitrary $v_1,\dots,v_n\in V.$ Then \left[\bigwedge^n T^*(\alpha_1\wedge\dots\wedge\alpha_n)\right](v_1\wedge\dots\wedge ...
Only top voted, non community-wiki answers of a minimum length are eligible
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https://en.m.wikibooks.org/wiki/Fundamentals_of_Transportation/Mode_Choice/Solution2
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# Fundamentals of Transportation/Mode Choice/Solution2
Problem:
Prior to the collapse, there were two modes serving the Marcytown-Rivertown corridor: driving alone (d) and carpool (c), which takes advantage of an uncongested carpool lane. The utilities of the modes are as given below.
${\displaystyle U_{d}=-t_{d}\,\!}$
${\displaystyle U_{c}=-12-t_{c}\,\!}$
where t is the travel time
Assuming a multinomial logit model, and
A) That the congested time by driving alone was 15 minutes and time by carpool was 5 minutes. What was the modeshare prior to the collapse?
B) How would you interpret the constant of -12 in the expression for Uc?
C) After the collapse, because of a shift in travelers from other bridges, the travel time by both modes increased by 12 minutes. What is the post-collapse modeshare?
D) The transit agency decides to run a bus to help out the commuters after the collapse. Again assuming the multinomial logit model holds, without knowing how many travelers take the bus, what proportion of travelers on the bus previously took the car? Why? Comment on this result. Does it seem plausible?
Solution:
A) That the congested time by driving alone was 15 minutes and time by carpool was 5 minutes. What was the modeshare prior to the collapse?
Ud = -15
Uc = -17
Pd = 0.88
Pc = 0.12
B) How would you interpret the constant of -12 in the expression for Uc?
The constant -12 is an alternative specific constant. In this example, even if the travel time for the drive and carpool modes were the same, the utility of the carpool mode is lesser than the drive alone due to the negative constant -12. This indicates that there is a lesser probability of an individual choosing the carpool mode due to its lower utility.
C) After the collapse, because of a shift in travelers from other bridges, the travel time by both modes increased by 12 minutes. What is the post-collapse modeshare?
In this question since the travel time for both modes increase by the same 12 minutes, the post-collapse mode share will be the same as before
D) The transit agency decides to run a bus to help out the commuters after the collapse. Again assuming the multinomial logit model holds, without knowing how many travelers take the bus, what proportion of travelers on the bus previously took the car? Why? Comment on this result. Does it seem plausible?
The logit model will indicate that 88% of the bus riders previously drove alone due to the underlying Independence of Irrelevant Alternatives (IIA) property. The brief implication of IIA is that when you add a new mode, it will draw from the existing modes in proportion to their existing shares. This doesnt seem plausible since the bus is more likely to draw from the carpool mode than the drive alone mode.
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https://en.wikipedia.org/wiki/Mason_Equation
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# Mason equation
(Redirected from Mason Equation)
The Mason equation is an approximate analytical expression for the growth (due to condensation) or evaporation of a water droplet—it is due to the meteorologist B. J. Mason.[1] The expression is found by recognising that mass diffusion towards the water drop in a supersaturated environment transports energy as latent heat, and this has to be balanced by the diffusion of sensible heat back across the boundary layer, (and the energy of heatup of the drop, but for a cloud-sized drop this last term is usually small).
## Equation
In Mason's formulation the changes in temperature across the boundary layer can be related to the changes in saturated vapour pressure by the Clausius–Clapeyron relation; the two energy transport terms must be nearly equal but opposite in sign and so this sets the interface temperature of the drop. The resulting expression for the growth rate is significantly lower than that expected if the drop were not warmed by the latent heat.
Thus if the drop has a size r, the inward mass flow rate is given by[1]
${\displaystyle {\frac {dM}{dt}}=4\pi r_{p}D_{v}(\rho _{0}-\rho _{w})\,}$
and the sensible heat flux by[1]
${\displaystyle {\frac {dQ}{dt}}=4\pi r_{p}K(T_{0}-T_{w})\,}$
and the final expression for the growth rate is[1]
${\displaystyle r{\frac {dr}{dt}}={\frac {(S-1)}{[(L/RT-1)\cdot L\rho _{l}/KT_{0}+(\rho _{l}RT_{0})/(D\rho _{v})]}}}$
where
## References
1. ^ a b c d 1. B. J. Mason The Physics of Clouds (1957) Oxford Univ. Press.
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https://www.maplesoft.com/support/help/errors/view.aspx?path=object/builtins&L=E
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• An object may override a routine by exporting a method of the same name. Any routine implemented in Maple code can be overridden. However, not all routines of type builtin can be overridden. This page discusses how to override those builtin routines. Operators that can be overridden are discussed on the page object,operators.
Overridable builtin Routines
• The following builtin functions can be overridden by object methods:
Special Considerations
• If an object implements a method to override a builtin routine, that method is still a procedure that follows the normal binding rules within the object declaration. This means that Maple may call the override even when the programmer wanted to call the top-level routine. To make sure that a function call invokes the top-level routine, use the fully qualified name. (Even when using the fully qualified name, if any of the arguments are objects exporting that name, the override will typically be called from within the builtin function.)
Overriding Particular Routines
• Special considerations for overriding particular operators are described in the object,operators help page.
andmap, ormap, and xormap
• The andmap (and ormap and xormap) method expects two or more arguments:
> export andmap::static := proc( p::appliable, self ) ... end proc:
• The p argument is the procedure to be applied to each element of the object, and is expected to return true, false, or FAIL. The method should check the validity of the return value. When p returns false in andmap, the method should immediately return false.
• If a container object does not export andmap (or ormap or xormap), and one of these functions is called with such an object as the second argument, Maple will attempt to use either the object's ModuleIterator method if it exists, or its lowerbound, upperbound, and ?[] methods to iterate over the object, calling p on the object's behalf, just as if the function had been called on a built-in container (such as a list).
convert
• A convert method needs to be able to deal with three possibilities: converting to the object from another type, converting from an object to another type, and applying a conversion where the object is an extra parameter (the third or later argument).
diff
• A diff method needs to handle three possibilities: differentiating an object, differentiating with respect to an object, or both.
• If an object exports a diff method, it should also export a has method. Maple uses has to determine if an expression contains the variable of differentiation. If has returns false, 0 is returned immediately. The built-in version of has does not look inside of objects, and thus will return false.
entries and indices
• The entries and indices methods should return a sequence of the entries and indices of a container object respectively. There should be a one-to-one correspondence between the indices and the entries, that is, the i-th index should yield the i-th element when passed to the ?[] method.
• Each element of the sequence must be a list containing the actual entry or index. The nolist option of these builtins is handled automatically by Maple, and need not be considered when implementing these methods.
• In order for the pair option of indices and/or entries to work with an object, both methods must be implemented. Again, Maple itself handles this option; the methods need not consider it.
• The indexorder option of entries and indices is not supported.
eval
• There are two calling sequences for the built-in eval.
> eval( expr );
> eval( expr, substitutions );
• An object's eval method only overrides the second calling sequence.
• As eval works recursively, if expr contains an object that implements eval, that object's eval method will be called.
• In the second calling sequence of the built-in eval, the substitutions can be specified in various ways. The eval method will have each equation passed as a separate argument.
evalf
• An evalf method should convert the object into a floating-point value.
• The evalf method is often called with an index (evalf[digits]) to specify the number of digits the expression should be evaluated to. When the object method is called, the value of the Digits environment variable will have been set if a value was given.
evalhf
• Implementing an evalhf method allows an object to be used in Maple's evalhf subsystem. An evalhf method should convert the object into one of the types that evalhf can manipulate. For the best performance, one of the following should be returned:
–
– An hfarray
– A Maple procedure that does not use lexical scoping
has
• The has method checks to see if an object contains an expression, if an expression contains an object, or if one object is contained in another.
• When declaring an object that exports a has method that uses the object name as a type, the named object syntax
> module Obj() ... end module:
should be used. Using the assignment syntax
> Obj := module() ... end module:
will cause an error to be raised during the assignment if the has method uses Obj as a type. The has routine is invoked when a top-level assignment occurs, to check if the name being assigned to is contained in the value being assigned to it. This is an attempt to avoid recursive assignments. The has method will be called for this assignment, but as the object's name has not been assigned, the type checks will fail.
lowerbound, upperbound, and ?[]
• These three can be used together to implement iteration over an object, as an alternative to implementing a ModuleIterator procedure. See ModuleIterator for more details, and object,operators for special considerations when implementing ?[].
map, map2, and map[n]
• The map, map2 and map[n] functions are all overridden by a single map method. The calling sequence of the map method is:
> export map::static := proc( oindex::integer, inplace::truefalse, func ) ... end proc:
oindex: corresponds to the index of the expression to be mapped over.
inplace: determines if the map should occur in-place. If in-place mapping is not supported, then an exception should be raised if inplace is true.
func: the function to be mapped.
• If the parameter declaration given above is used, then the special sequence _rest are the arguments to be passed to func and the element _rest[oindex] is the element to be mapped over. If e is an element of _rest[oindex] then the mapped value should be:
> func( _rest[..oindex-1], e, _rest[oindex+1..] )
max and min
• To override the max and min routines, export methods with the following declaration:
> export max::static := proc( definedOnly::truefalse, a, b:=NULL, $) ... end proc; > export min::static := proc( definedOnly::truefalse, a, b:=NULL,$ ) ... end proc;
definedOnly: corresponds to max['defined']( .. ) and determines the behavior when undefined values are compared. When definedOnly is true, undefined values should be ignored (that is, a defined value should be returned). When definedOnly is false, the routines should return FAIL when an undefined value is encountered.
• In Maple the max and min routines work on a combination of containers and elements. To handle these cases, the corresponding methods must be able to handle the case where b is NULL, indicating that it should return the maximum (or minimum) value stored in container object a, or a itself if it is not a container. In the general case, a and b will have a value and at least one of a or b will be an object. If the object is a container, then the maximum (or minimum) value between the elements in the container and the other argument should be returned. Otherwise the maximum (or minimum) value of a and b should be returned.
• If a container object is empty, the max or min method should return NULL, not -infinity or infinity, as the container may be nested in other containers having values that are not numeric (e.g. strings). Maple will convert the final value of the initial call of max or min into the appropriate infinity if no values were found at all in any of the arguments.
• Likewise, if a container object contains only empty sub-containers (either similar objects, or ordinary lists, sets, or Arrays), the result should be NULL as well. This is best achieved using the nodefault index option when recursively calling max or min on these sub-containers.
• If an object does not define min or max, Maple will assume it represents a value instead of a container, and will attempt to determine the correct element using an overloaded < (less than) operator, if it is defined.
member
• The member method determines if a container contains a value. If the container does contain the value, member should return the index that can be used by ?[] to retrieve that element. If the container does not contain the value, 0 should returned.
• If an object wants to implement member but does not implement the ?[] method, it should return undefined if the value is in the container, and 0 if it is not.
• More information on the consequences of implementing ?[] can be found in object,operators.
• Evaluating an expression of the form $a\in b$ can result in a call to member. More details can be found in object,operators.
normal
• The normal method has the following signature:
> export normal::static := proc( self, { expanded::truefalse = false }, $) ... end proc: expanded: true or false depending on if the expanded option was given to normal. select, remove, and selectremove • The select and remove methods have the following signature: > export select::static := proc( inplace::truefalse, fn, self ) > export remove::static := proc( inplace::truefalse, fn, self ) > export selectremove::static := proc( inplace::truefalse, fn, self ) inplace: determines that the result (the first result in the case of selectremove) should be computed in-place. If the object cannot support in-place selection or removal, an exception should be raised. • Any additional arguments to select, remove, or selectremove will be passed as additional arguments to the corresponding method, and can be accessed via _rest. sort • The sort method has the following signature: > export sort :: static := proc( inplace::truefalse, self ) ... end proc: inplace: determines if the sorting should be done in-place if possible. • Any additional arguments to sort will be passed as additional arguments to the sort method, and can be accessed via _rest. subs • The subs method has the following signature: > export subs :: static := proc( inplace::truefalse, eqns::{list,MyObject}, expr::anything,$ ) ... end proc:
inplace: determines if the substitutions should happen in-place if possible.
eqns: either a list of substitutions or an object whose subs method was invoked.
• If eqns is a list, then the third argument (expr) is the object whose subs method was invoked. If the second argument is an object with a subs method, then the third parameter can be anything.
type
• Objects can be used directly as types and an Object can define a ModuleType method to further refine this test. However, this does not allow an object to be tested by types that are not aware of the object. You can accomplish this by overriding the type method.
• When the first argument of a call to type is an object that exports a type method and the second argument is not a module type and not the name module, then the type override will be called.
> export type :: static := proc( self::MyObject, t, \$ ) :-type( self:-value, t ) end proc:
• The first argument is the object, the second argument is the given type.
• The type override should return one of three values:
– true : the object does match the given type
– false : the object does not match the given type
– NULL : undecided, the type checking continues as if the type override had not been written.
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http://mathoverflow.net/users/46114/j-l
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# J.L.
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https://philpapers.org/browse/decision-theoretic-frameworks-misc
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# Decision-Theoretic Frameworks, Misc
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1. Knowledge in Action.Jonathan Weisberg - 2013 - Philosophers' Imprint 13.
Recent proposals that frame norms of action in terms of knowledge have been challenged by Bayesian decision theorists. Bayesians object that knowledge-based norms conflict with the highly successful and established view that rational action is rooted in degrees of belief. I argue that the knowledge-based and Bayesian pictures are not as incompatible as these objectors have made out. Attending to the mechanisms of practical reasoning exposes space for both knowledge and degrees of belief to play their respective roles.
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2. In this paper, I argue for a new normative theory of rational choice under risk, namely expected comparative utility (ECU) theory. I show that for any choice option, a, and for any state of the world, G, the measure of the choiceworthiness of a in G is the comparative utility (CU) of a in G—that is, the difference in utility, in G, between a and whichever alternative(s) to a carry the greatest utility in G. On the basis of this principle, (...)
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3. A Companion to Rationality.David Robert - manuscript
This book is divided into 2 sections. In Section 1 (How to think rationally), I address how to acquire rational belief attitudes and, on that basis, I consider the question whether one ought to be skeptical of climate change. In Section 2 (How to act rationally), I address how to make rational choices and, on that basis, I consider the questions whether one is rationally required to do what one can to support life-extension medical research and, more broadly, whether one (...)
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4. Ex ante predicted outcomes should be interpreted as counterfactuals (potential histories), with errors as the spread between outcomes. But error rates have error rates. We reapply measurements of uncertainty about the estimation errors of the estimation errors of an estimation treated as branching counterfactuals. Such recursions of epistemic uncertainty have markedly different distributial properties from conventional sampling error, and lead to fatter tails in the projections than in past realizations. Counterfactuals of error rates always lead to fat tails, regardless of (...)
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5. A choice function C is rational iff: if it allows a path through a sequence of decisions with a particular outcome, then that outcome is amongst the ones that C would have chosen from amongst all the possible outcomes of the sequence. This implies, and it is the strongest definition that implies, that anyone who is irrational could be talked out of their own preferences. It also implies weak but non-vacuous constraints on choices over ends. These do not include alpha (...)
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6. This paper argues that we need to look beyond Bayesian decision theory for an answer to the general problem of making rational decisions under uncertainty. The view that Bayesian decision theory is only genuinely valid in a small world was asserted very firmly by Leonard Savage [18] when laying down the principles of the theory in his path-breaking Foundations of Statistics. He makes the distinction between small and large worlds in a folksy way by quoting the proverbs ”Look before you (...)
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7. Credal Imprecision and the Value of Evidence.Nilanjan Das - forthcoming - Noûs.
This paper is about a tension between two theses. The first is Value of Evidence: roughly, the thesis that it is always rational for an agent to gather and use cost-free evidence for making decisions. The second is Rationality of Imprecision: the thesis that an agent can be rationally required to adopt doxastic states that are imprecise, i.e., not representable by a single credence function. While others have noticed this tension, I offer a new diagnosis of it. I show that (...)
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8. Rational Intransitive Preferences.Peter Baumann - 2022 - Politics, Philosophy and Economics 21 (1):3-28.
According to a widely held view, rationality demands that the preferences of a person be transitive. The transitivity assumption is an axiom in standard theories of rational choice. It is also prima facie very plausible. I argue here that transitivity is not a necessary condition of rationality; it is a constraint only in some cases. The argument presented here is based on the non-linearity of differential utility functions. This paper has four parts. First, I present an argument against the transitivity (...)
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9. Escaping the Cycle.J. Dmitri Gallow - 2022 - Mind 131 (521):99-127.
I present a decision problem in which causal decision theory appears to violate the independence of irrelevant alternatives (IIA) and normal-form extensive-form equivalence (NEE). I show that these violations lead to exploitable behavior and long-run poverty. These consequences appear damning, but I urge caution. This decision should lead causalists to a better understanding of what it takes for a decision between some collection of options to count as a subdecision of a decision between a larger collection of options. And with (...)
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10. Tough Enough? Robust Satisficing as a Decision Norm for Long-Term Policy Analysis.Andreas L. Mogensen & David Thorstad - 2022 - Synthese 200 (1):1-26.
This paper aims to open a dialogue between philosophers working in decision theory and operations researchers and engineers working on decision-making under deep uncertainty. Specifically, we assess the recommendation to follow a norm of robust satisficing when making decisions under deep uncertainty in the context of decision analyses that rely on the tools of Robust Decision-Making developed by Robert Lempert and colleagues at RAND. We discuss two challenges for robust satisficing: whether the norm might derive its plausibility from an implicit (...)
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11. Expected Utility Theory on Mixture Spaces Without the Completeness Axiom.David McCarthy, Kalle Mikkola & Joaquin Teruji Thomas - 2021 - arXiv:2102.06898 [Econ.TH].
A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a mixture preorder has a multi-representation that consists of real-valued, mixture-preserving functions. If it does, it must satisfy the mixture continuity axiom of Herstein and Milnor (1953). Mixture continuity is sufficient for a mixture-preserving multi-representation when the dimension of the mixture space (...)
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12. A Restatement of Expected Comparative Utility Theory: A New Theory of Rational Choice Under Risk.David Robert - 2021 - Philosophical Forum 52 (3):221-243.
In this paper, I argue for a new normative theory of rational choice under risk, namely expected comparative utility (ECU) theory. I first show that for any choice option, a, and for any state of the world, G, the measure of the choiceworthiness of a in G is the comparative utility (CU) of a in G—that is, the difference in utility, in G, between a and whichever alternative to a carries the greatest utility in G. On the basis of this (...)
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13. Transformative Experiences.Marcus Arvan - 2020 - In International Encyclopedia of Ethics. Wiley-Blackwell.
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14. Avoiding Risk and Avoiding Evidence.Catrin Campbell-Moore & Bernhard Salow - 2020 - Australasian Journal of Philosophy 98 (3):495-515.
It is natural to think that there is something epistemically objectionable about avoiding evidence, at least in ideal cases. We argue that this thought is inconsistent with a kind of risk-avoidance...
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15. Accurate Updating for the Risk Sensitive.Catrin Campbell-Moore & Bernhard Salow - 2020 - British Journal for the Philosophy of Science:axaa006.
Philosophers have recently attempted to justify particular belief revision procedures by arguing that they are the optimal means towards the epistemic end of accurate credences. These attempts, however, presuppose that means should be evaluated according to classical expected utility theory; and there is a long tradition maintaining that expected utility theory is too restrictive as a theory of means–end rationality, ruling out too many natural ways of taking risk into account. In this paper, we investigate what belief-revision procedures are supported (...)
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16. Newcomb University: A Play in One Act.Adam Elga - 2020 - Analysis 80 (2):212-221.
Counter-intuitive consequences of both causal decision theory and evidential decision theory are dramatized. Each of those theories is thereby put under some pressure to supply an error theory to explain away intuitions that seem to favour the other. Because trouble is stirred up for both sides, complacency about Newcomb’s problem is discouraged.
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17. Freedom, Indeterminism, and Fallibilism.Danny Frederick - 2020 - Cham, Switzerland: Palgrave Macmillan.
This book uses the concepts of freedom, indeterminism, and fallibilism to solve, in a unified way, problems of free will, knowledge, reasoning, rationality, personhood, ethics and politics. Presenting an overarching theory of human freedom, Frederick argues for an account of free will as the capacity for undetermined acts. Knowledge, rationality, and reasoning, both theoretical and practical, as well as personhood, morality and political authority, are all shown to be dependent at their roots on indeterminism and fallibility, and to be connected (...)
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18. On the Individuation of Choice Options.Roberto Fumagalli - 2020 - Philosophy of the Social Sciences 50 (4):338-365.
Decision theorists have attempted to accommodate several violations of decision theory’s axiomatic requirements by modifying how agents’ choice options are individuated and formally represented. In recent years, prominent authors have worried that these modifications threaten to trivialize decision theory, make the theory unfalsifiable, impose overdemanding requirements on decision theorists, and hamper decision theory’s internal coherence. In this paper, I draw on leading descriptive and normative works in contemporary decision theory to address these prominent concerns. In doing so, I articulate and (...)
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19. The Causal Decision Theorist's Guide to Managing the News.J. Dmitri Gallow - 2020 - Journal of Philosophy 117 (3):117-149.
According to orthodox causal decision theory, performing an action can give you information about factors outside of your control, but you should not take this information into account when deciding what to do. Causal decision theorists caution against an irrational policy of 'managing the news'. But, by providing information about factors outside of your control, performing an act can give you two, importantly different, kinds of good news. It can tell you that the world in which you find yourself is (...)
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20. The Intrinsic Value of Risky Prospects.Zeev Goldschmidt & Ittay Nissan-Rozen - 2020 - Synthese 198 (8):7553-7575.
We study the representation of attitudes to risk in Jeffrey’s decision-theoretic framework suggested by Stefánsson and Bradley :602–625, 2015; Br J Philos Sci 70:77–102, 2017) and Bradley :231–248, 2016; Decisions theory with a human face, Cambridge University Press, Cambridge, 2017). We show that on this representation, the value of any prospect may be expressed as a sum of two components, the prospect’s instrumental value and the prospect’s intrinsic value. Both components have an expectational form. We also make a distinction between (...)
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21. Structuring Decisions Under Deep Uncertainty.Casey Helgeson - 2020 - Topoi 39 (2):257-269.
Innovative research on decision making under ‘deep uncertainty’ is underway in applied fields such as engineering and operational research, largely outside the view of normative theorists grounded in decision theory. Applied methods and tools for decision support under deep uncertainty go beyond standard decision theory in the attention that they give to the structuring of decisions. Decision structuring is an important part of a broader philosophy of managing uncertainty in decision making, and normative decision theorists can both learn from, and (...)
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22. The Reality of Free Will.Claus Janew - 2020 - Journal of Consciousness Exploration and Research 11 (1):1-16.
The uniqueness of each viewpoint, each point of effect, can be "overcome" only by changing the viewpoint to other viewpoints and returning. Such an alternation, which can also appear as constant change, makes up the unity of the world. The wholeness of an alternation, however, is a consciousness structure because of the special relationship between the circumscribing periphery and the infinitesimal center. This process structure unites determinacy and indeterminacy at every point also totally. We are dealing, therefore, with forms of (...)
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23. to appear in Lambert, E. and J. Schwenkler (eds.) Transformative Experience (OUP) -/- L. A. Paul (2014, 2015) argues that the possibility of epistemically transformative experiences poses serious and novel problems for the orthodox theory of rational choice, namely, expected utility theory — I call her argument the Utility Ignorance Objection. In a pair of earlier papers, I responded to Paul’s challenge (Pettigrew 2015, 2016), and a number of other philosophers have responded in similar ways (Dougherty, et al. 2015, Harman (...)
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24. 由于金蒂斯是一位资深经济学家,而且我饶有兴趣地阅读了他的一些以前的书,所以我期待对行为有更多的见解。可悲的是,他把群体选择和现象学的死手变成了他行为理论的核心,这在很大程度上使工作无效。更糟糕的是,由 于他在这里表现出了如此糟糕的判断,这就使他对以前的所有工作都提出了质疑。几年前,他在哈佛、诺瓦克和威尔逊的朋友试图重新选择团体,这是过去十年中生物学领域的重大丑闻之一,我在《利他主义、耶稣和世界末日》 一文中讲述了这个悲惨的故事——邓普顿·福 foundation 买下了哈佛大学教授职位,攻击了进化、理性和文明——对E.O.威尔逊的《地球的社会征服》(2012年)和诺瓦克和高菲尔德"超级合作者"(2012年)的回顾。与诺瓦克不同,金提人似乎并 非出于宗教狂热,而是强烈希望为人性的严峻现实创造一种替代方案,而(几乎普遍)缺乏对人类基本生物学的理解和空白石板主义的使之变得容易。行为科学家、其他学者和一般公众。 Gintis正确地攻击(正如他以前多次)经济学家、社会学家和其他行为科学家没有一个连贯的框架来描述行为。当然,理解行为所需的框架是一个进化的框架。不幸的是,他未能提供一个自己(根据他的许多批评家,我同 意),并试图嫁接腐烂的尸体的群体选择到任何经济和心理理论,他在他的几十年的工作,只是使他的整个项目无效。 虽然金蒂斯勇敢地努力去理解和解释遗传学,比如威尔逊和诺瓦克,但他远非专家,和他们一样,数学只是使他看不到生物学上的不可能性,当然这是科学的常态。正如维特根斯坦在《文化与价值》第一页中著名的指出的那样: "没有宗教派别滥用形而上学的表达方式像在数学中那样造成如此多的辛德。 一直很清楚,导致行为降低其自身频率的基因不能持久,但这是群体选择概念的核心。此外,众所周知,并经常证明,群体选择只是减少到包容性健身(亲属选择),正如道金斯指出,这只是另一个名字进化的自然选择。和威尔 逊一样,金蒂斯在这个舞台上工作了大约50年,但至今还没有掌握,但是丑闻爆发后,我只用了3天时间就找到、阅读和理解了最相关的专业工作,就像我的文章所详述的。想到金蒂斯和威尔逊在近半个世纪里未能实现这一点 ,这令人费解。 我讨论了群体选择和现象学的错误,这是学术界的常态,是几乎普遍不理解正在毁灭美国和世界的人性的特殊情况。 那些希望从现代两个系统的观点来看为人类行为建立一个全面的最新框架的人,可以查阅我的书《路德维希的哲学、心理学、Min d和语言的逻辑结构》维特根斯坦和约翰·西尔的《第二部》(2019年)。那些对我更多的作品感兴趣的人可能会看到《会说话的猴子——一个末日星球上的哲学、心理学、科学、宗教和政治——文章和评论2006-20 19年第3次(2019年)和自杀乌托邦幻想21篇世纪4日 (2019) .
