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http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/sylow-fractals
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# Sylow Fractals
by Ben Brewster (Binghamton University) and Michael B. Ward (Bucknell University)
Mathematics Magazine
December, 1995
Subject classification(s): Groups
Applicable Course(s): 4.2 Mod Algebra I & II
An analogy is used to relate the Sylow $$p$$-subgroups of $$S_{p^n}$$ and the symmetric group on the numbers $$1$$ through $$p^n$$.
A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.
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https://math.stackexchange.com/questions/4175914/why-1n-1-fracn3n-1-is-divergent/4175919
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# Why $(-1)^{n-1} \frac{n}{3n + 1}$ is divergent?
I am wondering the reason $$(-1)^{n-1} \frac{n}{3n + 1}$$ is divergent although the limit of $$\frac{n}{3n + 1}$$ is $$1/3.$$
Any explanation will be greatly appreciated!
• @DonThousand: The sequence can't converge since the limit is not $0$ and it does not have an ultimately constant sign. Jun 17, 2021 at 20:48
• A sequence is divergent if it doesn't converge. Since $n/(3n+1)$ converges to $1/3$, your sequence looks like $1/3,-1/3,1/3,-1/3,...$, which is osscilating.
– pax
Jun 17, 2021 at 20:49
Let $$a_n = (-1)^{n-1} \frac{n}{3n+1}$$. Then $$a_{2n} = -\frac{2n}{6n+1}$$ and $$a_{2n+1} = \frac{2n+1}{6n+4}$$. Observe that $$\lim_{n\to \infty}a_{2n} = -\frac{1}{3} \qquad \lim_{n\to \infty}a_{2n+1} = \frac{1}{3}$$
Since the limits along two subsequences differ, then $$a_n$$ diverges.
• Hi, what is the criterium that have you used? At this moment I have forgotten it. +1 Jun 17, 2021 at 21:00
• @Sebastiano If $x_n \to a$ , then any subsequence satisfies $x_{n_k} \to a$. If the conclusion does not hold for a sequence, by contrapositive it must be that the parent sequence does not converge. Jun 17, 2021 at 21:01
• Thank you very much for your collaboration....thank you again. Jun 17, 2021 at 21:04
Consider two subsequences of the given sequence, viz. the even subsequence, and the odd subsequence.
• For even $$n$$, we may write $$n=2k$$ for $$k\in\mathbb{N}$$. Then we have : $$\lim_{n\to\infty}(-1)^{n-1} \frac{n}{3n + 1} = \lim_{k\to\infty}(-1)^{2k-1} \frac{2k}{6k + 1} = -\lim_{k\to\infty} \frac{1}{3 + \frac{1}{2k}} = -\frac{1}{3}$$
• For odd $$n$$, we may write $$n=2k+1$$ for $$k\in\mathbb{N}$$. Then we have : $$\lim_{n\to\infty}(-1)^{n-1} \frac{n}{3n + 1} = \lim_{k\to\infty}(-1)^{2k+1-1} \frac{2k+1}{6k + 3 + 1} = \lim_{k\to\infty} \frac{1}{3 + \frac{1}{2k+1}} = \frac{1}{3}$$
So, the odd and the even subsequences of the original sequence converge to two different limit points. Thus, the sequence is not convergent.
Convergence implies that there exists a singular limit to the sequence, which itself requires that for all $$\epsilon > 0$$, there exists an $$N \in \mathbb{N}$$ such that $$|a_n - a| < \epsilon, \quad \forall n \geq N.$$ This convergence condition does not hold true for the sequence $$a_n = \frac{(-1)^{n-1}n}{3n+1}$$ purely due to its oscillatory nature and the fact that its limit when the $$(-1)^n$$ is removed, is nonzero.
Since the sequence $$\frac{n}{3n+1}$$ converges to a nonzero value, convergence of $$(-1)^n\frac{n}{3n+1}$$ would imply convergence of $$(-1)^n.$$ However, this sequence is known to be divergent.
Suppose a limit $$L$$ exists.
Case $$1$$: $$L\ge 0$$. Then for all $$\epsilon > 0$$, there is some $$N\in\mathbb N$$ such that for all $$n\ge N$$
$$|a_n-L|<\epsilon.$$
Choose $$\epsilon = 1/5$$, and find such an $$N$$ as above. Then as $$n=2N > N$$ we must have $$|a_{2N}-L|<1/5$$ or
$$-1/5 < L-1/5 < -\dfrac{N}{3N+1}=a_{2N} < L+1/5$$
but $$a_{2N}=-\dfrac{N}{3N+1} <-\dfrac{N}{3N+N} = -\dfrac{N}{4N} = -\dfrac{1}{4} \not > -\dfrac{1}{5}$$.
Case $$2$$: $$L<0$$. Apply similar thinking.
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https://www.tutorialspoint.com/What-are-Self-Invoking-Anonymous-Functions-in-JavaScript
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# What are Self-Invoking Anonymous Functions in JavaScript?
In JavaScript, the functions wrapped with parenthesis are called “Immediately Invoked Function Expressions" or "Self Executing Functions.
The purpose of wrapping is to the namespace and control the visibility of member functions. It wraps the code inside a function scope and decreases clashing with other libraries. This is what we call Immediately Invoked Function Expression (IIFE) or Self Executing Anonymous Function.
## Syntax
Here’s the syntax −
(function() {
// code
})();
As you can see above, the following pair of parentheses converts the code inside the parentheses into an expression −
function(){...}
In addition, the next pair, i.e. the second pair of parentheses continues the operation. It calls the function, which resulted from the expression above.
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http://www.maplesoft.com/support/help/Maple/view.aspx?path=Ore_algebra/Ore_to_diff
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Ore_algebra - Maple Programming Help
Home : Support : Online Help : Mathematics : Algebra : Skew Polynomials : Ore Algebra : Ore_algebra/Ore_to_diff
Ore_algebra
Ore_to_diff
convert a differential operator to a differential equation
Ore_to_shift
convert a shift operator to a recurrence equation
Ore_to_DESol
convert a differential operator to a DESol structure
Ore_to_RESol
convert a shift operator to an RESol structure
Calling Sequence Ore_to_diff(G, f, A) Ore_to_diff(G, f, A, 'D') Ore_to_shift(G, u, A) Ore_to_shift(G, u, A, 'indexed') Ore_to_DESol(P, f, A) Ore_to_RESol(P, u, A)
Parameters
G - list of operators of the Ore algebra A P - operator of the Ore algebra A f - expression denoting a mathematical function A - Ore algebra table
Description
• The Ore_to_diff command converts a differential operator or a list of differential operators of the skew algebra A into a differential equation or a list of differential equations in the function f. The output is expressed in terms of the diff function by default, or in terms of the D function when the optional parameter is set.
• The Ore_to_DESol command converts a single differential operator of the skew algebra A into a DESol structure in the function f.
• The Ore_to_shift command converts a shift operator or a list of shift operators of the skew algebra A into a recurrence equation or a list of recurrence equations in the sequence u. The output is expressed in functional notation ( $u\left(n\right),...$ ) by default, or in the indexed notation ( ${u}_{n},...$ ) when the optional argument is set.
• The Ore_to_RESol command converts a single recurrence operator of the skew algebra A into an RESol structure in the sequence u.
Examples
> $\mathrm{with}\left(\mathrm{Ore_algebra}\right):$
Differential case.
> $A≔\mathrm{diff_algebra}\left(\left[\mathrm{Dx},x\right],\left[\mathrm{comm},\mathrm{μ}\right]\right):$
> $P≔{x}^{2}{\mathrm{Dx}}^{2}+x\mathrm{Dx}+{x}^{2}-{\mathrm{μ}}^{2}:$
> $\mathrm{Ore_to_diff}\left(P,f,A\right)$
${{x}}^{{2}}{}\left(\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}{}{f}{}\left({x}\right)\right){+}{x}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}{}{f}{}\left({x}\right)\right){+}\left({-}{{\mathrm{μ}}}^{{2}}{+}{{x}}^{{2}}\right){}{f}{}\left({x}\right)$ (1)
> $\mathrm{Ore_to_diff}\left(P,f,A,\mathrm{D}\right)$
${{x}}^{{2}}{}{{\mathrm{D}}}^{\left({2}\right)}{}\left({f}\right){}\left({x}\right){+}{x}{}{\mathrm{D}}{}\left({f}\right){}\left({x}\right){+}\left({-}{{\mathrm{μ}}}^{{2}}{+}{{x}}^{{2}}\right){}{f}{}\left({x}\right)$ (2)
> $\mathrm{Ore_to_DESol}\left(P,f,A\right)$
${\mathrm{DESol}}{}\left(\left\{{{x}}^{{2}}{}\left(\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}{}{f}{}\left({x}\right)\right){+}{x}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}{}{f}{}\left({x}\right)\right){+}\left({-}{{\mathrm{μ}}}^{{2}}{+}{{x}}^{{2}}\right){}{f}{}\left({x}\right)\right\}{,}\left\{{f}{}\left({x}\right)\right\}\right)$ (3)
> $\mathrm{normal}\left(\mathrm{applyopr}\left(P,,A\right)\right)$
${0}$ (4)
Euler case.
> $A≔\mathrm{skew_algebra}\left(\mathrm{euler}=\left[\mathrm{Tx},x\right],\mathrm{comm}=\mathrm{μ}\right):$
> $P≔{\mathrm{Tx}}^{2}+{x}^{2}-{\mathrm{μ}}^{2}:$
> $\mathrm{Ore_to_diff}\left(P,f,A\right)$
${x}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}{}{f}{}\left({x}\right){+}{x}{}\left(\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{x}}^{{2}}}{}{f}{}\left({x}\right)\right)\right){+}\left({-}{{\mathrm{μ}}}^{{2}}{+}{{x}}^{{2}}\right){}{f}{}\left({x}\right)$ (5)
Recurrence case.
> $A≔\mathrm{shift_algebra}\left(\left[\mathrm{Sn},n\right],\left[\mathrm{comm},\mathrm{α}\right]\right):$
> $P≔{\mathrm{Sn}}^{2}+\mathrm{α}\mathrm{Sn}+1:$
> $\mathrm{Ore_to_shift}\left(P,u,A\right)$
${u}{}\left({n}{+}{2}\right){+}{\mathrm{α}}{}{u}{}\left({n}{+}{1}\right){+}{u}{}\left({n}\right)$ (6)
> $\mathrm{Ore_to_shift}\left(P,u,A,\mathrm{indexed}\right)$
${\mathrm{α}}{}{{u}}_{{n}{+}{1}}{+}{{u}}_{{n}}{+}{{u}}_{{n}{+}{2}}$ (7)
> $\mathrm{Ore_to_RESol}\left(P,u,A\right)$
${\mathrm{RESol}}{}\left(\left\{{u}{}\left({n}{+}{2}\right){+}{\mathrm{α}}{}{u}{}\left({n}{+}{1}\right){+}{u}{}\left({n}\right){=}{0}\right\}{,}\left\{{u}{}\left({n}\right)\right\}{,}\left\{{u}{}\left({0}\right){=}{u}{}\left({0}\right){,}{u}{}\left({1}\right){=}{u}{}\left({1}\right)\right\}{,}{\mathrm{INFO}}\right)$ (8)
Multivariate differential case.
> $A≔\mathrm{diff_algebra}\left(\left[\mathrm{Dx},x\right],\left[\mathrm{Dy},y\right],\left[\mathrm{comm},\mathrm{μ}\right]\right):$
> $G≔\left[-2\mathrm{Dx}x+\mathrm{Dy}y,-4\left(\mathrm{μ}-x{y}^{2}\right)\left(\mathrm{μ}+x{y}^{2}\right)+2\mathrm{Dx}x+{y}^{2}{\mathrm{Dy}}^{2},-2\left(\mathrm{μ}-x{y}^{2}\right)\left(\mathrm{μ}+x{y}^{2}\right)+\mathrm{Dy}\mathrm{Dx}yx,-\left(\mathrm{μ}-x{y}^{2}\right)\left(\mathrm{μ}+x{y}^{2}\right)+\mathrm{Dx}x+{\mathrm{Dx}}^{2}{x}^{2}\right]:$
These are operators for BesselJ(mu,x*y^2).
> $\mathrm{Ore_to_diff}\left(G,f,A\right)$
$\left[{-}{2}{}{x}{}\left(\frac{{\partial }}{{\partial }{x}}{}{f}{}\left({x}{,}{y}\right)\right){+}{y}{}\left(\frac{{\partial }}{{\partial }{y}}{}{f}{}\left({x}{,}{y}\right)\right){,}{-}{4}{}\left({-}{x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}\left({x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}{f}{}\left({x}{,}{y}\right){+}{{y}}^{{2}}{}\left(\frac{{{\partial }}^{{2}}}{{\partial }{{y}}^{{2}}}{}{f}{}\left({x}{,}{y}\right)\right){+}{2}{}{x}{}\left(\frac{{\partial }}{{\partial }{x}}{}{f}{}\left({x}{,}{y}\right)\right){,}{-}{2}{}\left({-}{x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}\left({x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}{f}{}\left({x}{,}{y}\right){+}{y}{}{x}{}\left(\frac{{{\partial }}^{{2}}}{{\partial }{y}{}{\partial }{x}}{}{f}{}\left({x}{,}{y}\right)\right){,}{-}\left({-}{x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}\left({x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}{f}{}\left({x}{,}{y}\right){+}{x}{}\left(\frac{{\partial }}{{\partial }{x}}{}{f}{}\left({x}{,}{y}\right)\right){+}{{x}}^{{2}}{}\left(\frac{{{\partial }}^{{2}}}{{\partial }{{x}}^{{2}}}{}{f}{}\left({x}{,}{y}\right)\right)\right]$ (9)
> $\mathrm{Ore_to_diff}\left(G,f,A,\mathrm{D}\right)$
$\left[{-}{2}{}{x}{}{\mathrm{D}}{[}{1}{]}{}\left({f}\right){}\left({x}{,}{y}\right){+}{y}{}{\mathrm{D}}{[}{2}{]}{}\left({f}\right){}\left({x}{,}{y}\right){,}{-}{4}{}\left({-}{x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}\left({x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}{f}{}\left({x}{,}{y}\right){+}{{y}}^{{2}}{}{\mathrm{D}}{[}{2}{,}{2}{]}{}\left({f}\right){}\left({x}{,}{y}\right){+}{2}{}{x}{}{\mathrm{D}}{[}{1}{]}{}\left({f}\right){}\left({x}{,}{y}\right){,}{-}{2}{}\left({-}{x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}\left({x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}{f}{}\left({x}{,}{y}\right){+}{y}{}{x}{}{\mathrm{D}}{[}{1}{,}{2}{]}{}\left({f}\right){}\left({x}{,}{y}\right){,}{-}\left({-}{x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}\left({x}{}{{y}}^{{2}}{+}{\mathrm{μ}}\right){}{f}{}\left({x}{,}{y}\right){+}{x}{}{\mathrm{D}}{[}{1}{]}{}\left({f}\right){}\left({x}{,}{y}\right){+}{{x}}^{{2}}{}{\mathrm{D}}{[}{1}{,}{1}{]}{}\left({f}\right){}\left({x}{,}{y}\right)\right]$ (10)
No conversion is available to a multivariate DESol.
> $\mathrm{Ore_to_DESol}\left(G,f,A\right)$
|
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https://en.m.wikipedia.org/wiki/One-repetition_maximum
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# One-repetition maximum
One-repetition maximum (one rep maximum or 1RM) in weight training is the maximum amount of weight that a person can possibly lift for one repetition. It may also be considered as the maximum amount of force that can be generated in one maximal contraction.[1] One repetition maximum can be used for determining an individual's maximum strength and is the method for determining the winner in events such as powerlifting and weightlifting competitions. One repetition maximum can also be used as an upper limit, in order to determine the desired "load" for an exercise (as a percentage of the 1RM).
## Calculating 1RM
This chart compares the different formulas
The 1RM can either be calculated directly using maximal testing or indirectly using submaximal estimation. The submaximal estimation method is preferred as it is safer, quicker, and less unnerving for inexperienced exercisers;[2] however, it may underestimate the actual 1RM.[3] One rep maximum calculators are used to predict a one rep maximum lift. The degree of accuracy can vary largely depending on the weight training experience and muscular composition of the athlete. Also, most one rep maximum calculators are designed for seasoned strength trainers, and those with little experience may find their actual one rep maximum is much lower because their nervous system cannot handle the stress of a high weight. This test should be performed with a spotter for reasons of safety.
Weight training protocols often use 1RM when programming to ensure the exerciser reaches resistance overload, especially when the exercise objective is muscular strength, endurance or hypertrophy. By understanding the maximal potential of the muscle, it is possible to reach resistance overload by increasing the number of repetitions for an exercise.
Determining the 1 rep max can be done directly through trial and error and simply requires the exerciser to complete one full repetition with the maximum weight. There are several common formulas used to estimate 1RM using the submaximal method, the Epley and the Brzycki being the most common.[4] In the formulas below, ${\displaystyle r}$ is the number of repetitions performed and ${\displaystyle w}$ is the amount of weight used (note that ${\displaystyle w}$ is a factor of each formula, so the unit of measurement doesn't matter).
### Epley formula
${\displaystyle 1{\text{ RM}}=w\left(1+{\frac {r}{30}}\right),}$ assuming ${\displaystyle r>1.}$ [5]
### Brzycki
This version of the one rep maximum calculation is often referred to as the Brzycki Formula after its creator, Matt Brzycki,[6] and can be written either in terms
${\displaystyle 1{\text{ RM}}=w\cdot {\frac {36}{37-r}}={\frac {w}{{\frac {37}{36}}-{\frac {1}{36}}r}}\approx {\frac {w}{1.0278-0.0278r}}}$
Formula 1 (Epley) and formula 2 (Brzycki) return identical results for 10 repetitions. However, for fewer than 10 reps, formula 1 returns a slightly higher estimated maximum. For example, if a person can lift 100 pounds on a given exercise for 10 reps, the estimated one rep max would be 133 pounds for both formulae. However, if the person were to complete only 6 reps, then formula 1 would estimate a one rep maximum of approximately 120 pounds, while formula 2 would return an estimate of approximately 116 pounds.
These types of calculations may not always produce accurate results, but can be used as starting points. The weight can then be changed as needed to perform the number of reps called for by the training protocol.
Several more complex formulae have been proposed which use different coefficients for different rep numbers and sometimes even for different exercises.[7]
### McGlothin
${\displaystyle 1{\text{ RM}}={\frac {100w}{101.3-2.67123r}}}$
### Lombardi
${\displaystyle 1{\text{ RM}}=wr^{0.10}}$
### Mayhew et al.
${\displaystyle 1{\text{ RM}}={\frac {100w}{52.2+41.9e^{-0.055r}}}}$
### O'Conner et al.
${\displaystyle 1{\text{ RM}}=w\left(1+{\frac {r}{40}}\right)}$
### Wathen
${\displaystyle 1{\text{ RM}}={\frac {100w}{48.80+53.8e^{-0.075r}}}}$
## References
1. ^ Marchese, Rosemary; Hill, Andrew (2011). The essential guide to fitness: for the fitness instructor. Sydney, NSW: Pearson Australia. p. 135. ISBN 9781442510203.
2. ^ Marchese, Rosemary; Hill, Andrew (2011). The essential guide to fitness: for the fitness instructor. Sydney, NSW: Pearson Australia. pp. 158–159. ISBN 9781442510203.
3. ^ Knutzen, Kathleen; Brilla, Lorraine; Caine, Dennis (August 1999). "Validity of 1RM Prediction Equations for Older Adults". The Journal of Strength & Conditioning Research. p. Vol 13, Issue 3, Page 242–246. Retrieved 11 July 2014.
4. ^ Calculate your One Rep Max (1RM).
5. ^ Epley, Boyd (1985). "Poundage Chart". Boyd Epley Workout. Lincoln, NE: Body Enterprises. p. 86.
6. ^ Brzycki, Matt (1998). A Practical Approach To Strength Training. McGraw-Hill. ISBN 978-1-57028-018-4.
7. ^ LeSuer, Dale A.; McCormick, James H.; Mayhew, Jerry L.; Wasserstein, Ronald L.; Arnold, Michael D. (November 1997). "The Accuracy of Prediction Equations for Estimating 1-RM Performance in the Bench Press, Squat, and Deadlift". Journal of Strength and Conditioning Research. 11 (4): 211–213. doi:10.1519/00124278-199711000-00001. S2CID 144001941.
• Lesuer, DA, Mccormick, JH, Mayhew, JL; et al. (1997). "The accuracy of prediction equations for estimating 1-RM performance in the bench press, squat, and deadlift". J Strength Cond Res. 11: 211–213.{{cite journal}}: CS1 maint: multiple names: authors list (link)
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https://www.physicsforums.com/threads/logic-gate-xor-and-xnor.263261/
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# Logic gate XOR and XNOR
1. Oct 10, 2008
### speck
I want to simplfy M'(A'B'C+ABC')+M(AB'C'+A'BC) to as simple a circuit as possible.
I don't know the boolean algebra to simplfy the ABC terms. Help please, Speck
2. Oct 10, 2008
### rootX
Tried K-maps?
From quick Venn inspection of (A'B'C+ABC') and (AB'C'+A'BC), I don't think you can simplify them further using AND, OR, NOT only
3. Oct 10, 2008
### speck
K-map is how I initial got the Eq. , right, it won't simplify with AND, OR, NOT. I want to use XOR with XNOR gates. I would really like it to simplify to something like (AB Oplus C) using XOR, but it does not. Thks, Speck
4. Oct 12, 2008
### speck
Does anyone think that the (A'B'C+ABC') part of the Eq. will reduce to (A Oplus B Oplus C)?
5. Oct 12, 2008
### Phrak
By simple, do you mean the least number of packages? It's trivial with a single PLA, but you'd need a burner...
Last edited: Oct 12, 2008
6. Oct 13, 2008
### rootX
I tried to put it into XOR/XNOR but I really couldn't find any way.
P.S. (I learned this stuff few weeks ago, so all I know is that there should be checkboard pattern)
Now that I said that I realized that there is infact a pattern and it is easier to isolate it when you look at it. You gotta approach it differently.
See K-Map When A = 0 and C = 1
A = 1 C = 0
I get something like
A!C!(B XOR M) + A!C (M XOR B)
So far, I look at K-Map and try to isolate 2 literal K-Maps that look like XOR and "and" it with conditions like A = 1 and C = 0 .. It works so far
Last edited: Oct 13, 2008
7. Nov 15, 2008
### Enthalpy
Another PLA-type cheater's answer: use a multiplexer. Input ABCM as the addresses, hardwire the 16 inputs to 1 or 0 to synthetise the desired logic function. The 4067 is such a 16-to-1 mux-demux and seems to be still relatively common (hey, I just feel younger!). One single package, no programming needed.
For a non-cheater answer, you'll have to wait a bit more. M and B have similar roles, as do A and C, so combining these pairs first could bring something.
Last edited: Nov 15, 2008
8. Nov 15, 2008
### Enthalpy
(A xnor C) nor (B xor M)
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https://xianblog.wordpress.com/tag/la-recherche/
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## the ABC conjecture
Posted in Books, University life with tags , , , , on November 27, 2012 by xi'an
Both Pour la Science and La Recherche, two French science magazines, had an entry this month on the abc conjecture! However, ABC being a common accronym, it is alas unrelated with my research theme. The abc conjecture is a number theory conjecture that states that if a and b are integers with no common factor and a small number of prime dividers, this does not hold for c=a+b. This is the abc triplet. (More precisely, the conjecture states that the quality of the triplet abc:
$q(a,b,c) = \log c / \log \text{rad}(abc)$
is larger than 1+ε for a finite number of triplets abc.) A proof of the conjecture by Shinichi Mochizuki was recently proposed, hence the excitment in the community. In La Recherche, I read that this conjecture is associated with an interesting computing challenge, namely to find the exhaustive collection of triplets with a quality more than a given bound 1+ε.