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25. Is risk aversion irrational? Examining the “fallacy” of large numbers.H. Orri Stefánsson - 2020 - Synthese 197 (10):4425-4437.
A moderately risk averse person may turn down a 50/50 gamble that either results in her winning $200 or losing$100. Such behaviour seems rational if, for instance, the pain of losing $100 is felt more strongly than the joy of winning$200. The aim of this paper is to examine an influential argument that some have interpreted as showing that such moderate risk aversion is irrational. After presenting an axiomatic argument that I take to be the strongest case for (...)
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26. Conflicting Intentions: Rectifying the Consistency Requirements.Hein Duijf, Jan Broersen & John-Jules Ch Meyer - 2019 - Philosophical Studies 176 (4):1097-1118.
Many philosophers are convinced that rationality dictates that one’s overall set of intentions be consistent. The starting point and inspiration for our study is Bratman’s planning theory of intentions. According to this theory, one needs to appeal to the fulfilment of characteristic planning roles to justify norms that apply to our intentions. Our main objective is to demonstrate that one can be rational despite having mutually inconsistent intentions. Conversely, it is also shown that one can be irrational despite having a (...)
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27. Measuring Belief and Risk Attitude.Sven Neth - 2019 - Electronic Proceedings in Theoretical Computer Science 297:354–364.
Ramsey (1926) sketches a proposal for measuring the subjective probabilities of an agent by their observable preferences, assuming that the agent is an expected utility maximizer. I show how to extend the spirit of Ramsey's method to a strictly wider class of agents: risk-weighted expected utility maximizers (Buchak 2013). In particular, I show how we can measure the risk attitudes of an agent by their observable preferences, assuming that the agent is a risk-weighted expected utility maximizer. Further, we can leverage (...)
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28. Since Gintis is a senior economist and I have read some of his previous books with interest, I was expecting some more insights into behavior. Sadly, he makes the dead hands of group selection and phenomenology into the centerpieces of his theories of behavior, and this largely invalidates the work. Worse, since he shows such bad judgement here, it calls into question all his previous work. The attempt to resurrect group selection by his friends at Harvard, Nowak and Wilson, a (...)
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29. What Is Risk Aversion?H. Orii Stefansson & Richard Bradley - 2019 - British Journal for the Philosophy of Science 70 (1):77-102.
According to the orthodox treatment of risk preferences in decision theory, they are to be explained in terms of the agent's desires about concrete outcomes. The orthodoxy has been criticised both for conflating two types of attitudes and for committing agents to attitudes that do not seem rationally required. To avoid these problems, it has been suggested that an agent's attitudes to risk should be captured by a risk function that is independent of her utility and probability functions. The main (...)
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30. Equal Opportunity and Newcomb’s Problem.Ian Wells - 2019 - Mind 128 (510):429-457.
The 'Why ain'cha rich?' argument for one-boxing in Newcomb's problem allegedly vindicates evidential decision theory and undermines causal decision theory. But there is a good response to the argument on behalf of causal decision theory. I develop this response. Then I pose a new problem and use it to give a new 'Why ain'cha rich?' argument. Unlike the old argument, the new argument targets evidential decision theory. And unlike the old argument, the new argument is sound.
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31. Newcomb's Problem.Arif Ahmed (ed.) - 2018 - Cambridge University Press.
Newcomb's Problem is a controversial paradox of decision theory. It is easily explained and easily understood, and there is a strong chance that most of us have actually faced it in some form or other. And yet it has proven as thorny and intractable a puzzle as much older and better-known philosophical problems of consciousness, scepticism and fatalism. It brings into very sharp and focused disagreement several long-standing philosophical theories on practical rationality, on the nature of free will, and on (...)
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32. What Decision Theory Provides the Best Procedure for Identifying the Best Action Available to a Given Artificially Intelligent System?Samuel A. Barnett - 2018 - Dissertation, University of Oxford
Decision theory has had a long-standing history in the behavioural and social sciences as a tool for constructing good approximations of human behaviour. Yet as artificially intelligent systems (AIs) grow in intellectual capacity and eventually outpace humans, decision theory becomes evermore important as a model of AI behaviour. What sort of decision procedure might an AI employ? In this work, I propose that policy-based causal decision theory (PCDT), which places a primacy on the decision-relevance of predictors and simulations of agent (...)
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33. Success-First Decision Theories.Preston Greene - 2018 - In Arif Ahmed (ed.), Newcomb's Problem. Cambridge University Press. pp. 115–137.
The standard formulation of Newcomb's problem compares evidential and causal conceptions of expected utility, with those maximizing evidential expected utility tending to end up far richer. Thus, in a world in which agents face Newcomb problems, the evidential decision theorist might ask the causal decision theorist: "if you're so smart, why ain’cha rich?” Ultimately, however, the expected riches of evidential decision theorists in Newcomb problems do not vindicate their theory, because their success does not generalize. Consider a theory that allows (...)
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34. Influences on Primary Care Provider Imaging for a Hypothetical Patient with Low Back Pain.Hh le, Matt DeCamp, Amanda Bertram, Minal Kale & Zackary Berger - 2018 - Southern Journal of Medicine 12 (111):758-762.
OBJECTIVE: How outside factors affect physician decision making remains an open question of vital importance. We sought to investigate the importance of various influences on physician decision making when clinical guidelines differ from patient preference. -/- METHODS: An online survey asking 469 primary care providers (PCPs) across four practice sites whether they would order magnetic resonance imaging for a patient with uncomplicated back pain. Participants were randomized to one of four scenarios: a patient's preference for imaging (control), a patient's preference (...)
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35. Continuity and Completeness of Strongly Independent Preorders.David McCarthy & Kalle Mikkola - 2018 - Mathematical Social Sciences 93:141-145.
A strongly independent preorder on a possibly in finite dimensional convex set that satisfi es two of the following conditions must satisfy the third: (i) the Archimedean continuity condition; (ii) mixture continuity; and (iii) comparability under the preorder is an equivalence relation. In addition, if the preorder is nontrivial (has nonempty asymmetric part) and satisfi es two of the following conditions, it must satisfy the third: (i') a modest strengthening of the Archimedean condition; (ii') mixture continuity; and (iii') completeness. Applications (...)
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36. Transformative Decisions.Kevin Reuter & Michael Messerli - 2018 - Journal of Philosophy 115 (6):313-335.
Some decisions we make—such as becoming a parent or moving to a different part of the world—are transformative. According to L. A. Paul, transformative decisions pose a major problem to us because they fall outside the realm of rationality. Her argument for that conclusion rests on the premise that subjective value is central in transformative decisions. This paper challenges that premise and hence the overall conclusion that transformative decisions usually are not rational. In the theoretical part of the paper, we (...)
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37. Expected Comparative Utility Theory: A New Theory of Rational Choice.David Robert - 2018 - Philosophical Forum 49 (1):19-37.
In this paper, I argue for a new normative theory of rational choice under risk, namely expected comparative utility (ECU) theory. I first show that for any choice option, a, and for any state of the world, G, the measure of the choiceworthiness of a in G is the comparative utility (CU) of a in G—that is, the difference in utility, in G, between a and whichever alternative to a carries the greatest utility in G. On the basis of this (...)
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38. Counterfactual Desirability.Richard Bradley & H. Orii Stefansson - 2017 - British Journal for the Philosophy of Science 68 (2):485-533.
The desirability of what actually occurs is often influenced by what could have been. Preferences based on such value dependencies between actual and counterfactual outcomes generate a class of problems for orthodox decision theory, the best-known perhaps being the so-called Allais Paradox. In this paper we solve these problems by extending Richard Jeffrey's decision theory to counterfactual prospects, using a multidimensional possible-world semantics for conditionals, and showing that preferences that are sensitive to counterfactual considerations can still be desirability maximising. We (...)
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39. Normative Theories of Rational Choice: Expected Utility.Rachael Briggs - 2017 - The Stanford Encyclopedia of Philosophy.
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40. The Sure-Thing Principle and P2.Yang Liu - 2017 - Economics Letters 159:221-223.
This paper offers a fine analysis of different versions of the well known sure-thing principle. We show that Savage's formal formulation of the principle, i.e., his second postulate (P2), is strictly stronger than what is intended originally.
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41. We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infi nite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfi es a condition that we call Polarization.
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42. Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail not (...)
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43. Newcomb Meets Gettier.Ittay Nissan-Rozen - 2017 - Synthese 194 (12):4799-4814.
I show that accepting Moss’s claim that features of a rational agent’s credence function can constitute knowledge, together with the claim that a rational agent should only act on the basis of reasons that he knows, predicts and explains evidential decision theory’s failure to recommend the right choice for the Newcomb problem. The Newcomb problem can be seen, in light of Moss’s suggestion, as a manifestation of a Gettier case in the domain of choice. This serves as strong evidence for (...)
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44. Decisions and Higher‐Order Knowledge.Moritz Schulz - 2017 - Noûs 51 (3):463-483.
A knowledge-based decision theory faces what has been called the prodigality problem : given that many propositions are assigned probability 1, agents will be inclined to risk everything when betting on propositions which are known. In order to undo probability 1 assignments in high risk situations, the paper develops a theory which systematically connects higher level goods with higher-order knowledge.
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45. Risk Writ Large.Johanna Thoma & Jonathan Weisberg - 2017 - Philosophical Studies 174 (9):2369-2384.
Risk-weighted expected utility theory is motivated by small-world problems like the Allais paradox, but it is a grand-world theory by nature. And, at the grand-world level, its ability to handle the Allais paradox is dubious. The REU model described in Risk and Rationality turns out to be risk-seeking rather than risk-averse on one natural way of formulating the Allais gambles in the grand-world context. This result illustrates a general problem with the case for REU theory, we argue. There is a (...)
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46. Generalized Regret Based Decision Making.Ronald R. Yager - 2017 - Engineering Applications of Artificial Intelligence 65:400-405.
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47. Review of Lara Buchak, *Risk and Rationality*. [REVIEW]Arif Ahmed - 2016 - British Journal for the Philosophy of Science Review of Books.
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48. Law as Trope: Framing and Evaluating Conceptual Metaphors.Lloyd Harold Anthony - 2016 - Pace Law Review 37.
Like others who work with language, many lawyers no doubt appreciate good kennings. However, metaphors also play a much deeper role in thought and law than style, ornament, or verbal virtuosity. As we shall see, metaphors play a necessary role in our categories of thought. As a result, metaphors are a necessary part of thought itself, including legal thought.
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49. Choice-Based Cardinal Utility. A Tribute to Patrick Suppes.Jean Baccelli & Philippe Mongin - 2016 - Journal of Economic Methodology 23 (3):268-288.
We reexamine some of the classic problems connected with the use of cardinal utility functions in decision theory, and discuss Patrick Suppes's contributions to this field in light of a reinterpretation we propose for these problems. We analytically decompose the doctrine of ordinalism, which only accepts ordinal utility functions, and distinguish between several doctrines of cardinalism, depending on what components of ordinalism they specifically reject. We identify Suppes's doctrine with the major deviation from ordinalism that conceives of utility functions as (...)
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http://www.logic.univie.ac.at/2017/Talk_03-09_a.html
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# 2017 seminar talk: Projective sets and inner models
Talk held by Yizheng Zhu (Universität Münster, Germany) at the KGRC seminar on 2017-03-09.
### Abstract
The collection of projective sets of reals is the smallest one containing all the Borel sets and closed under complements and continuous images. The Axiom of Projective Determinacy (PD) is the correct axiom that settles the regularity properties of projective sets. Inner model theory provides a systematic way of studying the projective sets under PD. In this talk, we describe some recent progress in this direction. A key theorem is the following inner-model-theoretic characterization of the canonical model associated to $\Sigma^1_3$:
Let $\mathcal{O}_{\Sigma^1_{3}}$ be the universal $\Sigma^1_3$ subset of $u_\omega$ in the sharp codes for ordinals in $u_\omega$. Let $M_{1,\infty}$ be the direct limit of iterates of $M_1$ via countable trees and let $\delta_{1,\infty}$ be the Woodin cardinal of $M_{1,\infty}$. Then $M_{1,\infty}|\delta_{1,\infty} = L_{u_\omega}[\mathcal{O}_{\Sigma^1_{3}}]$.
This theorem paves the way for further study of $\Sigma^1_3$ sets using inner model theory. It also generalizes to arbitrary $\Sigma^1_{2n+1}$ and $M_{2n-1,\infty}$.
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https://regions.danielantal.eu/news/index.html
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# regions 0.0.0.9000 Unreleased
• Added a NEWS.md file to track changes to the package.
• Preparing a release candidate with Travis-CI integration.
# regions 0.1.0 Unreleased
• Submitted to CRAN
# regions 0.1.0.0001 Unreleased
• Adding the google_nuts_matchtable by Istvan Zsoldos for joining data from the Google Mobility Reports with Eurostat datasets.
# regions 0.1.1 Unreleased
• Adding further documentation items at request of CRAN reviewer (Thanks!).
# regions 0.1.2 Unreleased
• New function impute_down_nuts for less general cases, i.e. EU NUTS imputations.
• Contributor attribution consistent in DESCRIPTION and source file.
• Release candidate on CRAN.
# regions 0.1.3 2020-06-04
• Further improvements in the Google typology: adding the United Kingdom, Portugal, Greece, Malta, parts of Latvia, Italy and Reunion.
• recode_nuts slightly altered to follow changes in dependency dplyr.
# regions 0.1.4 Unreleased
• Documentation improvements.
• validate_country_nuts_countries is now follows dplyr 1.0, this makes the code more readable.
• validate_nuts_regions is validating non-EU NUTS-like regions as valid if they will be added to NUTS2021. These regional codes, while legally not part of the NUTS2016 typology, are valid and can be placed on the maps created by EuroGeographics maps provided by Eurostat.
• Italy, Portugal, the United Kingdom, Estonia, Slovenia,Latvia pseudo-NUTS3 codes in google_nuts_matchtable.
• New correspondence table for conversion between Local Administration Units (LAUs) and NUTS within the European Union and some other European countries.
# regions 0.1.5 2020-06-23
• Correction of a small bug with input data frames that already have columns that the validation result should contain.
• Wordlist added for spell checking with geographical exceptions.
# regions 0.1.6 Unreleased
• Exception handling partly moved to assertthat.
• New test_geo_code of for performance enhancement.
• Changing non-standard evaluation to dplyr 1.0+
• Master repo moving to rOpenGov.
• Added the regional_rd_personnel dataset and the Maping Regional Data, Maping Metadata Problems vignette.
• A new function, validate_parameters() takes over several parameter validations. The aim of this function is to provide consistent error messages, and thorough validation of function parameters whenever they must conform to a closed vocabulary or parameter range.
• Removing a bottleneck from validate_geo_code(). The NUTS exceptions are essentially constants, and it was unnecessary to calculate them each time these functions were running. They were moved to the nuts_exceptions dataset.
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https://www.physicsforums.com/threads/ising-cell-hamiltonian.627842/
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# Ising cell hamiltonian
1. Aug 13, 2012
### LagrangeEuler
I don't understand this idea. For example we have cubic crystal which has a lot of unit cells. We define spin variable of center of cell like $$S_c$$. And spin variable of nearest neighbour cells with $$S_{c+r}$$. So the cell hamiltonian is
$$\hat{H}=\frac{1}{2}J\sum_{c}\sum_{r}(S_c-S_{c+r})^2+\sum_cU(S_c^2)$$
This model is simulation of uniaxial feromagnet.
I have three question:
1. What's the difference between Ising model and 1d Heisenberg model?
2. Why this model is better than Ising model with no cells? Where we have just spins which interract.
$$\hat{H}=-J\sum_iS_{i}S_{i+1}$$
3. What $$\sum_cU(S_c^2)$$ means physically?
Tnx.
2. Aug 13, 2012
### cgk
If I am not mistaken, in the Heisenberg model the spins can have an arbitrary polarization, not just up or down (and there are Heisenberg models with different J paramters in different directions, like the XXZ Heisenberg model). The "1d" in the model then applies to the /lattice/ dimension. That is, for the 1d Heisenberg model, you might think of a one-dimensional lattice in 3d space, where the spins are not actually one-dimensional.
I have little knowledge of spin models, but the model you wrote down looks to me like it includes some variant of a "Hubbard U" term. In electron models, such terms represent a strong local interaction which gives a penalty for two electrons occupying the same lattice site (a kind of screened Coulomb interaction, if you wish). In such models the U is used to tune a system between weakly correlated limits (simple metals) to strongly correlated limits (Mott-insulating anti-ferromagnet), and maybe other phases depending on the lattice type.
In the Hubbard case, the U term is normally written as $$U\cdot n_{c\uparrow}\cdot n_{c\downarrow}$$ where the n are the up/down spin occupation number operators of electrons (thus giving only a contribution if there are both up and down electrons on the same site). But this form can be re-formulated into a similar form involving the total electron number operator and squared spins: $$\langle n_{c\uparrow}\cdot n_{c\downarrow}\rangle=\langle n\rangle - 2/3 \langle S_c^2\rangle$$ (or something to that degree..don't nail me on the prefactors). In spin models the site occupation is of course normally fixed at one spin per site, but maybe the squared spin term still can fulfill a similar role.
3. Aug 13, 2012
### LagrangeEuler
Tnx for the answer. So I can say in 1 - dimensional Heisenberg spin can pointed in any direction.
I'm not quite sure about Hubbard but I will look at it.
Do you know maybe the answer of second question?
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https://www.educator.com/chemistry/physical-chemistry/hovasapian/looking-back-over-everything_-all-the-equations-in-one-place.php
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Raffi Hovasapian
Looking Back Over Everything: All the Equations in One Place
Slide Duration:
Section 1: Classical Thermodynamics Preliminaries
The Ideal Gas Law
46m 5s
Intro
0:00
Course Overview
0:16
Thermodynamics & Classical Thermodynamics
0:17
Structure of the Course
1:30
The Ideal Gas Law
3:06
Ideal Gas Law: PV=nRT
3:07
Units of Pressure
4:51
Manipulating Units
5:52
Atmosphere : atm
8:15
Millimeter of Mercury: mm Hg
8:48
SI Unit of Volume
9:32
SI Unit of Temperature
10:32
Value of R (Gas Constant): Pv = nRT
10:51
Extensive and Intensive Variables (Properties)
15:23
Intensive Property
15:52
Extensive Property
16:30
Example: Extensive and Intensive Variables
18:20
Ideal Gas Law
19:24
Ideal Gas Law with Intensive Variables
19:25
Graphing Equations
23:51
Hold T Constant & Graph P vs. V
23:52
Hold P Constant & Graph V vs. T
31:08
Hold V Constant & Graph P vs. T
34:38
Isochores or Isometrics
37:08
More on the V vs. T Graph
39:46
More on the P vs. V Graph
42:06
Ideal Gas Law at Low Pressure & High Temperature
44:26
Ideal Gas Law at High Pressure & Low Temperature
45:16
Math Lesson 1: Partial Differentiation
46m 2s
Intro
0:00
Math Lesson 1: Partial Differentiation
0:38
Overview
0:39
Example I
3:00
Example II
6:33
Example III
9:52
Example IV
17:26
Differential & Derivative
21:44
What Does It Mean?
21:45
Total Differential (or Total Derivative)
30:16
Net Change in Pressure (P)
33:58
General Equation for Total Differential
38:12
Example 5: Total Differential
39:28
Section 2: Energy
Energy & the First Law I
1h 6m 45s
Intro
0:00
Properties of Thermodynamic State
1:38
Big Picture: 3 Properties of Thermodynamic State
1:39
Enthalpy & Free Energy
3:30
Associated Law
4:40
Energy & the First Law of Thermodynamics
7:13
System & Its Surrounding Separated by a Boundary
7:14
In Other Cases the Boundary is Less Clear
10:47
State of a System
12:37
State of a System
12:38
Change in State
14:00
Path for a Change in State
14:57
Example: State of a System
15:46
Open, Close, and Isolated System
18:26
Open System
18:27
Closed System
19:02
Isolated System
19:22
Important Questions
20:38
Important Questions
20:39
Work & Heat
22:50
Definition of Work
23:33
Properties of Work
25:34
Definition of Heat
32:16
Properties of Heat
34:49
Experiment #1
42:23
Experiment #2
47:00
More on Work & Heat
54:50
More on Work & Heat
54:51
Conventions for Heat & Work
1:00:50
Convention for Heat
1:02:40
Convention for Work
1:04:24
Schematic Representation
1:05:00
Energy & the First Law II
1h 6m 33s
Intro
0:00
The First Law of Thermodynamics
0:53
The First Law of Thermodynamics
0:54
Example 1: What is the Change in Energy of the System & Surroundings?
8:53
Energy and The First Law II, cont.
11:55
The Energy of a System Changes in Two Ways
11:56
Systems Possess Energy, Not Heat or Work
12:45
Scenario 1
16:00
Scenario 2
16:46
State Property, Path Properties, and Path Functions
18:10
Pressure-Volume Work
22:36
When a System Changes
22:37
Gas Expands
24:06
Gas is Compressed
25:13
Pressure Volume Diagram: Analyzing Expansion
27:17
What if We do the Same Expansion in Two Stages?
35:22
Multistage Expansion
43:58
General Expression for the Pressure-Volume Work
46:59
Upper Limit of Isothermal Expansion
50:00
Expression for the Work Done in an Isothermal Expansion
52:45
Example 2: Find an Expression for the Maximum Work Done by an Ideal Gas upon Isothermal Expansion
56:18
Example 3: Calculate the External Pressure and Work Done
58:50
Energy & the First Law III
1h 2m 17s
Intro
0:00
Compression
0:20
Compression Overview
0:34
Single-stage compression vs. 2-stage Compression
2:16
Multi-stage Compression
8:40
Example I: Compression
14:47
Example 1: Single-stage Compression
14:47
Example 1: 2-stage Compression
20:07
Example 1: Absolute Minimum
26:37
More on Compression
32:55
Isothermal Expansion & Compression
32:56
External & Internal Pressure of the System
35:18
Reversible & Irreversible Processes
37:32
Process 1: Overview
38:57
Process 2: Overview
39:36
Process 1: Analysis
40:42
Process 2: Analysis
45:29
Reversible Process
50:03
Isothermal Expansion and Compression
54:31
Example II: Reversible Isothermal Compression of a Van der Waals Gas
58:10
Example 2: Reversible Isothermal Compression of a Van der Waals Gas
58:11
Changes in Energy & State: Constant Volume
1h 4m 39s
Intro
0:00
Recall
0:37
State Function & Path Function
0:38
First Law
2:11
Exact & Inexact Differential
2:12
Where Does (∆U = Q - W) or dU = dQ - dU Come from?
8:54
Cyclic Integrals of Path and State Functions
8:55
Our Empirical Experience of the First Law
12:31
∆U = Q - W
18:42
Relations between Changes in Properties and Energy
22:24
Relations between Changes in Properties and Energy
22:25
Rate of Change of Energy per Unit Change in Temperature
29:54
Rate of Change of Energy per Unit Change in Volume at Constant Temperature
32:39
Total Differential Equation
34:38
Constant Volume
41:08
If Volume Remains Constant, then dV = 0
41:09
Constant Volume Heat Capacity
45:22
Constant Volume Integrated
48:14
Increase & Decrease in Energy of the System
54:19
Example 1: ∆U and Qv
57:43
Important Equations
1:02:06
Joule's Experiment
16m 50s
Intro
0:00
Joule's Experiment
0:09
Joule's Experiment
1:20
Interpretation of the Result
4:42
The Gas Expands Against No External Pressure
4:43
Temperature of the Surrounding Does Not Change
6:20
System & Surrounding
7:04
Joule's Law
10:44
More on Joule's Experiment
11:08
Later Experiment
12:38
Dealing with the 2nd Law & Its Mathematical Consequences
13:52
Changes in Energy & State: Constant Pressure
43m 40s
Intro
0:00
Changes in Energy & State: Constant Pressure
0:20
Integrating with Constant Pressure
0:35
Defining the New State Function
6:24
Heat & Enthalpy of the System at Constant Pressure
8:54
Finding ∆U
12:10
dH
15:28
Constant Pressure Heat Capacity
18:08
Important Equations
25:44
Important Equations
25:45
Important Equations at Constant Pressure
27:32
Example I: Change in Enthalpy (∆H)
28:53
Example II: Change in Internal Energy (∆U)
34:19
The Relationship Between Cp & Cv
32m 23s
Intro
0:00
The Relationship Between Cp & Cv
0:21
For a Constant Volume Process No Work is Done
0:22
For a Constant Pressure Process ∆V ≠ 0, so Work is Done
1:16
The Relationship Between Cp & Cv: For an Ideal Gas
3:26
The Relationship Between Cp & Cv: In Terms of Molar heat Capacities
5:44
Heat Capacity Can Have an Infinite # of Values
7:14
The Relationship Between Cp & Cv
11:20
When Cp is Greater than Cv
17:13
2nd Term
18:10
1st Term
19:20
Constant P Process: 3 Parts
22:36
Part 1
23:45
Part 2
24:10
Part 3
24:46
Define : γ = (Cp/Cv)
28:06
For Gases
28:36
For Liquids
29:04
For an Ideal Gas
30:46
The Joule Thompson Experiment
39m 15s
Intro
0:00
General Equations
0:13
Recall
0:14
How Does Enthalpy of a System Change Upon a Unit Change in Pressure?