## genetics
Posted in Books, Kids, Travel, University life with tags , , , , , , , , , , on April 9, 2012 by xi'an
Today, I was reading in the science leaflet of Le Monde about a new magnitude in sequencing cancerous tumors (wrong link, I know…). This made me wonder whether the sequence of (hundreds of) mutations leading from a normal cell to a cancerous one could be reconstituted in the way a genealogy is. (This reminds me of another exciting genetic article I read in the Eurostar back from London on Thursday, in the Economist, about the colonization of Madagascar by 30 women from the Malay archipelago: “The island was one of the last places on Earth to be settled, receiving its earliest migrants in the middle of the first millennium AD…“)
As a double coincidence, I was reading La Recherche yesterday in the métro to Dauphine, which central theme this month is about heredity beyond genetics. (Double because this also connected with the meeting in London.) The keyword is epigenetics, namely the activation or inactivation of a gene and the hereditary transmission of this character w/o a genetic mutation. This is quite interesting as it implies the hereditability of some adopted traits, i.e. forces one to reconsider the nature versus nurture debate. (This sentence is another input due to Galton!) It also implies that a much faster rate of species differentiation due to environmental changes (than the purely genetic one) is possible, which may sound promising in the light of the fast climate changes we are currently facing. However, what I do not understand is why the journal included a paper on the consequences of epigenetics on the Darwinian theory of evolution and… intelligent design. Indeed, I do not see why the inclusion of different vectors in the hereditary process would contradict Darwin’s notion of natural selection. Or even why considering a scientific modification or replacement of the current Darwinian theory of evolution would be an issue. Charles Darwin wrote his book in 1859, prior to the start of genetics, and the immense advances made since then led to modifications and adjustments from his original views. Without involving any irrational belief in the process.
## 2012, Turing year
Posted in R, Statistics, University life with tags , , , , , , on January 3, 2012 by xi'an
Buying the special issue of La Recherche on “La révolution des mathématiques”, I discovered that this is the Alan Turing Year in celebration of the 100th anniversary of Turing‘s birth. The math department at the University of Leeds has a webpage on all the events connected with this celebration. From all over the World. (There is even a Turing relay in Cambridge, unfortunately it is not open to the general public… Unless you are attending the Isaac Newton Institute at the time.) Quite fitting a tribute. (Given Turing’s contributions to Bayesian analysis, as depicted e.g. in the theory that would not die, ISBA could have included a special session in the ISBA 2012 meeting in Kyoto. I will certainly dedicate the session I co-organise there on parallel computing to his memory.)
## How quickly does randomness appear?
Posted in Statistics, University life with tags , , , , , , , , on November 10, 2011 by xi'an
This was the [slightly off-key] title of the math column in the November issue of La Recherche, in any case intriguing enough for me to buy this general public science magazine on the metro platform and to read it immediately while waiting for an uncertain train, thanks to the nth strike of the year on my train line… But this was the occasion for an exposition of the Metropolis algorithm in a general public journal! The column actually originated from a recently published paper by Persi Diaconis, Gilles Lebeaux, and Laurent Michel, Geometric analysis for the Metropolis algorithm on Lipschitz domain, in Inventiones Mathematicae [one of the top pure math journals]. The column in La Recherche described the Metropolis algorithm (labelled there a random walk on Markov chains!), alluded to the use of MCMC methods in statistics, told the genesis of the paper [namely the long-term invitation of Persi Diaconis in Nice a few years ago] and briefly explained the convergence result, namely the convergence of the Metropolis algorithm to the stationary measure at a geometric rate, with an application to the non-overlapping balls problem.
If you take a look at the paper, you will see it is a beautiful piece of mathematics, establishing a spectral gap on the Markov operator associated with the Metropolis algorithm and deducing a uniformly geometric convergence [in total variation] for most regular-and-bounded-support distributions. A far from trivial and fairly general result. La Recherche however fails to mention the whole corpus of MCMC convergence results obtained in the 1990’s and 2000’s, by many authors, incl. Richard Tweedie, Gareth Roberts, Jeff Rosenthal, Eric Moulines, Gersende Fort, Randal Douc, Kerrie Mengersen, and others…
## Robin Ryder’s interview
Posted in Statistics, University life with tags , , , , on March 9, 2011 by xi'an
Robin Ryder—with whom I am sharing an office at CREST, and who is currently doing a postdoc on ABC methods—, got interviewed in the March issue of La Recherche. (The interviewer was Philippe Pajot who wrote “Parcours de mathématiciens”, reviewed in a recent post.) The interview is reproduced on Robin’s blog (in French) and gives in a few words the principles of Bayesian linguistics. This two-page interview also includes a few lines of a technical entry to MCMC (called Monte Carlo Markov chains rather than Markov chain Monte Carlo) that focus on the exploration of huge state-spaces associated with trees. Overall, a very good advertising for MCMC methods for the general public through the highly attractive story of the history of languages…
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http://mathhelpforum.com/number-theory/43856-modulo-proof.html
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Math Help - Modulo proof
1. Modulo proof
Let n E Z. and supposed that 5 does not divide n. Prove that n^4 is congruent to 1 mod 5.
2. Originally Posted by kel1487
Let n E Z. and supposed that 5 does not divide n. Prove that n^4 is congruent to 1 mod 5.
Nothing fancy here. For example,
$n \equiv 1~\text{ (mod 5)}$
so
$n^4 \equiv (1)^4 \equiv 1~\text{ (mod 5)}$
Similarly for $n \equiv 2~\text{ (mod 5)}$
$n^4 \equiv (2)^4 \equiv 16 \equiv 1~\text{ (mod 5)}$
etc.
-Dan
3. Thanks!! I was thinking too much into it!!
4. If n is not divisible by 5, then one of $n+1$, $n-1$, $n+2$, $n-2$ must be divisible by 5.
Hence the product $(n+1)(n-1)(n+2)(n-2)=(n^2-1)(n^2-4)$ must be divisible by 5.
Note however that $n^2-4\equiv n^2+1\pmod{5}$.
Hence $(n^2-1)(n^2+1)=n^4-1$ is divisible by 5; in other words $n^4\equiv1\pmod{5}$.
In general, Fermat's little theorem states that if p is prime and p does not divide n, then $n^{p-1}\equiv1\pmod{p}$.
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https://www.preprints.org/manuscript/201804.0137/v1
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Preprint Article Version 1 This version is not peer-reviewed
# The ECL Optimization and Experiment of HSPMSM with Improved Method
Version 1 : Received: 9 April 2018 / Approved: 11 April 2018 / Online: 11 April 2018 (05:45:35 CEST)
How to cite: Liu, X. The ECL Optimization and Experiment of HSPMSM with Improved Method. Preprints 2018, 2018040137 (doi: 10.20944/preprints201804.0137.v1). Liu, X. The ECL Optimization and Experiment of HSPMSM with Improved Method. Preprints 2018, 2018040137 (doi: 10.20944/preprints201804.0137.v1).
## Abstract
The eddy current loss should be optimized to be as less as possible for the stability of permanent magnet in high speed permanent magnet synchronous motor (HSPMSM) rotor and ensure the high efficiency and low temperature of the motor. This paper analyzes the eddy current distribution in rotor, with consideration of the conflict of the thickness of sleeve and diameter of the rotor, calculating the eddy current loss (ECL) and the thermal distribution via Separation of variables method for solving Maxwell's equations with analytical hieratical model of ECL constructed. The optimization result of ECL of the HSPMSM whose power and rated speed is 30kw 48000r/min can be got by multi-objective optimization method, combined weighting coefficient method and traversal algorithm based on chaotic local search particle swarm optimization (CLSPSO), utilizing ECL analytical model and other analytical constraints. Related experiment and measurement has been implemented with new approach of loss separation.
## Subject Areas
eddy current loss; multi-objective optimization (MOO); electromagnetic analysis; equivalent hierarchical method
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https://www.albert.io/ie/sat-physics-subject-test/physics-book-image-distance
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Free Version
Difficult
# Physics Book Image Distance
SATPHY-QVY5KG
A physics book is located $25.0\ cm$ in front of a convex mirror. The (virtual) focal length of the mirror is $20.0\ cm$.
Where is the image of the book formed, relative to the mirror?
A
$100.0\ cm$ in front of the mirror.
B
$11.1\ cm$ in back of the mirror.
C
$5.0\ cm$ in front of the mirror.
D
$100.0\ cm$ in back of the mirror.
E
$11.1\ cm$ in front of the mirror.
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https://kb.osu.edu/dspace/handle/1811/8221
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# THE FAR INFRARED SPECTRUM OF HYDROGEN $PEROXIDE^{*}$
Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/8221
Files Size Format View
1963-E-05.jpg 75.45Kb JPEG image
Title: THE FAR INFRARED SPECTRUM OF HYDROGEN $PEROXIDE^{*}$ Creators: Hunt, R. H.; Peters, C. W. Issue Date: 1963 Publisher: Ohio State University Abstract: “The far infra-reel spectrum of $H_{2}O_{2}$ has been obtained in the region $14--690\;cm^{-1}$ with an average resolution of $0.3\;cm^{-1}$. Seven hindered rotation bands have been identified and the first five excited states of the internal rotation found to be; 11:43, 254.2, 370.8, 569.3, 7760.0 (in $cm^{-1}$ above the ground state). A good fit to these levels is obtained, in accordance with the theory of Leacock and Hecht (see above abstract), using the hindering potential $V(x) = 993 \cos x + 636 \cos 2x + 44 \cos 3x$ and the bond parameters of Redington, Olsen, and $Cross^{1}$. This potential has a \emph{cis} harrier of $2460\;cm^{-1}$ a \emph{trans} Earner of $386\;cm^{-1}$ and a potential minimum $111.5^{\circ}$ from the \emph{cis} configuration.” Description: $^{*}$Work supported in part U. S. Air Force. $^{1}$Reddington, Olsen and Cross, J. Chem. Phys. 36, 1311 (1962). Author Institution: Randall Laboratory, University of Michigan URI: http://hdl.handle.net/1811/8221 Other Identifiers: 1963-E-5
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https://crypto.stackexchange.com/questions/86038/malleability-for-varying-length-message
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# Malleability for varying length message
Given ciphertext for a message encrypted using $$AES-CTR$$ along with actual, desired message and IV, I need to perform malleability attack on the ciphertext to change the original message from $$M$$ to $$M'$$. But the message length of $$M$$ and $$M'$$ isn't the same. Since CTR doesn't use padding and the ciphertext is same length as the message then should I remove the extra bytes from ciphertext in the forged cipher to get $$M'$$ as its shorter than $$M$$?
To explain this better please see the following example of what I have done so far!
$$M$$ = "Pay alex \$100" $$M'$$ = "Pay \$900"
$$C$$ = Ciphertext with first block as IV
• Calculate $$x = M ⊕ M'$$ (I padded $$M'$$ before XOR to match length of $$M$$)
• $$C' = C[17... n]$$ (Exclude initial 16 bytes as it corresponds to IV)
• $$C'' = C' ⊕ x$$
• Forged Cipher $$C^* = C[1.. 16]||C''$$ (First 16 bytes is the IV)
When I decrypt the forged ciphertext $$C^*$$ I get the expected message but with extra characters in the end as "Pay \$900.....".
So in the forged cipher-text if I remove the last 10 hex characters I get the exact message $$M'$$ that I was expecting. Is it right approach to get rid of the extra bits in the forged cipher-text to match the message length or what I've done is incorrect?
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https://walkccc.me/LeetCode/problems/0957/
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# 957. Prison Cells After N Days
• Time:
• Space: $O(1)$
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 class Solution { public: vector prisonAfterNDays(vector& cells, int n) { vector firstDayCells; vector nextDayCells(cells.size()); for (int day = 0; n-- > 0; cells = nextDayCells, ++day) { for (int i = 1; i + 1 < cells.size(); ++i) nextDayCells[i] = cells[i - 1] == cells[i + 1]; if (day == 0) firstDayCells = nextDayCells; else if (nextDayCells == firstDayCells) n %= day; } return cells; } };
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 class Solution { public int[] prisonAfterNDays(int[] cells, int n) { int[] firstDayCells = new int[cells.length]; int[] nextDayCells = new int[cells.length]; for (int day = 0; n-- > 0; cells = nextDayCells.clone(), ++day) { for (int i = 1; i + 1 < cells.length; ++i) nextDayCells[i] = cells[i - 1] == cells[i + 1] ? 1 : 0; if (day == 0) firstDayCells = nextDayCells.clone(); else if (Arrays.equals(nextDayCells, firstDayCells)) n %= day; } return cells; } }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 class Solution: def prisonAfterNDays(self, cells: List[int], n: int) -> List[int]: nextDayCells = [0] * len(cells) day = 0 while n > 0: n -= 1 for i in range(1, len(cells) - 1): nextDayCells[i] = 1 if cells[i - 1] == cells[i + 1] else 0 if day == 0: firstDayCells = nextDayCells.copy() elif nextDayCells == firstDayCells: n %= day cells = nextDayCells.copy() day += 1 return cells
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https://www.electricalclassroom.com/conductance-what-is-conductance/
|
# Conductance | What is conductance?
Every material in the universe is believed to be made up of atoms. In an atom, electrons are bound to its nucleus by a strong force of attraction by the protons in the nuclei. In some materials few free electrons are available. These electrons can move freely along the material. Such materials with free electrons can conduct electricity.
When a charge (i.e., an excess or deficit of electrons) is applied to one side of such a conducting material, the electrons throughout will realign themselves, spreading out by virtue of their mutual repulsion, and thus conduct the charge to the other side.
Most of the conducting materials are metals. In metals, some electrons are always free for available for conduction. But the conductivity of these metals also depends on the amount of energy the electrons can transfer without colliding on the neighbouring atoms.
## Conductivity
Conductivity is the reciprocal of resistance. When resistance is the opposition to the current flow, conductance is the amount of current that a material can conduct. Therefore, conductance can be defined as the ability of a material to conduct electric current. For example, a material with low resistance is highly conductive and vice Versa. Conductivity is denoted by the letter G.
## Unit of conductance
As conductance is the reciprocal of resistance it is mentioned in “mho” or “ Ω−1 ” or “℧”. Sometimes it is mentioned in “siemens” which is the derived unit of ℧ .
where Ω is the ohm, A is the ampere, and V is the volt.
## Superconductors
Superconductivity is a property of a material to conduct without any resistance. Some material can conduct electricity at zero resistance when they are supercooled. For example, some ceramic metals can turn to superconductors when they are cooled to -319 deg. F. At this stage, the free electrons can move more easily losing their energy by collisions. Scientists are working on superconducting material and are finding ways how they can be used for electric power transmission.
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http://aimsciences.org/article/doi/10.3934/dcdsb.2018317?viewType=html
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# American Institute of Mathematical Sciences
## A new model of groundwater flow within an unconfined aquifer: Application of Caputo-Fabrizio fractional derivative
1 African Institute for Mathematical Sciences-Cameroon, Limbe Crystal Gardens, South West Region, P.O. Box 608, Cameroon 2 Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of Free Staye, Bloemfontein, 9300, South Africa
* Corresponding author: Atangana Abdon
Received July 2017 Revised March 2018 Published January 2019
Fund Project: The first author was supported by AIMS-Cameroon Scholarship grant 2015-2016.
The second author was supported by AIMS-Cameroon tutor fellowship grant 2015-2016
In this paper, the groundwater flow equation within an unconfined aquifer is modified using the concept of new derivative with fractional order without singular kernel recently proposed by Caputo and Fabrizio. Some properties and applications are given regarding the Caputo-Fabrizio fractional order derivative. The existence and the uniqueness of the solution of the modified groundwater flow equation within an unconfined aquifer is presented, the proof of the existence use the definition of Caputo-Fabrizio integral and the powerful fixed-point Theorem. A detailed analysis on the uniqueness is included. We perform on the numerical analysis on which the Crank-Nicolson scheme is used for discretisation. Then we present in particular the proof of the stability of the method, the proof combine the Fourier and Von Neumann stability analysis. A detailed analysis on the convergence is also achieved.
Citation: Pierre Aime Feulefack, Jean Daniel Djida, Atangana Abdon. A new model of groundwater flow within an unconfined aquifer: Application of Caputo-Fabrizio fractional derivative. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2018317
##### References:
[1] R. T. Alqahtani, Fixed-point theorem for Caputo-Fabrizio fractional Nagumo equation with nonlinear diffusion and convection, in J. Nonlinear Sci. Appl, 9 (2016), 1991-1999. doi: 10.22436/jnsa.009.05.05. [2] A. Atangana and B. S. T. Alkahtani, New model of groundwater flowing within a confine aquifer: Application of Caputo-Fabrizio derivative, in Arabian Journal of Geosciences, Springer, 9 (2016), 8pp. [3] A. Atangana and B. S. T. Alkahtani, Analysis of the Keller-Segel model with a fractional derivative without singular kernel, in Entropy, Multidisciplinary Digital Publishing Institute, 17 (2015), 4439-4453. doi: 10.3390/e17064439. [4] A. Atangana and N. Bildik, The use of fractional order derivative to predict the groundwater flow, in Hindawi Publishing Corporation, Mathematical Problems in Engineering, 2013 (2013), Art. ID 543026, 9 pp. doi: 10.1155/2013/543026. [5] A. Atangana and P. D. Vermeulen, Analytical solutions of a space-time fractional derivative of groundwater flow equation, in Hindawi, 2014 (2014), Art. ID 381753, 11 pp. doi: 10.1155/2014/381753. [6] A. Atangana and J. F. Botha, A generalized groundwater flow equation using the concept of variable-order derivative, in Boundary Value Problems, Springer, 2013 (2013), 1-11. doi: 10.1186/1687-2770-2013-53. [7] A. Atangana and J. J. Nieto, Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel, in Advances in Mechanical Engineering, SAGE Publications 7 (2015), 1687814015613758. [8] N. S. Boulton, Unsteady radial flow to a pumped well allowing for delayed yield from storage, in Int. Assoc. Sci. Hydrol. Publ, 2 (1954), 472-477. [9] H. Brezis, Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2011. [10] M. Caputo and M. Fabrizio, A new definition of fractional derivative without singular kernel, in Progr. Fract. Differ. Appl, 1 (2015), 1-13. [11] C.-M. Chen, et al, A Fourier method for the fractional diffusion equation describing subdiffusion, in Journal of Computational Physics, 227 (2007), 886-897. doi: 10.1016/j.jcp.2007.05.012. [12] C.-M. Chen, et al, Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation, in Mathematics of Computation, 81 (2012), 345-366. doi: 10.1090/S0025-5718-2011-02447-6. [13] A. Cloot and J. F. Botha, A generalised groundwater flow equation using the concept of non-integer order derivatives, in Water SA, Water Research Commission (WRC), 32 (2007), 1-7. [14] K. Diethelm, N. J. Ford and A. D. Freed, Detailed error analysis for a fractional Adams method, in Numerical algorithms, Springer, 36 (2004), 31-52. doi: 10.1023/B:NUMA.0000027736.85078.be. [15] Eng. Deeb Abdel-Ghafour, Pumping test for groundwater aquifers analysis and evaluation, 2005, available from: https://docplayer.net/11404875-Pumping-test-for-groundwater-aquifers-analysis-and-evaluation-by-eng-deeb-abdel-ghafour.html. [16] G. Gambolati, Analytic element modeling of groundwater flow, in Eos, Transactions Ameriocan Geophysical Union, 77 (1995), 103-103. [17] G. Garven and R. A. Freeze, Theoretical analysis of the role of groundwater flow in the genesis of stratabound ore deposits, in Mathematical and Numerical Model, American Journal of Science, 284 (1984), 1085-1124. [18] H. M. Haitjema, Analytic element modeling of groundwater flow, in nc San Diego, CA, USA Google Scholar, Academic Press, (1995), 33-75. [19] L. F. Konikow and D. B. Grove, Derivation of equations describing solute transport in ground water, in US Geological Survey, Water Resources Division, 77 (1977). [20] J. Losada and J. J. Nieto, Properties of a new fractional derivative without singular kernel, in Progr. Fract. Differ. Appl, 1 (2015), 87-92. [21] P. K. Mishra and K. L. Kuhlman, Unconfined aquifer flow theory: from Dupuit to present, in Advances in Hydrogeology, Springer, New York, NY (2013), 185-202. [22] Pollock and W. David, Documentation of computer programs to compute and display pathlines using results from the US Geological Survey modular three-dimensional finite-difference ground-water flow model, in US Geological Survey, 89 (1989). [23] J. R. Prendergast, R. M. Quinn and J. H. Lawton, The gaps between theory and practice in selecting nature reserves, Conservation Biology, Wiley Online Library, 13 (1999), 484-492. [24] S. A. Sauter and C. Schwab, Boundary Element Methods, Springer Series in Computational Mathematics, 39. Springer-Verlag, Berlin, 2011. doi: 10.1007/978-3-540-68093-2. [25] C. V. Theis, The relation between the lowering of the Piezometric surface and the rate and duration of discharge of a well using ground-water storage, in Eos, Transactions American Geophysical Union, Wiley Online Library, 16 (1935), 519-524. [26] G. K. Watugala, Sumudu transform: A new integral transform to solve differential equations and control engineering problems, in Integrated Education, TaylorFrancis, 24 (1993), 35-43. doi: 10.1080/0020739930240105. [27] S. B. Yuste and L. Acedo, An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations, in Journal on Numerical Analysis, SIAM, 42 (2005), 1862-1874. doi: 10.1137/030602666. [28] I. S. Zektser, E. Lorne and others, Groundwater Resources of the World: And Their Use, IhP Series on groundwater, 6nd edition, Unesco, 2004.
show all references
##### References:
[1] R. T. Alqahtani, Fixed-point theorem for Caputo-Fabrizio fractional Nagumo equation with nonlinear diffusion and convection, in J. Nonlinear Sci. Appl, 9 (2016), 1991-1999. doi: 10.22436/jnsa.009.05.05. [2] A. Atangana and B. S. T. Alkahtani, New model of groundwater flowing within a confine aquifer: Application of Caputo-Fabrizio derivative, in Arabian Journal of Geosciences, Springer, 9 (2016), 8pp. [3] A. Atangana and B. S. T. Alkahtani, Analysis of the Keller-Segel model with a fractional derivative without singular kernel, in Entropy, Multidisciplinary Digital Publishing Institute, 17 (2015), 4439-4453. doi: 10.3390/e17064439. [4] A. Atangana and N. Bildik, The use of fractional order derivative to predict the groundwater flow, in Hindawi Publishing Corporation, Mathematical Problems in Engineering, 2013 (2013), Art. ID 543026, 9 pp. doi: 10.1155/2013/543026. [5] A. Atangana and P. D. Vermeulen, Analytical solutions of a space-time fractional derivative of groundwater flow equation, in Hindawi, 2014 (2014), Art. ID 381753, 11 pp. doi: 10.1155/2014/381753. [6] A. Atangana and J. F. Botha, A generalized groundwater flow equation using the concept of variable-order derivative, in Boundary Value Problems, Springer, 2013 (2013), 1-11. doi: 10.1186/1687-2770-2013-53. [7] A. Atangana and J. J. Nieto, Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel, in Advances in Mechanical Engineering, SAGE Publications 7 (2015), 1687814015613758. [8] N. S. Boulton, Unsteady radial flow to a pumped well allowing for delayed yield from storage, in Int. Assoc. Sci. Hydrol. Publ, 2 (1954), 472-477. [9] H. Brezis, Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2011. [10] M. Caputo and M. Fabrizio, A new definition of fractional derivative without singular kernel, in Progr. Fract. Differ. Appl, 1 (2015), 1-13. [11] C.-M. Chen, et al, A Fourier method for the fractional diffusion equation describing subdiffusion, in Journal of Computational Physics, 227 (2007), 886-897. doi: 10.1016/j.jcp.2007.05.012. [12] C.-M. Chen, et al, Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation, in Mathematics of Computation, 81 (2012), 345-366. doi: 10.1090/S0025-5718-2011-02447-6. [13] A. Cloot and J. F. Botha, A generalised groundwater flow equation using the concept of non-integer order derivatives, in Water SA, Water Research Commission (WRC), 32 (2007), 1-7. [14] K. Diethelm, N. J. Ford and A. D. Freed, Detailed error analysis for a fractional Adams method, in Numerical algorithms, Springer, 36 (2004), 31-52. doi: 10.1023/B:NUMA.0000027736.85078.be. [15] Eng. Deeb Abdel-Ghafour, Pumping test for groundwater aquifers analysis and evaluation, 2005, available from: https://docplayer.net/11404875-Pumping-test-for-groundwater-aquifers-analysis-and-evaluation-by-eng-deeb-abdel-ghafour.html. [16] G. Gambolati, Analytic element modeling of groundwater flow, in Eos, Transactions Ameriocan Geophysical Union, 77 (1995), 103-103. [17] G. Garven and R. A. Freeze, Theoretical analysis of the role of groundwater flow in the genesis of stratabound ore deposits, in Mathematical and Numerical Model, American Journal of Science, 284 (1984), 1085-1124. [18] H. M. Haitjema, Analytic element modeling of groundwater flow, in nc San Diego, CA, USA Google Scholar, Academic Press, (1995), 33-75. [19] L. F. Konikow and D. B. Grove, Derivation of equations describing solute transport in ground water, in US Geological Survey, Water Resources Division, 77 (1977). [20] J. Losada and J. J. Nieto, Properties of a new fractional derivative without singular kernel, in Progr. Fract. Differ. Appl, 1 (2015), 87-92. [21] P. K. Mishra and K. L. Kuhlman, Unconfined aquifer flow theory: from Dupuit to present, in Advances in Hydrogeology, Springer, New York, NY (2013), 185-202. [22] Pollock and W. David, Documentation of computer programs to compute and display pathlines using results from the US Geological Survey modular three-dimensional finite-difference ground-water flow model, in US Geological Survey, 89 (1989). [23] J. R. Prendergast, R. M. Quinn and J. H. Lawton, The gaps between theory and practice in selecting nature reserves, Conservation Biology, Wiley Online Library, 13 (1999), 484-492. [24] S. A. Sauter and C. Schwab, Boundary Element Methods, Springer Series in Computational Mathematics, 39. Springer-Verlag, Berlin, 2011. doi: 10.1007/978-3-540-68093-2. [25] C. V. Theis, The relation between the lowering of the Piezometric surface and the rate and duration of discharge of a well using ground-water storage, in Eos, Transactions American Geophysical Union, Wiley Online Library, 16 (1935), 519-524. [26] G. K. Watugala, Sumudu transform: A new integral transform to solve differential equations and control engineering problems, in Integrated Education, TaylorFrancis, 24 (1993), 35-43. doi: 10.1080/0020739930240105. [27] S. B. Yuste and L. Acedo, An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations, in Journal on Numerical Analysis, SIAM, 42 (2005), 1862-1874. doi: 10.1137/030602666. [28] I. S. Zektser, E. Lorne and others, Groundwater Resources of the World: And Their Use, IhP Series on groundwater, 6nd edition, Unesco, 2004.
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2017 Impact Factor: 0.972
Article outline
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http://web2.0calc.com/questions/let-f-x-displaystyle-frac-1-ax-b-where-a-and-b-are
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+0
# Let $f(x) = \displaystyle \frac{1}{ax+b}$ where $a$ and $b$ are nonzero constants. Find all solutions to $f^{-1}(x) = 0$. Express your answe
0
40
1
+409
Let $f(x) = \displaystyle \frac{1}{ax+b}$ where $a$ and $b$ are nonzero constants. Find all solutions to $f^{-1}(x) = 0$. Express your answer in terms of $a$ and/or $b$.
michaelcai Oct 29, 2017
Sort:
#1
+78540
+1
y = ax + b
y - b = ax
[ y - b] / a = x swap x and y and for y write f-1 (x)
So
f-1 (x) = [ x - b ] / a = 0 when b = x
CPhill Oct 29, 2017
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https://chemistry.stackexchange.com/questions/96545/why-dont-i-get-the-same-value-of-percentage-ionic-character-of-a-particular-mol
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# Why don't I get the same value of percentage ionic character of a particular molecule from different equations?
About the ionic character of a polar covalent compound Pauling gave two equations as
1. [1-$e^{.25(x_a - x_b)}]$%
1. [18$(x_a-x_b)^{1.4}$]%
Hanary and Smith gave the equation
1. [$16(x_a-x_b)+3.5(x_a-x_b)^2$]%
Where $x_a$ and $x_b$ stands for the electronegativity of $a$ and $b$ atom in bond $a-b$.
Now if I put $x_a-x_b = 2,$ The 1st, 2nd & 3rd equations respectively give the value as -.648%, 47.5% & 46%. What is the reason behind these different values of percentage ionic character of the same molecule? At where am I wrong?
• You are wrong in thinking that percentage of ionic character is a real observable thing, like mass or energy. It isn't. (Neither is electronegativity, BTW.) – Ivan Neretin May 8 '18 at 5:29
• @IvanNeretin then how Pauling gave the equations and how do we have an electronegativity table? – user187604 May 8 '18 at 11:01
• When Pauling gave the equations, he knew their limitations. As for the electronegativity table, we surely have not one, but many such tables, all subtly different. – Ivan Neretin May 8 '18 at 11:16
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https://scottlocklin.wordpress.com/category/physics/econophysics/
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# Locklin on science
## BTC bubbles
Posted in econophysics by Scott Locklin on April 17, 2013
Not surprisingly, Bitcoin prices are well described by the log periodic power laws describing the dynamics of bubbles. A reminder of what a LPPL model looks like; here is a simple one:
$\log(p(t)) = A + B(t_c - t)^\beta + C(t_c - t)^\beta \cos( \omega \log(t_c-t)+\phi)$
I didn’t profit from this. I thought of applying LPPL to the BTC bubble well before the crash during a bullshit session with a friend, but I didn’t run the analysis until after. I have better things to do with my time than play with weird monopoly money, and the “exchanges” presently offering shorts are not even close to useful. I also think anyone who trades on LPPL is basically gambling. The most interesting parameter, $t_c$ is hardest to fit, and, well, with all those parameters I could fit a whole lot of elephants. Just the same it is a useful enough concept to justify further research. No, I won’t be telling the world about that research on my blog. A man’s got to eat, after all. Doing bubble physics costs money.
If you don’t know about LPPL models, click on these two helpful links. The “hand wavey” idea is, if the price is formed by market participants looking at what other market participants are doing, as with Dutch tulips, pets.com, and market prices in various eras, the price is an irrational bubble which will eventually burst. This isn’t an original idea: Charles Mackay was talking about it 180 years ago. The original idea is mapping this behavior onto an Ising model, running some renormalization group theory on it, and fitting to the result to get a forecast of bubble burstings. Sornette, Ledoit, Johanson, Bouchaud and Freund did it and told the world about it; may the eternal void bless them with healthy returns for being kind enough to share this interesting idea with us.
Here’s a plot of BTC close prices from MtGox (via quandl), with the LPPL model fit 10 days before the bubble pop. I wasn’t real careful with the fit; no unit root tests were done, no probabilistic estimates were made and no Ornstein Uhlenbeck processes were taken into account. This is just curve fitting. The result is compelling enough to talk about. As you can see, with these parameters, the out of sample top is fit fairly well. Amusingly, so is the decline.
What can we learn from this? You can see a “fair value” of around $20/BTC due to be hit in a few weeks, with perhaps a full mean reversion to$10/BTC. BTC doesn’t seem to have a helpful “anti-bubble” decay; if anything, it is decaying faster than expected so far (it is possible I mis-fit the $\omega$). The fit parameters for this version of the model tell us a few interesting things about the herding behavior which you can read about in Sornette’s book.
I don’t have any strong opinions about using BTC as a currency. I think most of its enthusiasts are naive and do not understand the nature of money and what it is good for. I do think BTC would work a lot better as a store of value with a properly functioning foreign exchange futures market. There are no properly functioning BTC futures exchanges at present; just an assortment of dreamers and borderline crooks cashing in on hype. This is more of an engineering and legal problem than it is an inherent problem with using BTC as a currency. The way things are presently set up, without shorts, any extra media attention will result only in people buying the damn things. Without the ability to easily short them, price discovery is impossible, and herding behavior is the rule. It ain’t a market without shorts. It’s a bubble maker. Shorts don’t guarantee there will be no bubbles; we see plenty in shortable markets, but a lack of shorts will virtually guarantee future BTC bubbles.
## What is a bubble? (econophysics, part 2)
Posted in econophysics by Scott Locklin on August 14, 2011
“In science there is only physics; all the rest is stamp collecting.“-Lord Kelvin
In long ago (it took me this long to figure out how to make LaTeX in wordpress) part 1, I discussed the random field Ising model for opinion diffusion. What motivates this model? Well, we observe in nature that people’s opinions are influenced by the opinions of people around them. The random field Ising model is one very sensible way of modeling this. It’s particularly useful in systems where the statistical or geometric properties of the social network are well understood.
The nice thing about physics-like approaches is you don’t always need to know details, like what the geometric properties of the social network are. You can figure out a lot by just thinkin’. Didier Sornette’s ideas are like this. Effectively, in bubbles, people stop taking positions based on underlying fundamentals information, and start taking positions based on price. In other words, the entire market becomes trend following. If you take a position based on price, and everyone else starts to do the same thing, the prices will rise faster than exponentially via feedback. So, if you take the log of the price series, and notice stuff with super linear growth: those are bubbles.
One of the things my pals the economists don’t realize about markets is who the market consists of. There are a lot of ways to think about markets that flatter our egos, but a very useful way of thinking about markets is a group of people with edge versus a bunch of people who don’t know what they’re doing -who I’ll call “noise traders” because that’s what Fisher Black called them. This isn’t very charitable, as a lot of the “people who don’t know what they’re doing” have other priorities, like hedging or forming an index, or just buying and selling when some dope tells him to. But for the purposes of argument, since they’re not profit takers, they’re trading on what amounts to noise. When you get informed versus noise traders, you get a reversion to the fair value of the instrument fairly rapidly. The profit takers will trade with the noise traders who give them the price they want, and the price will move towards a place where profit takers can no longer make a profit.
Now, I’m asking you to take my word for these facts, but they’re stuff you can derive using freshman calculus. Some more advanced trickery (renormalization group theory -not as scary as it sounds: mostly, this is a trick for looking at symmetries in systems, a handy trick, used everywhere in physics) gets you the loq periodic power law (LPPL). Using the LPPL, we can potentially forecast things like when the bubble pops. How do you forecast something like this? Well, you use the following price evolution equation to find the crash point $t_c$:
$\log(p(t)) = A + B(t_c - t)^\beta + C(t_c - t)^\beta \cos( \omega \log(t_c-t)+\phi)$
“With three parameters, I can fit an elephant.” -Lord Kelvin
The first thing you should notice is all the parameters there are to fit here. With three parameters, I can fit an elephant, said Lord Kelvin; he wasn’t kidding. Wolfram has a useful demo. Given the hairiness of this function and the lack of data, this should give you pause. Seven parameters! Then … things actually get worse. We know that price time evolution follows an Ornstein–Uhlenbeck process which means our equation isn’t really an equation: there is stochastic calculus built into it. One can ignore this and blindly fit anyway, but this isn’t how the pros do it: Sornette and company account for it in various ways, using moving windows, bits of Black Scholes, multiple fits to isolate the range of the “less hairy” parameters (aka, $A, B, C$ are relatively easy to fit assuming you get everything else right -the interesting bits are $\omega, \beta, t_c$), multiple constrained fits on parameters (aka, constrain potential values to make sure $\omega$ and $t_c$ isn’t being fit to noise and $A$ doesn’t call the top of the market at some absurdly high value), Lomb periodograms, various GARCHy and Black Scholesey time series models with the log periodic piece baked in. Oh, and they use optimizer/fitters from Annealing to genetic algorithms and various other optimization tricks of the trade. It’s a tough function.
Interesting things to make note of: $A$ is important, as it calls the top. $t_c$ obviously is important as it calls the date of the crash. Most important, though, is $\beta$ and $\omega$, without which, you can’t identify whether or not you’re in a bubble regime. No power law growth with oscillations: no bubble. The meaning of these parameters is also interesting. It’s obvious what they mean from a fitting standpoint, but some of those numbers come from the actual physics of markets. For example, $\omega$ contains microstructure information about the “herdiness” of the market. $\beta$ actually comes from the structure of human markets, and seems to remain similar across many examples.
Does all this stuff work? I dunno. Certainly, running the rude implementation of it I found on Rnabble looks … evocative at least.
Might be interesting to build an oscillator which only fits the run-ups (though of course, the ones here are fit in sample, and so they look better than they probably are), and gets you out of the trade as they get closer together. Better yet: use lazy learning -maybe something like Dynamic Time Warping on time series which have been post-facto identified as bubble-like, with LPPL oscillations in the run-up. Or, generate LPPL time series using the model and DTW your way onto new ones to forecast burst bubbles. To my mind (and considering some interesting unexploited time scales), the log periodicity itself is interesting, and probably represents a common “orbit” in market dynamics which does not necessarily end in crashes, and which could be captured via some variants on the usual techniques.
Or maybe it’s all horse shit. Personally, I think the most productive looking route for research into this subject is not going to fit parametric models like the above using ML and what not: the basic insight of Sornette and company is to give you a vague idea of what groups of noise traders and informed traders will do to a price series in the presence of different populations of each. Indeed, in Sornette’s early research (which he seems to have made some money speculating on), most of those parameters were not present. Paring the equation down and trying to get the $\omega$ and $\beta$ right might pay a few dividends; as I said above -simple oscillator might work better.
One of the problems with this model as a model is that these populations of market participants are themselves a dynamic quantity. Think about what happens in a market collapse in a healthy market: informed traders move in to buy when the noise traders freak out and sell off. Those numbers slosh around a lot. The really big collapses happen when, whether because of tight credit or severe uncertainty, informed traders decide to stay home. But then, sometimes they don’t stay home. This isn’t really “modelable” in any way I can think of. This is something that requires the big picture judgement of a Monroe Trout or Paul Tudor Jones.
Generally though, such fitted models are not useful to speculators, as getting the fit right (in any model) is an art form, and when the parameters change over time, it becomes rather hopeless. That’s one of the reasons why people who trade end up using moving averages instead of GARCH. We know that volatility can be modeled with GARCH … but can it be forecasted by models fit to GARCH? Well, sometimes, but not really. However, ideas like GARCH are crucial to our understanding of how markets function. I’d say at some point, log periodic power laws will also be considered similarly useful. But right now, we’re still figuring it out.
http://quantivity.wordpress.com/2011/02/08/curiosity-of-lppl/
Everything you always wanted to know about Log Periodic Power Laws but were afriad to ask. -my favorite review article on the subject thus far.
## Conservation laws in the Ising universe: Econophysics breakthroughs
Posted in econophysics by Scott Locklin on May 11, 2011
Toffoli is one of my favorite physicists. His research has been consistently excellent, and he has been a pioneer in a number of fields. Unlike most physicists, who are content to mine their little niche, Toffoli is a risk taker: a would-be conquerer of new worlds. As Borel said of Poincare; he is a conquerer, not a colonist. His latest paper has tremendous implications in all kinds of interesting areas in Finance, econophysics, sociology and machine learning.
Remember way back when I blathered about the random field Ising model as a model for collective human behavior about a year ago? Well, Toffoli has forged ahead and derived conservation laws for this model. What does this mean for the science of social groups? Well, it means you can derive global behavior from first principles, aka microstructure. Sometimes you’ll be able to derive microstructure from observed global behavior. All this has rather large implications in fields which map well onto the Ising model.
One of the fields, of course, is econophysics: a developing branch of science which studies group behavior in an economic setting. Another is sociology, of which econophysics is a subset. Finally, there is machine learning: the Hopfield net a sort of ur-version of the Neural net, is an Ising model. It’s also a special case of Bayesian networks.
What does this sort of thing mean? Conservation laws are more or less how physicists think about the world. Should we develop a more detailed mathematical framework for the Ising model, it may be possible to analyze all kinds of orderly behavior which takes place naturally in systems which are well modeled by the Ising model. It’s entirely possible there are all manner of conservation laws derivable about Ising models, based on their geometry and other detailed aspects of their structures.
This could mean humans may some day understand some of the spooky behaviors of crowds. We can already understand lots of these spooky behaviors via numeric simulation and thermodynamic arguments. Imagine knowing how to spook a crowd into doing what you want? OK, this is kind of science fiction stuff (though looking around … maybe not so much; the RFIM reduces to something real simple when the driver field, aka mass media, is really strong). Consider a more pedestrian application: how do you pick the right kind of machine learning algorithm for a given task? How does one architect a neural net in order to solve a problem? Conservation laws *will* help people to do this, based on the symmetries of the problems at hand. If this doesn’t result in some breakthroughs in machine learning, it’s because people aren’t paying attention.
On a more pragmatic level, trending systems can be understood in the RFIM framework, and energy/time invariance conservation makes these sorts of models much easier to think about. Gentlemen: start your automated theorem provers.
## The compass rose pattern: microstructure on daily time scales
Posted in chaos, econophysics, microstructure by Scott Locklin on August 12, 2010
One of the first things I did when I fired up my Frankenstein’s monster was plot a recurrence map between equity returns and their lagged value. This is something every dynamical systems monkey will do. I did. In physics, we call it, “looking at the phase space.” If you can find an embedding dimension (in this case, a lag which creates some kind of regularity), you can tell a lot about the dynamical system under consideration. I figured plotting returns against their lags would be too simple to be interesting, but I was dead wrong. I saw this:
A high quality compass rose can be seen on Berkshire Hathaway preferred stock
I convinced myself that nothing this simple could be important (and that it went away with decimalization), and moved on to more productive activities, like trying to get indexing working on my time series class, or figuring out how to make some dude’s kd-tree library do what I wanted it to. I realized just today, this was a mistake, as other people have also seen the pattern, and think it’s cool enough to publish papers on. None other than Timothy Falcon Crack, bane of wannabe quants (and their employers) everywhere, was a coauthor of the first paper to overtly notice this phenomenon.
A slightly later epoch pre-decimalization
You can sort of see why this pattern would fade out with decimalization. If you’re trading in “pieces of 8” (aka 1/8ths of a dollar), returns which don’t neatly divide into 1/8ths will not be possible. In other words, there are only 7 prices between $20 and$21, as opposed to 100 like there are now. Therefore you’d expect to see some gaps in the lagged returns, which are just price ratios. Roughly speaking, if the average variance is small compared to the size of the tick, you’ll be able to see the pattern. At least that’s what most people seem to think. Weird that Berkshire Hathaway should be effected by this, but as it turns out, it had an effective tick size which was fairly large compared to daily motion, because the people trading it were lazy apes who wouldn’t quote a price at market defined tick size (which, even at 1/8ths was very small compared to Berkshire Hathaway’s share price of several tens of thousands of dollars).
Here you can still see some evidence of Compass Rose in the early decimalization era
One of the interesting implications of all this: if ticks are important enough to show up in a simple plot like this, what happens when you apply models which assume real numbers (aka virtually all models) to data which are actually integers? This is something I’ve wondered about since I got into this business. Anyone who notices his model returning something which has many decimal points at the end …. when the thing you’re measuring should be measured in integers should notice this. I don’t think this sort of issue has ever been resolved to anyone’s satisfaction; people just assume the generating process uses real numbers underneath, and average up to the nearest integer; sort of like trusting the floating point processor in your computer to do the right thing. The compass rose points out dramatically that you can’t really do that. It also demonstrates that, in a very real way, the models are wrong: they can’t reproduce this pattern. For example, what do you do when you’re testing for a random walk on something like this? Can it possibly be a random walk if the returns are probabilistically “loitering” at these critical angles? Does this bias models we use? Smart people think it does. Traders don’t seem to worry about it.
Finally, the compass rose is completely gone in the more recent epoch of decimalization for Berkshire Hathaway series A
Some other guys have attempted to tease some dynamics out of the pattern. Not sure I buy the arguments, since I don’t understand their denoising techniques. Others (Koppl and Nardone) have speculated that “big players” like central banks cause this sort of effect by creating confusion, though I can’t for the life of me see why central bank interventions would cause these patterns in equities. Their argument seems sound statistically. It was done on the Rouble market during periods of credit money versus gold backed. Unfortunately, they never bother relating the pattern in the different regimes to central bank interventions, other than to notice they coincidentally seem to happen at the same times. That doesn’t make any sense to me. It’s a regression on two numbers.
My own guess, developed over a half day of thinking about this and fiddling with plots in R, is that these patterns arise from dealer liquidity issues and market dislocations. How?
1. Human beings like round numbers. Machines don’t care. Lots of the market in ye olden pre-decimalization days was organized by actual human beings, like my pal Moe. Thus, even if there was no reason to pin a share at a round number, people often would anyway, because $22.00 is more satisfying than$22.13. Since liquidity peddling is now done by machines, most of which assume random walk, I’d expect compass rose patterns to go away in cases where it persisted for a long time, like with \$100k Berkshire Hathaway preferred shares, which are all that is pictured above. Voila, I am right. At least in my one stock guess, though the effect can be seen elsewhere also.
2. The plethora of machine-run strategies has made the market much more tightly coupled than it used to be. What does this mean? For example: at the end of the day, something like an ETF has to be marked to its individual components. One of the things which causes a burst in end of the day trading is the battle between the ETF traders trying to track an index, and arbs trying to make a dollar off of them. Similarly with the volatility of the index. With all this going on, there isn’t much “inertia” pinning the closing price to a nice, human round value. It was observed early on that indexes don’t follow the compass rose pattern, and it’s very easy to understand why if you think of it from the behavioral point of view; add together a lot of numbers, even if they’re mostly round numbers, and chances are high you will not get a round number as a result (especially if you weight the numbers, like in most indexes). You could look at the dissolution of this pattern over time as increasing the entropy of stock prices. High frequency traders make the market “hotter.” As such, the lovely crystaline compass rose pattern “melts” at higher temperatures, just like an ice cube in a glass of rum. With the Berkshire Hathaway preferred shares patterns above, you can see the pattern fading out as the machines take over: while some compass rose remains post-decimalization, it’s completely gone after 2006. You might see it at shorter time scales, however.
Relating it back to the Rouble analysis of Koppl and Nardone, I’d say they saw the compass rose in times of credit money simply because the market moved a lot slower than it did when it was based on gold. When it was credit money, there were effectively fewer people in the trade, and so, monkey preferences prevailed. When it was gold, there were lots of people in the trade, and the “end of day” for trading the Rouble was less meaningful, since gold was traded around the world.
One of the things that bothered me about the original paper is the insistence that one couldn’t possibly make money off of this pattern. I say, people probably were making money off the pattern: mostly market makers. What is more, I posit that, where the pattern exists (on whatever time scale), one could make money probabilistically. What you’re doing here is bidding on ebay. Everyone on ebay knows that it’s a win to not bid on round numbers, because the other apes will bid there. If you bid off the round number, you are more likely to win the auction. Similarly, if you’re a market maker, you might win the trade by bidding off the round number, and giving the customer a slightly better price. Duh. My four hours worth of hypothesis would predict thinly traded stocks which aren’t obviously important components in any index would continue to show this end of day pattern, since they won’t be as subject to electronic market making. And, in fact, that’s what I saw in the first one I saw, WVVI, which appears to be a small winery of some kind. Even in the most recent era, it has a decent compass rose evident. Second one I looked at, ATRO (a small aerospace company) similarly showed the compass rose during the 2001-2006 regime. I’m pretty sure there are simple ways to data mine for this pattern in the universe of stocks using KNN, though I don’t feel like writing the code to do it for a dumb blog post; someone’s grad student can look into it.
All of this is pure speculation after too much coffee, but it’s a very simple and evocative feature of markets which is deeper than I first thought. Maybe with some research one could actually use such a thing to look for trading opportunities (probably it’s just a bad proxy for “low volume”). Or maybe the excess coffee is making me crazy, and these patterns are actually just meaningless. None the less, in this silly little exercise, we can see effects of the integer nature of money, behavioral economics, visible market microstructure on a daily time scale, and very deep issues into the dynamics of financial instruments.
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https://c21.phas.ubc.ca/article/stretching-rubber-bands/
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# Stretching Rubber Bands
We can use common household objects to measure properties that match physical laws. This experiment takes a very common household item, the rubber band, and applies physical laws (Hooke’s Law and the Young’s Modulus) to them in a hands-on way.
Purpose:
To describe the stretching action of rubber bands, and explore the connection between Hooke’s Law and Young’s modulus.
Introduction:
Rubber bands stretch when we pull on them, but pulling as hard as you can on a 2-by-4 will probably have no visible effect. The stretchability of solid materials is expressed as their Young’s Modulus (a.k.a. “Elastic Constant”), $Y$. Here is the formula for Young’s modulus (Eqn.1):
$Y=\dfrac{\dfrac{F}{A}}{\dfrac{\ \Delta L\ }{L_0}} \tag{1}$
• $F$ = Force applied to solid [N]
• $A$ = Cross-sectional area of solid [m$^2$]
• $L$ = stretched length of solid [m]
• $L_0$ = original length of solid [m]
A simple way to understand this formula is $Y = \frac{\text{stress}}{\text{strain}}$. The stress is the amount of force applied to the object, per unit area ($F/A$). The strain is the relative change in the length of the solid ($\Delta L/L_0$). Therefore, a solid with a greater value of $Y$ will stretch less than a solid with a smaller $Y$, when the same force is applied.