2:58
For Liquids & Solids
12:11
For Ideal Gases
14:08
For Real Gases
16:58
The Joule Thompson Experiment
18:37
The Joule Thompson Experiment Setup
18:38
The Flow in 2 Stages
22:54
Work Equation for the Joule Thompson Experiment
24:14
Insulated Pipe
26:33
Joule-Thompson Coefficient
29:50
Changing Temperature & Pressure in Such a Way that Enthalpy Remains Constant
31:44
Joule Thompson Inversion Temperature
36:26
Positive & Negative Joule-Thompson Coefficient
36:27
Joule Thompson Inversion Temperature
37:22
Inversion Temperature of Hydrogen Gas
37:59
Adiabatic Changes of State
35m 52s
Intro
0:00
Adiabatic Changes of State
0:10
Adiabatic Changes of State
0:18
Work & Energy in an Adiabatic Process
3:44
Pressure-Volume Work
7:43
Adiabatic Changes for an Ideal Gas
9:23
Adiabatic Changes for an Ideal Gas
9:24
Equation for a Fixed Change in Volume
11:20
Maximum & Minimum Values of Temperature
14:20
18:08
18:09
21:54
22:34
Fundamental Relationship Equation for an Ideal Gas Under Adiabatic Expansion
25:00
More on the Equation
28:20
Important Equations
32:16
32:17
Reversible Adiabatic Change of State Equation
33:02
Section 3: Energy Example Problems
1st Law Example Problems I
42m 40s
Intro
0:00
Fundamental Equations
0:56
Work
2:40
Energy (1st Law)
3:10
Definition of Enthalpy
3:44
Heat capacity Definitions
4:06
The Mathematics
6:35
Fundamental Concepts
8:13
Isothermal
8:20
8:54
Isobaric
9:25
Isometric
9:48
Ideal Gases
10:14
Example I
12:08
Example I: Conventions
12:44
Example I: Part A
15:30
Example I: Part B
18:24
Example I: Part C
19:53
Example II: What is the Heat Capacity of the System?
21:49
Example III: Find Q, W, ∆U & ∆H for this Change of State
24:15
Example IV: Find Q, W, ∆U & ∆H
31:37
Example V: Find Q, W, ∆U & ∆H
38:20
1st Law Example Problems II
1h 23s
Intro
0:00
Example I
0:11
Example I: Finding ∆U
1:49
Example I: Finding W
6:22
Example I: Finding Q
11:23
Example I: Finding ∆H
16:09
Example I: Summary
17:07
Example II
21:16
Example II: Finding W
22:42
Example II: Finding ∆H
27:48
Example II: Finding Q
30:58
Example II: Finding ∆U
31:30
Example III
33:33
Example III: Finding ∆U, Q & W
33:34
Example III: Finding ∆H
38:07
Example IV
41:50
Example IV: Finding ∆U
41:51
Example IV: Finding ∆H
45:42
Example V
49:31
Example V: Finding W
49:32
Example V: Finding ∆U
55:26
Example V: Finding Q
56:26
Example V: Finding ∆H
56:55
1st Law Example Problems III
44m 34s
Intro
0:00
Example I
0:15
Example I: Finding the Final Temperature
3:40
Example I: Finding Q
8:04
Example I: Finding ∆U
8:25
Example I: Finding W
9:08
Example I: Finding ∆H
9:51
Example II
11:27
Example II: Finding the Final Temperature
11:28
Example II: Finding ∆U
21:25
Example II: Finding W & Q
22:14
Example II: Finding ∆H
23:03
Example III
24:38
Example III: Finding the Final Temperature
24:39
Example III: Finding W, ∆U, and Q
27:43
Example III: Finding ∆H
28:04
Example IV
29:23
Example IV: Finding ∆U, W, and Q
25:36
Example IV: Finding ∆H
31:33
Example V
32:24
Example V: Finding the Final Temperature
33:32
Example V: Finding ∆U
39:31
Example V: Finding W
40:17
Example V: First Way of Finding ∆H
41:10
Example V: Second Way of Finding ∆H
42:10
Thermochemistry Example Problems
59m 7s
Intro
0:00
Example I: Find ∆H° for the Following Reaction
0:42
Example II: Calculate the ∆U° for the Reaction in Example I
5:33
Example III: Calculate the Heat of Formation of NH₃ at 298 K
14:23
Example IV
32:15
Part A: Calculate the Heat of Vaporization of Water at 25°C
33:49
Part B: Calculate the Work Done in Vaporizing 2 Mols of Water at 25°C Under a Constant Pressure of 1 atm
35:26
Part C: Find ∆U for the Vaporization of Water at 25°C
41:00
Part D: Find the Enthalpy of Vaporization of Water at 100°C
43:12
Example V
49:24
Part A: Constant Temperature & Increasing Pressure
50:25
Part B: Increasing temperature & Constant Pressure
56:20
Section 4: Entropy
Entropy
49m 16s
Intro
0:00
Entropy, Part 1
0:16
Coefficient of Thermal Expansion (Isobaric)
0:38
Coefficient of Compressibility (Isothermal)
1:25
Relative Increase & Relative Decrease
2:16
More on α
4:40
More on κ
8:38
Entropy, Part 2
11:04
Definition of Entropy
12:54
Differential Change in Entropy & the Reversible Path
20:08
State Property of the System
28:26
Entropy Changes Under Isothermal Conditions
35:00
Recall: Heating Curve
41:05
Some Phase Changes Take Place Under Constant Pressure
44:07
Example I: Finding ∆S for a Phase Change
46:05
Math Lesson II
33m 59s
Intro
0:00
Math Lesson II
0:46
Let F(x,y) = x²y³
0:47
Total Differential
3:34
Total Differential Expression
6:06
Example 1
9:24
More on Math Expression
13:26
Exact Total Differential Expression
13:27
Exact Differentials
19:50
Inexact Differentials
20:20
The Cyclic Rule
21:06
The Cyclic Rule
21:07
Example 2
27:58
Entropy As a Function of Temperature & Volume
54m 37s
Intro
0:00
Entropy As a Function of Temperature & Volume
0:14
Fundamental Equation of Thermodynamics
1:16
Things to Notice
9:10
Entropy As a Function of Temperature & Volume
14:47
Temperature-dependence of Entropy
24:00
Example I
26:19
Entropy As a Function of Temperature & Volume, Cont.
31:55
Volume-dependence of Entropy at Constant Temperature
31:56
Differentiate with Respect to Temperature, Holding Volume Constant
36:16
Recall the Cyclic Rule
45:15
Summary & Recap
46:47
Fundamental Equation of Thermodynamics
46:48
For Entropy as a Function of Temperature & Volume
47:18
The Volume-dependence of Entropy for Liquids & Solids
52:52
Entropy as a Function of Temperature & Pressure
31m 18s
Intro
0:00
Entropy as a Function of Temperature & Pressure
0:17
Entropy as a Function of Temperature & Pressure
0:18
Rewrite the Total Differential
5:54
Temperature-dependence
7:08
Pressure-dependence
9:04
Differentiate with Respect to Pressure & Holding Temperature Constant
9:54
Differentiate with Respect to Temperature & Holding Pressure Constant
11:28
Pressure-Dependence of Entropy for Liquids & Solids
18:45
Pressure-Dependence of Entropy for Liquids & Solids
18:46
Example I: ∆S of Transformation
26:20
Summary of Entropy So Far
23m 6s
Intro
0:00
Summary of Entropy So Far
0:43
Defining dS
1:04
Fundamental Equation of Thermodynamics
3:51
Temperature & Volume
6:04
Temperature & Pressure
9:10
Two Important Equations for How Entropy Behaves
13:38
State of a System & Heat Capacity
15:34
Temperature-dependence of Entropy
19:49
Entropy Changes for an Ideal Gas
25m 42s
Intro
0:00
Entropy Changes for an Ideal Gas
1:10
General Equation
1:22
The Fundamental Theorem of Thermodynamics
2:37
Recall the Basic Total Differential Expression for S = S (T,V)
5:36
For a Finite Change in State
7:58
If Cv is Constant Over the Particular Temperature Range
9:05
Change in Entropy of an Ideal Gas as a Function of Temperature & Pressure
11:35
Change in Entropy of an Ideal Gas as a Function of Temperature & Pressure
11:36
Recall the Basic Total Differential expression for S = S (T, P)
15:13
For a Finite Change
18:06
Example 1: Calculate the ∆S of Transformation
22:02
Section 5: Entropy Example Problems
Entropy Example Problems I
43m 39s
Intro
0:00
Entropy Example Problems I
0:24
Fundamental Equation of Thermodynamics
1:10
Entropy as a Function of Temperature & Volume
2:04
Entropy as a Function of Temperature & Pressure
2:59
Entropy For Phase Changes
4:47
Entropy For an Ideal Gas
6:14
Third Law Entropies
8:25
Statement of the Third Law
9:17
Entropy of the Liquid State of a Substance Above Its Melting Point
10:23
Entropy For the Gas Above Its Boiling Temperature
13:02
Entropy Changes in Chemical Reactions
15:26
Entropy Change at a Temperature Other than 25°C
16:32
Example I
19:31
Part A: Calculate ∆S for the Transformation Under Constant Volume
20:34
Part B: Calculate ∆S for the Transformation Under Constant Pressure
25:04
Example II: Calculate ∆S fir the Transformation Under Isobaric Conditions
27:53
Example III
30:14
Part A: Calculate ∆S if 1 Mol of Aluminum is taken from 25°C to 255°C
31:14
Part B: If S°₂₉₈ = 28.4 J/mol-K, Calculate S° for Aluminum at 498 K
33:23
Example IV: Calculate Entropy Change of Vaporization for CCl₄
34:19
Example V
35:41
Part A: Calculate ∆S of Transformation
37:36
Part B: Calculate ∆S of Transformation
39:10
Entropy Example Problems II
56m 44s
Intro
0:00
Example I
0:09
Example I: Calculate ∆U
1:28
Example I: Calculate Q
3:29
Example I: Calculate Cp
4:54
Example I: Calculate ∆S
6:14
Example II
7:13
Example II: Calculate W
8:14
Example II: Calculate ∆U
8:56
Example II: Calculate Q
10:18
Example II: Calculate ∆H
11:00
Example II: Calculate ∆S
12:36
Example III
18:47
Example III: Calculate ∆H
19:38
Example III: Calculate Q
21:14
Example III: Calculate ∆U
21:44
Example III: Calculate W
23:59
Example III: Calculate ∆S
24:55
Example IV
27:57
Example IV: Diagram
29:32
Example IV: Calculate W
32:27
Example IV: Calculate ∆U
36:36
Example IV: Calculate Q
38:32
Example IV: Calculate ∆H
39:00
Example IV: Calculate ∆S
40:27
Example IV: Summary
43:41
Example V
48:25
Example V: Diagram
49:05
Example V: Calculate W
50:58
Example V: Calculate ∆U
53:29
Example V: Calculate Q
53:44
Example V: Calculate ∆H
54:34
Example V: Calculate ∆S
55:01
Entropy Example Problems III
57m 6s
Intro
0:00
Example I: Isothermal Expansion
0:09
Example I: Calculate W
1:19
Example I: Calculate ∆U
1:48
Example I: Calculate Q
2:06
Example I: Calculate ∆H
2:26
Example I: Calculate ∆S
3:02
Example II: Adiabatic and Reversible Expansion
6:10
Example II: Calculate Q
6:48
Example II: Basic Equation for the Reversible Adiabatic Expansion of an Ideal Gas
8:12
Example II: Finding Volume
12:40
Example II: Finding Temperature
17:58
Example II: Calculate ∆U
19:53
Example II: Calculate W
20:59
Example II: Calculate ∆H
21:42
Example II: Calculate ∆S
23:42
Example III: Calculate the Entropy of Water Vapor
25:20
Example IV: Calculate the Molar ∆S for the Transformation
34:32
Example V
44:19
Part A: Calculate the Standard Entropy of Liquid Lead at 525°C
46:17
Part B: Calculate ∆H for the Transformation of Solid Lead from 25°C to Liquid Lead at 525°C
52:23
Section 6: Entropy and Probability
Entropy & Probability I
54m 35s
Intro
0:00
Entropy & Probability
0:11
Structural Model
3:05
Recall the Fundamental Equation of Thermodynamics
9:11
Two Independent Ways of Affecting the Entropy of a System
10:05
Boltzmann Definition
12:10
Omega
16:24
Definition of Omega
16:25
Energy Distribution
19:43
The Energy Distribution
19:44
In How Many Ways can N Particles be Distributed According to the Energy Distribution
23:05
Example I: In How Many Ways can the Following Distribution be Achieved
32:51
Example II: In How Many Ways can the Following Distribution be Achieved
33:51
Example III: In How Many Ways can the Following Distribution be Achieved
34:45
Example IV: In How Many Ways can the Following Distribution be Achieved
38:50
Entropy & Probability, cont.
40:57
More on Distribution
40:58
Example I Summary
41:43
Example II Summary
42:12
Distribution that Maximizes Omega
42:26
If Omega is Large, then S is Large
44:22
Two Constraints for a System to Achieve the Highest Entropy Possible
47:07
What Happened When the Energy of a System is Increased?
49:00
Entropy & Probability II
35m 5s
Intro
0:00
Volume Distribution
0:08
Distributing 2 Balls in 3 Spaces
1:43
Distributing 2 Balls in 4 Spaces
3:44
Distributing 3 Balls in 10 Spaces
5:30
Number of Ways to Distribute P Particles over N Spaces
6:05
When N is Much Larger than the Number of Particles P
7:56
Energy Distribution
25:04
Volume Distribution
25:58
Entropy, Total Entropy, & Total Omega Equations
27:34
Entropy, Total Entropy, & Total Omega Equations
27:35
Section 7: Spontaneity, Equilibrium, and the Fundamental Equations
Spontaneity & Equilibrium I
28m 42s
Intro
0:00
Reversible & Irreversible
0:24
Reversible vs. Irreversible
0:58
Defining Equation for Equilibrium
2:11
Defining Equation for Irreversibility (Spontaneity)
3:11
TdS ≥ dQ
5:15
Transformation in an Isolated System
11:22
Transformation in an Isolated System
11:29
Transformation at Constant Temperature
14:50
Transformation at Constant Temperature
14:51
Helmholtz Free Energy
17:26
Define: A = U - TS
17:27
Spontaneous Isothermal Process & Helmholtz Energy
20:20
Pressure-volume Work
22:02
Spontaneity & Equilibrium II
34m 38s
Intro
0:00
Transformation under Constant Temperature & Pressure
0:08
Transformation under Constant Temperature & Pressure
0:36
Define: G = U + PV - TS
3:32
Gibbs Energy
5:14
What Does This Say?
6:44
Spontaneous Process & a Decrease in G
14:12
Computing ∆G
18:54
Summary of Conditions
21:32
Constraint & Condition for Spontaneity
21:36
Constraint & Condition for Equilibrium
24:54
A Few Words About the Word Spontaneous
26:24
Spontaneous Does Not Mean Fast
26:25
Putting Hydrogen & Oxygen Together in a Flask
26:59
Spontaneous Vs. Not Spontaneous
28:14
Thermodynamically Favorable
29:03
Example: Making a Process Thermodynamically Favorable
29:34
Driving Forces for Spontaneity
31:35
Equation: ∆G = ∆H - T∆S
31:36
Always Spontaneous Process
32:39
Never Spontaneous Process
33:06
A Process That is Endothermic Can Still be Spontaneous
34:00
The Fundamental Equations of Thermodynamics
30m 50s
Intro
0:00
The Fundamental Equations of Thermodynamics
0:44
Mechanical Properties of a System
0:45
Fundamental Properties of a System
1:16
Composite Properties of a System
1:44
General Condition of Equilibrium
3:16
Composite Functions & Their Differentiations
6:11
dH = TdS + VdP
7:53
dA = -SdT - PdV
9:26
dG = -SdT + VdP
10:22
Summary of Equations
12:10
Equation #1
14:33
Equation #2
15:15
Equation #3
15:58
Equation #4
16:42
Maxwell's Relations
20:20
Maxwell's Relations
20:21
Isothermal Volume-Dependence of Entropy & Isothermal Pressure-Dependence of Entropy
26:21
The General Thermodynamic Equations of State
34m 6s
Intro
0:00
The General Thermodynamic Equations of State
0:10
Equations of State for Liquids & Solids
0:52
More General Condition for Equilibrium
4:02
General Conditions: Equation that Relates P to Functions of T & V
6:20
The Second Fundamental Equation of Thermodynamics
11:10
Equation 1
17:34
Equation 2
21:58
Recall the General Expression for Cp - Cv
28:11
For the Joule-Thomson Coefficient
30:44
Joule-Thomson Inversion Temperature
32:12
Properties of the Helmholtz & Gibbs Energies
39m 18s
Intro
0:00
Properties of the Helmholtz & Gibbs Energies
0:10
Equating the Differential Coefficients
1:34
An Increase in T; a Decrease in A
3:25
An Increase in V; a Decrease in A
6:04
We Do the Same Thing for G
8:33
Increase in T; Decrease in G
10:50
Increase in P; Decrease in G
11:36
Gibbs Energy of a Pure Substance at a Constant Temperature from 1 atm to any Other Pressure.
14:12
If the Substance is a Liquid or a Solid, then Volume can be Treated as a Constant
18:57
For an Ideal Gas
22:18
Special Note
24:56
Temperature Dependence of Gibbs Energy
27:02
Temperature Dependence of Gibbs Energy #1
27:52
Temperature Dependence of Gibbs Energy #2
29:01
Temperature Dependence of Gibbs Energy #3
29:50
Temperature Dependence of Gibbs Energy #4
34:50
The Entropy of the Universe & the Surroundings
19m 40s
Intro
0:00
Entropy of the Universe & the Surroundings
0:08
Equation: ∆G = ∆H - T∆S
0:20
Conditions of Constant Temperature & Pressure
1:14
Reversible Process
3:14
Spontaneous Process & the Entropy of the Universe
5:20
Tips for Remembering Everything
12:40
Verify Using Known Spontaneous Process
14:51
Section 8: Free Energy Example Problems
Free Energy Example Problems I
54m 16s
Intro
0:00
Example I
0:11
Example I: Deriving a Function for Entropy (S)
2:06
Example I: Deriving a Function for V
5:55
Example I: Deriving a Function for H
8:06
Example I: Deriving a Function for U
12:06
Example II
15:18
Example III
21:52
Example IV
26:12
Example IV: Part A
26:55
Example IV: Part B
28:30
Example IV: Part C
30:25
Example V
33:45
Example VI
40:46
Example VII
43:43
Example VII: Part A
44:46
Example VII: Part B
50:52
Example VII: Part C
51:56
Free Energy Example Problems II
31m 17s
Intro
0:00
Example I
0:09
Example II
5:18
Example III
8:22
Example IV
12:32
Example V
17:14
Example VI
20:34
Example VI: Part A
21:04
Example VI: Part B
23:56
Example VI: Part C
27:56
Free Energy Example Problems III
45m
Intro
0:00
Example I
0:10
Example II
15:03
Example III
21:47
Example IV
28:37
Example IV: Part A
29:33
Example IV: Part B
36:09
Example IV: Part C
40:34
Three Miscellaneous Example Problems
58m 5s
Intro
0:00
Example I
0:41
Part A: Calculating ∆H
3:55
Part B: Calculating ∆S
15:13
Example II
24:39
Part A: Final Temperature of the System
26:25
Part B: Calculating ∆S
36:57
Example III
46:49
Section 9: Equation Review for Thermodynamics
Looking Back Over Everything: All the Equations in One Place
25m 20s
Intro
0:00
Work, Heat, and Energy
0:18
Definition of Work, Energy, Enthalpy, and Heat Capacities
0:23
Heat Capacities for an Ideal Gas
3:40
Path Property & State Property
3:56
Energy Differential
5:04
Enthalpy Differential
5:40
Joule's Law & Joule-Thomson Coefficient
6:23
Coefficient of Thermal Expansion & Coefficient of Compressibility
7:01
Enthalpy of a Substance at Any Other Temperature
7:29
Enthalpy of a Reaction at Any Other Temperature
8:01
Entropy
8:53
Definition of Entropy
8:54
Clausius Inequality
9:11
Entropy Changes in Isothermal Systems
9:44
The Fundamental Equation of Thermodynamics
10:12
Expressing Entropy Changes in Terms of Properties of the System
10:42
Entropy Changes in the Ideal Gas
11:22
Third Law Entropies
11:38
Entropy Changes in Chemical Reactions
14:02
Statistical Definition of Entropy
14:34
Omega for the Spatial & Energy Distribution
14:47
Spontaneity and Equilibrium
15:43
Helmholtz Energy & Gibbs Energy
15:44
Condition for Spontaneity & Equilibrium
16:24
Condition for Spontaneity with Respect to Entropy
17:58
The Fundamental Equations
18:30
Maxwell's Relations
19:04
The Thermodynamic Equations of State
20:07
Energy & Enthalpy Differentials
21:08
Joule's Law & Joule-Thomson Coefficient
21:59
Relationship Between Constant Pressure & Constant Volume Heat Capacities
23:14
One Final Equation - Just for Fun
24:04
Section 10: Quantum Mechanics Preliminaries
Complex Numbers
34m 25s
Intro
0:00
Complex Numbers
0:11
Representing Complex Numbers in the 2-Dimmensional Plane
0:56
Addition of Complex Numbers
2:35
Subtraction of Complex Numbers
3:17
Multiplication of Complex Numbers
3:47
Division of Complex Numbers
6:04
r & θ
8:04
Euler's Formula
11:00
Polar Exponential Representation of the Complex Numbers
11:22
Example I
14:25
Example II
15:21
Example III
16:58
Example IV
18:35
Example V
20:40
Example VI
21:32
Example VII
25:22
Probability & Statistics
59m 57s
Intro
0:00
Probability & Statistics
1:51
Normalization Condition
1:52
Define the Mean or Average of x
11:04
Example I: Calculate the Mean of x
14:57
Example II: Calculate the Second Moment of the Data in Example I
22:39
Define the Second Central Moment or Variance
25:26
Define the Second Central Moment or Variance
25:27
1st Term
32:16
2nd Term
32:40
3rd Term
34:07
Continuous Distributions
35:47
Continuous Distributions
35:48
Probability Density
39:30
Probability Density
39:31
Normalization Condition
46:51
Example III
50:13
Part A - Show that P(x) is Normalized
51:40
Part B - Calculate the Average Position of the Particle Along the Interval
54:31
Important Things to Remember
58:24
Schrӧdinger Equation & Operators
42m 5s
Intro
0:00
Schrӧdinger Equation & Operators
0:16
Relation Between a Photon's Momentum & Its Wavelength
0:17
Louis de Broglie: Wavelength for Matter
0:39
Schrӧdinger Equation
1:19
Definition of Ψ(x)
3:31
Quantum Mechanics
5:02
Operators
7:51
Example I
10:10
Example II
11:53
Example III
14:24
Example IV
17:35
Example V
19:59
Example VI
22:39
Operators Can Be Linear or Non Linear
27:58
Operators Can Be Linear or Non Linear
28:34
Example VII
32:47
Example VIII
36:55
Example IX
39:29
Schrӧdinger Equation as an Eigenvalue Problem
30m 26s
Intro
0:00
Schrӧdinger Equation as an Eigenvalue Problem
0:10
Operator: Multiplying the Original Function by Some Scalar
0:11
Operator, Eigenfunction, & Eigenvalue
4:42
Example: Eigenvalue Problem
8:00
Schrӧdinger Equation as an Eigenvalue Problem
9:24
Hamiltonian Operator
15:09
Quantum Mechanical Operators
16:46
Kinetic Energy Operator
19:16
Potential Energy Operator
20:02
Total Energy Operator
21:12
Classical Point of View
21:48
Linear Momentum Operator
24:02
Example I
26:01
The Plausibility of the Schrӧdinger Equation
21m 34s
Intro
0:00
The Plausibility of the Schrӧdinger Equation
1:16
The Plausibility of the Schrӧdinger Equation, Part 1
1:17
The Plausibility of the Schrӧdinger Equation, Part 2
8:24
The Plausibility of the Schrӧdinger Equation, Part 3
13:45
Section 11: The Particle in a Box
The Particle in a Box Part I
56m 22s
Intro
0:00
Free Particle in a Box
0:28
Definition of a Free Particle in a Box
0:29
Amplitude of the Matter Wave
6:22
Intensity of the Wave
6:53
Probability Density
9:39
Probability that the Particle is Located Between x & dx
10:54
Probability that the Particle will be Found Between o & a
12:35
Wave Function & the Particle
14:59
Boundary Conditions
19:22
What Happened When There is No Constraint on the Particle
27:54
Diagrams
34:12
More on Probability Density
40:53
The Correspondence Principle
46:45
The Correspondence Principle
46:46
Normalizing the Wave Function
47:46
Normalizing the Wave Function
47:47
Normalized Wave Function & Normalization Constant
52:24
The Particle in a Box Part II
45m 24s
Intro
0:00
Free Particle in a Box
0:08
Free Particle in a 1-dimensional Box
0:09
For a Particle in a Box
3:57
Calculating Average Values & Standard Deviations
5:42
Average Value for the Position of a Particle
6:32
Standard Deviations for the Position of a Particle
10:51
Recall: Energy & Momentum are Represented by Operators
13:33
Recall: Schrӧdinger Equation in Operator Form
15:57
Average Value of a Physical Quantity that is Associated with an Operator
18:16
Average Momentum of a Free Particle in a Box
20:48
The Uncertainty Principle
24:42
Finding the Standard Deviation of the Momentum
25:08
Expression for the Uncertainty Principle
35:02
Summary of the Uncertainty Principle
41:28
The Particle in a Box Part III
48m 43s
Intro
0:00
2-Dimension
0:12
Dimension 2
0:31
Boundary Conditions
1:52
Partial Derivatives
4:27
Example I
6:08
The Particle in a Box, cont.