Let’s return to rubber bands. Rubber bands are elastic solids and can be described with Hooke’s Law (Eqn.2). We can think of Hooke’s Law as a simplified version of Young’s Modulus, and it is classically applied to spring systems. However, it can also, to some extent, describe the stretch patterns observed for rubber bands.
$F=k \Delta L \tag{2}$
• $F$ = Force applied to elastic material [N]
• $k$ = spring constant [N/m]
• $ΔL$ = change in length of the elastic material [m]
If you compare the two equations, you will find (try this as an exercise) that the spring constant $k$ contains Young’s modulus $Y$ (which describes the material), the length $L_0$, and the cross-sectional area $A$ of the material, can be related as in Eqn.3.
$k=Y\dfrac{A}{L_0} \tag{3}$
This allows us now to make predictions before we do an experiment. For example, a thicker rubber band should have a larger spring constant due to its larger cross-sectional area. In this experiment you can check this prediction and investigate the way in which Hooke’s Law applies to rubber bands. You can also think about what happens if you use two rubber bands at the same time, either to hang an object from both bands in parallel or to create a longer band by knotting one band to the end of the other band. Write down your hypothesis and test it with an experiment.
The Challenge:
Design an experiment to measure the constant $k$ for rubber bands. Use items of known mass to provide the applied force. Measure the change in length and the original length for each rubber band; also record the physical properties of each band.
Key Concepts:
• Young’s modulus is a measure of stress over strain.
• Hooke’s Law takes only applied force and change in length into account.
• Different rubber bands will have different constants for both laws.
Skills:
• Applying Hooke’s Law
• Relating graphs of experimental data to given equations
• Understanding relationship between Hooke’s Law and Young’s modulus
• Simple graphical analysis
• Assigning errors and understanding error calculations
Materials/Equipment:
• Three rubber bands of different sizes and thicknesses
• Objects of given weight (granola bars, packaged foods, etc.)
• Small metal hanger
• Pushpin
• Ruler (30cm) or flexible tape measure
Suggested assigned time: 2 weeks
• Why does Hooke’s law not apply for greater forces?
• Why is Young’s modulus a more general descriptor of rubber band action than Hooke’s law?
Variations:
• Try the experiment with something other than a rubber band.
• Compare rubber band action with spring action. How do the graphs for Hooke’s law compare?
• Combine multiple rubbers bands and analyze stretching action.
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http://link.springer.com/article/10.1007%2FBF02480328
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, Volume 32, Issue 1, pp 241-245
# Nonparametric estimation of Matusita's measure of affinity between absolutely continuous distributions
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* Final gross prices may vary according to local VAT.
## Abstract
LetF andG be two distribution functions defined on the same probability space which are absolutely continuous with respect to the Lebesgue measure with probability densitiesf andg, respectively. Matusita [3] defines a measure of the closeness, affinity, betweenF andG as: $\rho = \rho (F,G) = \int {[f(x)g(x)]^{1/2} } dx$ . Based on two independent samples fromF andG we propose to estimate ρ by $\hat \rho = \int {[\hat f(x)\hat g(x)]^{1/2} } dx$ , where $\hat f(x)$ and $\hat g(x)$ are taken to be the kernel estimates off(x) andg(x), respectively, as given by Parzen [5].
In this note sufficient conditions are given such that (i) $E(\hat \rho - \rho )^2 \to 0$ asx→∞ and (ii) $\hat \rho - \rho$ with probability one, asn→∞.
Research supported in part by the National Research Council of Canada and by McMaster University Science and Engineering Research Board.
The author is presently with the Department of Mathematical Sciences, Memphis State University, Memphis, Tennessee 38152.
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http://math.stackexchange.com/questions/708373/for-every-rational-number-does-there-exist-a-sequence-of-irrationals-which-conv
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# For every rational number, does there exist a sequence of irrationals which converges to it?
I can think of of examples where a sequence of irrationals converges to $0$. But if we pick any rational will there always exist a sequence of irrationals which converges to it?
I cannot find a straight answer to this question.
-
Let $r$ be our rational. Look at $r+\frac{\sqrt{2}}{n}$. This may be the example you had in mind, "shifted" by $r$. – André Nicolas Mar 11 '14 at 18:47
Assume your number is $\frac{p}{q}$. Then the sequence $$a_n=\frac{\pi}{n}+\frac{p}{q}$$ converges to the given number and is irrational (any irrational number in the place of $\pi$ would do).
-
this is assuming $\lim_{n\to\inf}$, right? – Cole Johnson Mar 11 '14 at 23:47
@ColeJohnson Yes, right! – Stef Mar 11 '14 at 23:49
Yes, take a sequence consisting of your sequence of irrationals converging to $0$ plus your desired rational limit.
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Yes: If $r\in\Bbb Q$, then $\forall n\in\Bbb N$: ${rn\over n+\sqrt2}\in{\Bbb Q}^c$ and $$\lim_{n\to\infty}{rn\over n+\sqrt2}=r.$$
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For any rational number $x=\frac{p}{q}$ with $\gcd(p,q)=1$, just consider: $$x_n = \frac{p}{q}\cdot\frac{n}{\sqrt{n^2+1}}.$$ Clearly any $x_n$ belong to $\mathbb{R}\setminus\mathbb{Q}$ and we have $\lim_{n\to +\infty} x_n = x$.
-
Yes. Consider
$\frac{p}{q} - \frac{\sqrt{2}}{n}$
-
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https://astronomy.stackexchange.com/questions/35142/is-there-a-distinction-between-neos-and-near-earth-asteroids-is-there-a-differe
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# Is there a distinction between NEOs and near-Earth asteroids? Is there a difference?
My "real question" is in Space Exploration Meta (neo (near-earth-object) and near-earth-asteroid tags, do we need both?), but I think that astronomers will be able to help understand the situation and terminology.
Question: Is there a distinction between NEOs and near-Earth asteroids? Is there a difference? Or is it a distinction without a difference?
I noticed for example that here in Astronomy SE there is just .
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http://www.tug.org/twg/mfg/mail-html/1993-08/msg00115.html
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# Re: technical question
• To: [email protected]
• Subject: Re: technical question
• From: Michael Downes <[email protected]>
• Date: 11 Aug 1993 11:53:33 -0400 (EDT)
> Would it be possible, using the existant macro in plain to produce an
> estensible integral sign ?
>
> on a font and charlist point of view, there is no problem !
> But i'm wondering if the \left\int bit would work.
> how should \int be defined ?
Is it possible, that in a paper where \left\int is used, it will be
desired to have \int always act as a delimiter, and never in the plain
TeX way? If so, changing the definition and syntax of \int might
be the best approach, so that the \left is built-in. For example:
\def\int#1#2{\left\intdelim #1\right.#2}
with usage:
\int{f(x)}{dx}
(I don't recall from previous mail, is the differential placed after
the \right. or before?)
Of course there are complications with subscripts and superscripts
that would have to be dealt with.
As a syntax of this sort could also handle non-delimiter integrals,
the obvious next thought is a question: whether the old integral
syntax should be retired in favor of a new syntax. The old
backward-compatibility viper rears its ugly head. Using a new name
e.g. \integral would help, but at the cost of taking longer to type.
As for backward compatibility in general: Of course it is very
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http://www.maths.lu.se/english/research/seminars/oresundseminar-2018/
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lunduniversity.lu.se
# Öresund seminar 2018
## Thursday 15 November
Hörmander auditorium, Centre for Mathematical Sciences, Sölvegatan 18A
## Registration
Please register here by Wednesday, November 7.
## 13.15–14.05 Jan-Fredrik Olsen, Lund University
Balian-Low type theorems for finite sequences
This talk is based on a joint work with Shahaf Nitzan, where we formulate and prove finite dimensional analogues for the classical Balian-Low theorem as well as for a quantitative version previously obtained by Nitzan and Olsen. In particular, this answers the Finite Balian-Low conjecture'' posed in 2015 by Lammers and Stampe.
## 14.15–15.05 Magnus Goffeng, Chalmers/University of Gothenburg
The magnitude of geometry
Around a decade ago, Leinster introduced the notion of magnitude as a generalization of the Euler characteristic of a finite category. It has since been extended to an invariant of compact metric spaces. Taking these ideas one step further, one often considers the magnitude function: the magnitude of the space rescaled by a variable R>0, which captures several of the space's geometric features. I will recall this invariant and, focusing on the case of Riemannian manifolds with boundaries, describe the structure of the magnitude function. There are surprisingly few computations of magnitude that have been done. It was nevertheless conjectured by Leinster-Willerton that for convex domains, the magnitude function is a polynomial in R where the coefficients are the intrinsic volumes of the convex body (e.g.\ volume, surface volume, total mean curvature, ..., Euler characteristic). We prove an asymptotic version of this conjecture and show that the magnitude function extends meromorphically to the complex plane. For surfaces, we prove that the magnitude function recovers the Euler characteristic.
Based on joint work with Heiko Gimperlein.
## 15.45–16.35 Gerd Grubb, University of Copenhagen
Heat problems for operators of fractional order
When $P$ is a strongly elliptic pseudodifferential operator of order $2a>0$ for noninteger $a$, $P$ is nonlocal, but one can define a realization of the homogeneous Dirichlet problem on an open subset $\Omega$ of $\mathbb R^n$ by a variational construction. This includes the example $(-\Delta)^a$, which has been much studied in recent years because of its interest in finance and probability as well as mathematical physics. When $P$ moreover has even symbol, the regularity properties of solutions are well understood, always involving a power $d^a$, where $d(x)$ is the distance to the boundary (assumed $C^\infty$). In particular, a solution $u$ with data in $C^\infty$ has $u/d^a$ in $C^\infty$.
After recalling these results, we shall discuss the associated heat equation $Pu(x,t) + \partial_t u(x,t) = f(x,t)$, $t>0$. Here regularity of solutions can be obtained in relatively low-order function spaces, but one meets the surprising fact that the smoothness in $x$ at the boundary cannot in general be lifted beyond a certain point, even when $f(x,t)$ is $C^\infty$ up to the boundary. This is contrary to the properties of standard differential operator heat equations.
## 16.45–17.35 John Wheater, University of Oxford
Sums of Random Matrices and the Potts Model on Random Planar Maps
I will start by briefly reviewing the random matrix method for understanding spin systems on quantum geometry represented by random planar maps. Then I will describe some improved techniques and new results for the case of the q-state Potts Model which enable the calculation of an extended set of correlation functions. These reveal some unexpected features.
## CONTACT
Erik Wahlén
Associate Professor
[email protected]
+46 46 222 81 43
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http://math.stackexchange.com/questions/8113/two-basic-question-on-set-theory
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# Two basic question on set theory
1.How many proper subset of {1,2,3,4,5,6,7} contain the numbers 1 and 7 ?
Lets consider {1,7} as a single element then the number of possible subset is $2^6$ and hence the number of proper subset is 62.
2.A survey show that 63% of the Americans like cheese where as 73% like apples.If x% of Americans like both cheese and apples, then we have :
(A) $x \ge 39$ (B) $x \le 63$ (C) $39 \le x \le 63$ (D) None of these
if a% and b% like only cheese and only apples then we have, $a + x + x + b = 100$ ,$a + x = 63$ and $b + x = 63$ solving we get $x = 39%$. So (D) is my answer.
Am I correct ?
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I think you probably meant $b+x=39$. – VelvetThunder Oct 28 '10 at 5:50
Using your own logic, how can you get 62 proper subsets out 2^6 total subsets? Why are you subtracting two and not one? – crasic Oct 28 '10 at 6:24
1. No, the subsets must have 1 and 7. The other five elements are optional, but you can't have them all.
2. You have $a + b + x + \text{those who like neither cheese nor apples} =100%$. Don't count x twice when adding to 100%. But you are right that $a+x=63, b+x=39$
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(1)I don't understand what you mean & for (2) now I have no idea how to solve it ?! – Damir Frezivioski Oct 27 '10 at 23:52
What!? Who couldn't like either cheese or apples? – Mateen Ulhaq Oct 27 '10 at 23:54
@damir Number 1 is $2^5\space=\space32$ – Mateen Ulhaq Oct 28 '10 at 2:55
@muntoo not quite. It calls for proper subsets. – Ross Millikan Oct 28 '10 at 3:31
@damir so the legal subsets are {1,7} plus all subsets of {2,3,4,5,6} except the one that is all of them. That would not give a proper subset. As there are five elements, there are 2^5-1=31 possibilities. The empty set is a proper subset. – Ross Millikan Oct 28 '10 at 3:32
On #1, you are over counting. You have thought of {1,7} as a single elements but your answer has included the possibility that it is not in there. Think of it as we are setting 1 and 7 to the side. Now for each remaining element, we can either include it or exclude it from a subset. If you still don't see how to obtain the answer, I would recommend the following short explanation of the multiplication principle
On #2, you are correct in thinking that each person must fall into 1 of four groups: people who like apples and cheese, people who just like cheese, people who like just apples, and people who like neither. If you think abut the information you are given, you should see an upper bound for x. For a lower bound on x, assume that everyone either likes apple or cheese and use the inclusion exclusion principle
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In (1) I really don't understand why and how you are using multiplication principle. In (2) The lower bound determination is quite understandable but I am facing some troubles to understand how are you getting the upper bound ...:) – VelvetThunder Oct 28 '10 at 5:45
For the upper bound, we know that 63% of people like cheese and 73% of people like apples. The 'worst case' is that everyone who likes cheese also likes apples. Hence, at most 63% could like both. – WWright Oct 28 '10 at 5:50
I meant multiplication principle in the sense that the for each of the 5 sets they can be either in or out (2 options per element) hence we have 2^5 total, but we require proper subsets so subtract 1 off. Is this more clear? – WWright Oct 28 '10 at 5:51
+1, Aha ! so it's just a different way to look at the problem :) – VelvetThunder Oct 28 '10 at 5:55
1. Say {1,7} is a single element, then total number of subsets possible = $2^6$ Now, how many subsets among these don't have {1,7} ? It will be $2^5$.
Hence,number of subsets having {1,7} is $2^6$ - $2^5$ = 32.But since you have asked for proper subset so the answer would be 31.
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You could also get there directly, by asking how many subsets you can make out of {2,3,4,5,6} which 2^5 then subtract the one which is the whole set and get 2^5 - 1 = 31 – crasic Oct 28 '10 at 5:58
Hm yes,but I showed him that way to match his way of thinking :) – VelvetThunder Oct 28 '10 at 6:00
1. crasic has taken the words out of my mouth. It's the same as the number of proper subsets of {2, 3, 4, 5, 6}, i.e. 2^5 - 1 = 31.
2. Only 63% like cheese, so there cannot be more than 63% who like both cheese and apples. So B is correct.
37% don't like cheese, and 27% don't like apples (which I personally find hard to imagine). The lower bound for x is found in the case where these two sets are disjoint - 64% either don't like cheese or don't like apples, leaving 36%.
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http://postfactualpolitics.org/atl-v-the-usa/
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# As Atlanta flies, so flies the nation
The following was written for an exercise I did as an application for a job at the Brookings Institute. I thought the data was interesting and worth posting. I also mapped the change.
Something is happening in Georgia. The Atlanta Metropolitan Area is the 9th largest in the United States and has grown at a rate three times higher than the national median. [1] Between 2006 and 2016, only two other metropolitan areas saw a larger total increase in number of passengers boarding commercial flights. Yet in 2016 Atlanta’s sole major airport, ATL, had just over 34,000 fewer yearly departures than it did in 2006, and it lost eight direct routes over the same period; based on these two measures ATL is the 13th and 10th fastest shrinking airport.[2]
ATL is not an anomaly. Nationally there are fewer departures and direct flights than a decade ago while the total number of passengers rises. This is largely an unintended consequence of the 1978 Airline Deregulation Act. Since 1978, the airline industry has seen continued consolidation such that today just four airlines control over 65% of the domestic US market.[3] With consolidation comes less competition, allowing the industry to pursue otherwise potentially untenable business strategies. The hub-and-spoke model is an example of this: major airlines have routed more of their flights through their hub airports while decreasing their presence in other airlines’ hubs at passengers’ expense.
Returning to Georgia, Delta Airlines uses ATL as one of its hubs and is responsible for over 70% of the passenger traffic in the airport.[4] Without serious competition between airlines, ATL has lost ground in terms of total direct flights and departures. Meanwhile, Delta has increased the number of seats in its planes and the percentage of seats sold in each flight to keep pace with the growing number of passengers. The same trend appears in the national data where the median number of seats per departure has risen by 15 from 91 to 107 and the percentage of those seats occupied by passengers rose by 6 percentage-points from 74% to 81%.[5] This leaves passengers with fewer choices, increasingly crowded planes and no tenable response on the market.
The internet has made it easier for individuals and companies to work across geographic boundaries. But for personal and business purposes the internet can only go so far and there comes a point when physical meetings are necessary. The airline industry thus has a crucial role to play in the globalization of our society and economy. Unfortunately, airlines too often engage in practices that hamper this integration and the continuing trend from consolidation to competition since 1978 has only enabled them.
While reinstating pre-1978 regulations is neither a good idea nor likely possible, federal policymakers need to look seriously at the state of the airline industry and increase scrutiny on any future mergers. Strengthening and applying anti-trust laws to the industry in order to create space for smaller airlines and force greater head-to-head competition between major carriers would serve as a good first step. Otherwise crowded flights at inopportune hours without alternatives will further define domestic air travel.
### Table II: Atlanta compared to the nation
[1] Unless otherwise noted, all statistics come from analysis of the American Community’s Survey 2006 estimates and 2016 5-year estimates or from analysis of data on all commercial flights from the 100 largest metropolitan areas in 2006 and 2016, downloaded from the Bureau of Transportation Statistics (BTS).
[2] Table II provides a simple comparison between trends at ATL and nationally.
[3] According to analysis of 2017 BTS data by Statista, accessible at https://bit.ly/2fMUXkn
[4] Based on ATL’s Monthly Airport Traffic Report, accessible at https://bit.ly/2szyKxF
[5] Planes from ATL have a median of 22 more seats than they did in 2006 (from 117 to 139), and the occupancy rate of those seats has risen by 8 percentage-points (from 77% to 85%).
Scroll to top
Insert math as
$${}$$
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https://qanda.ai/en/search/%5Cleft(%20%202x%20%5E%7B%204%20%20%7D%20%20%2B25x%20%5E%7B%203%20%20%7D%20%20%2B4x%2B10%20%5Cright)%20%20%20%5Cdiv%20%20%20%5Cleft(%20%202x%2B1%20%5Cright)?search_mode=expression
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# Calculator search results
Formula
Calculate the value
Use the synthetic division to find the quotient and the remainder
$\left( 2x ^{ 4 } +25x ^{ 3 } +4x+10 \right) \div \left( 2x+1 \right)$
$\dfrac { 2 x ^ { 4 } + 25 x ^ { 3 } + 4 x + 10 } { 2 x + 1 }$
Arrange the rational expression
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 25 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ \div } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
Calculate the multiplication expression
$\color{#FF6800}{ \dfrac { 2 x ^ { 4 } + 25 x ^ { 3 } + 4 x + 10 } { 2 x + 1 } }$
Quotient $: x ^ { 3 } + 12 x ^ { 2 } - 6 x + 5 \\$ Remainder $: 5$
Use the synthetic division to find the quotient and the remainder
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ + } \color{#FF6800}{ 25 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \right ) \color{#FF6800}{ \div } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
Divide $2 x ^ { 4 } + 25 x ^ { 3 } + 4 x + 10$ by $2 x + 1$ using the synthetic division
Quotient $: x ^ { 3 } + 12 x ^ { 2 } - 6 x + 5 \\$ Remainder $: 5$
Solution search results
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https://morethingsjapanese.com/what-is-nomological-thinking/
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# What is nomological thinking?
## What is nomological thinking?
The nomology of mind is the branch of science and philosophy concerned with the laws or principles governing the thought processes and operation of the mind, especially as defined by custom or culture.
## What is a Nomological net in psychology?
A nomological network (or nomological net) is a representation of the concepts (constructs) of interest in a study, their observable manifestations, and the interrelationships between these.
What is deductive Nomological?
Deductive-Nomological Explanation The deductive-nomological model used to be the standard conception of explanation: one explains a phenomenon by deducing the description of the phenomenon from a law and a description of the particular circumstances in which the phenomenon in question occurs.
### What is nomological network analysis?
A nomological network (or nomological net) is a representation of the concepts (constructs) of interest in a study, their observable manifestations, and the interrelationships between these. The term “nomological” derives from the Greek, meaning “lawful”, or in philosophy of science terms, “law-like”.
### What is a Nonology?
Nonology is one of several nonce words created by analogy with trilogy (along with duology, heptalogy and other [Greek number prefix]+logy constructions).
Is Behaviourism idiographic or nomothetic?
Idiographic vs Nomothetic It is a nomothetic approach as it views all behavior governed by the same laws of conditioning. However, it does account for individual differences and explain them in terms of difference of history of conditioning.
## How do you describe a Nomological network?
A nomological network (or nomological net) is a representation of the concepts (constructs) of interest in a study, their observable manifestations, and the interrelationships between these. Correspondence rules, allowing each construct to be measured empirically.
## Which is the best definition of the word nomological?
Definition of nomological. : relating to or expressing basic physical laws or rules of reasoning. nomological universals.
What’s the difference between a merely universal and a nomological statement?
The difference between a nomological and a merely universal statement is that from the universal all As are Bs one cannot, but from the nomological all As must be Bs one can, infer the counterfactual if this were an A it would (have to) be a B
### What are the principles of the nomological network?
The nomological network is founded on a number of principles that guide the researcher when trying to establish construct validity. They are: Scientifically, to make clear what something is or means, so that laws can be set forth in which that something occurs.
### Why did Cronbach and Meehl create the nomological network?
The nomological network was Cronbach and Meehl’s view of construct validity. That is, in order to provide evidence that your measure has construct validity, Cronbach and Meehl argued that you had to develop a nomological network for your measure.
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https://www.longqi.cf/
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# New Site 新的网站
Hi everyone! I am happy to announce I have a new version of this website. It is a new iteration of the website. Most of the old articles will still be here, and the new articles will be published in the new website here. You can find several new articles there now, and some of them are actually published months ago. One of the article is related to a major update of WriteTeX. For further update of WriteTeX, please also refer to new website. Clearly, the new website is not full functional, and more updates are on the way. Welcome to visit the new website @ longqi.ga.
# Release of WriteTeX v 1.00
Everything That Has A Beginning Has An End. From “The Matrix Revolutions”
# 打假：印度是强奸之国
## 均值分析
globalmean <- rape %>%
group_by(Year) %>%
summarise(mean=round(mean(Events,na.rm=T),2),
median=median(Events,na.rm=T),
sd=round(sd(Events,na.rm=T),2))
# How to parallelize 'do' computation in dplyr
## Introduction
Recently, I took apart in the IJCAI-17 Customer Flow Forecasts. It is an interesting competition in some extent. The datasets provided include:
1. shop_info: shop information data
2. user_pay: users pay behavior
3. user_view: users view behavior
4. prediction：test set and submission format
Because the nature of this problem is to predict time series, methods specifically designed for this task should be tested. The well-known ones include:
1. ARIMA series models
2. ETS series models
3. Regression models
And it is not hard to find out that customer flow is a seasonal time series. Therefore, time series decomposition such as X12 and STL may be useful tools in analysis.
### Preprocessing
The datasets include plenty of information such as the user_id make a payment to shop_id at time. Because the goal is to predict the flow of each shop and it is hard to build a user_id profile based model with only this amount of data provided, a shop_id profile based solution appears to be a better choice, i.e., we will build a model for each shop, and do the prediction. Therefore, for the preprocessing, the user_id should be aggregated. This is a pretty entry level task for dpylr(R) or pandas(Python) user. Therefore, I do not share code for this part, the results are organized as following dataset:
library(psych)
summary(tc2017)
## shop_id time_stamp date_week nb_pay
## Min. : 1 Min. :2015-06-26 Monday :86544 Min. : 1.0
## 1st Qu.: 504 1st Qu.:2016-02-03 Tuesday :84851 1st Qu.: 51.0
## Median :1019 Median :2016-05-22 Wednesday:85283 Median : 82.0
## Mean :1008 Mean :2016-05-04 Thursday :85643 Mean : 116.3
## 3rd Qu.:1512 3rd Qu.:2016-08-15 Friday :86041 3rd Qu.: 135.0
## Max. :2000 Max. :2016-10-31 Saturday :84902 Max. :4704.0
## Sunday :86011
describe(tc2017)
## vars n mean sd median trimmed mad min max
## shop_id 1 599275 1007.58 577.88 1019 1008.69 747.23 1 2000
## time_stamp* 2 599275 NaN NA NA NaN NA Inf -Inf
## date_week* 3 599275 4.00 2.00 4 4.00 2.97 1 7
## nb_pay 4 599275 116.26 132.04 82 93.64 54.86 1 4704
## range skew kurtosis se
## shop_id 1999 -0.02 -1.22 0.75
## time_stamp* -Inf NA NA NA
## date_week* 6 0.00 -1.25 0.00
## nb_pay 4703 7.06 105.67 0.17
### Exploratory
First, let us make some figures using off course ggplot2. Plots for first five shops:
Above two figures are quite messy. We can notice that the data have different range, which means that we may have to worry about NAs. Moreover, most of the series do not steady in the given range. For these five curves, the curves are more steady after April 2016. Then, above series are plotted into separated panels as follows:
p <- ggplot(tc2017 %>% filter(shop_id<6),aes(time_stamp,nb_pay)) +
geom_line() +
facet_wrap(~shop_id, ncol = 1, scales = "free")
print(p)
Some series have strong seasonal feature, such as curve for shop_id==4. We may need to consider the seasonal effect. A quick acf drawing is shown as below:
acf((tc2017 %>% filter(shop_id==4))$nb_pay) It can be observed that the periodic pattern is quite clear, the period is 7 and it is the length of one week. Therefore, we plot the data against the weekday: p <- ggplot(tc2017 %>% filter(shop_id==4), aes(time_stamp,nb_pay)) + geom_line(size=1) + facet_grid(date_week~.,scales = "fixed")+ theme_bw() print(p) It is shown in above figure, the number of customs is much steady when we investigate the flow on the same weekday. This pattern also appears in the data of other shops. p <- ggplot(tc2017 %>% filter(shop_id<6), aes(time_stamp,nb_pay,color = date_week)) + geom_line(size=1) + facet_grid(date_week~shop_id,scales = "free")+ scale_color_brewer(palette = "Set1")+ theme_bw()+ theme(legend.position = "none") print(p) Generally, the flows have quite different patterns between weekdays and weekends. However, the longtime trend also plays important role in the flow. Let's make some predictions here: library(forecast) library(xts) to.ts <- function (x) { ts(x$nb_pay,frequency = 7)
}
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https://okayama.pure.elsevier.com/en/publications/reduced-lattice-thermal-conductivity-of-fe-bearing-bridgmanite-in
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# Reduced lattice thermal conductivity of Fe-bearing bridgmanite in Earth's deep mantle
Wen Pin Hsieh, Frédéric Deschamps, Takuo Okuchi, Jung Fu Lin
Research output: Contribution to journalArticlepeer-review
28 Citations (Scopus)
## Abstract
Complex seismic, thermal, and chemical features have been reported in Earth's lowermost mantle. In particular, possible iron enrichments in the large low shear-wave velocity provinces (LLSVPs) could influence thermal transport properties of the constituting minerals in this region, altering the lower mantle dynamics and heat flux across core-mantle boundary (CMB). Thermal conductivity of bridgmanite is expected to partially control the thermal evolution and dynamics of Earth's lower mantle. Importantly, the pressure-induced lattice distortion and iron spin and valence states in bridgmanite could affect its lattice thermal conductivity, but these effects remain largely unknown. Here we precisely measured the lattice thermal conductivity of Fe-bearing bridgmanite to 120 GPa using optical pump-probe spectroscopy. The conductivity of Fe-bearing bridgmanite increases monotonically with pressure but drops significantly around 45 GPa due to pressure-induced lattice distortion on iron sites. Our findings indicate that lattice thermal conductivity at lowermost mantle conditions is twice smaller than previously thought. The decrease in the thermal conductivity of bridgmanite in mid-lower mantle and below would promote mantle flow against a potential viscosity barrier, facilitating slabs crossing over the 1000 km depth. Modeling of our results applied to LLSVPs shows that variations in iron and bridgmanite fractions induce a significant thermal conductivity decrease, which would enhance internal convective flow. Our CMB heat flux modeling indicates that while heat flux variations are dominated by thermal effects, variations in thermal conductivity also play a significant role. The CMB heat flux map we obtained is substantially different from those assumed so far, which may influence our understanding of the geodynamo.
Original language English 4900-4917 18 Journal of Geophysical Research: Solid Earth 122 7 https://doi.org/10.1002/2017JB014339 Published - Jul 2017
## Keywords
• bridgmanite
• geodynamics
• thermal conductivity
## ASJC Scopus subject areas
• Geophysics
• Geochemistry and Petrology
• Earth and Planetary Sciences (miscellaneous)
• Space and Planetary Science
## Fingerprint
Dive into the research topics of 'Reduced lattice thermal conductivity of Fe-bearing bridgmanite in Earth's deep mantle'. Together they form a unique fingerprint.
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https://uwaterloo.ca/nanotechnology/?uwb=281
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# Nanotechnology Engineering at the University of Waterloo
Nanotechnology Engineering is a multi-disciplinary engineering field, which draws from and benefits areas such as materials science and engineering, chemistry, physics, biology, and medicine.
Waterloo's Nanotechnology Engineering programs are offered collaboratively through the Department of Chemical Engineering and the Department of Electrical and Computer Engineering in the Faculty of Engineering, and the Chemistry Department in the Faculty of Science.
1. May 19, 2020Celebrating Capstone Design
Celebrating Capstone Design
When COVID-19 restrictions forced the Nanotechnology Engineering program to cancel its Capstone Design Symposium with just days’ notice, students quickly pivoted to present their own projects via online presentation seminars and honour the accomplishments of their classmates.
2. Apr. 14, 2020NE teams dominate Esch pitch competition
Congratulations to Nanotechnology Engineering’s iuvoderm, KnowStroke and Scope for their wins at the Norman Esch Entrepreneurship Awards for Capstone Design competition. These teams of fourth-year students brought home three of the six $10,000 prizes on offer at this annual pitch competition that recognizes innovative Capstone Design projects. 3. Apr. 6, 2020NE teams win Concept$5k pitch competition
Congratulations to the SMRT Coat and iuvoderm teams for their success in the Winter 2020 Concept \$5k Pitch Competition.
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http://crypto.stackexchange.com/questions/14592/shamirs-id-based-signatures-notation-issues
|
# Shamir's ID based signatures - Notation issues
I am currently implementing Shamir's ID Based signature scheme as defined in the original paper. The sign and verify operation are defined as follows:
Sign: $s = g * r^{f(t,m)} (\mod n)$
Verification: $s^e = i * t^{f(t, m)} (\mod n)$
I have some troubles to convert this to Java code, because I am unsure about the order of evaluation, i.e., I am unsure, what the modulus refers to in this context, the hole right hand side (including the multiplication) or the exponentiation operation, only?
Best regards,
Kwyjibo
PS: This post is related to this question.
-
Ok, lets look at the operations.
Sign: $s = g * r^{f(t,m)} \pmod n$
This is an assignment. You compute $(g * r^{f(t,m)}) \mod n$ and assign the resulting value to $s$. If you have a multiplication $(a \cdot b) \mod n$, this is equal to $((a \mod n)\cdot (b \mod n)) \mod n$. See for instance here.
Verification: $s^e = i * t^{f(t, m)} \pmod n$
This is no check for equality, but a check for congruence.
You can implement this by computing $s^e \mod n$ as well as $(i * t^{f(t, m)}) \mod n$ and check if these values are equal.
fgrieu has recently written an answer to a recent question on congruences which clarifies this nicely.
-
Thank you for your answer. Does (mod n) relate to the whole right hand side (i.e., [g*r^f(t,m)] mod n), or to the exponentiation, only (i.e., g * [r^f(t,m) mod n])? – Kwyjibo Feb 20 at 8:18
@Kwyijbo you can see this from my answer (below the sign operation). This applies always to the entire side. If you have a multiplication modulo $n$ then you can reduce any of the operands modulo $n$ and then the result modulo $n$. You may also read this for a description of modular exponentiation. I would strongly suggest to read up on modular arithmetic before implementing anything. If you implement this scheme in Java, BigInteger already provides all these methods. – DrLecter Feb 20 at 9:23
I haven't seen the Shamir ID-based signature algorithm, but I think you want to use .powMod(exponent, modulus), and not, for performance and/or OutOfMemory reasons, .pow(exponent).mod(modulus). E.g. for forming the signature BigInteger g=???; BigInteger r=???; BigInteger ftm=???; BigInteger n=???; BigInteger s=r.powMod(ftm, n).multiply(g).mod(n);
-
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https://socratic.org/questions/can-you-help-me-with-this-20-g-of-glucose-is-dissolved-in-150-g-of-water-calcula
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Chemistry
Questions Topics
# Can you help me with this? 20 g of glucose is dissolved in 150 g of water. Calculate the molarity, molality & mole fraction of glucose in solution.
Then teach the underlying concepts
Don't copy without citing sources
preview
?
#### Explanation
Explain in detail...
#### Explanation:
I want someone to double check my answer
16
Jul 8, 2015
Here's how you can go about solving this one.
#### Explanation:
The problem gives you all the information you need in order to solve for the molality and mole fraction of the solution. In order to determine its molarity, you're going to need the solution's volume.
To get the volume, you have to know what the density of the solution is. Determine the percent concentration by mass of the solution first
$\text{%w/w" = m_"solute"/m_"solution} \cdot 100$
In your case, the mass of the solution will be
${m}_{\text{solution" = m_"glucose" + m_"water}}$
${m}_{\text{solution" = 20 + 150 = "170 g}}$
This means that you get
$\text{%w/w" = (20cancel("g"))/(170cancel("g")) * 100 = "11.8%}$
The density of this solution will thus be
http://us.mt.com/us/en/home/supportive_content/application_editorials/D_Glucose_de_e.html
$\rho = \text{1.045 g/mL}$
Use glucose's molar mass to determine how many moles you have
20cancel("g") * "1 mole glucose"/(180.16cancel("g")) = "0.111 moles glucose"
The solution's volume will be
170cancel("g") * "1 mL"/(1.045cancel("g")) = "162.7 mL"
This means that its molarity is - do not forget to convert the volume to liters!
C = n/V = "0.111 moles"/(162.7 * 10^(-3)"L") = color(green)("0.68 M")
A solution's molality is defined as the number of moles of solute divided by the mass of the solvent - in kilograms! This means that you have
b = n/m_"water" = "0.111 moles"/(150 * 10^(-3)"kg") = color(green)("0.74 molal")
To get the mole fraction of sucrose, you need to know how many moles of water you have present. Once again, use water's molar mass
150cancel("g") * "1 mole water"/(18.02cancel("g")) = "8.24 moles water"
The total number of moles the solution contains is
${n}_{\text{total" = n_"glucose" + n_"water}}$
${n}_{\text{total" = 0.111 + 8.24 = "8.351 moles}}$
This means that the mole fraction of sucrose, which is defined as the number of moles of sucrose divided by the total number of moles in the solution, will be
chi_"sucrose" = n_"sucrose"/n_"total" = (0.111cancel("moles"))/(8.351cancel("moles")) = color(green)("0.013")
SIDE NOTE I've left the values rounded to two sig figs, despite the fact that you only gave one sig fig for the mass of glucose.
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##### Impact of this question
19979 views around the world
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|
http://tex.stackexchange.com/questions/72983/alias-for-verbatim-environment?answertab=votes
|
# Alias for verbatim environment
I'm trying to create an alias for the verbatim environment like this:
\newcommand{\vb}[1]{\begin{verbatim} #1 \end{verbatim}}
So I can use it like this:
\vb{
word.
}
But when using it, I get this error:
! Missing $inserted. <inserted text>$
l.93 \end{verbatim}
Where line 93 is the end of a verbatim environment I used after later down the file after closing the \vb. If I replace all verbatim environments with the \vb syntax, then I get this error:
Runaway argument?
zip([],B) = case ([],B) of ([],_) => [] | (_,[]) => [] | (x::L,y::R\ETC.
! File ended while scanning use of \@xverbatim.
<inserted text>
\par
So it seems like the \vb is not closing the environment correctly? How do I get this to work ? The end goal is to get a \vb command that I can use like I described above, and bonus points if I could indent the stuff in the \vb command by a few mm.
-
As far as I know, there’s no way in replacing the environment with a command. Nonetheless you should take a deep look into the fancyvrbdocumentation. – Speravir Sep 18 '12 at 2:29
If you just want oneline verbatim text, you could use a \Verb variant in Fancyvrb. – Speravir Sep 18 '12 at 2:32
Your statement "So it seems like the \vb is not closing the environment correctly" is absolutely correct. Tokens are scanned in search of \end{verbatim} and is never found. – Werner Sep 18 '12 at 5:26
Werner forgot to provide the following link (I found it in another answer of him) from the UK TeX FAQ: Why doesn’t verbatim work within …?. – Speravir Sep 18 '12 at 22:41
A general rule is that you can't have \begin{verbatim} or the \verb command in the argument to another command, including an argument to \newcommand.
If you really want to use that syntax, you of course can't have braces in the argument and hope that they will be printed as themselves: either they delimit the argument or they must be printed.
If this limitation satisfies you, then
\makeatletter
\newcommand{\vb}{%
\begingroup
\@verbatim
\catcode{=1 \catcode}=2 \catcode =10
\frenchspacing
\@vb}
\def\@vb#1{#1\endtrivlist\endgroup}
\makeatother
will allow you to write
\vb{
word.
}
I don't think this is a great improvement than saying
\begin{verbatim}
word.
\end{verbatim}
If you want a margin indent of the verbatim, look at the option xleftmargin in to the Verbatim environment provided by the package fancyvrb`.
-
|
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|
http://sage-doc.sis.uta.fi/reference/curves/sage/schemes/elliptic_curves/mod5family.html
|
# Elliptic curves with congruent mod-5 representation¶
AUTHORS:
• Alice Silverberg and Karl Rubin – original PARI/GP version
• William Stein – Sage version
sage.schemes.elliptic_curves.mod5family.mod5family(a, b)
Formulas for computing the family of elliptic curves with congruent mod-5 representation.
EXAMPLES:
sage: from sage.schemes.elliptic_curves.mod5family import mod5family
sage: mod5family(0,1)
Elliptic Curve defined by y^2 = x^3 + (t^30+30*t^29+435*t^28+4060*t^27+27405*t^26+142506*t^25+593775*t^24+2035800*t^23+5852925*t^22+14307150*t^21+30045015*t^20+54627300*t^19+86493225*t^18+119759850*t^17+145422675*t^16+155117520*t^15+145422675*t^14+119759850*t^13+86493225*t^12+54627300*t^11+30045015*t^10+14307150*t^9+5852925*t^8+2035800*t^7+593775*t^6+142506*t^5+27405*t^4+4060*t^3+435*t^2+30*t+1) over Fraction Field of Univariate Polynomial Ring in t over Rational Field
|
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|
https://chemistry.stackexchange.com/questions/8536/name-of-a-pharmaceutical-drug-used-in-dentistry-that-has-ionic-bonding-and-how
|
# name of a pharmaceutical drug used in dentistry that has Ionic bonding? and how this bounding is made?
Hello I am looking for this information and I did not find anything, the closest thing I have found it is Fluorocarbon, but I think it is wrong, does anybody know?. Help really appreciated I am still looking for this
• Prescription strength fluoride (Acidul), though it probably is not considered to be a pharmaceutical. – Uncle Al Feb 17 '14 at 21:40
The fluorocarbons that you mentioned do have polarized $\ce{C-F}$ bonds, but no ionic bonds. If you think ionic, think salts.
All these compounds have tertiary and secondary amino groups. (I've marked the relevant nitrogen atoms blue). When these compounds are treated with hydrogen chloride, the amines get protonated and the neutral compounds are converted to ionic hydrochlorides, $\ce{R3N ->[\textrm{HCl}] R3NH+ Cl-}$.
|
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|
http://export.arxiv.org/abs/1103.0038
|
cs.IT
(what is this?)
# Title: On the Sum-Capacity with Successive Decoding in Interference Channels
Abstract: In this paper, we investigate the sum-capacity of the two-user Gaussian interference channel with Gaussian superposition coding and successive decoding. We first examine an approximate deterministic formulation of the problem, and introduce the complementarity conditions that capture the use of Gaussian coding and successive decoding. In the deterministic channel problem, we find the constrained sum-capacity and its achievable schemes with the minimum number of messages, first in symmetric channels, and then in general asymmetric channels. We show that the constrained sum-capacity oscillates as a function of the cross link gain parameters between the information theoretic sum-capacity and the sum-capacity with interference treated as noise. Furthermore, we show that if the number of messages of either of the two users is fewer than the minimum number required to achieve the constrained sum-capacity, the maximum achievable sum-rate drops to that with interference treated as noise. We provide two algorithms (a simple one and a finer one) to translate the optimal schemes in the deterministic channel model to the Gaussian channel model. We also derive two upper bounds on the sum-capacity of the Gaussian Han-Kobayashi schemes, which automatically upper bound the sum-capacity using successive decoding of Gaussian codewords. Numerical evaluations show that, similar to the deterministic channel results, the constrained sum-capacity in the Gaussian channels oscillates between the sum-capacity with Han-Kobayashi schemes and that with single message schemes.
Comments: 32 pages, 21 figures Subjects: Information Theory (cs.IT) Cite as: arXiv:1103.0038 [cs.IT] (or arXiv:1103.0038v2 [cs.IT] for this version)
## Submission history
From: Yue Zhao [view email]
[v1] Mon, 28 Feb 2011 22:04:06 GMT (1827kb)
[v2] Tue, 29 Mar 2011 01:22:20 GMT (1940kb)
Link back to: arXiv, form interface, contact.
|
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|
https://getthingsdone.hk/2018/05/27/hot-to-build-a-robust-graphql.html
|
# How to build robust GraphQL APIs
Gilbert Wat (屈振鵬) · May 27, 2018
Just read this awesome article[1] in building GraphQL APIs. Github and facebook have created their own public facing GraphQL APIs. When I first dapple with this topic last year, one of the crucial question is resource management. Resource management is specifically the CPU and memory usage of data persistence layer.
In RESTful world, API designers can require the callers to bound the request. Take some naïve example in place I work, when the caller of /orders, we require them to specify the limit of number of orders or the date range. So the Swagger looks a bit like this.
/orders:
get:
security:
- CourierAuth: []
parameters:
- name: page
in: query
type: integer
description: 'default set to 1'
- name: limit
in: query
type: integer
description: 'default set to 30'
- name: status
in: query
type: string gtgt
required: true
enum:
- pending
- in_progress
- is_completed
responses:
'200':
description: OK
schema:
\$ref: '#/definitions/Orders'
summary: List orders
description: List orders
tags:
- Order
produces:
- application/json
But in the world of GraphQL, there is no elegant way to specify this. Also, the limit can be different, even for the same application, with different usage, the result set can be differ so much.
In the context of database, we can separate into 2 questions:
1. How can we make sure an arbitrary GraphQL query won’t run too long and use up all CPU of the database?
2. How can we make sure an arbitrary GraphQL query won’t return a yuuuuuuuggeeeeeee results and use up all memory / bandwidth of client?
Turns out there can be mathematical / academic ways to deal with these problem.
So first this paper established that for every queries in GraphQL, there is a way to transform it into non-redundant queries in ground-typed normal form. Sounds intimidating? Yes it is. I am still grasping what is that. Anyone has an idea let me know.
And then based on the algorithm mentioned in the original paper2, we can determine the size of the result in polynomial time. After that, we can choose to really run the query or just return an error of “result set too large”.
In the following weeks, I would like to have time to prototype it, but I cannot guarantee anything.
P.S: A little bit takeaway in reading this:
1. Formalization of problem really helps us to think about it. Formalization essentially separate convoluting concepts and parameters into mathematical notations. Real world socio-political or human dynamics problems may not be applicable but most other problems, I would argue, is at least partly applicable to this approach.
2. Everytime I read mathematical notations I got cognitive overload. Anyway to solve this? I am drawing mindmap but still very overloaded.
|
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|
https://hungary.pure.elsevier.com/en/publications/rheology-study-on-the-earths-mantle-application-of-quantitative-f
|
# A földköpeny reológiai kutatása: Mennyiségi fourier transzformációs infravörös spektrometria alkalmazása egy persány hegységi xenolit példáján
Translated title of the contribution: Rheology study on the earth’s mantle: Application of quantitative fourier transform infrared spectroscopyon upper mantle xenolith from the perşani mountains
Thomas Pieter Lange, Csaba Szabó, Nóra Liptai, Levente Patkó, Orsolya Gelencsér, László Előd Aradi, István János Kovács
Research output: Contribution to journalArticle
### Abstract
By studying mantle xenoliths we can obtain direct information about the chemical and physical state of the lithospheric mantle. With this information, some important geophysical properties (e.g. seismic velocity, conductivity and effective viscosity) can be calculated, which provide a tool to better understand the evolution of the studied region. In this paper, we present how even a small amount of ’water’ (more precisely structural hydroxyl) in nominally anhydrous minerals (NAMs) can affect the physical properties of the lithospheric mantle and how to quantify the amount of the structural hydroxyl. Fourier transform infrared (FTIR) spectroscopy is a useful technique to study NAMs for their ‘water’ content, which affects the rheology of the different rock types (e.g. melting temperature, deformation, conductivity). As demonstrated in petrologic experiments H+ can be incorporated in a lattice vacancy replacing a cation or incorporate together with another cation, called heteroelectronic incorporation (e.g. H+ + Al3+ or 2H+ + Ti4+). When H+ incorporates in a vacancy it binds to an O2– forming a structural hydroxyl (OH) group. In some cases, the OH can bind to a Li+ or Na+ ions within intersticial space. The type of incorporation depends on the composition of the system (e.g. Ti content), the oxygen, H2 O and SiO2 activity, oxygen fugacity and pressure. With the help of micro-FTIR one can measure the exact structural hydroxyl content of the nominally anhydrous minerals. This value is defined in ppm wt. or mol%. Non-polarized micro-FTIR gives a good opportunity to measure small, unoriented grains in a relatively short time compared to the traditional polarized micro-FTIR. The goal of our study is to provide a detailed description of the micro-FTIR method and how it is used to measure structural hydroxyl content in NAMs. Our study focuses on the lithospheric mantle xenoliths of the Perşani Mountains Volcanic Field and use the results to constrain the physical conditions. Comparing the results with xenoliths from other young volcanic fields (Styrian Basin and Nógrád–Gömör), we have a better understanding of the evolution of the Carpathian-Pannonian region (CPR).
Original language Hungarian 233-254 22 Foldtani Kozlony 149 3 https://doi.org/10.23928/foldt.kozl.2019.149.3.233 Published - Jan 1 2019
### ASJC Scopus subject areas
• Geology
• Geochemistry and Petrology
• Stratigraphy
• Palaeontology
|
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|
https://www.vedantu.com/ncert-solutions/ncert-solutions-class-7-science-chapter-1
|
# NCERT Solutions for Class 7 Science
## NCERT Solutions for Class 7 Science Chapter 1 - Nutrition in Plants
NCERT Class 7 Science Chapter 1 is based on different modes of nutrition in plants. Experts at Vedantu have made NCERT Solutions for Class 7 Science Chapter 1 PDF format available for students that will help them build a strong base on plant nutrition. The questions are selected covering topics of Science Class 7 Chapter 1 in a precise manner. Provided solutions are equally effective for a student as it's accessible from anywhere. You can also download NCERT Solutions for Class 7 Maths to help you to revise complete syllabus and score more marks in your examinations.
With Vedantu Learning App in your Mobile, you will get to attend FREE LIVE Master - Classes and FREE Conceptual videos. Not only that, but you will also have access to all the FREE PDFs of study materials and solutions along with absolutely FREE Online Tests to enhance your problem-solving speed.
NCERT Class 7 Science Chapter 1 is visually appealing as it exposes you to the world of plants. The curriculum includes a range of tasks that will encourage kids to love studying. You will like studying this Chapter since the curriculum introduces you to new vocabulary and concepts.
In the Class 7 Nourishment in Plants Chapter, students will learn about many new topics linked to plants and how they obtain nutrition for themselves. They will also learn about photosynthesis, chlorophyll, stomata, etc. Plants with different forms of sustenance, such as insectivorous plants are also discussed in this chapter.