11:28
Operator Notation
12:04
Symbol for the Laplacian
13:50
The Equation Becomes…
14:30
Boundary Conditions
14:54
Separation of Variables
15:33
Solution to the 1-dimensional Case
16:31
Normalization Constant
22:32
3-Dimension
28:30
Particle in a 3-dimensional Box
28:31
In Del Notation
32:22
The Solutions
34:51
Expressing the State of the System for a Particle in a 3D Box
39:10
Energy Level & Degeneracy
43:35
Section 12: Postulates and Principles of Quantum Mechanics
The Postulates & Principles of Quantum Mechanics, Part I
46m 18s
Intro
0:00
Postulate I
0:31
Probability That The Particle Will Be Found in a Differential Volume Element
0:32
Example I: Normalize This Wave Function
11:30
Postulate II
18:20
Postulate II
18:21
Quantum Mechanical Operators: Position
20:48
Quantum Mechanical Operators: Kinetic Energy
21:57
Quantum Mechanical Operators: Potential Energy
22:42
Quantum Mechanical Operators: Total Energy
22:57
Quantum Mechanical Operators: Momentum
23:22
Quantum Mechanical Operators: Angular Momentum
23:48
More On The Kinetic Energy Operator
24:48
Angular Momentum
28:08
Angular Momentum Overview
28:09
Angular Momentum Operator in Quantum Mechanic
31:34
The Classical Mechanical Observable
32:56
Quantum Mechanical Operator
37:01
Getting the Quantum Mechanical Operator from the Classical Mechanical Observable
40:16
Postulate II, cont.
43:40
Quantum Mechanical Operators are Both Linear & Hermetical
43:41
The Postulates & Principles of Quantum Mechanics, Part II
39m 28s
Intro
0:00
Postulate III
0:09
Postulate III: Part I
0:10
Postulate III: Part II
5:56
Postulate III: Part III
12:43
Postulate III: Part IV
18:28
Postulate IV
23:57
Postulate IV
23:58
Postulate V
27:02
Postulate V
27:03
Average Value
36:38
Average Value
36:39
The Postulates & Principles of Quantum Mechanics, Part III
35m 32s
Intro
0:00
The Postulates & Principles of Quantum Mechanics, Part III
0:10
Equations: Linear & Hermitian
0:11
Introduction to Hermitian Property
3:36
Eigenfunctions are Orthogonal
9:55
The Sequence of Wave Functions for the Particle in a Box forms an Orthonormal Set
14:34
Definition of Orthogonality
16:42
Definition of Hermiticity
17:26
Hermiticity: The Left Integral
23:04
Hermiticity: The Right Integral
28:47
Hermiticity: Summary
34:06
The Postulates & Principles of Quantum Mechanics, Part IV
29m 55s
Intro
0:00
The Postulates & Principles of Quantum Mechanics, Part IV
0:09
Operators can be Applied Sequentially
0:10
Sample Calculation 1
2:41
Sample Calculation 2
5:18
Commutator of Two Operators
8:16
The Uncertainty Principle
19:01
In the Case of Linear Momentum and Position Operator
23:14
When the Commutator of Two Operators Equals to Zero
26:31
Section 13: Postulates and Principles Example Problems, Including Particle in a Box
Example Problems I
54m 25s
Intro
0:00
Example I: Three Dimensional Box & Eigenfunction of The Laplacian Operator
0:37
Example II: Positions of a Particle in a 1-dimensional Box
15:46
Example III: Transition State & Frequency
29:29
Example IV: Finding a Particle in a 1-dimensional Box
35:03
Example V: Degeneracy & Energy Levels of a Particle in a Box
44:59
Example Problems II
46m 58s
Intro
0:00
Review
0:25
Wave Function
0:26
Normalization Condition
2:28
Observable in Classical Mechanics & Linear/Hermitian Operator in Quantum Mechanics
3:36
Hermitian
6:11
Eigenfunctions & Eigenvalue
8:20
Normalized Wave Functions
12:00
Average Value
13:42
If Ψ is Written as a Linear Combination
15:44
Commutator
16:45
Example I: Normalize The Wave Function
19:18
Example II: Probability of Finding of a Particle
22:27
Example III: Orthogonal
26:00
Example IV: Average Value of the Kinetic Energy Operator
30:22
Example V: Evaluate These Commutators
39:02
Example Problems III
44m 11s
Intro
0:00
Example I: Good Candidate for a Wave Function
0:08
Example II: Variance of the Energy
7:00
Example III: Evaluate the Angular Momentum Operators
15:00
Example IV: Real Eigenvalues Imposes the Hermitian Property on Operators
28:44
Example V: A Demonstration of Why the Eigenfunctions of Hermitian Operators are Orthogonal
35:33
Section 14: The Harmonic Oscillator
The Harmonic Oscillator I
35m 33s
Intro
0:00
The Harmonic Oscillator
0:10
Harmonic Motion
0:11
Classical Harmonic Oscillator
4:38
Hooke's Law
8:18
Classical Harmonic Oscillator, cont.
10:33
General Solution for the Differential Equation
15:16
Initial Position & Velocity
16:05
Period & Amplitude
20:42
Potential Energy of the Harmonic Oscillator
23:20
Kinetic Energy of the Harmonic Oscillator
26:37
Total Energy of the Harmonic Oscillator
27:23
Conservative System
34:37
The Harmonic Oscillator II
43m 4s
Intro
0:00
The Harmonic Oscillator II
0:08
Diatomic Molecule
0:10
Notion of Reduced Mass
5:27
Harmonic Oscillator Potential & The Intermolecular Potential of a Vibrating Molecule
7:33
The Schrӧdinger Equation for the 1-dimensional Quantum Mechanic Oscillator
14:14
Quantized Values for the Energy Level
15:46
Ground State & the Zero-Point Energy
21:50
Vibrational Energy Levels
25:18
Transition from One Energy Level to the Next
26:42
Fundamental Vibrational Frequency for Diatomic Molecule
34:57
Example: Calculate k
38:01
The Harmonic Oscillator III
26m 30s
Intro
0:00
The Harmonic Oscillator III
0:09
The Wave Functions Corresponding to the Energies
0:10
Normalization Constant
2:34
Hermite Polynomials
3:22
First Few Hermite Polynomials
4:56
First Few Wave-Functions
6:37
Plotting the Probability Density of the Wave-Functions
8:37
Probability Density for Large Values of r
14:24
Recall: Odd Function & Even Function
19:05
More on the Hermite Polynomials
20:07
Recall: If f(x) is Odd
20:36
Average Value of x
22:31
Average Value of Momentum
23:56
Section 15: The Rigid Rotator
The Rigid Rotator I
41m 10s
Intro
0:00
Possible Confusion from the Previous Discussion
0:07
Possible Confusion from the Previous Discussion
0:08
Rotation of a Single Mass Around a Fixed Center
8:17
Rotation of a Single Mass Around a Fixed Center
8:18
Angular Velocity
12:07
Rotational Inertia
13:24
Rotational Frequency
15:24
Kinetic Energy for a Linear System
16:38
Kinetic Energy for a Rotational System
17:42
Rotating Diatomic Molecule
19:40
Rotating Diatomic Molecule: Part 1
19:41
Rotating Diatomic Molecule: Part 2
24:56
Rotating Diatomic Molecule: Part 3
30:04
Hamiltonian of the Rigid Rotor
36:48
Hamiltonian of the Rigid Rotor
36:49
The Rigid Rotator II
30m 32s
Intro
0:00
The Rigid Rotator II
0:08
Cartesian Coordinates
0:09
Spherical Coordinates
1:55
r
6:15
θ
6:28
φ
7:00
Moving a Distance 'r'
8:17
Moving a Distance 'r' in the Spherical Coordinates
11:49
For a Rigid Rotator, r is Constant
13:57
Hamiltonian Operator
15:09
Square of the Angular Momentum Operator
17:34
Orientation of the Rotation in Space
19:44
Wave Functions for the Rigid Rotator
20:40
The Schrӧdinger Equation for the Quantum Mechanic Rigid Rotator
21:24
Energy Levels for the Rigid Rotator
26:58
The Rigid Rotator III
35m 19s
Intro
0:00
The Rigid Rotator III
0:11
When a Rotator is Subjected to Electromagnetic Radiation
1:24
Selection Rule
2:13
Frequencies at Which Absorption Transitions Occur
6:24
Energy Absorption & Transition
10:54
Energy of the Individual Levels Overview
20:58
Energy of the Individual Levels: Diagram
23:45
Frequency Required to Go from J to J + 1
25:53
Using Separation Between Lines on the Spectrum to Calculate Bond Length
28:02
Example I: Calculating Rotational Inertia & Bond Length
29:18
Example I: Calculating Rotational Inertia
29:19
Example I: Calculating Bond Length
32:56
Section 16: Oscillator and Rotator Example Problems
Example Problems I
33m 48s
Intro
0:00
Equations Review
0:11
Energy of the Harmonic Oscillator
0:12
Selection Rule
3:02
Observed Frequency of Radiation
3:27
Harmonic Oscillator Wave Functions
5:52
Rigid Rotator
7:26
Selection Rule for Rigid Rotator
9:15
Frequency of Absorption
9:35
Wave Numbers
10:58
Example I: Calculate the Reduced Mass of the Hydrogen Atom
11:44
Example II: Calculate the Fundamental Vibration Frequency & the Zero-Point Energy of This Molecule
13:37
Example III: Show That the Product of Two Even Functions is even
19:35
Example IV: Harmonic Oscillator
24:56
Example Problems II
46m 43s
Intro
0:00
Example I: Harmonic Oscillator
0:12
Example II: Harmonic Oscillator
23:26
Example III: Calculate the RMS Displacement of the Molecules
38:12
Section 17: The Hydrogen Atom
The Hydrogen Atom I
40m
Intro
0:00
The Hydrogen Atom I
1:31
Review of the Rigid Rotator
1:32
Hydrogen Atom & the Coulomb Potential
2:50
Using the Spherical Coordinates
6:33
Applying This Last Expression to Equation 1
10:19
Angular Component & Radial Component
13:26
Angular Equation
15:56
Solution for F(φ)
19:32
Determine The Normalization Constant
20:33
Differential Equation for T(a)
24:44
Legendre Equation
27:20
Legendre Polynomials
31:20
The Legendre Polynomials are Mutually Orthogonal
35:40
Limits
37:17
Coefficients
38:28
The Hydrogen Atom II
35m 58s
Intro
0:00
Associated Legendre Functions
0:07
Associated Legendre Functions
0:08
First Few Associated Legendre Functions
6:39
s, p, & d Orbital
13:24
The Normalization Condition
15:44
Spherical Harmonics
20:03
Equations We Have Found
20:04
Wave Functions for the Angular Component & Rigid Rotator
24:36
Spherical Harmonics Examples
25:40
Angular Momentum
30:09
Angular Momentum
30:10
Square of the Angular Momentum
35:38
Energies of the Rigid Rotator
38:21
The Hydrogen Atom III
36m 18s
Intro
0:00
The Hydrogen Atom III
0:34
Angular Momentum is a Vector Quantity
0:35
The Operators Corresponding to the Three Components of Angular Momentum Operator: In Cartesian Coordinates
1:30
The Operators Corresponding to the Three Components of Angular Momentum Operator: In Spherical Coordinates
3:27
Z Component of the Angular Momentum Operator & the Spherical Harmonic
5:28
Magnitude of the Angular Momentum Vector
20:10
Classical Interpretation of Angular Momentum
25:22
Projection of the Angular Momentum Vector onto the xy-plane
33:24
The Hydrogen Atom IV
33m 55s
Intro
0:00
The Hydrogen Atom IV
0:09
The Equation to Find R( r )
0:10
Relation Between n & l
3:50
The Solutions for the Radial Functions
5:08
Associated Laguerre Polynomials
7:58
1st Few Associated Laguerre Polynomials
8:55
Complete Wave Function for the Atomic Orbitals of the Hydrogen Atom
12:24
The Normalization Condition
15:06
In Cartesian Coordinates
18:10
Working in Polar Coordinates
20:48
Principal Quantum Number
21:58
Angular Momentum Quantum Number
22:35
Magnetic Quantum Number
25:55
Zeeman Effect
30:45
The Hydrogen Atom V: Where We Are
51m 53s
Intro
0:00
The Hydrogen Atom V: Where We Are
0:13
Review
0:14
Let's Write Out ψ₂₁₁
7:32
Angular Momentum of the Electron
14:52
Representation of the Wave Function
19:36
28:02
Example: 1s Orbital
28:34
Probability for Radial Function
33:46
1s Orbital: Plotting Probability Densities vs. r
35:47
2s Orbital: Plotting Probability Densities vs. r
37:46
3s Orbital: Plotting Probability Densities vs. r
38:49
4s Orbital: Plotting Probability Densities vs. r
39:34
2p Orbital: Plotting Probability Densities vs. r
40:12
3p Orbital: Plotting Probability Densities vs. r
41:02
4p Orbital: Plotting Probability Densities vs. r
41:51
3d Orbital: Plotting Probability Densities vs. r
43:18
4d Orbital: Plotting Probability Densities vs. r
43:48
Example I: Probability of Finding an Electron in the 2s Orbital of the Hydrogen
45:40
The Hydrogen Atom VI
51m 53s
Intro
0:00
The Hydrogen Atom VI
0:07
Last Lesson Review
0:08
Spherical Component
1:09
Normalization Condition
2:02
Complete 1s Orbital Wave Function
4:08
1s Orbital Wave Function
4:09
Normalization Condition
6:28
Spherically Symmetric
16:00
Average Value
17:52
Example I: Calculate the Region of Highest Probability for Finding the Electron
21:19
2s Orbital Wave Function
25:32
2s Orbital Wave Function
25:33
Average Value
28:56
General Formula
32:24
The Hydrogen Atom VII
34m 29s
Intro
0:00
The Hydrogen Atom VII
0:12
p Orbitals
1:30
Not Spherically Symmetric
5:10
Recall That the Spherical Harmonics are Eigenfunctions of the Hamiltonian Operator
6:50
Any Linear Combination of These Orbitals Also Has The Same Energy
9:16
Functions of Real Variables
15:53
Solving for Px
16:50
Real Spherical Harmonics
21:56
Number of Nodes
32:56
Section 18: Hydrogen Atom Example Problems
Hydrogen Atom Example Problems I
43m 49s
Intro
0:00
Example I: Angular Momentum & Spherical Harmonics
0:20
Example II: Pair-wise Orthogonal Legendre Polynomials
16:40
Example III: General Normalization Condition for the Legendre Polynomials
25:06
Example IV: Associated Legendre Functions
32:13
The Hydrogen Atom Example Problems II
1h 1m 57s
Intro
0:00
Example I: Normalization & Pair-wise Orthogonal
0:13
Part 1: Normalized
0:43
Part 2: Pair-wise Orthogonal
16:53
Example II: Show Explicitly That the Following Statement is True for Any Integer n
27:10
Example III: Spherical Harmonics
29:26
Angular Momentum Cones
56:37
Angular Momentum Cones
56:38
Physical Interpretation of Orbital Angular Momentum in Quantum mechanics
1:00:16
The Hydrogen Atom Example Problems III
48m 33s
Intro
0:00
Example I: Show That ψ₂₁₁ is Normalized
0:07
Example II: Show That ψ₂₁₁ is Orthogonal to ψ₃₁₀
11:48
Example III: Probability That a 1s Electron Will Be Found Within 1 Bohr Radius of The Nucleus
18:35
Example IV: Radius of a Sphere
26:06
Example V: Calculate <r> for the 2s Orbital of the Hydrogen-like Atom
36:33
The Hydrogen Atom Example Problems IV
48m 33s
Intro
0:00
Example I: Probability Density vs. Radius Plot
0:11
Example II: Hydrogen Atom & The Coulombic Potential
14:16
Example III: Find a Relation Among <K>, <V>, & <E>
25:47
Example IV: Quantum Mechanical Virial Theorem
48:32
Example V: Find the Variance for the 2s Orbital
54:13
The Hydrogen Atom Example Problems V
48m 33s
Intro
0:00
Example I: Derive a Formula for the Degeneracy of a Given Level n
0:11
Example II: Using Linear Combinations to Represent the Spherical Harmonics as Functions of the Real Variables θ & φ
8:30
Example III: Using Linear Combinations to Represent the Spherical Harmonics as Functions of the Real Variables θ & φ
23:01
Example IV: Orbital Functions
31:51
Section 19: Spin Quantum Number and Atomic Term Symbols
Spin Quantum Number: Term Symbols I
59m 18s
Intro
0:00
Quantum Numbers Specify an Orbital
0:24
n
1:10
l
1:20
m
1:35
4th Quantum Number: s
2:02
Spin Orbitals
7:03
Spin Orbitals
7:04
Multi-electron Atoms
11:08
Term Symbols
18:08
Russell-Saunders Coupling & The Atomic Term Symbol
18:09
Example: Configuration for C
27:50
Configuration for C: 1s²2s²2p²
27:51
Drawing Every Possible Arrangement
31:15
Term Symbols
45:24
Microstate
50:54
Spin Quantum Number: Term Symbols II
34m 54s
Intro
0:00
Microstates
0:25
We Started With 21 Possible Microstates
0:26
³P State
2:05
Microstates in ³P Level
5:10
¹D State
13:16
³P State
16:10
²P₂ State
17:34
³P₁ State
18:34
³P₀ State
19:12
9 Microstates in ³P are Subdivided
19:40
¹S State
21:44
Quicker Way to Find the Different Values of J for a Given Basic Term Symbol
22:22
Ground State
26:27
Hund's Empirical Rules for Specifying the Term Symbol for the Ground Electronic State
27:29
Hund's Empirical Rules: 1
28:24
Hund's Empirical Rules: 2
29:22
Hund's Empirical Rules: 3 - Part A
30:22
Hund's Empirical Rules: 3 - Part B
31:18
Example: 1s²2s²2p²
31:54
Spin Quantum Number: Term Symbols III
38m 3s
Intro
0:00
Spin Quantum Number: Term Symbols III
0:14
Deriving the Term Symbols for the p² Configuration
0:15
Table: MS vs. ML
3:57
¹D State
16:21
³P State
21:13
¹S State
24:48
J Value
25:32
Degeneracy of the Level
27:28
When Given r Electrons to Assign to n Equivalent Spin Orbitals
30:18
p² Configuration
32:51
Complementary Configurations
35:12
Term Symbols & Atomic Spectra
57m 49s
Intro
0:00
Lyman Series
0:09
Spectroscopic Term Symbols
0:10
Lyman Series
3:04
Hydrogen Levels
8:21
Hydrogen Levels
8:22
Term Symbols & Atomic Spectra
14:17
Spin-Orbit Coupling
14:18
Selection Rules for Atomic Spectra
21:31
Selection Rules for Possible Transitions
23:56
Wave Numbers for The Transitions
28:04
Example I: Calculate the Frequencies of the Allowed Transitions from (4d) ²D →(2p) ²P
32:23
Helium Levels
49:50
Energy Levels for Helium
49:51
Transitions & Spin Multiplicity
52:27
Transitions & Spin Multiplicity
52:28
Section 20: Term Symbols Example Problems
Example Problems I
1h 1m 20s
Intro
0:00
Example I: What are the Term Symbols for the np¹ Configuration?
0:10
Example II: What are the Term Symbols for the np² Configuration?
20:38
Example III: What are the Term Symbols for the np³ Configuration?
40:46
Example Problems II
56m 34s
Intro
0:00
Example I: Find the Term Symbols for the nd² Configuration
0:11
Example II: Find the Term Symbols for the 1s¹2p¹ Configuration
27:02
Example III: Calculate the Separation Between the Doublets in the Lyman Series for Atomic Hydrogen
41:41
Example IV: Calculate the Frequencies of the Lines for the (4d) ²D → (3p) ²P Transition
48:53
Section 21: Equation Review for Quantum Mechanics
Quantum Mechanics: All the Equations in One Place
18m 24s
Intro
0:00
Quantum Mechanics Equations
0:37
De Broglie Relation
0:38
Statistical Relations
1:00
The Schrӧdinger Equation
1:50
The Particle in a 1-Dimensional Box of Length a
3:09
The Particle in a 2-Dimensional Box of Area a x b
3:48
The Particle in a 3-Dimensional Box of Area a x b x c
4:22
The Schrӧdinger Equation Postulates
4:51
The Normalization Condition
5:40
The Probability Density
6:51
Linear
7:47
Hermitian
8:31
Eigenvalues & Eigenfunctions
8:55
The Average Value
9:29
Eigenfunctions of Quantum Mechanics Operators are Orthogonal
10:53
Commutator of Two Operators
10:56
The Uncertainty Principle
11:41
The Harmonic Oscillator
13:18
The Rigid Rotator
13:52
Energy of the Hydrogen Atom
14:30
Wavefunctions, Radial Component, and Associated Laguerre Polynomial
14:44
Angular Component or Spherical Harmonic
15:16
Associated Legendre Function
15:31
Principal Quantum Number
15:43
Angular Momentum Quantum Number
15:50
Magnetic Quantum Number
16:21
z-component of the Angular Momentum of the Electron
16:53
Atomic Spectroscopy: Term Symbols
17:14
Atomic Spectroscopy: Selection Rules
18:03
Section 22: Molecular Spectroscopy
Spectroscopic Overview: Which Equation Do I Use & Why
50m 2s
Intro
0:00
Spectroscopic Overview: Which Equation Do I Use & Why
1:02
Lesson Overview
1:03
Rotational & Vibrational Spectroscopy
4:01
Frequency of Absorption/Emission
6:04
Wavenumbers in Spectroscopy
8:10
Starting State vs. Excited State
10:10
Total Energy of a Molecule (Leaving out the Electronic Energy)
14:02
Energy of Rotation: Rigid Rotor
15:55
Energy of Vibration: Harmonic Oscillator
19:08
Equation of the Spectral Lines
23:22
Harmonic Oscillator-Rigid Rotor Approximation (Making Corrections)
28:37
Harmonic Oscillator-Rigid Rotor Approximation (Making Corrections)
28:38
Vibration-Rotation Interaction
33:46
Centrifugal Distortion
36:27
Anharmonicity
38:28
Correcting for All Three Simultaneously
41:03
Spectroscopic Parameters
44:26
Summary
47:32
Harmonic Oscillator-Rigid Rotor Approximation
47:33
Vibration-Rotation Interaction
48:14
Centrifugal Distortion
48:20
Anharmonicity
48:28
Correcting for All Three Simultaneously
48:44
Vibration-Rotation
59m 47s
Intro
0:00
Vibration-Rotation
0:37
What is Molecular Spectroscopy?
0:38
Microwave, Infrared Radiation, Visible & Ultraviolet
1:53
Equation for the Frequency of the Absorbed Radiation
4:54
Wavenumbers
6:15
Diatomic Molecules: Energy of the Harmonic Oscillator
8:32
Selection Rules for Vibrational Transitions
10:35
Energy of the Rigid Rotator
16:29
Angular Momentum of the Rotator
21:38
Rotational Term F(J)
26:30
Selection Rules for Rotational Transition
29:30
Vibration Level & Rotational States
33:20
Selection Rules for Vibration-Rotation
37:42
Frequency of Absorption
39:32
Diagram: Energy Transition
45:55
Vibration-Rotation Spectrum: HCl
51:27
Vibration-Rotation Spectrum: Carbon Monoxide
54:30
Vibration-Rotation Interaction
46m 22s
Intro
0:00
Vibration-Rotation Interaction
0:13
Vibration-Rotation Spectrum: HCl
0:14
Bond Length & Vibrational State
4:23
Vibration Rotation Interaction
10:18
Case 1
12:06
Case 2
17:17
Example I: HCl Vibration-Rotation Spectrum
22:58
Rotational Constant for the 0 & 1 Vibrational State
26:30
Equilibrium Bond Length for the 1 Vibrational State
39:42
Equilibrium Bond Length for the 0 Vibrational State
42:13
Bₑ & αₑ
44:54
The Non-Rigid Rotator
29m 24s
Intro
0:00
The Non-Rigid Rotator
0:09
Pure Rotational Spectrum
0:54
The Selection Rules for Rotation
3:09
Spacing in the Spectrum
5:04
Centrifugal Distortion Constant
9:00
Fundamental Vibration Frequency
11:46
Observed Frequencies of Absorption
14:14
Difference between the Rigid Rotator & the Adjusted Rigid Rotator
16:51
21:31
Observed Frequencies of Absorption
26:26
The Anharmonic Oscillator
30m 53s
Intro
0:00
The Anharmonic Oscillator
0:09
Vibration-Rotation Interaction & Centrifugal Distortion
0:10
Making Corrections to the Harmonic Oscillator
4:50
Selection Rule for the Harmonic Oscillator
7:50
Overtones
8:40
True Oscillator
11:46
Harmonic Oscillator Energies
13:16
Anharmonic Oscillator Energies
13:33
Observed Frequencies of the Overtones
15:09
True Potential
17:22
HCl Vibrational Frequencies: Fundamental & First Few Overtones
21:10
Example I: Vibrational States & Overtones of the Vibrational Spectrum
22:42
Example I: Part A - First 4 Vibrational States
23:44
Example I: Part B - Fundamental & First 3 Overtones
25:31
Important Equations
27:45
Energy of the Q State
29:14
The Difference in Energy between 2 Successive States
29:23
Difference in Energy between 2 Spectral Lines
29:40
Electronic Transitions
1h 1m 33s
Intro
0:00
Electronic Transitions
0:16
Electronic State & Transition
0:17
Total Energy of the Diatomic Molecule
3:34
Vibronic Transitions
4:30
Selection Rule for Vibronic Transitions
9:11
More on Vibronic Transitions
10:08
Frequencies in the Spectrum
16:46
Difference of the Minima of the 2 Potential Curves
24:48
Anharmonic Zero-point Vibrational Energies of the 2 States
26:24
Frequency of the 0 → 0 Vibronic Transition
27:54
Making the Equation More Compact
29:34
Spectroscopic Parameters
32:11
Franck-Condon Principle
34:32
Example I: Find the Values of the Spectroscopic Parameters for the Upper Excited State
47:27
Table of Electronic States and Parameters
56:41
Section 23: Molecular Spectroscopy Example Problems
Example Problems I
33m 47s
Intro
0:00
Example I: Calculate the Bond Length
0:10
Example II: Calculate the Rotational Constant
7:39
Example III: Calculate the Number of Rotations
10:54
Example IV: What is the Force Constant & Period of Vibration?