This chapter will cover the fundamentals of plant nutrition and how plants create their food, but reading it attentively will help students comprehend botany principles at a deeper level. As a result, it is strongly advised that students should make notes so that they may revise them while preparing this chapter for the exam.
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## Access NCERT Solutions for Science Chapter 1– Nutrition in Plants
Q1.Why Do Organisms Need To Take Food?
Ans: Organism needs food to:-
(i) Survive.
(ii) Growth.
(iii)Gain Energy.
(iv) Damage repair.
(v) Maintain bodily functions.
(vi) Other activities.
Q2. Distinguish Between a Parasite and Saprophyte.
Ans: Differences between Parasite and saprophytes are as follows:
Parasite Saprophyte Parasites are living entities that rely on their host to survive. Humans, animals, and plants all have parasites. They belong to the category of eukaryotic organisms.Examples- Tapeworm, barnacles. Saprophytes are organisms that feed on decomposing or dead substances. Saprophytes are found solely in plants and animals.Saprophytes can be eukaryotic or prokaryotic.Examples- Mushrooms, molds.
Q3. How Would You Test the Presence of Starch in Leaves?
Ans: When starch reacts with an iodine solution, it takes on a characteristic dark blue color. If a few drops of iodine solution are applied to a leaf and a dark blue color develops, the existence of starch in the leaf is confirmed.
Q4. Give a Brief Description of the Process of Synthesis of Food in Green Plants.
Ans: In green plants, the synthesis of food occurs by a process called photosynthesis. During this process, chlorophyll in the cells of the leaves uses carbon dioxide and water to synthesize carbohydrates in the presence of sunlight. The process can be represented by an equation:
$Carbon\:dioxide\:+\:\:Water\:\xrightarrow[Chlorophyll]{Sunlight}\:Carbohydrates\:+Oxygen$
During this process, oxygen is released, and the carbohydrates generated are stored as starch.
Q5. Show with the help of a sketch that the plants are the ultimate source of food.
Ans:
6. Fill in the blanks:
1. Green plants are called ----------- since they synthesize their own food.
Ans: Green plants are called autotrophs since they synthesize their own food.
1. The Food Synthesized by the Plants is Stored as ---------------.
Ans: The food synthesized by the plants is stored as starch.
1. In Photosynthesis, Solar Energy is Captured by the Pigment Called------------.
Ans: In photosynthesis, solar energy is captured by the pigment called chlorophyll.
1. During photosynthesis plants take in ------------- and release
-------------.
Ans: During photosynthesis, plants take in carbon dioxide and release oxygen.
Q7. Name the following:
1. A Parasitic Plant With a Yellow, Slender, and Tubular Stem.
Ans: Cuscuta- The Cuscuta plant is classified as a parasite since it lacks chlorophyll and feeds on the host. The host loses vital nutrients as a result of this process.
1. A Plant That Has Both Autotrophic and Heterotrophic Modes of Nutrition.
Ans: Pitcher plant - The pitcher plant is an autotrophic plant that performs photosynthesis, but it also has a partly heterotrophic method of nutrition because it grows in nitrogen-deficient soil.
1. The Pores Through Which Leaves Exchange Gases.
Ans: Stomata- Gases such as carbon dioxide, water vapor, and oxygen can diffuse into and out of the plant's interior tissues through stomata.
### Q8. Tick the Correct Answer:
1. Amarbel is an Example of:
(i)Autotroph
(ii) Parasite
(iii) Saprophyte
(iv) Host
Ans: (ii) Parasite-
Cuscuta or Dodder are other names for Amarbel. A parasite is an organism that grows on the body of another organism and feeds on its nutrition.
1. The Plant Which Traps and Feeds on Insects is:
(i) Cuscuta
(ii) China rose
(iii) Pitcher plant
(iv) Rose
Ans: (iii) Pitcher plant
The pitcher plant is a type of plant with trapping and digesting leaves. Medicine is made from the leaf and root.
Q9. Match the item in given column I with those in column II.
Column I Column II
1. Chlorophyll (a) Bacteria
2. Nitrogen (b) Heterotrophs
3. Amarbel (c) Pitcher plant
4. Animals (d) Leaf
5. Insects (e) Parasite
Ans: (i)-(d); (ii)-(a); (iii)-(e); (iv)-(b); (v)-(c)
Q10. Mark “T” if the statement is true and “F” if it is false:
1. Carbon dioxide is released during photosynthesis. (T/F)
Ans: False- Oxygen is released during photosynthesis.
1. Plants that synthesize their food themselves are called saprotrophs. (T/F)
Ans: False- Plants which synthesize their food themselves are called autotrophs.
1. The product of photosynthesis is not a protein. (T/F)
Ans: True- The product of photosynthesis is not a protein.
1. Solar energy is converted into chemical energy during photosynthesis. (T/F)
Ans: True- Solar energy is converted into chemical energy during photosynthesis.
Q11. Choose the Correct Option From the Following:
Which part of the plant gets carbon dioxide from the air for photosynthesis?
1. Root hair
2. Stomata
3. Leaf veins
4. Sepals
Ans: (b) Stomata gets carbon dioxide from the air for photosynthesis.
Q12. Choose the Correct Option From the Following:
Plants take carbon dioxide from the atmosphere mainly through their:
1. Roots
2. Stem
3. Flowers
4. Leaves
Ans: (d) Plants take carbon dioxide from the atmosphere mainly through their leaves.
Nutrition in plants Class 7 NCERT is a good conceptual chapter for the students of Class 7. The Official website has all Class 7 Science Chapter 1 Solution available in PDF format for students to get easy access. These solutions have the entire Ch 1 Science for Class 7 covered and will help students to score better marks in Science exams.
### Important Topics Covered in Chapter 1 of Class 7 Science- Nutrition in Plants
Nutrition in Plants Mode of Nutrition in Plants Photosynthesis – a food-making process in Plants The alternative mode of nutrition in Plants Saprophytes Nutrient replenishment in the soil
### 1.1 Mode of Nutrition in Plants
Among all living beings, plants are the only ones who can make their own food. They prepare their food from sunlight, minerals, water and carbon dioxide that exist in the surrounding. The nutrients help the plant to grow, build itself and repair damaged body parts. The nutrients also provide the required energy to perform vital life processes. The mode is nutrition by which an organism takes nutrients from its surroundings and utilizes it in its body.
There are two modes of nutrition- autotrophic and heterotrophic nutrition mode. Autotrophic nutrition mode enables the organisms to make their food from simpler substances from the surrounding. For example, plants are autotrophs. Heterotrophic nutrition mode allows the organism to derive their nutrients from other animals. For example, all animals are heterotroph.
Since plants are autotrophs, the next questions that will come to you are how do plants make their food.
### 1.2 Photosynthesis- Food Making Process in Plants
You must have learned that leaves are considered as food factories in plants. They synthesize the food for all parts of the plant. The different body parts transport different raw materials to the parts of the leaves. The roots absorb water and minerals from the soil and send it to leaves through vessels that run all over the root, stem and leaves. Tiny pores on the leaves, called stomata, absorb carbon dioxide. The guard cells control the opening and closing of stomata on the leaves.
All leaves contain chlorophyll. The chlorophyll is responsible for the green colour of the leaves. The chlorophyll traps sunlight and uses solar energy to produce food from carbon dioxide and water. Therefore, to produce food, plants require sunlight, water and carbon dioxide. The process by which plants produce their own food from sunlight, carbon dioxide and water is called photosynthesis. Photosynthesis is an exclusive process that takes place in plants and some algae. It uses solar energy.
Therefore, you can imagine the importance of photosynthesis for maintaining life on earth. Without photosynthesis, there will be no food, since all animals depend indirectly or directly on the plants for food. Without food for plants, life is impossible on earth.
At the time of photosynthesis, the chlorophyll present on the leaves uses sunlight, water and carbon dioxide to produce carbohydrates. Carbohydrate or starch is the food for the plant. The equation for photosynthesis is:
$\text{Carbon dioxide + water} \xrightarrow[Chlorophyll]{Sunlight} \text{Carbohydrate + oxygen}$
As you can see in the equation, oxygen is known to release during photosynthesis. The carbohydrate thus formed is converted to starch, which is another carbohydrate. Photosynthesis is indicated by the presence of starch in the leaves.
Green plants do not only conduct photosynthesis. Yellow, red or multicoloured leaves also perform photosynthesis. Chlorophyll is also present in the leaves that are of other colours.
If you look at the pond or any other stagnant water bodies, you will observe green slimy patches on the water surface. These slimy patches are algae and contain chlorophyll, which makes them green coloured. With the help of these chlorophylls, algae, too, can make their food by the process of photosynthesis.
Every living body is made up of numerous tiny building blocks called cells. Cells play numerous functions in the body. During photosynthesis, the stomata are responsible for gaseous exchange. The opening and closing of stomata are controlled by the guide cells.
### 1.3 Other Modes of Nutrition in Plants
Not all plants contain chlorophyll. For example, you will often find yellow tubular plants twining around the stem of other plants. It is called Cuscuta and they do not contain chlorophyll. Then how exactly do they get their food? Such plants that lack chlorophyll obtain food by heterotrophic nutrition mode. That means that the plants obtain food from other living organisms. The other living organism is called the host. If the plants deprive the valuable nutrients of the host, they are called parasites. You have often come across the word parasite in terms of insects and other animals. But can plants also be a parasite? Well, yes!
Do you know that plants can also eat animals? Yes, they do so. For example, a pitcher plant has a pitcher shaped structure which is a modification of a leaf. It has a lid at the top which closes when any insect (prey) falls into the pitcher. Some hairs directed downwards on the inside of the pitcher. These plants are insect-eating and known as insectivorous plants.
### 1.4 Saprotrophs
You must have seen mushrooms selling in the market. They are club-shaped structures mostly white or cream in colour. If they do not contain chlorophyll, then how do they prepare their food?
Mushrooms are fungi. They are not plants and they obtain food from other nutrition modes. They secrete digestive juices and chemicals on decaying or dead organic matters and extract nutrients from them. Such nutrition mode is called the saprophytic nutrition mode and the fungi are known as saprotrophs.
You will also find fungi growing on leather, pickle, bread and other surfaces, which are kept in hot and humid weather for a long time.
You will find most fungi in rainy seasons. These saprotrophs are the reasons why most food and clothes get spoiled in this season. The fungi propagate with the help of spores that can travel through the air. Once these spores come in contact with a wet surface, they can settle down, germinate and grow. So now you can understand why your food or wet clothes get spoiled in the rainy season.
There are other types of relationships between organisms. In one relationship, two organisms stay together since both of them are benefiting. For example, some fungi living in close association with the roots of some plants. They derive their nutrients from plants while providing nitrogen to the plants in return. Such a type of relationship where both the organisms are benefitted is called a symbiotic relationship.
In lichens, fungi and algae stay together. The alga delivers food it makes by photosynthesis. The fungus provides water, minerals, and shelter.
### 1.5 How Nutrients are Replenished in the Soil
If plants use all the minerals and nutrients from the soil, the levels of these nutrients in the soil are supposed to go down. To replenish the nutrient content of the soil, farmers often add manures and fertilizers to the soil. In this way, the nutrients are replenished, and it will support the continued growth of plants on this soil.
In general, soils require plenty of nitrogen for their growth. After each harvest, the soil gets devoid of nitrogen. To have further plantation on these soils, farmers often grow leguminous crops that can increase the nitrogen content of the soil. These leguminous crops like pulses, grams, dal, etc. are in a symbiotic relationship with a bacteria called rhizobium, which fixes atmospheric nitrogen into the soil. The bacteria obtain food and shelter in return from the plants. Growing leguminous crops in the field reduce the need to add nitrogen-containing artificial fertilizers in the soil.
In this CBSE Class 7 Science Chapter 1 nutrition in plants, you learned about plants that are autotrophs. You also learned about different nutrition modes amongst plants like heterotrophic, saprophytic, parasitic, insectivorous and symbiotic.
### Facts that Matter
• All organisms take food and utilize it to get energy for growth, maintenance and various life processes.
• Based on the mode of getting food, organisms are classified as autotrophs and heterotrophs.
• Autotrophs prepare their own food using simple inorganic materials like carbon dioxide and water.
• The essential requirements for photosynthesis are chlorophyll and sunlight.
• Heterotrophs are the organisms that cannot make food on its own and so they depend on autotrophs directly or indirectly for food.
• Parasitic, saprophytic, insectivorous and symbiotic are the different modes of heterotrophic nutrition in plants.
• Plants like Cuscuta are parasites as they take nutrition from the host plant.
• Saprotrophs like Fungi obtain nutrition from dead and decaying organic matter.
• Symbiotic relationship between Rhizobium and legumes helps in enriching the soil of the nitrogen that was lost.
• Leaves of the plants prepare the food so they are called the food factory of the plant.
• The important components of food are carbohydrates, fats, proteins, vitamins and minerals.
• Sun is the fundamental source of energy for all living organisms.
### Key Features of NCERT Solutions for Class 7 Science Chapter 1
Scoring good marks in the exam is essential for every student. To do so, students must have a clear idea about the subject. The next step would be to learn the solutions to important questions related to the subject. Experts at Vedantu have made Class 7th Science Chapter 1 solutions in a format that’s simple and easy to understand. Students can get benefits given below:
• Experts in the subject matter have designed the ch 1 Science Class 7 solutions. That is why the NCERT Class 7th Science Chapter 1 solutions can be considered as the most comprehensive, easy-to-understand, and to-the-point study materials for the students.
• Students have the unique facility of asking the experts whenever they face any problem.
• NCERT solution for Class 7 Science Chapter 1 has arranged all the concepts and equations in a proper sequence, thus saving the time for the students while they study.
• The students are encouraged to perform several Science experiments to understand the concepts.
• Since NCERT Class 7 Science Chapter 1 nutrition in plants can be downloaded, it allows the students to read and revise the concepts at their convenience.
• CBSE Class 7 Science Chapter 1 nutrition in plants PDF becomes more helpful when students plan for a quick revision before the examination.
• The NCERT solution for Class 7 Science Chapter 1 solutions promises a significant increase in marks for the students.
1. How does the fungus get its nutrition?
Fungus is a saprotroph. Its mode of nutrition is called the saprotrophic mode of nutrition. It takes its food from dead and decaying organic matter. The digestive juices of fungus convert the dead materials into soluble form that get absorbed.
2. Explain the process, how nutrients are replenished in the soil.
The plants absorb mineral nutrients from the soil. The fertilizers and manures containing various nutrients like nitrogen, potassium and phosphorus need to be added from time to time to enrich the soil. The nitrogen gas is available in large amounts in the soil but cannot use it directly from the air. The bacterium Rhizobium lives in the roots of the leguminous plants. Rhizobium bacteria convert the non-usable form. In this way the nutrients are replenished in the soil by using fertilizers, manures and by sowing leguminous plants.
3. Explain the mechanism of eating insects by a pitcher plant?
The leaves of the pitcher plants are tailored into a pitcher like structure. The tip of the leaves form a lid that can open and close the mouth of the pitcher like structure of the leaves. There is hair inside the pitcher, which is directed downwards. When an insect lands in the pitcher gets entangled into the hair. The pitcher secretes some digestive juices that help the plant to digest the insect. Such insects eating plants are insectivorous plants. These plants do not get all the necessary nutrients from the soil. So, they are called partial heterotrophs.
4. How do I get marks in the exams with Vedantu’s study guide?
Vedantu has a team of very proficient and experienced teachers who understand the academic needs of every student. The subject matter experts have developed the study material in such a way that it is self-explanatory. The materials are also developed as per the latest guidelines from the CBSE board. You can not only download the pdf of the study guide but also reach out to the teachers if you have any doubts relating to the subject. This will definitely help you score more marks than before.
5. What do you mean by autotrophic nutrition according to Chapter 1 of Class 7th Science NCERT Textbook?
In the presence of sunshine, autotrophic nutrition is a process in which an organism creates its own sustenance from basic inorganic elements such as water, carbon dioxide, and mineral salts. The autotrophic mechanism of feeding is found in all green plants. This is a very interesting topic and the related processes are very necessary and hence the students must pay heed to each process involved. Visit the Vedantu site in case of any doubt or query regarding the same.
6. What do you mean by heterotrophic nutrition according to Chapter 1 of Class 7th Science NCERT Textbook?
Heterotrophic nutrition is defined as a method of nutrition in which certain species rely on other organisms for their survival. Heterotrophs are creatures that cannot manufacture their own food. Animals, fungi, and bacteria are all examples of heterotrophs. Because this is such an intriguing subject, students should pay close attention to the many procedures that go along with it. If you have any questions on the same, you can visit the Vedantu website.
7. What do you mean by chlorophyll according to Chapter 1 of Class 7th Science NCERT Textbook?
The chemical that gives plants their green hue is chlorophyll. During the biological process known as photosynthesis, it aids plants in absorbing energy and obtaining nutrients from sunlight. Many green foods contain chlorophyll, and some individuals take it as a supplement or apply it topically. In order for plants to begin photosynthesis, they would need this energy. Photosynthesis is the process through which water and carbon dioxide are converted into starches that plants may utilise as food.
8. What do you understand by photosynthesis according to Chapter 1 of Class 7th Science NCERT Textbook?
During photosynthesis, the light energy is converted into chemical energy by green plants and other organisms. Chloroplasts are tiny particles found inside plant cells that perform photosynthesis. Plants absorb carbon dioxide from the air and water from the earth via their roots. The Sun gives out light energy. The leaves release the oxygen that has been generated into the air. Since it is an important topic, do understand it properly along with all its components such as chloroplasts and so on.
9. How can I download the Solutions of Chapter 1 of Class 7th Science NCERT Textbook?
The solutions are easily available on the Vedantu site.
1. Click on this NCERT Solutions of Class 7 Science and choose Chapter 1.
2. The webpage with Vedantu’s solutions for Chapter 1 of Class 7th Science NCERT Textbook will open.
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https://brilliant.org/problems/some-area-here/
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# Some area here
Calculus Level 4
What is the area of the gray region? Give you answer in three decimal decimal places.
×
Problem Loading...
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Set Loading...
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https://mathoverflow.net/questions/28157/breaking-the-circularity-in-the-definition-of-n
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# Breaking the circularity in the definition of N
Some days ago, I posted a question about models of arithmetic and incompleteness. I then made a mixture of too many scattered ideas. Thinking again about such matters, I realize that what really annoyed me was the assertion by Ken Kunen that the circularity in the informal definition of natural number (what one gets starting from 0 by iterating the successor operation a finite number of times) is broken “by formalizing the properties of the order relation on ω” ( page 23 of his “The Foundations of Mathematics”). What does actually “breaking the circularity” mean? Is there a precise model theoretic statement that expresses this meaning? And what about proving that statement? Is that possible?
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If possible, could you please quote a couple of sentences to give us the context? This is a relatively new book and therefore many readers will not have access to it. Since "breaking the circularity" doesn't sound like a technical mathematical term, some more information is necessary to determine what Kunen means by it. – Timothy Chow Jun 15 '10 at 1:04
– Halfdan Faber Jun 15 '10 at 4:52
Looking at the draft that was linked above, it's more clear what Kunen means. He is just saying that the informal "definition" of the natural numbers that you might think of in school is circular when examined closely. And it is, in the sense that you have to start with some undefined concept, be it "natural number", "finite set", "proof", etc., to capture finiteness.
However, Kunen does not dwell on that sort of philosohical point. He is simply saying that there is a formal and non-circular definition of ω in set theory, as the smallest infinite ordinal. This does give a rigorous definition, but it doesn't ensure that "finite" in an aribitrary model corresponds to our actual notion of finite. That is something that cannot be ensured in first-order logic.
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As Tim mentioned in his answer to my other post, sometimes model theorists studying nonstandad models of arithmetic refer to N as the standard model, and to Th(N) as "true arithmetic", i. e. the set of sentences in the language of PA true in that model. Then they prove things like that if M is a nonstandard model of PA then M contains an isomorphic copy of N (in fact an initial segment of M). When one thinks informally about the natural numbers one has in mind N, not omega, which as Harald says is but a formal definition not capable of capturing what N really is. Hence the confusion. – Marc Alcobé García Jun 15 '10 at 13:18
In other words, we avoid circularity at the expenses of precisely stating what we'd like to mean. – Marc Alcobé García Jun 15 '10 at 13:24
On notation: one convention in computability theory is to use ω to refer to the standard natural numbers and blackboard bold N to refer to an arbitrary model of (some fragment of) arithmetic. This is related to the use of the term "ω-model". But this convention is not universal; Kaye's book uses blackboard bold N for the standard model, and Kossak/Schmerl use both b.b. N and ω for the standard model. I have never seen a book that uses ω to refer to a nonstandard model, though. – Carl Mummert Jun 15 '10 at 13:31
@Carl, my impression was that $\omega$ is used when the emphasis is on the set or at most an ordered set and $\mathbb{N}$ is used when one wants to put emphasis on the structure of natural numbers usually including at least addition and multiplication and $N$ is used for possibly nonstandard objects in models satisfying those properties of $\mathbb{N}$ that are expressible in the language. – Kaveh Jul 15 '13 at 9:37
@Kaveh: in most of the reverse mathematics literature, $\mathbb{N}$ is used for an arbitrary, possibly nonstandard model and $\omega$ is used for the standard model. But although this is common in that field, it is not universal. – Carl Mummert Jul 15 '13 at 11:53
I don't have that book, but as far as I can understand, the “circularity” must mean this: in the phrase “iterating the successor operation a finite number of times”, we should mean a number of times corresponding to a natural number. But since the natural numbers are what we are defining, this is circular. So one has to define the natural numbers without reference to the concept of “finite”. Where the circularity is broken is if you rewrite your definition as follows:
1. 0 is a natural number,
2. the successor of any natural number is a natural number, and
3. nothing is a natural number unless it must be, by 1 and 2.
(All this stated in more technical language, of course.)
There is no reference to the notion of “finite” here. Instead, number 3 above gives us, by definition, the principle of induction. For example, how do you show that some object X is not a natural number? Well, if for some property P, you can show P(0) and you can also show that ∀n: P(n)⇒P(n') where the prime denotes the successor function, but X fails property P, then you can know for sure that X is not a natural number.
Edit: I see I did not answer all your questions. I am not a logician, so take this with a grain of salt. But basically, in first order logic (in which ZFC is expressed) it is impossible to make circular definitions, and if you can't make one, you can't repair it. The circularity, as I see it, all exists on the meta-level, before you have even gotten around to formalizing the theory. So “breaking the circularity” must in essence happen in the transition between the informal and the formal.
Strictly speaking, first order theories don't even allow definitions at all! What you have to do is to notice that there is a complicated formula NN(x) that we interpret as “x is the set of natural numbers”, and a theorem ∃!x NN(x) in ZFC (where ∃! is short for “there exists a unique …”); then we create a new theory by adding the symbol ω and adding the axiom NN(ω). Now, any formula A(ω) in the new theory can be rewritten in the old theory as ∃x:NN(x)∧A(x), so nothing new has really happened, except for a great amount of simplification.
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Yes, that is the circularity. But the inductive definition doesn't really help, in first-order logic: there are still nonstandard models that satisfy all the same first-order induction axioms as the standard model. These nonstandard models think that all their nonstandard numbers "must be" obtained by rule 3. Maybe what Kunen means is that, once we have axiomatized enough of the true properties of the natural numbers, we can use those axioms to prove interesting theorems, and we don't have to worry too much about nonstandard models at that point. But I also don't have the book. – Carl Mummert Jun 14 '10 at 22:48
@Harald: I would guess that "circularity" refers to the fact that the following three concepts are all mutually dependent: "natural number", "string of symbols", "proof". All three of these rely on the same notion of "finiteness", so in the end if you are doubtful about whether "finite" is well defined you cannot use any of the three concepts to clarify the other two. But this assumes that you are doubtful about what "finite" means. If we simply accept "finite" as an undefined term, and axiomatize the properties that "finite" things have, this starts to sound more like Kunen's proposal. – Carl Mummert Jun 14 '10 at 22:53
@Carl: Yes, the existence of nonstandard models are indeed a fact of life and there is no way out of that. I think you're right on in your first comment. Re your second comment, now you are talking about the meta level and the formalization of things like well-formed formulas and proof, right? Lacking Kunen's book I cannot be sure, but I did not get the impression that this sort of question is at issue here. – Harald Hanche-Olsen Jun 14 '10 at 23:04
## protected by François G. Dorais♦Jul 15 '13 at 15:12
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https://discussions.tomtom.com/en/discussion/1125593/tt550-i-dont-hear-all-messages-any-more
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# TT550, I don't hear ALL messages any more
Registered Users Posts: 2
New Seeker
Dear TT users,
small probably stupid question,
Using TT550, Schubert SC1 & iPhone,
the connection is ok, on the moment I switch on, it gives me an OK, If there is a Radar Control, it tells me (which is great) but lately I do not get messages on where to got to (the standard" take next one to the left in 500 m" or something like that).
So,
I have to assume (as it does give the other messages, I must have switched the "Directional" messages OFF (definitely unintentionally) so WHERE I can switch that "ON" again ?
regards,
Leon
• Registered Users Posts: 2
New Seeker
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https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/06%3A_The_Periodic_Table/6.01%3A_Early_History_of_the_Periodic_Table
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6.1: Early History of the Periodic Table
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When you go to the library to find a book, how do you locate it?
If it is a fiction book, you look by author since the fiction materials are filed by the author’s last name. If you are looking for a non-fiction publication, you look in a catalog (most likely on a computer these days). The book you are looking for will have a number by the title. This number refers to the Dewey Decimal system, developed by Melvil Dewey in 1876 and used in over 200,000 libraries throughout the world. Another system in wide use is the Library of Congress approach, developed in the late 1800s-early 1900s to organize the materials in the federal Library of Congress. This method is one of the most widely used ways to organize libraries in the world. Both approaches organize information so that people can easily find what they are looking for. Chemistry information also needs to be organized so we can see patterns of properties in elements.
Early Attempts to Organize Elements
By the year 1700, only a handful of elements had been identified and isolated. Several of these, such as copper and lead, had been known since ancient times. As scientific methods improved, the rate of discovery dramatically increased. With the ever-increasing number of elements, chemists recognized that there may be some kind of systematic way to organize the elements. The question was: how?
A logical way to begin grouping elements together was by their chemical properties. (In other words, putting elements in separate groups based on how they reacted with other elements.) In 1829, a German chemist, Johann Dobereiner (1780-1849), placed various groups of three elements into groups called triads. One such triad was lithium, sodium, and potassium. Triads were based on both physical, as well as chemical, properties. Dobereiner found that the atomic masses of these three elements, as well as other triads, formed a pattern. When the atomic masses of lithium and potassium were averaged together $$\left( \frac{\left( 6.94 + 39.10 \right)}{2} = 23.02 \right)$$, it was approximately equal to the atomic mass of sodium (22.99). These three elements also displayed similar chemical reactions, such as vigorously reacting with the members of another triad: chlorine, bromine, and iodine. While Dobereiner's system would pave the way for future ideas, a limitation of the triad system was that not all of the known elements could be classified in this way.
English chemist John Newlands (1838-1898) ordered the elements in increasing order of atomic mass and noticed that every eighth element exhibited similar properties. He called this relationship the "Law of Octaves". Unfortunately, there were some elements that were missing and the law did not seem to hold for elements that were heavier than calcium. Newlands' work was largely ignored and even ridiculed by the scientific community in his day. It was not until years later that another more extensive periodic table effort would gain much greater acceptance, and that the pioneering work of John Newlands would be appreciated.
Summary
• Johann Dobereiner organized elements into groups called triads.
• John Newlands proposed the "Law of Octaves" for organizing the elements.
Review
1. List some elements known since ancient times?
2. What properties were the basis of the triad system?
3. Why did Dobereiner believe that lithium, sodium, and potassium belonged in a triad?
4. What was a shortcoming of the triad system?
5. How did Newlands arrange the element?
6. What was a problem with the “Law of Octaves"?
6.1: Early History of the Periodic Table is shared under a CK-12 license and was authored, remixed, and/or curated by CK-12 Foundation via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
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https://mersenneforum.org/showthread.php?p=605427
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mersenneforum.org FastECPP software and 50000 digit primality proof (reposted from NMBRTHRY)
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2022-05-06, 21:16 #1
Batalov
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
100110101100012 Posts
FastECPP software and 50000 digit primality proof (reposted from NMBRTHRY)
Quote:
Originally Posted by Andreas Enge @inria.fr Dear colleagues, I am pleased to announce the release of a new free software for creating elliptic curve primality proofs using the fastECPP algorithm due to Morain, Franke, Kleinjung and Wirth [1, 2]. It is available under the GPL version 3 or later at https://www.multiprecision.org/cm/ It relies on the approach of computing class polynomials by complex approximations as described in [3]. Optimal class invariants are chosen derived from Weber functions [4], simple [5] or double eta quotients [6], including cases where it is enough to compute lower-degree subfields of the class field [7]. The evaluation of modular functions, which is the most important part of the class polynomial computation, is optimised following [3, 8]. To ease the step of factoring class polynomials modulo primes, the class fields are then represented as a tower of cyclic Galois extensions of prime degree following [9]. The software relies on a number of libraries from the GNU project, notably GMP [10], MPFR [11] and MPC [12], and on PARI/GP [13] for computations with class groups and for root finding modulo a prime. The code has been used to prove a record prime of about 50000 digits; indeed it has shown that 10^50000+65859 is the smallest prime with 50001 digits. The certificate is available at https://www.multiprecision.org/downl...cert-50000.bz2 in PARI/GP format [13] and at https://www.multiprecision.org/downl...0000.primo.bz2 in Primo format [14] as converted by PARI/GP code written by J. Asuncion, who is also the author of the fastECPP implementation in PARI/GP. Parallelisation uses MPI. Computations have been carried out on the PlaFRIM [15] and MCIA [16] clusters in Bordeaux. The first phase of the record, in which a list of discriminants and candidate orders of points on elliptic curves is produced, has taken about 26 days of wallclock time and 67 years of CPU time, in several runs on clusters with 752 to 1328 cores. Of this CPU time, about 8% has been devoted to the computation of square roots modulo a prime by the Tonelli-Shanks algorithm, about 12% to solving quadratic equations by Cornacchia's algorithm, about 65% to removing smooth factors from curve cardinalities, and about 15% to internal primality tests. This imbalance probably indicates non-optimal choices of parameters. On the other hand, it leads to very short certificates: We reach a length of only 1645 steps, as opposed to the 3794 steps in the recent 49000 digits record [17], which implies that verification time is proportionally lower. For the specialists, the parameters were as follows: Discriminants with absolute value up to about 6.9*10^9, leading to class numbers with prime factors up to 157 (and no bound on the class numbers themselves), and a smoothness bound of about 5.5*10^11 for partial factorisation of point orders. The second phase of the record, in which complex multiplication produces a list of elliptic curves and points of (recursively shown to be) prime orders on them, has taken about 74 days of wallclock time and less than 4 years of CPU time on a few machines with 32 to 256 cores in total. Depending on the largest factor of the class number, each step may take a vastly differing amount of time. The longest step has taken close to 10 days for factoring a class polynomial for the discriminant -345992327 of class number 13112=2^3*11*149 for an intermediate prime of about 47800 digits; this would also have been the wallclock time for this phase had it been run sufficiently in parallel. Of the total CPU time, about 96% has been devoted to finding roots of class polynomials, about 3% to verifying point orders, and only about 1% to the construction of the class polynomials. Verification of the certificate takes a little over 4 hours using PARI/GP on a machine with 128 cores. Andreas Enge [1] F. Morain: "Implementing the asymptotically fast version of the elliptic curve primality proving algorithm", Mathematics of Computation 76 (257), 2007, pp. 493-505 [2] J. Franke, T. Kleinjung, F. Morain and T. Wirth: "Proving the Primality of Very Large Numbers with fastECPP", in Duncan Buell: "Algorithmic Number Theory - ANTS-VI", Lecture Notes in Computer Science 3076, Springer-Verlag, Berlin 2004, pp. 194-207 [3] A. Enge: "The complexity of class polynomial computation via floating point approximations", Mathematics of Computation 78 (266), 2009, pp. 1089-1107 [4] R. Schertz: "Die singulären Werte der Weberschen Funktionen $f$, $f_1$, $f_2$, $\gamma_2$, $\gamma_3$", Journal für die reine und angewandte Mathematik 286/287, 1976, pp. 46-74 [5] A. Enge and F. Morain: "Generalised Weber Functions", Acta Arithmetica 164 (4), 2014, pp. 309-341 [6] A. Enge and R. Schertz: "Constructing elliptic curves over finite fields using double eta-quotients", Journal de Théorie des Nombres de Bordeaux 16, 2004, pp. 555-568 [7] A. Enge and R. Schertz: "Singular values of multiple eta-quotients for ramified primes", LMS Journal of Computation and Mathematics 16, 2013, 407-418 [8] A. Enge, W. Hart and F. Johansson: "Short addition sequences for theta functions", Journal of Integer Sequences 18 (2), 2018, pp. 1-34 [9] A. Enge and F. Morain: "Fast Decomposition of Polynomials with Known Galois Group", in Marc Fossorier, Tom Høholdt and Alain Poli (editors): "Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - AAECC-15", Lecture Notes in Computer Science 2643, Springer-Verlag, Berlin 2003, pp. 254-264 [10] Torbjörn Granlund et al.: "GMP - The GNU Multiple Precision Arithmetic Library", release 6.2.1, 2020, http://gmplib.org/ [11] Guillaume Hanrot, Vincent Lefèvre, Patrick Pélissier, Paul Zimmermann et al.: "GNU MPFR - A library for multiple-precision floating-point computations with exact rounding", release 4.1.0, 2020, http://www.mpfr.org/ [12] A. Enge, M. Gastineau, P. Théveny and P. Zimmermann: "GNU MPC - A library for multiprecision complex arithmetic with exact rounding", release 1.2.1, 2020, https://www.multiprecision.org/mpc/ [13] PARI Group: "PARI/GP", release 2.13.4, 2022, https://pari.math.u-bordeaux.fr/ [14] M. Martin: "Primo", release 4.3.3, 2020, http://www.ellipsa.eu/public/primo/primo.html [15] PlaFRIM, Plateforme Fédérative pour la Recherche en Informatique et Mathématiques, https://www.plafrim.fr/ [16] MCIA, Mésocentre de Calcul Intensif Aquitain, https://www.mcia.fr/ [17] https://primes.utm.edu/primes/page.php?id=133761
Exciting development. The early preview was visible since last August:
Quote:
rank prime digits who when comment 64129 U(148091) 30949 x49 Sep 2021 Fibonacci number, ECPP 66197 (2^95369 + 1)/3 28709 x49 Aug 2021 Generalized Lucas number, Wagstaff, ECPP
2022-05-06, 22:05 #2 paulunderwood Sep 2002 Database er0rr 22·1,063 Posts An amazing feat! Such parallelism and clever mathematics run on some very big hardware. I take my hat off to these provers.
2022-05-06, 23:17 #3 ATH Einyen Dec 2003 Denmark 1101000101112 Posts So 71 years of CPU time for 51,000 digits vs 20 months * 64 cores ~ 107 years of CPU time for 49,081 digits. But depends on how comparable those CPU core years are. 51,000 digits is supposed to take (51000/49081)^3.75 ~ 15% longer ? At least with Primo.
2022-05-06, 23:29 #4 Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 5·7·283 Posts Note in their text that they say "This <<...>> probably indicates non-optimal choices of parameters. On the other hand, it leads to very short certificates: We reach a length of only 1645 steps" (!!). They call it a pre-release. They will likely optimize it even more. Btw, I had to "massage" their cert a little bit, but then factorDB took it. Took 3 iterations slightly reformatting the file (and to rename it into .out file)
2022-05-06, 23:31 #5
paulunderwood
Sep 2002
Database er0rr
425210 Posts
Quote:
Originally Posted by ATH So 71 years of CPU time for 51,000 digits vs 20 months * 64 cores ~ 107 years of CPU time for 49,081 digits. But depends on how comparable those CPU core years are. 51,000 digits is supposed to take (51000/49081)^3.75 ~ 15% longer ? At least with Primo.
It is 50,001 digits. My estimate for Primo is (50001/49081)^4 = 1.077 or 7.7% longer.
I used quad channel DDR 2400MHz for R49081's certification. I guess they were using octa channel most of the time, but that does not explain their speed fully. There is marginal gain by having fewer stage 2 steps to do.
Last fiddled with by paulunderwood on 2022-05-06 at 23:53
2022-05-06, 23:33 #6
paulunderwood
Sep 2002
Database er0rr
22×1,063 Posts
Quote:
Originally Posted by Batalov Note in their text that they say "This <<...>> probably indicates non-optimal choices of parameters. On the other hand, it leads to very short certificates: We reach a length of only 1645 steps" (!!). They call it a pre-release. They will likely optimize it even more. Btw, I had to "massage" their cert a little bit, but then factorDB took it. Took 3 iterations slightly reformatting the file (and to rename it into .out file)
Last fiddled with by paulunderwood on 2022-05-06 at 23:37
2022-05-06, 23:50 #7 Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 5×7×283 Posts I made a shorter jump and forwarded NMBRTHRY email to Caldwell. (though he is surely on the list.*) ________ * Funny story: a few years ago a ton (literally!) of porn links started coming every day via NMBRTHRY email list. It went on for quite a while. Many folks, I am afraid, unsubscribed from it at that point. Since then it has been moderated with huge delays. One curious example was when an invitation to a December conference was sent out in March.
2022-05-07, 00:33 #8 ixfd64 Bemusing Prompter "Danny" Dec 2002 California 46558 Posts This is great news for two reasons: 1. It's a new ECPP world record. 2. We finally have an open-source ECPP implementation that can compete with Primo. I'm aware that Marcel has no obligation to make Primo open source, but I do feel that closed-source software goes against the spirit of science. Last fiddled with by ixfd64 on 2022-05-07 at 02:14
2022-05-07, 07:31 #9 Puzzle-Peter Jun 2009 23·3·29 Posts Holy s**t! Hats off and congrats to all those involved. That is some serious soft- and hardware. I wonder how big the code can go? There are so many interesting numbers from 50K to 100K digits. Just the electricity cost alone will make such a number pretty valuable
2022-05-07, 13:51 #10 mathwiz Mar 2019 5×59 Posts Fantastic! It would seem this page needs an update?
2022-05-07, 15:15 #11 paulunderwood Sep 2002 Database er0rr 10000100111002 Posts Some entity should set up fastECPP for a proof-over-the-net. Clients could latch onto the main server. This way a 60k proof might be computed in a reasonable amount of time. Last fiddled with by paulunderwood on 2022-05-07 at 15:22
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https://mathzsolution.com/surprise-exam-paradox/
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I just remembered about a problem/paradox I read years ago in the fun section of the newspaper, which has had me wondering often times. The problem is as follows:
A maths teacher says to the class that during the year he’ll give a surprise exam, so the students need be prepared the entire year. One student starts thinking though:
1. The teacher can’t wait until the last day of school, because then the exam won’t be unexpected. So it can’t be the last day.
2. Since we’ve removed the last day from the list of possible days, the same logic applies to the day before the last day.
3. By applying 1) and 2) we remove all the days from the list of possible days.
4. So, it turns out that the teacher can’t give a surprise exam at all.
Following this logic, our student doesn’t prepare for this test and is promptly flunked when the teacher does give it somewhere during the middle of the year (but that’s my own creative addition to the problem).
This problem reminds me about the prisoner’s dilemma for finite number of turns – you have to betray at the last turn because tit-for-tat retaliation is no longer relevant (no next turn), but then that means that you have to betray at the turn before that, and so on, until you reach the conclusion that you can’t cooperate at all.
So is the student’s reasoning correct or not? Mathematically it looks like it should be, but that would imply that surprise exams are not possible (and they are).
There is a model of knowledge, essentially due to Robert Aumann, in which knowledge is represented by a partition $$Π\Pi$$ of a set of states of the world $$Ω\Omega$$. If the true state of the world is $$ω\omega$$, the agent with partition $$Π\Pi$$ only knows that some state in the cell $$π(ω)\pi(\omega)$$ (the value of the projection at $$ω\omega$$) obtained. An event is simply a subset of $$Ω\Omega$$. We say that an agent knows that the event $$EE$$ obtains at $$ω\omega$$ if $$π(ω)⊆E\pi(\omega)\subseteq E$$. Now let the state space be $$Ω={1,2,…,T}\Omega=\{1,2,\ldots,T\}$$, where we interpret $$tt$$ as “there is an exam at $$tt$$“. Now there is no partition $$Π\Pi$$ such that the following holds:
2. If there was no exam at $${1,…,t−1}\{1,\ldots,t-1\}$$, then the student knows this at $$tt$$.
Proof: Let $$tt$$ be an element in $$Ω\Omega$$ such that $$π(t)\pi(t)$$ is not a singleton. Such an element must exist by 1. Let $$t′t'$$ be the largest element in $$π(t)\pi(t)$$. By assumption $$t′>tt'>t$$ and so by 2., $${1,…,t′−1}\{1,\ldots,t'-1\}$$ is a union of cells in $$Π\Pi$$ that contains $$tt$$. Since $$Π\Pi$$ is a partition, $$π(t)⊆{1,…,t′−1}\pi(t)\subseteq\{1,\ldots,t'-1\}$$, contradicting $$t′∈π(t)t'\in\pi(t)$$.
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https://www.transtutors.com/questions/exercise-9-14-flexible-budget-lo1-pierr-manufacturing-inc-has-provided-the-following-1364171.htm
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# EXERCISE 9–14 Flexible Budget [LO1] Pierr Manufacturing Inc. has provided the following...
EXERCISE 9–14 Flexible Budget [LO1]
Pierr Manufacturing Inc. has provided the following information concerning its manufacturing costs:
Direct materials . . . . . . . . . . . $5.70 Direct labor . . . . . . . . . . . . . .$42,800 Supplies . . . . . . . . . . . . . . . . $0.20 Utilities . . . . . . . . . . . . . . . . .$1,600 $0.15 Depreciation . . . . . . . . . . . . .$14,900 Insurance . . . . . . . . . . . . . . . $11,400 For example, utilities should be$1,600 per month plus \$0.15 per machine-hour. The company expects to work 4,000 machine-hours in July. Note that the company’s direct labor is a fixed cost.
Required:
Prepare the company’s planning budget for manufacturing costs for July.
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https://geekyisawesome.blogspot.com/2015/07/probabilities-are-average-proportions.html
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## Wednesday, July 8, 2015
### Probabilities are average proportions (expected value)
Intuitively, if a coin flip has a probability of 1/2 of turning out heads, and we flipped the coin 100 times, we expect that 1/2 of those 100 flips will be heads. What is meant by "expect" is that if we do this 100 coin flip experiment for many times, count the number of times it turns out heads for each 100 flip trial, and take the average of these counts, the average will be close to 1/2 of 100. Furthermore, the more 100 flip trials we include in our average, the closer the average will be 1/2 of 100.
If this were the case, then a probability can be treated as an average proportion, because if a probability of something happening is, say, 1/100, then after 1000 attempts we should find that, on average, 1/100 of those 1000 attempts would be the thing happening. In general, if the probability of an outcome is "p", and "n" attempts are made, then we should have "pn" positive outcomes. That probability is acting as a proportion of the average number of attempts made which will result in a positive outcome out of the attempts made. In fact, semantically speaking, the phrase "This outcome occurs with probability 1/100" and the phrase "This outcome occurs once every 100 times" are identical.
A simple proof of this is in the way we estimate the probability of an outcome. We attempt to produce the outcome (such as a coin flip resulting in heads) for a number of times "n", count the number of times "x" the outcome is positive (heads), and then just find x/n. But in order for this probability to be reliable, the quotient must remain constant for different values of "n" (the value "x" will change according to "n" to keep x/n equal). Given this statement, if we know a reliable probability x/n, and have performed the experiment "m" times, then the number of positive outcomes "y" can be predicted as follows:
For x/n to be reliable, x/n = y/m
Therefore, y = m(y/m) = m(x/n)
That is, since x/n is known and "m" is known, "y" can be found using those two values only.
Of course this is not a rigorous proof. To get a rigorous proof we need to turn to a field of probability called expected value. The expected value of a random variable (such as a coin flip) is the average of the values (assumed to be numerical) of the outcomes after a large number of trials. It is defined as the sum of each outcome multiplied by its probability. For example, the expected value of the value on a die is
1*1/6 + 2*1/6 + 3*1/6 + 4*1/6 + 5*1/6 + 6*1/6
because for each outcome from 1 to 6, the probability is 1/6.
In general, if the probability of outcome "o_i" is "p_i", then the expected outcome is
sum(o_i*p_i for all i)
But this isn't useful for proving the statement in the title. The proof is in this Math Exchange answer which explains that the expected number of positive outcomes out of "n" attempts, given that the probability of each outcome each time is "p", is "pn". It goes like this:
Let the random variable "U_i" be the outcome of the "i"th attempt (heads or tails). If the outcome is positive (heads), "U_i" is 1, otherwise it is 0. Given "n" attempts, the number of positive outcomes is
U_1 + U_2 + U_3 + ... + U_n
Call this actual number of positive outcomes "X", that is
X = U_1 + U_2 + U_3 + ... + U_n
The expected value of "X", written as E(X) is
E(X) = E(U_1 + U_2 + U_3 + ... + U_n)
Since the expected value is a linear operator,
E(X) = E(U_1) + E(U_2) + E(U_3) + ... + E(U_n)
Now, given the above definition of what an expected value is,
E(U_i) = 1*(probability of U_i = 1) + 0*(probability of U_i = 0)
If the probability of "U_i" being 1 is "p_i", then
E(U_i) = p_i
But for all "i", the probability of "U_i" is the same. That is
E(U_i) = p
So that means that
E(X) = p + p + p + ... + p
E(X) = pn
And there we have it, the expected number of positive outcomes out of "n" attempts, each of which has a probability of "p", is "pn", which means that the probability "p" can be treated exactly as if it was the proportion of positive outcomes out of a number of trials.
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https://alice-publications.web.cern.ch/node/3881
|
# Two-pion Bose-Einstein correlations in central Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
The first measurement of two-pion Bose--Einstein correlations in central Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV at the Large Hadron Collider is presented. We observe a growing trend with energy now not only for the longitudinal and the outward but also for the sideward pion source radius. The pion homogeneity volume and the decoupling time are significantly larger than those measured at RHIC.
|
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https://www.computer.org/csdl/trans/td/2012/11/ttd2012112024-abs.html
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The Community for Technology Leaders
Issue No. 11 - Nov. (2012 vol. 23)
ISSN: 1045-9219
pp: 2024-2032
Gregory D. Peterson , University of Tennessee, Knoxville
Junqing Sun , Marvell Semiconductor, Santa Clara
ABSTRACT
In performance modeling of parallel synchronous iterative applications, the longest individual execution time among parallel processors determines the iteration time and often must be estimated for performance analysis. This involves the mean maximum calculation which has been a challenge in computer modeling for a long time. For large systems, numerical methods are not suitable because of heavy computation requirements and inaccuracy caused by rounding. On the other hand, previous approximation methods face challenges of accuracy and generality, especially for heterogeneous computing environments. This paper presents an interesting property of extreme values to enable Effective Mean Maximum Approximation (EMMA). Compared to previous mean maximum execution time approximation methods, this method is more accurate and general to different computational environments.
INDEX TERMS
Program processors, Random variables, Approximation methods, Computational modeling, Mathematical model, Distribution functions, Shape, heterogeneous computing, Performance modeling, extreme value, mean maximum, execution time
CITATION
Gregory D. Peterson, Junqing Sun, "An Effective Execution Time Approximation Method for Parallel Computing", IEEE Transactions on Parallel & Distributed Systems, vol. 23, no. , pp. 2024-2032, Nov. 2012, doi:10.1109/TPDS.2012.21
FULL ARTICLE
CITATIONS
SHARE
153 ms
(Ver 3.3 (11022016))
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http://tex.stackexchange.com/questions/94056/space-between-letter-and-lowercase-in-latex-math-mode
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# Space between letter and lowercase in latex math mode
is there a way to remove the space between the variable and the lowercase letter as standard in math environment?
by now i'm using this:
$$a\;b_{\! c}\;d$$
Without \! the space looks to big. Now i thought, if it is possible to set this by default in the math environment.
-
## migrated from stackoverflow.comJan 16 '13 at 12:17
This question came from our site for professional and enthusiast programmers.