16:31
Example V: Part A - Calculate the Fundamental Vibration Frequency
21:42
Example V: Part B - Calculate the Energies of the First Three Vibrational Levels
24:12
Example VI: Calculate the Frequencies of the First 2 Lines of the R & P Branches of the Vib-Rot Spectrum of HBr
26:28
Example Problems II
1h 1m 5s
Intro
0:00
Example I: Calculate the Frequencies of the Transitions
0:09
Example II: Specify Which Transitions are Allowed & Calculate the Frequencies of These Transitions
22:07
Example III: Calculate the Vibrational State & Equilibrium Bond Length
34:31
Example IV: Frequencies of the Overtones
49:28
Example V: Vib-Rot Interaction, Centrifugal Distortion, & Anharmonicity
54:47
Example Problems III
33m 31s
Intro
0:00
Example I: Part A - Derive an Expression for ∆G( r )
0:10
Example I: Part B - Maximum Vibrational Quantum Number
6:10
Example II: Part A - Derive an Expression for the Dissociation Energy of the Molecule
8:29
Example II: Part B - Equation for ∆G( r )
14:00
Example III: How Many Vibrational States are There for Br₂ before the Molecule Dissociates
18:16
Example IV: Find the Difference between the Two Minima of the Potential Energy Curves
20:57
Example V: Rotational Spectrum
30:51
Section 24: Statistical Thermodynamics
Statistical Thermodynamics: The Big Picture
1h 1m 15s
Intro
0:00
Statistical Thermodynamics: The Big Picture
0:10
Our Big Picture Goal
0:11
Partition Function (Q)
2:42
The Molecular Partition Function (q)
4:00
Consider a System of N Particles
6:54
Ensemble
13:22
Energy Distribution Table
15:36
Probability of Finding a System with Energy
16:51
The Partition Function
21:10
Microstate
28:10
Entropy of the Ensemble
30:34
Entropy of the System
31:48
Expressing the Thermodynamic Functions in Terms of The Partition Function
39:21
The Partition Function
39:22
Pi & U
41:20
Entropy of the System
44:14
Helmholtz Energy
48:15
Pressure of the System
49:32
Enthalpy of the System
51:46
Gibbs Free Energy
52:56
Heat Capacity
54:30
Expressing Q in Terms of the Molecular Partition Function (q)
59:31
Indistinguishable Particles
1:02:16
N is the Number of Particles in the System
1:03:27
The Molecular Partition Function
1:05:06
Quantum States & Degeneracy
1:07:46
Thermo Property in Terms of ln Q
1:10:09
Example: Thermo Property in Terms of ln Q
1:13:23
Statistical Thermodynamics: The Various Partition Functions I
47m 23s
Intro
0:00
Lesson Overview
0:19
Monatomic Ideal Gases
6:40
Monatomic Ideal Gases Overview
6:42
Finding the Parition Function of Translation
8:17
Finding the Parition Function of Electronics
13:29
Example: Na
17:42
Example: F
23:12
Energy Difference between the Ground State & the 1st Excited State
29:27
The Various Partition Functions for Monatomic Ideal Gases
32:20
Finding P
43:16
Going Back to U = (3/2) RT
46:20
Statistical Thermodynamics: The Various Partition Functions II
54m 9s
Intro
0:00
Diatomic Gases
0:16
Diatomic Gases
0:17
Zero-Energy Mark for Rotation
2:26
Zero-Energy Mark for Vibration
3:21
Zero-Energy Mark for Electronic
5:54
Vibration Partition Function
9:48
When Temperature is Very Low
14:00
When Temperature is Very High
15:22
Vibrational Component
18:48
Fraction of Molecules in the r Vibration State
21:00
Example: Fraction of Molecules in the r Vib. State
23:29
Rotation Partition Function
26:06
Heteronuclear & Homonuclear Diatomics
33:13
Energy & Heat Capacity
36:01
Fraction of Molecules in the J Rotational Level
39:20
Example: Fraction of Molecules in the J Rotational Level
40:32
Finding the Most Populated Level
44:07
Putting It All Together
46:06
Putting It All Together
46:07
Energy of Translation
51:51
Energy of Rotation
52:19
Energy of Vibration
52:42
Electronic Energy
53:35
Section 25: Statistical Thermodynamics Example Problems
Example Problems I
48m 32s
Intro
0:00
Example I: Calculate the Fraction of Potassium Atoms in the First Excited Electronic State
0:10
Example II: Show That Each Translational Degree of Freedom Contributes R/2 to the Molar Heat Capacity
14:46
Example III: Calculate the Dissociation Energy
21:23
Example IV: Calculate the Vibrational Contribution to the Molar heat Capacity of Oxygen Gas at 500 K
25:46
Example V: Upper & Lower Quantum State
32:55
Example VI: Calculate the Relative Populations of the J=2 and J=1 Rotational States of the CO Molecule at 25°C
42:21
Example Problems II
57m 30s
Intro
0:00
Example I: Make a Plot of the Fraction of CO Molecules in Various Rotational Levels
0:10
Example II: Calculate the Ratio of the Translational Partition Function for Cl₂ and Br₂ at Equal Volume & Temperature
8:05
Example III: Vibrational Degree of Freedom & Vibrational Molar Heat Capacity
11:59
Example IV: Calculate the Characteristic Vibrational & Rotational temperatures for Each DOF
45:03
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1 answerLast reply by: Professor HovasapianFri Mar 23, 2018 5:19 AMPost by Richard Lee on March 23, 2018Thank you for your wonderful lectures!
### Looking Back Over Everything: All the Equations in One Place
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
• Intro 0:00
• Work, Heat, and Energy 0:18
• Definition of Work, Energy, Enthalpy, and Heat Capacities
• Heat Capacities for an Ideal Gas
• Path Property & State Property
• Energy Differential
• Enthalpy Differential
• Joule's Law & Joule-Thomson Coefficient
• Coefficient of Thermal Expansion & Coefficient of Compressibility
• Enthalpy of a Substance at Any Other Temperature
• Enthalpy of a Reaction at Any Other Temperature
• Entropy 8:53
• Definition of Entropy
• Clausius Inequality
• Entropy Changes in Isothermal Systems
• The Fundamental Equation of Thermodynamics
• Expressing Entropy Changes in Terms of Properties of the System
• Entropy Changes in the Ideal Gas
• Third Law Entropies
• Entropy Changes in Chemical Reactions
• Statistical Definition of Entropy
• Omega for the Spatial & Energy Distribution
• Spontaneity and Equilibrium 15:43
• Helmholtz Energy & Gibbs Energy
• Condition for Spontaneity & Equilibrium
• Condition for Spontaneity with Respect to Entropy
• The Fundamental Equations
• Maxwell's Relations
• The Thermodynamic Equations of State
• Energy & Enthalpy Differentials
• Joule's Law & Joule-Thomson Coefficient
• Relationship Between Constant Pressure & Constant Volume Heat Capacities
• One Final Equation - Just for Fun
### Transcription: Looking Back Over Everything: All the Equations in One Place
Hello and welcome to www.educator.com and welcome back to Physical Chemistry.0000
Today, we are going to look back over absolutely everything that we have done in this thermodynamics portion of Physical Chemistry.0004
It is going to be all the equations in one place.0013
Let us just jump right on in and get started.0016
You can consider this as a quick general review.0020
We started off with the definition of work and we set the work is equal to the external pressure.0025
The change in work DW is equal to the external pressure × the change in volume.0031
With the definition of energy so it is DU = DQ – DW.0039
This is absolutely very important.0044
I'm probably going to go ahead and put circles around the equations that I think are the ones that you need to memorize,0046
the ones that you need to bring to the table when you solve a particular problem.0052
Let me go ahead and do that in red actually.0058
This is a very important equation, the definition of work is absolutely fundamental and of course the definition of energy.0062
Recall, that we took heat from the systems point of view.0072
In other words, if heat goes into the system heat is positive.0075
If heat leaves the system, it is negative.0079
We took work from the surroundings point of view.0082
If work is done on the surroundings then work is positive.0085
If work is done on the system then work is negative.0091
It is the reverse of what some people do, often in chemistry we see this DQ + DW.0095
Again, this is the reason for the minus sign above equation that is different from what you are used to seeing or for what you do see.0101
Absolutely everything else is completely the same.0108
The only thing that this minus sign does is, when I get value of work and let us say it is positive, the only thing you have to do is change the sign.0111
That is the only thing because all you are doing is changing a particular perspective.0120
It is the magnitude that actually matters.0125
Should I say the direction does not matter.0128
The direction matters but in terms of the equation, it is just a question of point of view.0130
In chemistry we take the systems point of view for work and for heat.0134
What I have done here is take the systems point of view for heat, the surroundings point of view from work.0141
And if you go back to those lessons where I discussed it, I talked about why I actually did that.0146
But as far as your problems are concerned, nothing changes.0152
You are going to use the same equations.0155
It is just your sign for work is just going to be the opposite of what you get here.0157
The definition of enthalpy.0165
The enthalpy of the system is a measure of the energy + the energy of the system + the pressure of the system × the volume of the system at a given point.0166
It is just a combined, it is a derived unit.0178
It is a compound unit H = U + PV.0180
We wanted to find the heat capacities.0185
The constant volume heat capacity is the change in heat at constant volume ÷ the change in temperature0188
which happened to be DU/ DT at constant volume, the change in energy per unit change in temperature.0195
Constant pressure heat capacity, the same thing, is the amount of heat that is transferred0205
under conditions of constant pressure ÷ the differential change in heat or it is the DH DT at constant P.0210
These are the definitions of the heat capacities.0217
A relationship between the two heat capacities for an ideal gas CP - CV = RN.0223
I think this is absolutely important one to remember.0229
I should have circled the ones for the heat capacities but that is okay.0232
Heat and work are path properties.0237
Remember, their values depend on the path taken to go from some initial state to some final state.0240
They actually change the values of the heat and work change depending on the path that you take.0245
Energy is a state property, along with all the other thermodynamic properties.0250
H is a state property, G is a state property, S is a state property.0256
Energy is a state property also called the state function.0263
Its value does not depend on the path taken to go from an initial state to a final state.0266
It only depends on the initial and final states.0271
It is actually pretty extraordinary given the definition of energy.0274
You have energy is equal to DQ – DW.0279
Heat and work are path functions.0282
How is it that the difference of two path functions ends up with a state function that is actually very extraordinary and very profound.0285
State properties are exact differentials.0293
It has profound consequences for the mathematics.0296
We want to express changes in the energy of a system in terms of properties of the system.0307
We decided on temperature volume and temperature pressure.0313
I think there is a little bit of typo here, that is not a problem I will fix it.0320
The energy differential is this, this is the total differential.0323
Just a straight mathematical form for the total differential.0326
DU DT being the definition of constant volume heat capacity, you end up with this equation.0330
One of the important equations to know.0339
As for enthalpy is concerned, enthalpy was going to be for temperature and pressure so I apologize here.0341
Let me go to black, let me erase this, this should be DP.0348
It looks like I have DP here so it was just a little typo there.0354
This is the differential expression for the δ H.0359
The DH DT being the constant pressure heat capacity, we end up with this equation.0365
If I change the temperature, if I change the pressure, how does the enthalpy of the system change?0374
We went on to discuss Joules law.0384
The Joules law for an ideal gas DU DV = 0, this is the second term in the equations that we just saw for energy.0386
The change in energy per unit change in volume for an ideal gas that is 0.0394
The Joule Thompson coefficient, change in enthalpy per unit change in pressure = -CP × the Joule Thompson coefficient.0399
For an ideal gas, the DH DPT that was equal to 0.0411
This is the second term in the previous equation that we saw for the enthalpy differential.0416
The coefficient of thermal expansion, these are very important to know as it keep coming up.0422
Coefficient of thermal expansion is Α 1/ DV DT.0430
Basically, it measures the change in volume per unit change in temperature at constant pressure.0434
The coefficient of compressibility measures the change in volume per unit change in pressure at constant temperature.0439
The enthalpy of a substance at any other temperature, besides the temperature that we know, we have tabulated enthalpy.0451
In the tables of thermodynamic data, they are done at 25°C or 298°K.0458
If you want to know the enthalpy of a particular substance at any other temperature, this is what you would use.0463
You would take the enthalpy of the standard temperature and0470
then you would integrate the constant pressure heat capacity with respect to temperature from 298 to the new temperature.0473
The enthalpy of reaction at any other temperature, the enthalpy of a reaction is the δ H.0482
The enthalpy of the products - the enthalpy of the reactants.0488
That is again, the δ H at 298 + the integral 298 δ CP.0491
This is a little different, this is just the sum of the heat capacities of the products - the sum of the heat capacities of the reactors including these coefficients.0498
You do the same thing that you do with δ H, δ G, δ S.0511
Products – reactants, just make sure to include these coefficients.0513
Of δ H for elements and δ G for elements is 0.0520
You remember from general chemistry that is not the case here.0523
There is always going to be some number for the heat capacity even for an element, it is never 0.0526
We are going to discuss entropy and our definition of entropy was DS = DQ reversible/ T.0536
The differential change in entropy of the system is equal to the heat transferred by reversible process ÷ the temperature at which that takes place.0543
The Clausius inequality says DS is greater than DQ irreversible/ T.0552
For any spontaneous process this has to be satisfied.0557
This is for reversible process, this is at equilibrium.0561
Any particular process, an irreversible process, the heat transfer ÷ the temperature0566
at which the transformation takes place is going to be less than the entropy change.0573
This is for a spontaneous process.0581
Entropy changes in an isothermal system, we said that an isothermal system temperature stays the same.0586
The temperature actually comes out of this one, we integrate these two equations and we get the following.0592
The change in entropy of a vaporization process is equal to the δ H of the vaporization ÷ the boiling temperature.0598
And the δ S of fusion is equal to the δ H of fusion ÷ the melting temperature.0605
The fundamental equation of thermodynamics expressed as DS.0614
This expresses the relationship between entropy, temperature, energy, pressure, and volume.0618
That is why it is called the fundamental equation of thermodynamics.0625
We will see it again in another form expressed in terms of DU rearranged.0628
It is DU over here alone a little bit later.0633
Let us see what we have got and how far are we.0640
We did the same thing with entropy that we did with energy.0644
We want to express it in terms of properties of the system.0647
Once again, we do temperature volume and we do temperature pressure.0650
This is the differential expression that ends up being this,0656
a very important equation, these right here, the Α/ Κ, let us go ahead and leave this alone.0662
This is the change in entropy when I change temperature volume, the change in entropy when I change temperature pressure.0672
These are the two equations that are really important to know.0679
Entropy changes in the ideal gas, you have this equation and you have this equation.0684
These equations can be derived from these just using PV = nrt.0690
That takes care of that.0699
Third law entropies.0701
Basically, the entropies that you see, the entropy values that you see in your table of thermodynamic data, these are third law entropies.0706
The only thing that you need to know is that if I want to measure the entropy of the substance at any particular temperature,0712
depending on what it is, whether it is in the gas state, liquid state, the solid state.0720
Let us say you know the entropy at 25°C from the table of thermodynamic data and you want to find the entropy at let us say 75°C.0728
It is 50° higher.0744
What you actually ended up doing is, because you are not changing state all you are going to do is0746
integrate the change in the particular heat capacity for the solid, for the liquid, for the gas ÷ the temperature, going from one temperature to the next.0753
Essentially what this says is that going from Z to some melting temperature 0°K, this is going to be my entropy.0767
I have to include the entropy of the melting process.0777
I have to include the entropy of going from the melting temperature to the boiling temperature.0781
I have to include the entropy of the vaporization process.0786
I have to include the entropy in going from the boiling temperature to another temperature.0790
What you are going to be doing is, if you want to find the entropy at some temperature,0798
you are going to take the entropy of some temperature that you know0804
and you are just going to be integrating from the initial temperature to0809
your new temperature of the constant pressure heat capacities ÷ T DT whatever state that is in.0812
If it is in a liquid state and you want to find the entropy of liquid water 25°, 75°.0819
In that range, the 25 to 75 is still liquid water so you would use the constant pressure heat capacities of liquid water.0827
You have to account for every single phase change and any temperature difference.0835
The entropy change in a chemical reaction, same sort of thing.0843
For chemical reaction, we have products – reactants.0847
It is going to be the entropy that you know at a particular temperature which for us is 25°C.0850
And you are going to integrate from that 25°C to the next temperature of this δ CP.0858
And again this is just the sum of the heat capacities of the products - the sum of the heat capacities of the reactants.0864
We will go on to discuss entropy from a statistical point of view.0876
The statistical definition of entropy was this, S = KB LN O.0881
KB is the Boltzmann constant.0885
The ω for the spatial distribution was this one.0888
Here N, this is the number of spaces available.0892
It is N sub A which is the number of particles.0904
A good approximation when the number of particles is a lot less than the number of spaces available.0912
A gas in a big volume is this, this is a good approximation to that.0919
The ω for the energy distribution is the one that we are actually going to use later on after we have discussed quantum mechanics.0924
When we come back and talk about statistical thermodynamics.0932
This is the one we are going to be concerned with not so much this one.0936
This is just the ω for the energy distribution, that is all.0940
Spontaneity and equilibrium, we went on to define this thing called the Helmholtz energy that was U – TS.0946
We did the definition of Gibbs energy.0953
The Gibbs energy was defined as the energy of the system + the pressure × the volume - the temperature × the entropy.0955
This is a compound thermodynamic properties made up of these three things.0963
U + PV happen to equal H as enthalpy.0969
G is also equal to H - TS or it is equal to A + PV.0972
All of these three are all definitions, this is the definition of G.0977
You can also use these two, if you need to.0981
Now under conditions of constant temperature and pressure, the condition of spontaneity was that δ G.0985
A little bit of problem here, it is not supposed to be greater than 0.0991
I’m thinking about entropy here, sorry about that.0997
For conditions of spontaneity, in order for a particular process, a particular reaction to be spontaneous, we need the δ G to be less than 0.1001
The condition for equilibrium is that DG or δ G is equal to 0.1012
These are very important to know.1017
One the most important equations and probably the most significant in chemists δ G = δ H - T δ S.1022
Your δ G in enthalpy term, in entropy term, and the temperature term.1029
The δ G for a reaction is the maximum amount of energy above and1036
beyond expansion of work that can be extracted from a spontaneous process and harnessed to do useful work.1041
That is what δ G is, it gives you an upper limit on the amount of energy that you can actually use to do useful work.1049
Think of δ G as ordered energy, all the rest of the energy of the system is spent on the entropy, it is disordered energy.1057
Δ G is ordered energy that you can actually use to do useful work if δ G happens to be negative.1068
The conditions of spontaneity with respect to entropy.1079
The δ S of the universe = δ S of the surroundings + the δ S of the system.1081
The δ S of the surroundings is - the δ H of the system ÷ T.1087
The δ S of the universe was - δ G ÷ T this was the relationship.1092
Δ G' is for spontaneity, δ G has to be less than 0.1098
It is the same as δ S of the universe having to be greater than 0.1102
The fundamental equations.1111
These set of equations here and on the next page, they are the ones that basically tie everything together.1114
DU = T DS – P DV.1121
DH = T DS + V DP.1125
DA = - S DT – PDV.1128
DG = - S DT + V DP.1132
Energy, enthalpy, Helmholtz energy, Gibbs energy.1136
Maxwell's relations, these establish relationships between the rates of change from the fundamental equations that we just saw.1146
We have this one which is the rate of change of temperature per unit change in volume at a constant entropy1155
is equal to the negative of the rate of change of pressure per unit change in entropy at constant volume.1162
These are relationships that exist and these relationships that we actually end up using as substitutions.1169
For example maybe we have this one here and perhaps this one here if it shows up in an equation,1178
because it is equal to this we go ahead and we use this one because this is actually really easy to measure, volume, temperature, pressure.1187
Entropy, pressure and temperature entropy, things involving entropy are difficult to deal with so it is nice that we have these relationships.1194
Anytime something like the shows up, we can use this one.1200
If something like this shows up we can use this one.1203
That is exactly what we are going to do.1206
The thermodynamic equations of state are profoundly important.1209
You do not necessarily need to memorize them but basically instead of PV = nrt or the Van Der Waals gas law or the equation of state for a liquid, the equation of state for a solid.1213
Instead all of these equations, these equations they apply to every single state and every single situation.1226
These are the thermodynamic equations of state.1234
These are the most general expressions of the state of the system.1237
Rearranging these and using Α and Κ from above, remember the coefficient of compressibility and the coefficient of thermal expansion,1243
we end up finding that the DU DV is the term that showed up in the energy differential expression.1253
The DH DP is the one that showed up in the enthalpy differential, it is actually equal to this.1259
You do not have to memorize these are good to now.1265
Now, you can substitute these values back in the equations for energy and enthalpy and you end up with this.1270
What makes these extraordinary is that these equations express changes in the energy and enthalpy of1279
the system entirely in terms of values that we can either measure or obtain from a table.1283
Measurable measurable, table table.1290
That is fantastic, easily measurable quantities or easily something that I can look up in a table.1301
I can tell you that if I change the temperature and volume, or if I change the temperature and pressure of a system,1307
I can tell you what the change in energy or the change in enthalpy is.1311
Profoundly beautiful.1315
Joules is DU DV =0 for an ideal gas.1321
The Joule Thompson coefficient, this one right here and the DH DPT is 0 for an ideal gas.1327
When we substitute from above, what we just got regarding the DU DV, we end up with this.1337
We end up with this equation CP nrt = Α TV – V.1344
Once again, in terms of something which is measurable, something that you can look up, I can find out what the Joule Thompson coefficient is.1349
That is absolutely extraordinary.1360
We have expressed a very important quantity, the Joule Thompson coefficient in terms of easily measurable and or easily retrievable quantities.1365
That is the running theme, this is why we have manipulated the equations the way that we have1373
because we want to express these thermodynamic properties.1378
These really esoteric things in terms of things that we can measure, volume, temperature, heat capacity are the running theme.1381
That is what we have done all this mathematics.1392
The general expression for the relationship between the constant pressure and constant volume heat capacities was this equation.1396
You absolutely do not have to know that but again using values for the partial derivatives from above, you come up with this.1402
For an ideal gas we said that CP - CV = nr.1410
For any other thing, this is just TV Α²/ Κ, that is the relationship between the heat capacities.1417
This is profoundly important for relationship between the constant pressure and constant volume heat capacities.1423
Once again, we have expressed a very important relationship in terms of easily measurable and or easily retrievable quantities.1429
Much of science is dedicated to these, taking things that are abstract and esoteric and1435
expressing them in terms of things that we can touch, that we can measure.1440
We actually come to the end here.1448
One final equation just for fun.1451
We expressed entropy in terms of temperature and volume.1454
We had a differential expression in terms of temperature and pressure.1459
Mixing and matching and using all these partial derivative relations we have between Maxwell's relation and Α and Κ,1465
We are actually able to express the entropy change in terms of pressure and volume.1472
If for some reason, I wanted to do that and there you go, this is the differential expression1480
and this is the expression based on all the things that we can measure and or look up.1485
It ends up looking like this.1490
You absolutely do not have to memorize this, I just want to throw in there to let you know1492
that now we have close the circle on all of this beautiful thermodynamics, energy, entropy,1497
temperature, volume, pressure, free energy, Helmholtz energy, and enthalpy.1504
All of these come together really beautifully.1513
Thank you so much for joining us here at www.educator.com.1516
We will see you next time, bye.1519
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http://math-doc.ujf-grenoble.fr/cgi-bin/sps?kwd=MARTIN+BOUNDARY&kwd_op=contains
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Browse by: Author name - Classification - Keywords - Nature
3 matches found
II: 11, 175-199, LNM 51 (1968)
MEYER, Paul-André
Compactifications associées à une résolvante (Potential theory)
Let $E$ be a locally compact space, $(U_p)$ be a submarkovian resolvent, with a potential kernel $U=U_0$ which maps $C_k$ (the continuous functions with compact support) into continuous bounded functions. Let $F$ be a compact space containing $E$ as a dense subset, but inducing possibly a coarser topology. It is assumed that all potentials $Uf$ with $f\in C_k$ extend to continuous functions on $F$, and that points of $F$ are separated by continuous functions on $F$ whose restriction to $E$ is supermedian. Then it is shown how to extend the resolvent to $F$ and imitate the construction of a Ray semigroup and a strong Markov process. This was an attempt to compactify the space using only supermedian functions, not $p$-supermedian for all $p>0$. An application to Markov chains is given
Comment: This method of compactification suggested by Chung's boundary theory for Markov chains (similarly Doob, Trans. Amer. Math. Soc., 149, 1970) never superseded the standard Ray-Knight approach
Keywords: Resolvents, Ray compactification, Martin boundary, Boundary theory
Nature: Original
Retrieve article from Numdam
V: 19, 196-208, LNM 191 (1971)
MEYER, Paul-André
Représentation intégrale des fonctions excessives. Résultats de Mokobodzki (Markov processes, Potential theory)
Main result: the convex cone of excessive functions for a resolvent which satisfies the absolute continuity hypothesis is the union of convex compact metrizable hats''\ in a suitable topology, and therefore has the integral representation property. The original proof of Mokobodzki, self-contained and unpublished, is given here
Comment: See Mokobodzki's work on cones of potentials, Séminaire Bourbaki, May 1970
Keywords: Minimal excessive functions, Martin boundary, Integral representations
Nature: Exposition
Retrieve article from Numdam
IX: 13, 305-317, LNM 465 (1975)
FÖLLMER, Hans
Phase transition and Martin boundary (Miscellanea)
To be completed
Comment: To be completed
Keywords: Random fields, Martin boundary
Nature: Original
Retrieve article from Numdam
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https://mathoverflow.net/questions/254391/does-the-p-part-of-the-level-of-a-newform-appear-in-its-attached-p-adic-repr
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Does the $p$-part of the level of a newform appear in its attached $p$-adic representation?
Let $f$ a newform of weight $2$ on $\Gamma_0(Np^r)$, $N$ coprime to $p$, and consider its $p$-adic Galois representation $$\rho:G_{\mathbb Q}\longrightarrow GL_2(\bar{\mathbb Q}_p)$$ It's a theorem of Carayol that the prime-to-$p$ conductor $N(\rho)$ of $\rho$ equals $N$. Hence, one can recover $N$ from $\{\rho\vert_{I_q}\}_{q\mid N}$.
The question is:
Can $r$ be read in $\rho\vert_{I_p}$?
• Could $p^r$ be the conductor of the Weil-Deligne representation attached to $\rho|G_{\mathbb{Q_p}}$ by Fontaine? – Aurel Nov 11 '16 at 0:59
• What Aurel says is true -- a theorem of Takeshi Saito. – wrigley Nov 11 '16 at 17:19
• @wrigley It was a guess; thanks for confirming it. Do you have a precise reference? – Aurel Nov 14 '16 at 18:51
• "modular forms and p-adic Hodge theory" 1997 Inventiones. – wrigley Nov 25 '16 at 12:04
The answer to the question in the title is yes, as explained in the last paragraph below.
However, under a literal interpretation of "can" (implying actual feasibility), I believe the answer to the question in the body of the text is no.
Assume for instance that $f$ and $g$ are two is $p$-ordinary eigencuspforms ($p$-ordinary means that under a fixed embedding of $\bar{\mathbb Q}$ into $\bar{\mathbb Q}_{p}$, the $p$-adic valuation of $a_{p}(f)$ and of $a_{p}(g)$ is zero), that $\pi(f)_p$ (the automorphic representation of $\operatorname{GL}_{2}(\mathbb Q_{p})$ attached to $f$) is unramified principal series and that $\pi(g)_{p}$ (same notation) is unramified Steinberg.
Then the conductor of $f$ at $p$ is trivial ($r=0$) whereas the conductor at $p$ of $g$ is $p$ ($r=1$). However, after restriction to $I_{p}$, both $\rho_f$ and $\rho_g$ are equivalent to $$\begin{pmatrix} 1&*\\ 0&\chi^{-1} \end{pmatrix}$$ where $\chi$ is the cyclotomic character. I don't know how to distinguish between them using the class of the extension of $\chi^{-1}$ by $1$ (the $*$, so to speak) and it seems hard to me though I admit I also don't know that it is definitely not possible.
One can construct many such examples of ambiguous $I_{p}$-representation, so I doubt one can reconstruct $p^{r}$ in general. As more generally the representation $\rho_f|G_{\mathbb Q_{p}}$ is the representation $V_{2,a_p}$ in the notation of C.Breuil Sur quelques représentations modulaires et $p$-adiques de $\operatorname{GL}_{2}(\mathbb Q_{p})$ II (Journal de l'IMJ, 2003) it might be a good idea to have a look at this article if you want a definite answer.
As Aurel points out, $p^{r}$ is the conductor of the Weil-Deligne representation attached to $D_{\operatorname{pst}}(\rho_f|G_{\mathbb Q_{p}})$ so you certainly can reconstruct $r$ from $\rho_{f}|G_{\mathbb Q_{p}}$ and what you are missing in your setting are the eigenvalues of the image of $\operatorname{Fr}(p)$ through $\rho_f$. In the case above for instance, both eigenvalues would have the same $p$-adic valuations in the first case and different valuations in the second.
• That's really not that hard. Such a class is an element of $H^1(\mathbb Q_p, \chi)$, i.e., by Kummer theory, an element of $\mathbb Q_p^ \times \otimes \mathbb Q_p = \mathbb Q_p \times \mathbb Q_p$ where the first coordinate comes from the valuation and the second comes from the logarithm. The unramified extensions necessarily form a one-dimensional subspace. I claim the image of the logarithm map is the unramified one. – Will Sawin Nov 11 '16 at 3:55
• A really silly way to check this is to note that every other one-dimensional subspace contains the image of an element $q$ in $\mathbb Q_p$ with positive valuation, and thus is the $p$-adic Tate module of the elliptic curve with uniformization $\mathbb Q_p^\times / q$, which has multiplicative reduction at $p$ and hence has ramified Weil-Deligne representation. – Will Sawin Nov 11 '16 at 3:56
• Oh, I see. I'll let my example stand for the moment though, and maybe someone can give a definite answer. – Olivier Nov 11 '16 at 4:55
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https://www.physicsforums.com/threads/trig-problem.162369/
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# Trig Problem
1. Mar 24, 2007
### ][nstigator
Hey guys, got a small problem and need some help
The problem statement, all variables and given/known data
Show that
$$\arctan{\left( \frac{x}{2} \right)} = \arccos{\left(\frac{2}{\sqrt{4+x^2}}\right)} \ \mbox{for x}\epsilon\mbox{R}$$
The attempt at a solution
Honestly Im pretty stumped from the very beginning....
The only thing I can currently think of to do is go...
$$\arctan{\frac{x}{2}} = \frac{\arcsin{\frac{x}{2}}}{\arccos{\frac{x}{2}}}$$
but Im not sure if that is even correct....
Even still, if that is valid, Im still pretty unsure what Im meant to do next..
Any hints to point me in the right direction would be much appreciated
I hope I did the Latex stuff right, its my first time using it..
Last edited: Mar 25, 2007
2. Mar 24, 2007
### symbolipoint
Draw a right-triangle and label the sides until you can form a triangle which give s the relationship that you are looking for in your equation. This may give you another formulable relationship which permits you to solve the problem.
3. Mar 24, 2007
### symbolipoint
I misunderstood the meaning of the problem. You are probably looking for identity relationships to PROVE that your given relation is an identity. Of course, when you draw a right-triangle, you will be able to derive the relationship but you are trying to use a trail of identities to prove this. I wish I could offer better help.
The best that I could do right now is to draw a triangle; I label one of the non-right angles; the side opposite I give as "x"; the side between the referenced angle and the right-angle I give as length 2; pythagorean theorem gives the hypotenuse as (4 + x^2)^(1/2). Continued reference to this triangle gives the arcos expression which you wanted -------- I am not well with being able to prove as you wanted, but maybe you might be able to now?
4. Mar 25, 2007
### VietDao29
Are you sure you've copies the problem correctly?
What if $$x = -2$$?
$$\arctan \left( \frac{-2}{2} \right) = \arctan (-1) = -\frac{\pi}{4}$$
Whereas:
$$\arccos \left( \frac{2}{\sqrt{4 + (-2) ^ 2}} \right) = \arccos \left( \frac{1}{\sqrt{2}} \right) = \frac{\pi}{4}$$
So:
$$\arctan \left( \frac{-2}{2} \right) \neq \arccos \left( \frac{2}{\sqrt{4 + (-2) ^ 2}} \right)$$ (Q.E.D)
5. Mar 25, 2007
### ][nstigator
Yup, I definately copied the problem down correctly... weird huh :(
6. Mar 25, 2007
### f(x)
Either you are not working in principle values or the question is copied down incorrectly.
because $cos \frac{\pi}{4}= cos \frac{- \pi}{4}$
but the inverse doesnt hold as $cos^{-1} \mbox{has principle range as} [0,\pi]$
7. Mar 25, 2007
### ][nstigator
Show that $$\arctan{\left( \frac{x}{2} \right)} = \arccos{\left(\frac{2}{\sqrt{4+x^2}}\right)} \ \mbox{for x}\epsilon\mbox{R}$$
..is the question, character for character
8. Mar 25, 2007
### VietDao29
Well, then, the problem cannot be proven. Because, it's... you know, false.
Similar Discussions: Trig Problem
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http://motls.blogspot.co.uk/2012/04/royal-status-of-11-dimensional.html
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## Saturday, April 07, 2012 ... /////
### The royal status of 11-dimensional supergravity
A few days ago, I discussed the maximally supersymmetric gauge theory, the Darth Vader theory, which is exceptional.
I mentioned that the $\NNN=4$ gauge theory in $d=4$ dimensions is a beautiful, fully consistent (at the quantum level) dimensional reduction of the 10-dimensional supersymmetric gauge theory which has many hidden virtues and symmetries. All these theories have 16 supercharges.
A portrait of eleven-dimensional supergravity. As Dilaton knows, "elf" means "eleven". ;-)
There's one more royal family that is, in some sense, comparably fundamental as the family descended from the ten-dimensional supersymmetric gauge theory. This additional family of theories has 32 real supercharges and not just 16 of them.
The master theory's spacetime has $d=11$ dimensions rather than $d=10$. It is not renormalizable and none of its compactifications is fully consistent at the quantum level, either. These theories are only meaningful at a classical level (or in some low-energy expansion). All of these theories contain gravity and they are limits of string/M-theory which had to be the case because string/M-theory is the only consistent quantum theory of gravity.
Even though the eleven-dimensional gravity is just a low-energy limit of the full string/M-theory, it (and its compactifications) already knows quite something about the wisdom of string/M-theory in its most symmetric incarnation.
First of all, the previous text looked at gauge theories. We saw that supersymmetry implied some pairing between fermionic and bosonic degrees of freedom. Because the fermions have to be organized as $j=1/2$ spinors whose number of components grows exponentially, it's only possible to match them for $d=3,4,6,10$. In particular, $d=10$ was the maximum dimension in which a supersymmetric and pure gauge theory may exist.
Allowing gravity
Now we will allow massless fields with spin up to $j\leq 2$. We know that Einstein's gravity predicts gravitational waves. Their energy has to be quantized i.e. these waves have to be composed of gravitons of energy $E=\hbar\omega$. The spin of the gravitons is $j=2$ essentially because the metric field $g_{\mu\nu}$ has two indices.
If we linearize the metric tensor around a background, e.g. the flat Minkowski background, we obtain a dynamical spin-2 field. Much like spin-1 fields, it contains timelike components (in particular, components with an odd number of indices being timelike) which create negative-norm excitations. Much like in the Yang-Mills case, there has to be a gauge symmetry that decouples these dangerous excitations that could make the probabilities of many processes negative if they weren't killed.
For spin-1 fields, the possible gauge symmetries that do this job are Yang-Mills symmetries; we may choose the gauge group which also influences the number of components of the gauge fields (via the dimension of the gauge group). However, the gauge field of gravity – the metric tensor – has a spin that is greater by one. So the conserved charges – the generators of the symmetries – have to carry an additional Lorentz index. The generator of this symmetry can't be an "electric charge" or its non-Abelian generalization; it has to be a spacetime vector.
The only conserved vector that still allows realistic theories is the energy-momentum vector, i.e. the integral of the stress-energy tensor. Its conservation is linked to the translational symmetries of the spacetime via Emmy Noether's theorem; however, we are making this symmetry local or gauge so the translational symmetry is going to be promoted to all diffeomorphisms. If we required the conservation of yet another vector or even higher-spin tensors, the theory would be so constrained by the conservation laws (so many components) that it would essentially have to be non-interacting.
(Winding numbers of macroscopic strings and membranes may be a loophole and may be additional conserved quantities aside from the energy-momentum vector; this loophole is possible because pointlike excitations of the theory – and those are studied by the Coleman-Mandula theorem – carry vanishing values of these charges.)
If you think about these words, you will see that $j=2$ is the maximum spin of a field for which you will be able to propose a reasonable gauge symmetry that kills the negative-norm excitations while allowing at least some interactions in the theory. Moreover, the $j=2$ massless field has to be unique. There's only one translational symmetry of the spacetime so there's only one stress-energy tensor and it can only couple to one "gauge field" for this symmetry, the metric tensor.
The spin $j=5/2$ would already give too many components.
Maximizing the number of supercharges
Fine. So we want to construct a supersymmetric theory of massless particles that has the maximum spacetime dimension and the maximum number of supercharges. Let me say in advance that we will be led to $d=11$ dimensions and $N=32$ supercharges by this maximization procedure. Why?
Imagine a supermultiplet of massless particles in such a theory. One-half of the supercharges i.e. $N/2$ of them will annihilate the whole supermultiplet; all of the components will be invariant under one-half of the supercharges. The rest of the supercharges, $N/2$ real supercharges, may be recombined into $N/4$ raising operators and $N/4$ lowering operators; the latter group may be composed of the Hermitian conjugates of the former group. Each of these complexified supersymmetry generators changes a chosen projection of the spin by $\Delta j=\pm 1/2$.
We want to maximize the number of supercharges so we must allow the set of $N/4$ raising operators to be able to climb from the minimum allowed component of the spin, e.g. $j_{12}$, i.e. from $j_{12}=-2$ (graviton), to the maximum allowed one, $j_{12}=+2$, by those $\Delta j=1/2$ steps. We therefore see that $\frac{N}{4} = \frac{(+2)-(-2)}{\frac{1}{2}}=8,\qquad N=32.$ If the supersymmetry algebra is capable of climbing from one extreme component of the graviton to the opposite one, we must have $N=32$ real supercharges. Now, recall that the Dirac spinor in $d=10$ has $2^{10/2}=32$ components so in $d=10$, we actually find a 32-component spinor. However, the Dirac spinor is reducible, to the left-handed and right-handed chiral components, if you wish. That's not really a problem but it's a sign that we may go higher.
And indeed, the spinor in $d=11$ has 32 real components. There's no chirality in $d=11$ because eleven is an odd number. The $d=11$ spinor simply becomes the Dirac spinor if you dimensionally reduce the theory by one dimension. So $d=11$ is the right number of dimensions in which we should expect a nice maximally supersymmetric theory of gravity or supergravity.
Representation of the massless multiplet
So far I haven't said anything about interactions and even in this section, we will assume that we're considering the free limit of the theory only. The question we want to answer is how do the excitations of the massless gravitational supermultiplet transform under spacetime rotations.
In $d=11$, the massless particles move in a direction. Their nonzero energy prevents us from mixing time with other coordinates while preserving the energy-momentum vector of the particle; the direction of the particle's motion removes one spatial dimension as well. So there are only $d-2=9$ transverse dimensions that may be rotated into each other so that the energy-momentum vector is unchanged. (There are actually some light-like boosts as well but I only want to discuss compact groups here.)
So the little group is $SO(9)$. As we have already said, the multiplet is annihilated by 16 supercharges while the remaining 16 "active" supercharges play the role of 8 raising and 8 lowering operators. The algebra satisfied by these 16 "active" Hermitian supercharges is $\{Q_a,Q_b\} = \delta_{ab} E, \qquad a,b\in\{1,2,\dots , 16\}$ if we normalize the supercharges so that there's no extra coefficient. The Kronecker delta arises from a Dirac gamma matrix reduced to the simpler 16-dimensional space relevant for the little group. My point is that these 16 "active" supercharges transform as a spinor of the little group, $SO(9)$, because they're a remnant of a spinor of $SO(10,1)$, the Lorentz group of the 11-dimensional theory.
Do you know another way how to look at the anticommutators above? Well, you should. They're the same anticommutators as the algebra of Dirac gamma matrices:$\{\Gamma_a,\Gamma_b\} = \delta_{ab},\qquad a,b\in\{1,2,\dots , 16\}$ up to the obvious change of the normalization. But we know what we get from the algebra above if we "quantize it", right? We get a 256-dimensional spinor of $SO(16)$ or $Spin(16)$, to be more accurate. It's 256-dimensional because each of the 8 raising operators (that exists besides the 8 lowering operators) may be either applied to the "ground state" or not. The mathematical problem we're solving here is completely $Spin(16)$-symmetric so we know that the states we get by "quantizing" the raising and lowering operators must produce a nice representation of $Spin(16)$. Clearly, it has to be $2^8$-dimensional and it's nothing else than the spinor of $SO(16)$.
Moreover, one may define the operator of chirality $\Gamma_{17}$, to use a notation analogous to $\Gamma_5$ in $d=4$, that anticommutes with the sixteen $\Gamma_a$ matrices. This operator makes it clear that the 256-dimensional representation is reducible; it decomposes at least to 128 components that have $\Gamma_{17}=+1$ and 128 components with $\Gamma_{17}=-1$.
If we return from the $\Gamma_a$ notation to $Q_a$, it's clear that $\Gamma_{17}$ is nothing else than the operator remembering whether a state of the representation is bosonic or fermionic. That's the only conclusion from the fact that $\Gamma_{17}$ anticommutes with all $Q_a$ operators and those are fermionic ones.
We have just determined that the gravitational supermultiplet contains 128 bosonic and 128 fermionic states. We know that they transform as the full Dirac spinor (or the sum of the two chiral spinors) under $SO(16)$. However, the little group $SO(9)$ is "bizarrely" embedded into this $SO(16)$ in such a way that the "vector" ${\bf 16}$ of $SO(16)$ is the "spinor" ${\bf 16}$ of $SO(9)$ whose vector is ${\bf 9}$, of course. So how do the 128-dimensional chiral spinors of $SO(16)$ decompose under $SO(9)$ which is a subgroup of $SO(16)$?
Getting the three fields of $d=11$ SUGRA
Let's start with the fermionic ones. We should get a representation of $Spin(9)$ which is 128-dimensional. This representation inevitably contains some states with $j_{12}=3/2$, as expected for gravitinos. What are the representations of $Spin(9)$ with this property?
Well, the answer is that there is a unique 128-dimensional representation of this kind and it is irreducible. Why? Take the tensor product of the vector and the spinor of $Spin(9)$, ${\bf 9} \otimes {\bf 16}.$ It's 144-dimensional which is too many for us. Is it irreducible? Well, it is not. We may require$\chi_{ia}\gamma^i_{ab}=0$ That's the only linear, rotationally invariant condition we may demand from the spin-3/2 object $\chi_{ia}$ which doesn't make it identically vanish. The condition above has a free $b$ index so it eliminates sixteen components of the tensor with one vector index and one spinor index. So the number of independent surviving components is $8\times 16=128$ rather than $9\times 16=144$ and that's exactly what we need. The gravitino in $d=11$ forms an irreducible 128-dimensional representation of the little group
$Spin(9)$.
They must contain the graviton which comes from transverse excitations of the metric tensor, $h_{ij}$, where $i,j=1,2,\dots,9$. This would have $9\times 10/2\times 1=45$ components; count the number of squares in a symmetric matrix or a triangle that includes the diagonal. However, this 45-dimensional representation isn't irreducible. Again, we may demand an extra condition, namely tracelessness$\sum_{i=1}^9 h_{ii} = 0$ and general relativity actually does imply that the physical states are traceless which means that the $d=11$ graviton only has $\frac{9\times 10}{2\times 1} - 1 = 44$ components. Where are the remaining 84 components?
I have already mentioned that the spin-2 states have to be unique. But the gravitational multiplet may still contain $j=1$ and $j=0$ states. Well, there have to be some additional $j=1$ states as well. I originally wrote an explanation in terms of weights but it would be too annoyingly technical so I erased it and you will only be told the sketched result. The representations with $j=1$ don't have to be just vectors; $p$-forms are fine, too. If you analyze the dimensions of the antisymmetric tensor representations, you will find out that $C_{ijk}$ with three $SO(9)$ indices has$\frac{9\times 8 \times 7}{3\times 2 \times 1} = 84$ components which is exactly what you need. So the 128 bosonic states decompose to 44 states of the graviton and 84 states of the 3-form. Everything seems to work at the level of the little group and its representations.
Writing the Lorentz, diff-invariant Lagrangian
The $d=11$ theory of supergravity should therefore contain the metric tensor $g_{\mu\nu}$, a gravitino Rarita-Schwinger field $\chi_{\mu\alpha}$, and a three-form $C_{\lambda\mu\nu}$. Let's use the convention in which the metric and the three-form potential are dimensionless and the fermionic field has the dimension ${\rm mass}^{1/2}$. What is the Lagrangian?
You combine the usual Einstein-Hilbert action $\LL_{EH} = \frac{1}{16\pi G} R$ i.e. the Ricci scalar with other terms. Note that its dimension is ${\rm mass}^2$ and when divided by Newton's constant which is ${\rm length}^9$, e.g. because $A/4G$ should be the dimensionless entropy, we get ${\rm mass}^{11}$, as expected from an 11-dimensional Lagrangian density. Aside from the Einstein-Hilbert action, there will also be some nice Maxwell-like kinetic term for the three-form potential,$\LL_{EM} = \frac{C}{G} F_{\lambda\mu\nu\pi} F^{\lambda\mu\nu\pi}$ where the 4-form $F$ is gotten as the antisymmetrized derivative, $F=*dC$, much like in the electromagnetic case. Finally, there have to be kinetic terms for the gravitino,$\LL_{RS} \sim \frac{C}{G} \chi^{\lambda \beta} (\Gamma\delta)_{\lambda}^{\mu\nu}{}^\alpha_\beta \partial_\nu \chi_{\mu\alpha}$ where I don't want to write all the required combinations of contractions of the indices and their right relative normalizations so I have unified the gamma matrices and a Lorentz-vector Kronecker delta into a "hybrid" object. Just like the Dirac Lagrangian, this fermionic kinetic term is linear in derivatives. Note that all the terms in the Lagrangian have the right units; and all of them are proportional to $1/G$.
You will find out that the theory above isn't supersymmetric. However, it's possible to systematically deduce all the additional interaction terms and the supersymmetry suddenly starts to hold. It's a kind of miracle. You will have to add gauge-fermion-like interactions $F\psi\psi$, the Chern-Simons term $C\wedge F\wedge F$ with the right coefficient (an 11-form), and a $\chi^4$ term as well. But when you add all of them, the total action may be verified to be locally supersymmetric! It's also diffeomorphism symmetric and symmetric under $\delta C = d\lambda$ where $\lambda$ is a 2-form parameter of a gauge transformation for the 3-form that generalizes the electromagnetic gauge symmetry (but is still Abelian).
Why does the supersymmetry work?
It's a kind of a miracle that the supersymmetry holds when you adjust a few coefficients. I guess that only dozens of people in the world have verified the supersymmetry of the 11-dimensional supergravity's action explicitly, without any help of a computer, and roughly 100 people have done so with the help of a computer or some other improvements of their brains.
Is there an intuitive explanation why it works? I admit that, paradoxically enough, the most straightforward and heavy-algebra-free approach to prove that this limit exists could actually start from (type IIA) string theory. If any reader has an explanation why such an interacting theory with such a huge symmetry principle exists at all, an explanation will be highly welcome.
M2-branes, M5-branes
The field content of the theory includes a 3-form bosonic field. One may naturally include another term in the action$S = \int \dd \Sigma_3 C_{(3)}$ that simply integrates the 3-form potential over some 3-dimensional manifold in the spacetime. Such privileged manifolds that do contribute to the action in this way may exist; they're of course the world volumes of the two-dimensional branes or membranes. The membranes in 11-dimensional supergravity or M-theory are known as M2-branes. They carry some specific "charge density" in the right direction. However, in electromagnetism, you know that you may also consider $*F$ instead of $F$ and study magnetic charges, too.
The same thing may be done here. The field strength $F_{(4)}$ which is a 4-form may be Hodge dualized in 11 dimensions to a 7-form and this 7-form may be, at least in regions without sources, written as $F_{(7)}=d\tilde C_{(6)}$. And this dual 6-potential may be integrated over 6-dimensional manifolds in spacetime: they're nothing else than the world volumes of M5-branes.
So the 11-dimensional theory predicts gravitational waves, generalizations of electromagnetic waves, black holes, M2-branes, and M5-branes, among other objects.
We're going to look at some dimensional reductions, perhaps oxidations, and dimensional chemistry. Song "Chemistry" is sung by Mr Xindl X.
Surprising richness of the compactifications
If you wanted the theory to be well-defined at the quantum level including the quantum corrections – which is the same as corrections that become strong at high energies – you would have to replace the 11-dimensional supergravity by its unique ultraviolet completion, M-theory. I don't want to do that in this article.
However, it's interesting to look at compactifications. The simplest compactifications are the toroidal ones, i.e. ones in which a couple of dimensions are periodically identified, i.e. points are identified with other points that are shifted by an element of a lattice.
$\RR^n / \Gamma^n=T^n$ is a torus. If its size is comparable to the Planck length, the length scale at which the quantum M-theory corrections become really important, it's obvious that the compactification will be a compactification with extremely short, microscopic periodicities that look like zero from the viewpoint of long-distance probes. So if you only consider SUGRA and not the full M-theory, these compactifications will be just dimensional reductions and the size and angles in the torus will be physically inconsequential (for all effects at low energies).
And indeed, this fact will manifest itself as a noncompact symmetry of the dimensionally reduced supergravity theory: changing the shape and size of the torus is actually changing nothing about the low-energy physics. The dimensional reductions still have 32 real supercharges but they're organized as extended supersymmetry in the lower-dimensional spacetimes. You will find out that there is a noncompact version of the $E_k$ symmetry if you dimensionally reduce the theory to $11-k$ large dimensions of spacetime. That's true for $k=6,7$ and, when you properly interpret some fields in 3 dimensions, even for $k=8$. Well, one could argue that some of those statements may even be done for the Kač-Moody case $k=9$ in $d=2$ if not the hyperbolic case $E_{10}$ in a 1-dimensional spacetime.
The groups $E_5, E_4, E_3, E_2, E_1$ should be understood as $SO(5,5)$, $SL(5,\RR)$, $SL(2,\RR)\times SL(3,\RR)$, $SL(2,\RR)$, $\RR$. If you study the full M-theory, using probes that can feel the Planckian physics, the shape of the torus matters and these noncompact symmetries are reduced to their discrete versions such as $E_{7(7)}(\ZZ)$ in the case of the $\NNN=8$ $d=4$ supergravity, i.e. to the so-called U-duality groups. The quotient of the continuous group and its discrete subgroup spans the moduli space. Various charges and scalar fields etc. know about the noncompact group or its maximal compact subgroup.
It's a shocking set of mathematical facts. There exist mathematical explanations why the moduli spaces have to be quotients, why the exceptional groups are the only solutions, and so on. But I think that no one knows of any "truly conceptual" explanation why the exceptional groups appear in the discussion of a maximally supersymmetric theory of gravity which didn't start with any components that would resemble exceptional groups. The exceptional groups were spitted out as one of the amazingly surprising outputs.
All these mathematical facts become even more stunning if you study those theories beyond the low-energy approximation i.e. if you investigate the whole structure of string/M-theory. The 11-dimensional spacetime of M-theory, the completion of the 11-dimensional supergravity, is the maximum-dimensional spacetime in string/M-theory that may exist which is why people often say that it's a "more fundamental" limit than others. Of course, a more politically correct assertion is that it's just another limit, on par with many others such as the five 10-dimensional string "theories" (vacua). Still, by its having a higher number of dimensions, the description in terms of 11-dimensional theory is "more geometric" than others.
(F-theory has 12 dimensions in some counting but 2 of them have to be infinitesimal and they're a bit different than the remaining 10 dimensions. From some perspectives, F-theory is more geometrical and higher-dimensional than M-theory; from others, it's the other way around. This discussion is similar to the question whether mothers or fathers are more fundamental. There's no unique answer. After all, it's not just an analogy because M-theory stands for Mother while F-theory stands for Father. M-theory compactified on a circle easily produces type IIA string theory; F-theory is a toolkit to construct sophisticated nonperturbative type IIB string vacua.)
Technical: Speed up your MathJax $\rm\LaTeX$ by a second per page, at least in Windows. Download these zipped OTF fonts, unzip them, and for each of the 22 OTF files, right-click Properties/General and "unblock". Then choose all the 22 OTF files and install them. It will display the same maths you're used from the web, but using your local copy of the fonts. (These are not STIX fonts which I consider uglier but the very same fonts you're used to.) Warning: the local $\rm \TeX$ fonts may produce imperfect output when applied by Internet Explorer to pages with Greek letters. You should learn how to uninstall the MathJax fonts, too.
This text has been proofread once and quickly.
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https://www.physicsforums.com/threads/review-q-3.430933/
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# Homework Help: Review Q #3
1. Sep 21, 2010
### TeenieWeenie
Problem solved! Thanks again Thaakisfox!
1. The problem statement, all variables and given/known data
A ball thrown horizontally at 2.2 m/s from the roof of a building lands 36 m from the base of the building. Calculate the height of the building.
Vox = 2.2 m/s
Xo = 0m
Vx = 0 m/s
X = 36m
2. Relevant equations
y = Vosin ao - (0.5)(g)(t^2)
3. The attempt at a solution
I tried plugging it in but then I have a missing time...?
Last edited: Sep 21, 2010
2. Sep 21, 2010
### Thaakisfox
This is a horizontal projection hence you dont need any sine etc. Just calculate the time of descent from the velocity and horizontal displacement by dividing them. And then the vertical component is simple freefall.
3. Sep 21, 2010
### TeenieWeenie
I'm kinda confused.
What formula would I use then?
x=Vo *CosAo * t
4. Sep 21, 2010
### Thaakisfox
No. It is a horizontal projection. You dont need any of those sine or cosine function.
You throw the ball with horizontal velocity Vo. Since it has no acceleration in the horizontal direction, the distance it travels is simply: x=Vo*t where x is given (the distance from the base of the building). from here you can get t. Now in the vertical plane it is just simple freefall, so use the formula which gives the distance when freefall takes place
5. Sep 21, 2010
### TeenieWeenie
36 m = 2.2 m/s * t
36/2.2 s = t
16.36 s = t
Formula for free fall: h(t) = Vo*t + 1/2 at^2
h(16.36) = 0*t + (0.5)(-9.8m/s^2)(16.36^2)
= -1311.48304 m ?
I think something went wrong... :(
6. Sep 21, 2010
### Thaakisfox
The calculation is correct. The given data seem insensible.
7. Sep 21, 2010
### TeenieWeenie
Insensible?
8. Sep 21, 2010
### Thaakisfox
That happens many times in textbooks, that the given data for a problem dont make sense. For example there probably arent many buildings taller than 1km, and especially someone throwing a ball off.
But your calculation is correct. (That minus sign doesnt matter, it just means that you took the y axis to point upwards, and thats why the acceleration has a negative sign. But you are searching for the absolute value of the height anyway, so just take that minus sign away.)
9. Sep 21, 2010
### TeenieWeenie
Oh! Good observation.
Problem solved! Thanks again Thaakisfox!
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https://brilliant.org/problems/ita-falling-ball/
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# Ball Falling On Inclined Ramp
From a resting state, a small ball falls vertically on an inclined ramp of angle $\theta$, in respect to the horizontal, resulting in several elastic collisions.
If $d$ is the initial vertical distance from the ball to the ramp, find the distance between the $n^{\text{th}}$ point of collision and the first point of collision in a function of $d$, $n$ and $\theta.$
This question appeared on ITA's 2014 Physics Paper, and is inspired by a question from Saraeva's book "Problemas Selecionados de Fisica Elementar".
×
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https://jira.lsstcorp.org/browse/DM-28860
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# Refactoring the configuration service of the Qserv Replication/Ingest system
XMLWordPrintable
#### Details
• Type: Improvement
• Status: Done
• Resolution: Done
• Fix Version/s: None
• Component/s:
• Labels:
None
• Story Points:
1
• Sprint:
DB_S21_12
• Team:
Data Access and Database
# Motivations
The present design of the Configuration service is quite complex. There are 5 classes (and a few hundred methods) in the core of the service:
================== +-------------> ConfigurationIFace | ================== | ^ ^ | | | | has +----------+ +----------+ | | | | ============= ================= +-- Configuration ConfigurationBase ============= ================= : public API ^ ^ | | +------+ +-------+ | | ================ ================== ConfigurationMap ConfigurationMySQL ================ ================== : unit testing : used at NCSA : and Kubernetes
The second issue is a distributed state of the transient configuration that's spread in between static data members of class Configuration and member data of class ConfigurationBase.
The third issue is related to how the default values of the parameters are stored and used. In the present implementation there are ~50 static members of class ConfigurationBase representing the defaults. The defaults are separate from the target variables (where the current state of the corresponding configuration parameters are stored).
All together, this makes it quite cumbersome to add new configuration parameters, or modify existing ones.
There is also a new requirement in the Replication/Ingest system that would be hard to address within the present paradigm of the service - serializing the state of the configuration and sending it over-the-wire protocol from the Master Controller to the Replication/Ingest workers.
## The proposed migration plan
The proposal is modeled after a similar effort made in a context of DM-26754.
To address the above stated issues, the following refactoring is proposed:
• Flatten the hierarchy of the existing classes into a single class Configuration.
• Keep the named methods as they are now to avoid modifying the dependent code.
• Implement the transient state as a single object of class nlohmann::json::object.
• Set defaults as initial value of the transient object. The defaults will be amended when the corresponding "external" source of the configuration will be used to set up the new state.
• Implements a few forms of the configuration construction from the following sources:
• MySQL (will require a connection string mysql://<user>:<password>@<host>:<port>/<database>).
• Transient JSON object.
• A JSON-formatted text file.
This approach will benefit from the existing features of the nlohmann::json library, such as: serialization/de-serialization into/from a string, json path capability.
Besides, the new implementation of the service won't affect existing code relying upon the configuration. Existing unit tests should also work. Though, they will need to be migrated from relying upon the "key-values" maps for setting the tested object state to use a transient JSON object.
#### Activity
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Andy Salnikov added a comment -
I have reviewed the PR but I did not approve it, so I 'm not marking this ticket as reviewed yet. We should probably talk about what needs to be done for schema migration and few other issues that I commeneted on.
Show
Andy Salnikov added a comment - I have reviewed the PR but I did not approve it, so I 'm not marking this ticket as reviewed yet. We should probably talk about what needs to be done for schema migration and few other issues that I commeneted on.
Hide
Igor Gaponenko added a comment - - edited
Andy Salnikov Please, have another look at the PR. I've reviewed all suggestions, answered your questions on the design decisions, and implemented most of what was requested. Specifically, the following major changes were made to the code:
• The built-in schema management was killed in anticipation that an appropriate schema migration mechanism will be implemented in the new Qserv containers. When it'll be ready, the code of the module will quickly adopt the mechanism as soon as we will switch to using the new containers and the build system. In the meantime, two SQL files were reintroduced into the package: the schema definition file and the initialization file for the default values of the general parameters. I should say I don't like the second file since what it does duplicates what's done in the JSON schema definition of class ConfigurationSchema. However, with no access to the schema from the transient code, this duplication is unavoidable. With my original attempt to put all schema operations into the code, I was hoping to avoid this and other related problems. I still think the built-in "smart" schema management approach is better than what's presently done in Qserv with the "external" schema management.
• The AKA "integration" test (better be called the "diagnostic" test for the MySQL backend) moved into a separate application qserv-replica-config-test.
• The use of JSON has been reduced to the general parameters only. Complex (object) definitions of workers, database families, and databases are now stored as traditional statically types structures/objects within class Configuration.
• Parsing of parameters from JSON or MySQL sources has been made scalable (nearly everything is driven by the transient JSON schema in class ConfigurationSchema). After that new general parameters would only need to be added to the schema definition (and, unfortunately, since I killed the built-in MySQL schema support, within an external SQL file) and into the unit tests.
• The class Configuration has been reduced by moving classes WorkerInfo, DatabaseFamilyInfo, and DatabaseInfo into dedicated files.
• The parser classes moved from file Configuration.cc into dedicated files: ConfigParserJSON and ConfigParserSQL. They were also refactored to avoid explicitly mentioning the names of the general parameters. Parsing of those is now completely driven by the transient schema definition.
Typos and spellings were corrected. I'm not sure why my VSCode setup didn't see them, even though I have the spelling checker installed. It sees some, but not others.
For sure more improvements could be made to the code to make it "perfect". However (and honestly) this won't worth additional efforts. What I have here covers all (but the one I killed) my needs.
UPDATED: I've realized that with the JSON-based transient schema (that also provides default values) there is no longer any need in preloading the defaults from an external SQL file. So, I'm removing the one from the module:
core/modules/replica/schema/replication_default_config.sql
Should any site/deployment-specific customization be needed, those would/should be done using a specialized configuration, that would presumably be in a separate Git package.
Thank you!
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Andy Salnikov added a comment -
Looks OK, few comments on PR.
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Andy Salnikov added a comment - Looks OK, few comments on PR.
#### People
Assignee:
Igor Gaponenko
Reporter:
Igor Gaponenko
Reviewers:
Andy Salnikov
Watchers:
Andy Salnikov, Fritz Mueller, Igor Gaponenko, Nate Pease
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https://www.gregschool.org/new-blog-20/2017/8/30/capacitance
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# Capacitance
The capacitance of a system (represented by $$C$$) is a measure of how efficient and quickly that system accumulates an amount of charge $$Q$$ and is defined as
$$C≡\frac{Q}{ΔV_{ab}}.\tag{1}$$
If we're charging a capacitor by an amount $$Q$$, the voltage $$ΔV_{ab}=\frac{ΔU}{q}$$ measures how much potential energy is transferred to the capacitor every time an amount of charge $$q$$ is transferred from one conductor in the capacitor to another. In Equation (1), $$Q$$ is the total amount of charge that gets stored in the capacitor.
(Let's, for arguments sake, just assume for the moment that the capacitor is charged to the amount $$Q=q$$.) Now, the important thing to know is that the capacitance $$C$$ is a number that we measure which only depends on the type of material comprising the conductors and the insulator of the capacitor. The value of $$C$$ does not depend on $$Q$$ or $$ΔV_{ab}$$. So, if $$C$$ has say a small value ($$C=\text{'small value'}$$) then if we charged the capacitor by an amount $$Q+q$$, then the amount of energy (or, to be more precise, the amount of electric potential energy) $$ΔV_{ab}=\frac{ΔU}{q}=ΔU=\frac{q}{C}=\frac{q}{text{'small value'}}$$ stored in the capacitor is large. If the capacitor is, however, made out of material for which $$C=\text{'big value'}$$, then if we charged the capacitor to an amount $$Q=q$$ the total energy $$ΔV_{ab}=\frac{q}{\text{'big value'}}=ΔU$$ stored in the capacitor would be small. So, in a certain sense, the capacitance of a capacitor can be viewed as how efficiently energy is transferred to the capacitor as you charge it. Capacitors for which the capacitance is lower accumulates energy faster and morre efficiently as you charge it up, whereas capacitors with a higher capacitance assumulates energy much slower and less efficiently as you charge it.
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https://cran.r-project.org/web/packages/modeval/vignettes/modeval.html
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# An introduction to the ‘modeval’ package
## Overview
Package modeval is designed to assist novice to intermediate analysts in choosing an optimal classification model, particularly for working with relatively small data sets. It provides cross-validated results comparing several different models at once using a consistent set of performance metrics, so users can hone in on the most promising approach rather than attempting single model fittings at a time. The package pre-defined 12 most common classification models, although users are free to select from the 200+ other options available in caret package. In total, these models have been proven to address a wide range of classification challenges. Pre-defined models are as follows:
#### Linear
• Generalized Linear Model (glm)
• Linear Discriminant Analysis (lda)
• Bayesian functions for generalized linear modeling (bayesglm)
#### Nonlinear
• K-nearest Neighbors (knn)
• Neural Networks (nnet)
#### Support Vector Machines
• Support Vector Machines with Linear Kernel (svmLinear)
• Support Vector Machines with Class Weights (svmRadialWeights)
#### Tree-based
• Random Forests (rf)
• CART (rpart)
• Bagged CART (treebag)
## Motivation
There are many different modeling options in R and each has particular syntax for model training and/or prediction. At the same time, model fit structures are also different, so it is challenging to consolidate results and efficiently compare performance between models. The caret package provides a uniform interface for more than 200 regression and classification models; modeval was largely built on that platform, and is intended to be an easier, simpler entry into solving classification problems.
Presented with a classification problem, one of the first questions facing an analyst is, what kinds of models should I try? With hundreds of options available, it is daunting to work through enough models and confidently pick the one that best suits a particular dataset and classification objective. So, analysts tend to rely on models that are familiar and easy to use, which may not necessarily yield the best possible result. modeval automates model evaluation and enables comparison of performance with minimal user manipulation.
Analysts may also enter into classification model fitting with assumptions of data normality and class balance, which can each threaten their ability to achieve a good result. This package includes automated checks and recommendations for transforming and subsampling data to address issues of non-normality and class imbalance, respectively.
## Capabilities
Following are some of the key features of modeval:
• Evaluate the normality of the predictor variables by calculating skew and kurtosis. The user is provided guidance regarding whether data tranformation is advised, and how well each of three tranformation options (Box-Cox, Yeo-Johnson, or PCA) does in reducing non-normality as compared to each other and the original, untransformed data set. Users can also compare the goodness of model fits based on transformed and untransformed data.
• Check required packages and automatically install needed packages.
• Check whether each function supports a two-class classification problem and ignore it if it doesn’t support it.
• Check if each function supports class probability and exclude it from performance comparision if it doesn’t support it.
• Functions supporting class probability also produce accuracy and Kappa metrics alongside Area Under the Curve (AUC). We can compare performance of those models that don’t support class probability.
• Determine if each function supports a function to evaluate variable importance and exclude it from variable importance comparision if it doesn’t.
• Provide the user with several subsampling options to address issues of class imbalance. Options include down-sampling, up-sampling, SMOTE, and ROSE, which are described below as parameters in function add_model.
## Examples
Below, several brief examples are included to demonstrate the workflow and general utility of modeval.
### Prepare or import dataset
Here we draw a sample from a data set called “PimaIndiansDiabetes,” which is embedded in R package mlbench and can also be downloaded from the University of California-Irvine’s Machine Learning Repository. Included are 8 predictor variables referencing various health characteristics and one outcome class variable indicating either a positive or negative test for diabetes.
library(modeval)
library(mlbench)
data(PimaIndiansDiabetes)
index <- sample(seq_len(nrow(PimaIndiansDiabetes)), 500)
trainingSet <- PimaIndiansDiabetes[index, ]
testSet <- PimaIndiansDiabetes[-index, ]
x <- trainingSet[, -9]
y <- trainingSet[, 9]
x_test <- testSet[, -9]
y_test <- testSet[, 9]
### Function suggest_transformation
One of the first things an analyst will want to do is inspect the data set to understand the characteristics of all the variables, including the distributions of the predictor variables and the prevalence of each class outcome.
Two common challenges with classifcation problems are: (1) significant non-normality in one or more variables, and (2) class imbalance. modeval not only automates checking for both issues, but also guides the user to select a remedy, if appropriate.
In the example below, we use the suggest_tranformation function to check for non-normality (skew and kurtosis), and view the results of applying three data transformations. (Options for addressing class imbalance are presented within function add_model, specifically the sampling parameter.)
suggest_transformation(x)
##
## Consider transforming data if skew or kurtosis of any variable is > 2 or < -2
##
## BoxCox : The distribution of an attribute can be shifted to reduce the skew and make it more Gaussian.
##
## Yeo-Johnson : Like the Box-Cox transform, but it supports raw values that are equal to zero and negative.
##
## PCA : Transform the data to the principal components.
Four plots are generated, each displaying the skewness (x-axis) and kurtosis (y-axis) of the predictor variables. The first plot presents the untransformed data, while the others demonstrate the impact on skew and kurtosis of applying three well-established tranformation approaches. Each is labled with a tag that can be applied in the add_model function described below, should the user wish to use one of the tranformations. The four plots:
• The untransformed data set.
• tf1 applies a Box-Cox transformation, which shifts the distribution to be more Gaussian.
• tf2 applies a Yeo-Johnson transformation, which is similar to Box-Cox but supports raw values that can be zero or negative.
• tf3 applies a Principal Components tranformation to ensure that variables are uncorrelated.
Skew and kurtosis values of >2 and <-2 are generally considered problematic, and each plot helps the user visually inspect the extent to which variables are outside those values, and thus transformation may be useful. First, a shaded square between -2 and +2 is presented. And second, variable points are colored red, blue, or purple if skew, kurtosis, or both are outside the boundaries, respectively.
In the above example, we see that all three transformation options reduce skew and kurtosis but only tf2 (Yeo-Johnson) gets all variables inside the desired boundaries.
### Function add_model
With add_model, users can conduct model training and add each model fit to the summary list. The function will check that the model and data supports classification. If model supports class probability, then the best model is choosen based on AUC. If model doesnt support class probabilities, the best model is choosen based on accuracy. Ten-fold cross validation is used by default.
In the example below, we specify four models. Although modeval supports 12 models, the user can use additional models if they choose, as long as they are supported in caret. Here, one of those non-native models, qrnn, is excluded from training because it only applicable to regression models, and the other, rpartScore will only produce Accuracy and Kappa metrics as it doesn’t support class probability prediction.
sSummary is a list of model fits and each model fit is named. The code below allows us to see the current contents of sSummary as defined above.
sSummary <- list() # empty list where we store model fit results
models = c("glm", "qrnn", "lda", "rpartScore") # create a character vector with function names
sSummary <- add_model(sSummary, x, y, models)
##
## Model: rpartScore
## >> Accuracy and Kappa metrics are available.
## >> Best model is selected based on accuracy.
##
##
## Model: glm, lda
## >> ROC, Sens, Spec, Accuracy and Kappa metrics are available.
## >> Best model is selected based on AUC.
##
##
## Model: qrnn
## >> Model(s) not support classification problem.
##
names(sSummary)
## [1] "glm" "lda" "rpartScore"
#### Arguments in add_model
• addTo - Summary list that will contain all model fit results. In our examples we use sSummary
• model - A vector of model names to train.
• x and y - A dataframe of input and output variables, respectively.
• tuneLength - The maximum number of tuning parameter combinations as generated by random search. Default = 5L.
• modelTag - A charactor value of tag that to be added to model name. Default = NULL.
• tf - A single charactor value for transformation options (see suggest_transformation). Default = NULL.
• sampling - A single character value to pass caret::trainControl. This handles subsampling, which can be desirable in cases of class imbalance. Default = NULL, which is the same as “none”. Values are as follows:
• “none” (No subsampling conducted)
• “down” (Down-sampling to randomly subset all classes such that class frequencies match the least prevalent class)
• “up” (Up-sampling to randomly sample (with replacement) the least prevalent class such that it becomes the same size as the majority class)
• “smote” (Generating new observations by randomly selecting points on the line connecting the rare class observation to one of its nearest neighbors in the feature space)
• “rose” (A smoothed bootstrapping approach that generates new samples from the feature space around the rare class observation)
Note that SMOTE and ROSE require the DMwR and ROSE packages, respectively.
#### Further Examples
Adding more models is easy. Simply run the add_model function. Here are a few examples:
sSummary <- add_model(sSummary, x, y, c("knn", "nnet", "qda"), modelTag = "Nonlinear", tf="tf2")
sSummary <- add_model(sSummary, x, y, c("rf", "rpart", "treebag"), modelTag = "TreeBased", sampling = "down")
sSummary <- add_model(sSummary, x, y, c("svmLinear", "svmRadial", "svmPoly"), modelTag = "svmFamily")
names(sSummary)
## [1] "glm" "lda" "rpartScore"
## [4] "knn_tf2_Nonlinear" "nnet_tf2_Nonlinear" "qda_tf2_Nonlinear"
## [7] "rf_TreeBased" "rpart_TreeBased" "treebag_TreeBased"
## [10] "svmLinear_svmFamily" "svmRadial_svmFamily" "svmPoly_svmFamily"
In this case, we notice that each model fit is labeled “modelname_modelTag.” The modelTag will be useful when we want to visualize results by the four main categories provided in this package (linear, nonlinear, tree-based, support vector machines).
### Evaluate results with functions suggest_auc and suggest_accuracy
Users can easily visualize performance with a single line of code and have the option of viewing average training time for a single tuning. Options with and without time are presented below.
suggest_auc(sSummary)
suggest_auc(sSummary, time = TRUE)
If a user wishes to select specific models to compare, they can leverage modelTag. Once modelTag is added, it only includes the model fits that includes modelTag in the name.
suggest_auc(sSummary, time = TRUE, "TreeBased")
Users can also indicate model names to grep the models for comparison. The following code grabs any model fits that include “glm” or “Tree.”
suggest_auc(sSummary, time = TRUE, "glm|Tree")
Users interested in visualizing accuracy and Kappa metrics can use the function suggest_accuracy, which uses the same syntax and arguments as suggest_auc above. As with suggest_auc, time=TRUE will generate a training time chart. Here’s an example:
suggest_accuracy(sSummary, "glm|Tree")
### Identify best-performing categories with suggest_category
With this function, users can get better understanding of caracteristics of each prediction model family. Users may also want to use modelTag to limit visualization to certain models. Example:
suggest_category(sSummary, "nnet|knn|rf")
### Explore variable performance with function suggest_variable
Some classification and regression models produce variable and importance indices based on their own algorithms. Weights and priorities are not always comparable across different model types, so average or median value from differnet models is not always useful and may be misleading. However, observing and comparing variable importance results can be very useful because we can check which variables are consistantly important across different models and which aren’t. This helps the analyst develop a deeper level of understanding of the caracteristic of each model and the problem itself. Users may wish to use tag to extract the models for comparison.
suggest_variable(sSummary)
suggest_variable(sSummary, "TreeBased")
## Compare performance with class probability
### Add prediction function with test dataset using function add_prob
To be able to use functions suggest_probPop, suggest_probCut and suggest_gain, users will need to add prediction functions with the test dataset suing the add_prob function. Using our sample data set, class probability predictions of a positive diabetes test (“pos”) are generated using x_test and y_test.
sSummary <- add_prob(sSummary, x_test, y_test, "pos")
## Calculating prediction: glm
## Calculating prediction: lda
## Calculating prediction: knn_tf2_Nonlinear
## Calculating prediction: nnet_tf2_Nonlinear
## Calculating prediction: qda_tf2_Nonlinear
## Calculating prediction: rf_TreeBased
## Calculating prediction: rpart_TreeBased
## Calculating prediction: treebag_TreeBased
## Calculating prediction: svmLinear_svmFamily
## Calculating prediction: svmPoly_svmFamily
### Explore population distribution and probability cuts with functions suggest_variable and suggest_probCut
While AUC demonstrates overall performance, sometimes analysts will be more interested in a specific area. By observing density distribution by population and by probability cut-off, we can more clearly understand each model’s predictive performance as well as similarities and differences between models.
suggest_probPop(sSummary, "pos")
suggest_probPop(sSummary, "pos", modelTag = "Tree")
suggest_probCut(sSummary, "pos")
suggest_probCut(sSummary, "pos", modelTag = "Tree")
### Visualize Gain and Lift with Function suggest_gain
Gain and Lift charts are widely used for marketing purposes. They indicate the effectiveness of predictive models compared to the results obtained without the predictive model. With modeval, users can create Gain, Lift, Accumulated Event Percent, and Event Percent for each population bucket.
suggest_gain(sSummary, "pos", modelTag = "Tree")
suggest_gain(sSummary, "pos", type = "Gain")
suggest_gain(sSummary, "pos", type = "Lift")
suggest_gain(sSummary, "pos", type = "PctAcc")
suggest_gain(sSummary, "pos", type = "Pct")
suggest_gain(sSummary, "pos", type = "Gain", modelTag = "Tree")
When single plots are created using the “type” argument, users can adjust the plot by adding ggplot2 syntax. In this example, we adjust the x-axis limit.
suggest_gain(sSummary, "pos", type = "Gain") + xlim(0, 0.5)
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|
https://www.elitedigitalstudy.com/11252/dihydrogen-gas-used-in-habers-process-is-produced-by-reacting-methane-from-natural-gas-with-high-temperature
|
Dihydrogen gas used in Haber’s process is produced by reacting methane from natural gas with high-temperature steam. The first stage of two-stage reaction involves the formation of CO and H2. In second stage, CO formed in first stage is reacted with more steam in water gas shift reaction,
$$CO(g)+H_{2}O(g) ⇌ CO_{2}(g)+H_{2}(g)$$
If a reaction vessel at 400°C is charged with an equimolar mixture of CO and steam such that Pco=PH2O= 4.0 bar, what will be the partial pressure of H2 at equilibrium? Kp= 10.1 at 400°C
Asked by Abhisek | 1 year ago | 116
##### Solution :-
Let the partial pressure of both carbon dioxide and hydrogen gas be p. The given reaction is:
CO(g) + H2O ⇌ CO2(g) + H2(g)
Initial conc. 4.0 bar 4.0 bar 0 0
At equilibrium 4.0-p 4.0-p p p
Given Kp = 10.1
So, partial pressure of His 3.04 bar at equilibrium.
Answered by Pragya Singh | 1 year ago
### Related Questions
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The concentration of sulphide ion in 0.1M HCl solution saturated with hydrogen sulphide is 1.0 × 10–19 M. If 10 mL of this is added to 5 mL of 0.04M solution of the following: FeSO4, MnCl2, ZnCl2 and CdCl2 . in which of these solutions precipitation will take place?
#### What is the minimum volume of water required to dissolve 1g of calcium sulphate at 298 K?
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#### What is the maximum concentration of equimolar solutions of ferrous sulphate and sodium sulphide
What is the maximum concentration of equimolar solutions of ferrous sulphate and sodium sulphide so that when mixed in equal volumes, there is no precipitation of iron sulphide? (For iron sulphide, Ksp = 6.3 × 10–18).
|
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http://www-old.newton.ac.uk/programmes/MLC/seminars/2013010910001.html
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# MLC
## Seminar
### On the cubic instability in the Q-tensor theory of nematics
Zarnescu, A (University of Sussex)
Wednesday 09 January 2013, 10:00-10:40
Seminar Room 1, Newton Institute
#### Abstract
Symmetry considerations, as well as compatibility with the Oseen-Frank theory, require the presence of a cubic term (involving spatial derivatives) in the Q-tensor energy functional used for describing variationally the nematics. However the presence of the cubic term makes the energy functional unbounded from below.
We propose a dynamical approach for addressing this issue, namely to consider the L^2 gradient flow generated by the energy functional and show that the energy is dynamically bounded, namely if one starts with a bounded, suitable, energy then the energy stays bounded in time. We discuss notions of suitability which are related to the preservation of a physical constraint on the eigenvalues of the Q-tensors (without using the Ball-Majumdar singular potential).
This is joint work with G. Iyer and X. Xu (Carnegie-Mellon).
#### Video
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
|
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http://reluctanthacker.rollett.org/content/setting-nagios3-send-prowl-notifications
|
# Setting up nagios3 to send prowl notifications
Updated 27.i.2010 to reflect mig5’s corrections
I spent a few minutes today setting up our nagios install at work to page me via prowl, instead of an email->sms gateway. Why? Because I’m cheap, that’s why - don’t like paying for any more texts than I must. I ran into a few gotchas, so I thought I would briefly document the process.
sudo mkdir -p /usr/local/bin
sudo wget -O /usr/local/bin/prowl.pl <a href="http://prowl.weks.net/static/prowl.pl
sudo">http://prowl.weks.net/static/prowl.pl
sudo</a> chmod +x /usr/local/bin/prowl.pl
Next, you will have to install the Crypt::SSLeay and LWP::UserAgent library for perl, so it can access https URLs.
# If you're running debian/ubuntu
sudo apt-get update; sudo apt-get install libcrypt-ssleay-perl liblwp-useragent-determined-perl
# otherwise find a package for your distro, or run:
# sudo cpan install Crypt::SSLeay
# sudo cpan install LWP::UserAgent
Now, try it out to be sure it works:
/usr/local/bin/prowl.pl -apikey='yourAPIkeyHere' -application='prowl.pl' -event='test' -notification='mic check 1 2'
You should get a ‘Notification successfully posted.’ message. (and a popup on your phone, of course!) If the script isn’t working, you’ll have to figure out the reason, because nagios depends on it.
Once you’ve ironed all that out, it’s time to configure nagios!
First, you need to set up your contact information. Edit whichever file you keep your contacts in, and modify an existing record, or add a new one, similar to this:
define contact{
_prowl_apikey yourAPIkeyGoesHere
}
It is very important that you leave the underscore in front of the _prowl_apikey variable, as Nagios’ custom variables depend on it.
Next, you’ll need to add the custom prowl notification commands. Edit the appropriate file, and add these commands:
define command{
command_name notify-host-by-prowl
command_line /usr/bin/perl -w /usr/local/bin/prowl.pl -apikey="$_CONTACTPROWL_APIKEY$" -priority=1 -application="Nagios" -event="Host" -notification="$HOSTNAME$ $HOSTDESC$ '$HOSTOUTPUT$'"
}
define command{
command_name notify-service-by-prowl
command_line /usr/bin/perl -w /usr/local/bin/prowl.pl -apikey="$_CONTACTPROWL_APIKEY$" -priority=1 -application="Nagios" -event="Service" -notification="$HOSTNAME$ $SERVICEDESC$ '$SERVICEOUTPUT$'"
}
If your perl binary doesn’t live in /usr/bin, be sure to give the correct path. (run ‘which perl’ to find this out if you don’t know) If you try to run the prowl.pl script directly, (without using the system perl binary) nagios uses its own perl interpreter, and you’ll get an error similar to this in the nagios logs:
*ePN failed to compile /usr/local/bin/prowl.pl: "Missing right curly or square bracket at (eval 1) line 95, at end of line syntax error at (eval 1) line 102, at EOF"
If you have any trouble, check the nagios debug logs, (you may need to turn up the nagios debug level) and try to run the command it’s producing as the nagios user.
Just a quick note…
I wanted to let you know this guide helped me a bunch when setting up Nagios to prowl. I was linked here from iNag (which is also an awesome app!)
Thanks for sharing! Rob
Just in the middle of setting up the same thing. Thanks for your excellent guide.
Just thought I’d note that if you’re on Debian/Ubuntu, you’ll also need to apt-get install liblwp-useragent-determined-perl if you haven’t got it already, or else Perl will die with this error:
Can't locate LWP/UserAgent.pm in @INC (@INC contains: /etc/perl /usr/local/lib/perl/5.10.0 /usr/local/share/perl/5.10.0 /usr/lib/perl5 /usr/share/perl5 /usr/lib/perl/5.10 /usr/share/perl/5.10 /usr/local/lib/site_perl .) at /usr/local/bin/prowl.pl line 33. BEGIN failed--compilation aborted at /usr/local/bin/prowl.pl line 33.
Sorry, just nitpicking..
Your host command definition in the example is using $SERVICEDESC$ ‘$SERVICEOUTPUT$’ instead of $HOSTDESC$ $HOSTOUTPUT$, these would result in empty variables in the prowl message.
Also the path to your prowl.pl in the command definitions is /usr/local/nagios3/libexec, but previously we wget it to /usr/local/bin
Otherwise, great! Thanks again.
I recently installed the notify by prowl code. I can get the test message through the linux console but, when i run it through nagios it does not work. any ideas? Here is the command verbage.
# ‘notify-host-by-prowl’ command definition
define command{ command_name notify-host-by-prowl command_line /usr/bin/perl -w /usr/local/bin/prowl.pl -apikey=”$_CONTACTPROWL_APIKEY$” -priority=1 -application=”Nagios” -event=”Host” -notification=”$HOSTNAME$ $HOSTDESC$ ‘$HOSTOUTPUT$’” }
# ‘notify-service-by-prowl’ command definition
define command{ command_name notify-service-by-prowl command_line /usr/bin/perl -w /usr/local/bin/prowl.pl -apikey=”$_CONTACTPROWL_APIKEY$” -priority=1 -application=”Nagios” -event=”Service” -notification=”$HOSTNAME$ $SERVICEDESC$ ‘$SERVICEOUTPUT$’” }
Hi! Thanks for this. Rocks on my system. Query about an improvement (that might not be possible).
Prowl on my iPhone let’s me quiet it during nights unless I get an “emergency”. I know I cant priority to 2 and get that. But is it possible, somehow, to set priority based on severity from Nagios?
Ie. Warning = Priority 1, Info = Priority 0, Critical = Priority 2.. If it is possible somehow.. I’d love it. Why? Because I don’t need to run to my computer if it’s a warning or information - only when theres an emergency..
glad it’s working for you! I can think of two ways to accomplish this - the first would be to write a wrapper script that sets the priority based on the input, and call that instead. The second is what I do - I use nagios escalations so that only the truly critical notifications get sent directly to my phone, and deal with the rest via email.
good luck!
thanks! works like a charm!
Awesome post, works great. But I am cheap and lazy (well too busy to edit cfg in vi every time I add a host)
Do you have any idea on how to incorporate prowl into Opsview ? I have tried but for the life of me, the cfg for Opsview is no where near Nagios, or Icinga or Monarch. I have gotten as far as finding where I should put the config for the custom notification, but actually getting it to work is another story.
Cheers for the help.
W
1. define contact{
|
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|
http://mathhelpforum.com/calculus/33296-particular-inegral.html
|
1. ## Particular Inegral
$m\frac {d^2x}{dt^2} + 5kx = -mgsin\alpha + 11kl_0
$
I am trying to find the general solution.
Setting
$\omega^2=\frac{k}{m}$, I found $x_c$ to be:
$x(t) = A~cos \left ( \sqrt 5 \omega t + \phi \right )
$
I have no idea how to find $x_p$...
What trial solution would you suggest using?
2. Hello,
You can consider that x is a constant. Thus its second derivate will be null and you'll have an equation with xp
I hope for you it's true that $\omega^2=\frac{5k}{m}$, because this is something i can't do ^^
3. I am totally new at this... I still have no idea.
I divided the original equation through by $m$ to get:
$\frac {d^2x}{dt^2} + 5\omega^2 x = -gsin\alpha + 11\omega^2 l_0$
am i getting any closer?
4. I really don't know for xc... I don't remember the rules for general solution ! If you're not sure, derivate again to see if you get xc so that xc is solution of d²xc/dt²+5w²xc=0
However, for xp :
xp is a particular solution. Let X be a constant satisfying the equation.
The second derivate of X is 0.
We have $5kX = -mgsin\alpha + 11kl_0$
-> $X=x_p=\frac{-mgsin\alpha + 11kl_0}{k}$
5. I don't get it. Where did the 5 go?
I did this:
$
m\frac {d^2x}{dt^2} + 5kx = -mgsin\alpha + 11kl_0
$
$
\frac {d^2x}{dt^2} + 5\omega^2 x = -gsin\alpha + 11\omega^2 l_0
$
$
\frac{d^2x}{dt^2} + 5\omega^2 x = \omega^2 (11l_0-\frac{mg}{k}sin\alpha)
$
$
x_p=\frac{1}{5}(11l_0-\frac{mg}{k}sin\alpha)
$
How's that? Anyone? Anyone?
6. Am sorry, i forgot the 5...
7. So we pretty much have the same answer. Thanks for the help!
8. Originally Posted by billym
I don't get it. Where did the 5 go?
I did this:
$
m\frac {d^2x}{dt^2} + 5kx = -mgsin\alpha + 11kl_0
$
$
\frac {d^2x}{dt^2} + 5\omega^2 x = -gsin\alpha + 11\omega^2 l_0
$
$
\frac{d^2x}{dt^2} + 5\omega^2 x = \omega^2 (11l_0-\frac{mg}{k}sin\alpha)
$
$
x_p=\frac{1}{5}(11l_0-\frac{mg}{k}sin\alpha)
$
How's that? Anyone? Anyone?
Relax guy. Be vague.
Moo dropped a 5. It was a simple error, easily spotted. As you did. If you understand what Moo was doing to get the particular solution, then all's well. So go back, put the 5 in where it's meant to go. There's the answer.
Life's full of small mistakes, most easily spotted and corrected for. The world keeps turning. Don't have cow, man.
9. Don't have cow, man.
Moo
Thanks for explaining it more precisely than i did ^^
10. I really wasn't having a cow man! I seriously wasn't sure if she dropped the 5 on purpose or not. This site feels like I'm doing my homework with God, so I just assume everyone else is right.
11. Originally Posted by billym
I really wasn't having a cow man! I seriously wasn't sure if she dropped the 5 on purpose or not. This site feels like I'm doing my homework with God, so I just assume everyone else is right.
Not at all, we're all equal in front of maths
errare humanum est
Btw, what does "have a cow" means ? ^^'
12. He was likening my concern over your missing 5 to the ordeal of giving birth to a cow.
|
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|
http://mathoverflow.net/questions/15370/tools-for-the-langlands-program/15388
|
# Tools for the Langlands Program?
Hi,
I know this might be a bit vague, but I was wondering what are the hypothetical tools necessary to solve the Langlands conjectures (the original statments or the "geometic" analogue). What I mean by this is the following: for the Weil Conjectures it became clear that, in order to prove them, one needed to develop a marvelous cohomology theory that would explain Weil's observations. Of course, we all know that etale cohomology is that marvelous tool. By analogy, what "black box" tools are necessary for the Langlands program? Broadly speaking what tools do we need for the Langlands program?
-
This question is too broad in my opinion. I'm sure there are good papers giving an overview of the Langlands program. I know that Mitya Boyarchenko and David Ben Zvi have some stuff about geometric Langlands that might help you get up to speed. – Harry Gindi Feb 15 '10 at 21:37
– Harry Gindi Feb 15 '10 at 21:39
No, I mean, it's a really really huge program. I think that any satisfying answer to this question either doesn't exist or could take tens if not hundreds of pages. – Harry Gindi Feb 15 '10 at 21:55
If you check out either of the links I gave you, you'll see just how much stuff is actually being used. – Harry Gindi Feb 15 '10 at 21:56
Here is my vague, limited and non-geometric understanding. There is not a black box theory whose existence would prove the conjectures of Langlands as there was with the Weil conjectures. However, one general strategy is to use the Arthur-Selberg trace formula on two different reductive groups, match up the geometric sides of the formula (as much as possible), and then use the spectral sides to relate the automorphic forms of the groups. There are several technical difficulties in getting this to work in general, with a major problem having been the Fundamental Lemma, finally resolved by Ngo. – Zavosh Feb 15 '10 at 22:53
There are all sorts of problems with the Langlands conjectures that we (as far as I know) have no idea at all how to approach. As a very simple example of an issue for $GL(2)$ over $\mathbf{Q}$ that we cannot do, consider this: there should be a canonical bijection between continuous even (i.e. det(complex conj)=+1) irreducible 2-dimensional representations $Gal(\overline{\mathbf{Q}}/\mathbf{Q})\to GL(2,\mathbf{C})$ and normalised algebraic cuspidal Maass new eigenforms on the upper half plane. This is a sort of non-holomorphic analogue of the Deligne-Serre theorem which relates the odd irreducible Galois representations to holomorphic weight 1 newforms. One way of nailing this bijection is that given a Maass newform, then for all primes $p$ not dividing the level, the eigenvalue of $T_p$ (suitably normalised) should be the trace of the representation evaluated at the Frobenius element in the Galois group.
You want a black box which will solve all of Langlands---then you need a black box which will solve this. Unfortunately it seems to me that firstly you'll need several good new ideas to resolve even this simple case, and secondly there is more than one strategy and it's not clear what will work first. As examples of the problems one faces: given the Galois representation, that's just a lump of algebra---a finite amount of data. However is one going to construct a bunch of analysis from it?? One way might be via the theory of base change, which works a treat for cyclic extensions, and just enough has been developed in order to resolve the problem for Galois representations with solvable image (one uses a lot more than the statement that the group is solvable---one uses that it is also "small"---this is not just a formal consequence of cyclic base change). This is the Langlands-Tunnell theorem, which gives the Maass form from the Galois representation if it has solvable image. In the non-solvable case one can dream of non-solvable base change, but non-solvable base change is really nothing but a dream at this point. So there's one big black box but that will only resolve one direction of one small fragment of the Langlands conjectures.
Now what about the other way? Well here we're even more in the dark. Given an algebraic Maass form, we can't even prove that its Hecke eigenvalues are algebraic numbers, let alone the sum of two roots of unity. In the holomorphic modular form case we can get bases of the spaces of forms using e.g. coherent cohomology of the modular curve considered as an algebraic curve over $\mathbf{Q}$, or (in weights 2 or more) singular cohomology of a (typically non-trivial) local system on the curve. Both these machines produce $\mathbf{Q}$-vector spaces with Hecke actions, and hence char polys are in $\mathbf{Q}[x]$ and so eigenvalues are algebraic. But with algebraic Maass forms we have no such luxury. They are not cohomological, so we can't expect to see them in singular cohomology of a local system, and they are not holomorphic, so we can't expect to see them in coherent cohomology either. So we, vaguely speaking, need a black box which, given certain finite-dimensional complex vector spaces with Hecke actions, produces finite-dimensional $\mathbf{Q}$-vector spaces out of thin air, which when tensored up to the complexes give us back our groups. People have tried using base change to do this, or other known instances of functoriality, but everything so far has failed and it's not clear to me that one even has a conjectural approach for doing this direction. And I'm only talking about proving that the eigenvalues are algebraic---not even coming close to attaching the Galois representation!
So one vague black box "non-abelian base change", and one hard problem that as far as I know no-one has ideas about, and, if you put these together, you would solve one teeny tiny insy winsy little part of the Langlands programme. Makes the Weil conjectures look like a walk in the park!
-
"Makes the Weil conjectures look like a walk in the park!" - This was exactly my point in my comment. That's why it's called the Langlands program rather than the Langlands conjecture(s). – Harry Gindi Feb 16 '10 at 0:10
Hey! We're making progress. It used to be called the Langlands philosopy. [Oops, this was meant to be a comment on fpqc's comment.] – JS Milne Feb 16 '10 at 0:44
+1 Just because why not. Wasn't it called the "philosophy of cusp forms" even before that? – Harry Gindi Feb 16 '10 at 0:52
I thought that the reason it's called the Langlands Programme rather than the Langlands conjectures was that actually many of the statements are quite vague, or come in several forms, so it's difficult to say really what is conjectured and what is just a good motivating idea. For example transfer of automorphic reps via a morphism of L-groups should obey local Langlands everywhere, but local Langlands is a bit vague: "there should be a canonical bijection..." and there are issues of strong mult 1 and so on. The true force is in the most powerful statements but these are typically ill-defined. – Kevin Buzzard Feb 16 '10 at 9:03
[grr I want to make longer comments!]. For example the existence of the global Langlands group is a conjecture that, it seems to me, is almost unfalsifiable. Langlands makes some conjecture in Corvallis of the form "this set (iso classes of reps of GL_n(adeles) for all n at once) should have the structure of a Tannakian category in some natural way" for example. Is that really a conjecture or just a really good idea? – Kevin Buzzard Feb 16 '10 at 9:05
This answer deals with the classical Langlands program (if you like, the Langlands program for number fields).
There are (at least) two aspects to this program:
(a) functoriality: this is Langlands original conjecture, explained in the letter to Weil, and further developed in "Problems in the theory of automorphic forms" and later writing. It is a conjecture purely about automorphic forms. Langlands has outlined an approach to proving it in general is his papers on the topic of "Beyond endoscopy" (available online at his collected works).
A proof of functoriality would imply, among other things, the non-solvable base-change discussed in Kevin's answer.
It seems that for the "beyond endoscopy" program to work as Langlands envisages it, one would need unknown (and seemingly out of reach) results in the analytic number theory of $L$-functions.
(b) reciprocity: this is the conjectured relationship between automorphic forms and Galois representations/motives. It has two steps: attaching Galois representations, or even motives, to (certain) automorphic forms, and, conversely, showing that all Galois representations of motives arise in this way. (This converse direction typically incorporates the Fontaine--Mazur conjecture as well, which posits a purely Galois-theoretic criterion for when a Galois representation should arise from a motive.)
If one is given the direction automorphic to Galois, then there are some techniques for deducing the converse direction, namely the Taylor--Wiles method. However this method is not a machine that automatically applies whenever one has the automorphic to Galois direction available; in particular, it doesn't seem to apply in any straightforward way to Galois representations/motives for which some $h^{p,q}$ is greater than 1 (in more Galois-theoretic terms, which have irregular Hodge--Tate weights). Thus in particular, even if one could attach Galois representations to (certain) Maass forms, one would still have the problem of proving that every even 2-dimensional Artin representation of $G_{\mathbb Q}$ arose in this way.
As to constructing Galois representations attached to automorphic forms, here the idea is to use Shimura varieties, and one can hope that, with the fundamental lemma now proved, one will be able to get a pretty comprehensive description of the Galois representations that appear in the cohomology of Shimura varieties. (Here one will also be able to take advantage of recent progress in the understanding of integral models of Shimura varieties, due to people like Harris and Taylor, Mantovan, Shin, Morel, and Kisin, in various different contexts.)
The overarching problem here is that, not only do not all automorphic forms contribute to cohomology (e.g. Maass forms, as discussed in Kevin's answer), but also, not all automorphic forms appear in any Shimura variety context at all. Since Shimura varieties are currently the only game in town for passing from automorphic forms to Galois representations, people are thinking a lot about how to move from any given context to a Shimura variety context, by applying functoriality (e.g. Taylor's construction of Galois reps. attached to certain cuspforms on $GL_2$ of a quadratic imaginary field), or trying to develop new ideas such as $p$-adic functoriality. While there are certainly ideas here, and one can hope for some progress, the questions seem to be hard, and there is no one black box that will solve everything.
In particular, one could imagine having functoriality as a black box, and asking if one can then derive reciprocity. (Think of the way that Langlands--Tunnell played a crucial role in the proof of modularity of elliptic curves.) Langlands has asked this on various occasions. The answer doesn't seem to be any kind of easy yes.
-
I happened to come across this paper yesterday, but haven't been able to read it because of the prohibitive price. You may access this article for 1 day for US$12.00. Ash, Avner; Gross, Robert Generalized non-abelian reciprocity laws: a context for Wiles' proof. Bull. London Math. Soc. 32 (2000), no. 4, 385--397. – Chandan Singh Dalawat Feb 16 '10 at 4:02 if you google for the title, the second link gives you the pdf file. The authors expanded on this in their book "fearless symmetry", btw. – Franz Lemmermeyer Feb 16 '10 at 8:33 For me it was the first search result. Vielen Dank. – Chandan Singh Dalawat Feb 16 '10 at 14:11 I don't know a whole lot about the Langlands program, but if there is one tool that seems to come up a lot in geometric Langlands, it's perverse sheaves. You see a lot of singular algebraic varieties in geometric Langlands, and perverse sheaves are meant as a singular generalization of a vector bundle with a flat connection. Ordinary sheaves are already a singular generalization of vector bundles, but not the relevant one. Perverse sheaves (which are made from sheaves but not sheaves themselves) are a more apropos generalization that incorporates and sort-of just is intersection (co)homology. I can also say that I wasn't going to learn about perverse sheaves until I had to. However, I have now seen several important papers, in the related categorification program, that read this way: "Perverse sheaves + necessary restrictions = a good solution". So now I might be slowly getting used to them. I can also see that even the formalism perverse sheaves or intersection homology is sort-of inevitable. In some of the simpler constructions, the varieties (over$\mathbb{C}$, say) are non-singular and certain answers arise as ordinary cohomology products or intersection products. For instance, the Schubert calculus in a Grassmannian manifold. What choice do you have if the Grassmannian is replaced by a singular variety$X$? For some of these categorification/Langlands questions, you can either propose wrong answers, or ad hoc answers, or you can automatically get the right answer by using intersection homology on$X\$. (With middle perversity, as they say.)
-
Intersection cohomology (either l-adic or Betti or Hodge) also plays a central role in the cohomological study of non-compact Shimura variety and the application of trace formula methods, see e.g Zucker's conjecture or Sophie Morel's PhD thesis. But I don't really see why this is a feature of the Langlands program, rather than a by-product of the fact that many interestingly singular varieties pop up in compactifications of moduli problems. – Simon Pepin Lehalleur Aug 8 '10 at 19:49
|
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|
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