Welcome to TeX.sx! Your post was migrated here from Stack Overflow. Please register on this site, too, and make sure that both accounts are associated with each other (by using the same OpenID), otherwise you won't be able to comment on or accept answers or edit your question. – Torbjørn T. Jan 16 '13 at 12:20
The spacing without the \! seems correct for the product. If you are looking for more of a row vector, see if \begin{matrix} a & b_{c} & d \end{matrix} is more to your liking. – Peter Grill Jan 19 '13 at 9:52
no no, its for normal equations – Los WochoS Jan 21 '13 at 9:24
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https://manualzz.com/doc/48852668/citrix%C2%AE-xenconvert%E2%84%A2-guide
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# Citrix® XenConvert™ Guide
```Citrix® XenConvert™ Guide
XenConvert 1.1
Revision 6
December 15, 2008
Use of the product documented in this guide is subject to your prior acceptance of the End User License Agreement.
Information in this document is subject to change without notice. Companies, names, and data used in examples herein are
fictitious unless otherwise noted. No part of this document may be reproduced or transmitted in any form or by any means,
electronic or mechanical, for any purpose, without the express written permission of Citrix Systems, Inc.
Xen and Citrix are registered trademarks, and Citrix Provisioning Server, XenConvert and XenServer are trademarks of Citrix
Systems, Inc. in the United States and other countries.
Microsoft, Windows, Windows Server are either registered trademarks or trademarks of Microsoft Corporation in the United
States and/or other countries.
All other trademarks and registered trademarks are the property of their respective owners.
Document Code: December 15, 2008 (MS)
C ONTENTS
Contents
Chapter 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
Intended Audience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
Related Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
Contact Us. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
Chapter 2
What’s New in This Release. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Converting from Microsoft Virtual Server 2005 . . . . . . . . . . . . . . . . . . . . . . . . .5
Additional Physical Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Upgrading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Consolidation of XenConvert Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Known Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Converting a VHD Containing a Windows OS That is Newer Than the Host OS
6
Windows Boot and System Drives Must be on the Same Volume . . . . . . . . . . .6
Source Disk Limited to Basic Disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Running From a Terminal Services Session. . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Known Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Converting a Workload with Files in Use. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Mapped Network Drive Can Interfere with Conversion. . . . . . . . . . . . . . . . .7
Autorun Can Interfere with Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Safe to Remove Messages During Physical to XVA Conversion . . . . . . . . . . . .8
XenConvert Fails When Automount is Disabled . . . . . . . . . . . . . . . . . . . . . . . . .8
Problem Ejecting Citrix Virtual Hard Disk Messages . . . . . . . . . . . . . . . . . . . . .8
Service or Device Specific to the Source Machine May Fail to Start in a Virtual
Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
VHD Appears to be Mounted After Cancelling XenConvert . . . . . . . . . . . . . . .9
Exception Message Appears on First Boot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
Virtual Display Adapter Driver is Not Installed Automatically. . . . . . . . . . . . .10
Unknown Device on Windows 2000 SP4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
2
Citrix XenConvert Guide
Chapter 3
Installing XenConvert
Obtaining the Installation File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
XenConvert System Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
Installing XenConvert Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
Upgrading XenConvert. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Remove XenConvert Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Chapter 4
Using XenConvert
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Converting From Physical Machines to Virtual Machines . . . . . . . . . . . . . . . .15
Converting From Microsoft Virtual Server . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Starting the XenConvert Wizard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
Conversion Summary Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
Controlling XenConvert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
Converting from a Physical Machine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
Before Converting From a Physical Machine. . . . . . . . . . . . . . . . . . . . . . . . . . .18
Enable Automount . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
Stop Security Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
Working with Provisioning Server . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
Physical to VHD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
Physical to XVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
Physical to XenServer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
Converting from Microsoft Virtual Server. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
Before Converting From Microsoft Virtual Server . . . . . . . . . . . . . . . . . . . . . .21
After Converting From Microsoft Virtual Server. . . . . . . . . . . . . . . . . . . . . . . .21
VMC to XVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
VMC to XenServer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
VHD to XVA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
VHD to XenServer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
XenServer Account Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
C HAPTER 1
This document provides instructions on installing and using Citrix XenConvert
software. This document is organized as follows:
•
“About XenConvert” provides information such as new features and known
issues.
•
“Installing XenConvert” describes how to install the XenConvert software.
•
“Using XenConvert” describes how to use XenConvert.
Introduction
Citrix® XenConvert™ converts a server or desktop workload from either a
physical machine or from another type of virtual machine, to a XenServer virtual
machine.
•
Converting to a XenServer VM produces an intermediate XVA containing a
bootable XenServer VM and automatically imports it into a XenServer.
•
Converting to an XVA produces an offline package of a bootable
XenServer VM ready to manually import into a XenServer.
•
Converting to a VHD produces a VHD compatible with Provisioning
Server 5.0 if the target device software included with Provisioning Server
5.0 was installed beforehand.
XenConvert includes a wizard, to use interactively, and a command line interface,
to use from a script.
Intended Audience
This document is intended for XenServer system administrators and software
installers. It is assumed that readers are familiar with basic installation and system
management tasks for Microsoft Windows systems.
4
Citrix XenConvert Guide
Related Information
Information on XenConvert is provided with the software in the form of an online
help file, which is available from the product, and as a PDF document.
may also be required during installation and use of this product. This information
can be found at the following locations:
•
XenServer: http://support.citrix.com/product/xens/
•
Provisioning Server: http://support.citrix.com/product/provsvr/
Your feedback on Citrix XenConvert documentation is important to us. Use the
http://support.citrix.com/docfeedback/
C HAPTER 2
This chapter contains information relevant to this release of XenConvert
software. This information includes:
•
“What’s New in This Release”
•
“Known Limitations”
What’s New in This Release
This section describes enhancements and other changes made to XenConvert in
this release.
Converting from Microsoft Virtual Server 2005
Convert a single VHD or an entire virtual machine to a XVA or XenServer:
•
“VHD to XVA”
Convert a single Virtual Hard Disk (VHD) to a XVA.
•
“VHD to XenServer”
Convert from a single VHD to a XenServer.
•
“VMC to XVA”
Convert an entire virtual machine to a XVA.
•
“VMC to XenServer”
Convert an entire virtual machine to a XenServer.
A source VHD can be of the fixed or dynamic type.
Physical conversion enhancements include converting a physical source machine
without any ATA devices (pure SCSI machine, such as a blade system).
6
Citrix XenConvert Guide
Run the XenConvert installer to upgrade XenConvert. It is no longer necessary to
remove the previous version.
Consolidation of XenConvert Documentation
The Release Notes, Installation Guide, and Help documents were consolidated
into a single document to create this guide. This consolidation increases usability
by making it easier to locate and search for XenConvert information.
Known Limitations
This section describes known limitations for the XenConvert software. Wherever
possible, a workaround for the problem is included.
Converting a VHD Containing a Windows OS That
is Newer Than the Host OS
If the Windows OS version of a VHD is newer than the host’s OS, XenConvert
cannot convert the VHD. For example, if the VHD contains Windows XP and the
host contains Windows 2000.
Issue # 7875
Windows Boot and System Drives Must be on the
Same Volume
XenConvert can only convert a workload from a source machine on which the
system drive is the same as the boot drive. For example, boot.ini and the
\Windows must both reside on C:.
Source Disk Limited to Basic Disk
The source disk is limited to a physical disk initialized as a basic disk. Converting
a physical disk initialized as a dynamic disk type is not yet supported.
Running From a Terminal Services Session
XenConvert cannot run from a Terminal Services session when the Terminal
Server is a Window 2000 operating system. Mounting a VHD either fails after
several minutes or does not appear to complete. This issue does not occur with
VNC.
To workaround this issue, run XenConvert from the Console.
Chapter 2
7
To change the amount of time that XenConvert waits to mount the VHD, change
the registry key value VhdPluginTimeoutAsMs described in “Controlling
XenConvert” section.
Known Problems
This section describes known problems for the XenConvert software. Wherever
possible, a workaround for the problem is included.
Converting a Workload with Files in Use
XenConvert cannot copy a file in use by another application or service. To ensure
that the file is included in the conversion, stop the respective service before
starting the conversion.
It is not recommended to convert a workload executing a critical service that
keeps critical files open that cannot be stopped (such as a Domain Controller with
Active Directory service).
Mapped Network Drive Can Interfere with
Conversion
If a network drive was mapped to the next available drive letter (e.g. F: when last
local drive was E), then XenConvert is unable to get the drive letter for the new
VHD that it just created, mounted, and formatted because Windows assigned it to
the same drive letter as the network drive. See http://support.microsoft.com/kb/
297694/ for a description of the same problem affecting other removable disks.
Although that KB pertains to Windows XP, the problem also affects Windows
Server 2003 when automount is enabled.
The workaround is to remap the network drive to a drive letter other than the
lowest available one before running XenConvert.
Autorun Can Interfere with Conversion
If enabled, Autorun can interfere when converting from a VHD. After a VHD
containing at least one file system is mounted, Autorun scans the file system and
leaves a dialog box open, causing the conversion to stall because the VHD cannot
be automatically dismounted.
To work around this issue, disable Autorun for fixed drives by setting the
following DWORD to 0x8:
HKLM\SOFTWARE\Microsoft\Windows\CurrentVersion\Policie
s\Explorer \NoDriveTypeAutoRun
8
Citrix XenConvert Guide
For details, refer to http://www.microsoft.com/technet/
prodtechnol/windows2000serv/reskit/regentry/
91525.mspx?mfr=true.
Issue # 7911
Safe to Remove Messages During Physical to XVA
Conversion
You may see a “safe to remove” balloon message on Windows XP and dialog box
on Windows 2000 after the file copy stage. The message occurs when the VHD
that was created is dismounted before creation of the XVA file. This is a normal
message and can be ignored.
Issue # 7307
XenConvert Fails When Automount is Disabled
The following message appears in the log file when XenConvert is run with
automount disabled:
Windows Automount may be disabled
Windows Server 2003 Enterprise and Datacenter editions disable automount by
default. This prevents programmatically formatting a volume without assigning a
drive letter or mount point.
You can work around this issue by enabling automount before running
XenConvert. Use the Windows diskpart program to enable automount:
C:\> DiskPart
DISKPART> automount enable
DISKPART> exit
Automount can be disabled after XenConvert completes. Note that automount
will be enabled in the VM you create and can be disabled from within the VM.
Issue # 7282
Problem Ejecting Citrix Virtual Hard Disk
Messages
The following messages may appear with a Problem Ejecting Citrix Virtual Hard
Disk during the VHD to XVA stage of a conversion.
•
The device 'Generic volume' cannot be stopped right now. Try stopping the
device again later.'
•
The device 'Citrix Virtual Hard Disk' cannot be stopped because of an
unknown error. Since the device is still being used, do not remove it.
Chapter 2
9
These messages may display if applications or services (for example, a virus scan
or the Windows Autorun feature) open a file on the mounted VHD. The open file
prevents a dismount, causing the messages to appear. Increasing the amount of
time that XenConvert waits to automatically dismount a VHD dismount time out
may resolve the issue. Refer to “Controlling XenConvert” for details on how to
change this value. Disabling Autorun may also resolve the issue.
Issue # 7308
Service or Device Specific to the Source Machine
May Fail to Start in a Virtual Machine
Messages similar to the following may be displayed when booting a virtual
machine:
"The Parallel port driver service failed to start due to the
following error: The service cannot be started, either because it is
disabled or because it has not enabled devices associated with it.”
This problem occurs when a service or a device on the physical machine fails to
start on the virtual machine. The failure may be caused by the fact that the
particular device or service is not available or supported on the machine that is
running the virtual machine.
Issue # 7337
VHD Appears to be Mounted After Cancelling
XenConvert
If you cancel a conversion while the VHD is being mounted, the VHD does not
appear to get unmounted after the cancel.
The VHD isn't actually mounted. Windows Explorer displays a stale view of the
drives, showing a red question mark over the device that was the VHD.
You can update the view by choosing “Refresh” from the “View” menu in
Windows Explorer.
Issue # 7394
Exception Message Appears on First Boot
After converting from a physical machine to a XenServer, the following message
may appear once after the virtual machine boots for the first time.
"An exception occurred while trying to run "newdev.dll,ClientSideInstall
\\.\pip\PNP_Device_Install_Pipe_0..."
You can ignore this message.
Issue # 7389
10
Citrix XenConvert Guide
Virtual Display Adapter Driver is Not Installed
Automatically
After converting a physical machine equipped with the Intel 82945G chipset or
Intel Q33 Express chipset, the virtual display adapter device may appear as an
unknown device in Device Manager in Windows Server 2003 R2 Standard
Edition.
A standard VGA mode driver is installed.
Issue # 7340
Unknown Device on Windows 2000 SP4
After a conversion to XVA on Windows 2000 SP4 systems, an unknown device
may be present. This device has no negative impact on the operation of the VM.
Issue # 7280
C HAPTER 1
Installing XenConvert
Obtaining the Installation File
Citrix XenConvert software is distributed electronically. Consult with your sales
representative for information on obtaining the software.
The product distribution contains this guide and the product installation wizard:
•
XenConvert_Install.exe
•
XenConvert_Install_x64.exe
XenConvert System Requirements
The system requirements for systems running the XenConvert software are listed
in the following table.
Requirements
XenConvert supports Microsoft Windows 64-bit:
the following
Windows Server 2003 Standard, Enterprise SP2
Operating Systems
Microsoft Windows 32-bit:
Windows Server 2003, Standard, Enterprise SP1/SP2/R2
Windows Small Business Server 2003 R2 SP2
Windows XP SP2/SP3
Windows 2000 SP4
CPU
Same as the requirements specified for the installed
operating system.
Memory
Same as the requirements specified for the installed
operating system.
12
XenConvert Installation Guide
Requirements
Disk space
requirements
When converting to VHD, the required amount of free space
is 101% of the used space on the source physical disk.
When converting to XVA or XenServer, the required amount
of free space is typically 115% of the used space on the
source disks. Note that these conversions involve
compression that depends on the disk contents. Therefore,
the required free space could be greater. The absolute worst
case would be 200% of the used space on the source
physical disk.
XenServer
XenServer Versions 4.0, 4.1, and 5.0 support import of VMs
created with XenConvert.
requirements
Microsoft .NET Framework version 2.0, which installs
automatically if necessary.
Installing XenConvert Programs
1.
On the target system, close all Windows applications.
2.
In My Computer or Windows Explorer, navigate to the directory where the
installer file: XenConvert_install.exe
3.
The XenConvert Welcome screen is displayed. Click Next to begin the
installation.
4.
The License Agreement screen appears. Click I accept..... and Next to
continue the installation. Click I do not accept to terminate the installation.
Click Print to print a copy of the License Agreement.
5.
The Destination Folder screen appears. Click Next to install XenConvert in
the default directory. Click Change to select a directory other than the
default. Click Next after the directory is selected.
6.
The Ready to Install the Program screen appears. Click Install to begin the
installation. The Installing XenConvert screen displays, showing the
installation progress.
7.
When the installation is complete, the InstallShield Wizard Complete
screen appears. Click Finish to exit the installer.
For details on using the XenConvert Wizard, refer to the chapter titled “Using
XenConvert”.
Chapter 1
Installing XenConvert
13
installer.
Remove XenConvert Programs
Use the Windows Control Panel to remove XenConvert programs.
1.
To remove XenConvert programs, access Control Panel > Add or
Remove Programs and select XenConvert.
2.
Click Remove to begin removing XenConvert programs.
3.
The ‘Are you sure you want to remove XenConvert from your computer?’
dialog box appears. Click Yes to uninstall the software from your system,
then wait for the uninstall to finish.
14
XenConvert Installation Guide
C HAPTER 2
Using XenConvert
This chapter provides the information necessary to use the XenConvert wizard
and command line interface.
Introduction
Citrix XenConvert converts a server or desktop workload from either a physical
machine, or from another type of virtual machine, to a XenServer virtual
machine.
Converting From Physical Machines to Virtual
Machines
XenConvert supports the following physical-to-virtual conversions:
•
“Physical to VHD”
•
“Physical to XVA”
•
“Physical to XenServer”
Converting From Microsoft Virtual Server
XenConvert supports the following virtual-to-virtual machine conversions:
•
“VMC to XVA”
•
“VMC to XenServer”
•
“VHD to XVA”
•
“VHD to XenServer”
Starting the XenConvert Wizard
Supported conversion methods are selected and performed using the XenConvert
Wizard.
16
Citrix XenConvert Guide
To start the wizard, click XenConvert.exe in directory that was selected
during the installation process. The default location is:
C:\Program Files\Citrix\XenConvert
The Citrix XenConvert Welcome screen appears. The information that the wizard
displays next will depend on the conversion method selected on this screen. Refer
to the appropriate conversion method for conversion specific details.
Conversion Summary Screen
After a conversion method is selected and the conversion information is entered
using the wizard, the conversion summary screen appears. This screen
summarizes and provides the conversion information and options that follow.
Conversion summary information includes:
Conversion method
The selected conversion method displays at the top of the screen.
The name given to this workload.
Source
The source directory where this unconverted workload currently resides.
Destination Folder
The destination folder where this converted workload will reside.
Status
The current step, user instructions, and status messages that are associated
with this conversion process.
Progress
The progress for this step of the conversion.
After reviewing conversion information on this screen, select one of the
following conversion options:
Back
Use the Back button to return to the previous window to make changes, or
to enter new parameters.
Convert
Click Convert to begin the conversion process.
Cancel
Chapter 2
Using XenConvert
17
Click Cancel to cancel a conversion that is in process. When you cancel a
conversion, a message displays in the status field and is written to the log
file. Files that were created during the conversion remain on the source
system.
Finish
Click Finish to exit XenConvert. This button displays after the conversion
completes or after cancelling the conversion process.
Log
Click Log to display the conversion log file in Notepad. For each
conversion run, detailed status information is stored in the log file. The log
file, XenConvert.txt, is created in the installation directory and
provides the following information:
•
Start and stop time stamps
•
Error and informational messages,
The Log button appears after you click the Convert button.
Controlling XenConvert
XenConvert reads the following parameters from the registry to manage some
functionality. These parameters may be changed to correct problems encountered
with VHDs and are located in:
HKEY_LOCAL_MACHINE\SOFTWARE\Citrix\XenConvert\Paramete
rs\.
Name
Type
Description
AutoDismountTimeoutAsMs DWORD
Number of milliseconds to wait before retrying to
automatically dismount a VHD. Default is 60
seconds.
VhdPluginTimeoutAsMs
Number of milliseconds to wait for a VHD to mount.
Default is 10 minutes.
DWORD
18
Citrix XenConvert Guide
Converting from a Physical Machine
This section describes the following physical-to-virtual conversion methods
supported by XenConvert:
•
“Physical to VHD”
•
“Physical to XVA”
•
“Physical to XenServer”
Before Converting From a Physical Machine
•
“Enable Automount”
•
“Stop Security Services”
•
“Working with Provisioning Server”
Enable Automount
On Windows Server 2003, enable the Windows Automount feature.
•
Enter the following command at a command shell prompt:
DISKPART
•
Enter the following command at the DISKPART prompt:
•
automount enable
Automount will be enabled in the VM you create and can be disabled from within
the VM.
Stop Security Services
Some security services such as anti-virus and end-point protection services can
interfere with a conversion. Stop these types of security services before
converting.
Working with Provisioning Server
XenConvert produces a virtualized instance of a workload usable with
XenServer. To produce a virtualized instance of a workload that is also usable
with Citrix Provisioning Server, install Provisioning Server Target Device
software on the physical source machine before using XenConvert. After a
conversion completes, use the Provisioning Server Console to add the new VHD
and configure a compatible target device to boot from it. Refer to the
Provisioning Server product documentation set for details.
Chapter 2
Using XenConvert
19
Physical to VHD
Select this method to convert a single partition of a physical disk to a partition
within a VHD.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
Name to use.
Source
Choose the physical disk to convert from the drop-down menu.
Destination Folder
Type or browse to the folder to contain the VHD related files. These files
are excluded from the conversion. The folder is created if it does not
After providing conversion information, select from the following options:
Empty Recycle Bin
Check this box to automatically empty the recycle bin before the
conversion process begins. The option is enabled by default. Emptying the
recycle bin reduces the disk space required by the conversion.
Cancel
Exit XenConvert.
Next
Advance to the “Conversion Summary Screen”.
Physical to XVA
Select this method to convert a single partition of a physical disk to a XVA.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
Name to use for the Xen virtual machine.
Source
Select the disk to convert from the drop-down menu.
Destination Folder
20
Citrix XenConvert Guide
Type or browse to the folder to contain the XVA related files. These files
are excluded from the conversion. The folder is created if it does not
After providing conversion information, select from the following options:
Empty Recycle Bin
Check this box to automatically empty the recycle bin before the
conversion process begins. The option is enabled by default. Emptying the
recycle bin reduces the disk space required by the conversion.
Cancel
Exit XenConvert.
Next
Advance to the “Conversion Summary Screen”.
Physical to XenServer
Select this method to convert a single partition of a physical disk to XenServer.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
Name to use for the Xen virtual machine.
Source
Choose the physical disk to convert from the drop-down menu.
Destination Folder
Specify or browse to the folder to contain the intermediate files. These files
are excluded from the conversion. The folder is created if it does not
After providing conversion information, select from the following options:
Empty Recycle Bin
Check this box to automatically empty the recycle bin before the
conversion process begins. The option is enabled by default. Emptying the
recycle bin reduces the disk space required by the conversion.
Cancel
Exit XenConvert.
Next
Advance to the “Conversion Summary Screen”.
Chapter 2
Using XenConvert
21
Converting from Microsoft Virtual Server
This section describes the methods available when converting from Microsoft
Virtual Server.
•
“VMC to XVA”
•
“VMC to XenServer”
•
“VHD to XVA”
•
“VHD to XenServer”
Before Converting From Microsoft Virtual Server
•
Disable Autorun
Consider disabling the Windows Autorun feature because it can interfere
with a conversion. One method of disabling this feature is to set the value of
the following registry value to 0x8 for fixed drives including VHD, or
0xFF for all drives.
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\Curr
entVersion\policies\Explorer\NoDriveTypeAutoRun
•
Shutdown VM
After Converting From Microsoft Virtual Server
1.
Boot the new XenServer VM.
2.
3.
Use Add/Remove Programs feature of Windows to remove the program
VMC to XVA
Select this method to convert a Microsoft Virtual Server 2005 VM to a XVA.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
VMC
Type or browse to the path of the VMC file.
Destination Folder
22
Citrix XenConvert Guide
Type or browse to the folder to contain the XVA. The folder is created if it
After providing conversion information, select from the following options:
Cancel
Exit XenConvert.
Next
Advance to the “Conversion Summary Screen”.
VMC to XenServer
Select this method to convert a Microsoft Virtual Server 2005 VM to a XenServer
VM. This conversion requires a XenServer accessible on the network and a valid
account on that XenServer. The conversion creates an intermediate XVA that
remains on the host.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
VMC
Type or browse to the path of the VMC file.
Destination Folder
Type or browse to the folder to contain the intermediate files. The folder is
created if it does not already exist.
After providing conversion information, select from the following options:
Cancel
Exit XenConvert.
Next
Advance to the “XenServer Account Screen”.
VHD to XVA
Select this method to convert a single VHD to a XVA.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
VHD
Type or browse to the path of the VHD file.
Destination Folder
Chapter 2
Using XenConvert
23
Type or browse to the folder to contain the XVA. The folder is created if it
After providing conversion information, select from the following options:
Cancel
Exit XenConvert.
Next
Advance to the “Conversion Summary Screen”.
VHD to XenServer
Convert a single VHD to a XenServer. This conversion requires a XenServer
accessible on the network and a valid account on that XenServer. The conversion
creates an intermediate XVA that remains on the host.
If this method is selected from the XenConvert wizard, provide the following
conversion information:
VHD
Type or browse to the path of the VHD file.
Destination Folder
Type or browse to the folder to contain the intermediate files. The folder is
created if it does not already exist.
After providing conversion information, select from the following options:
Cancel
Exit XenConvert.
Next
Advance to the “XenServer Account Screen”.
XenServer Account Screen
Enter the following information to identify the XenServer that will be used to
Hostname
Simple host name, fully qualified domain name, or IP address of the
XenServer.
User name
Name of the account with import privileges. Consult the XenServer product
documentation for information on account requirements.
24
Citrix XenConvert Guide
|
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8462910056114197, "perplexity": 704.5831528674925}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376825123.5/warc/CC-MAIN-20181214001053-20181214022553-00266.warc.gz"}
|
https://math.iitm.ac.in/publications/viewpublication/127
|
## Department of Mathematics
Indian Institute Of Technology Madras , Chennai
### Influence of mixed convection in an exponentially decreasing external flow velocity
#### Authors:
Patil, P.M. and Ramane, H.S. and Roy, S. and Hindasageri, V. and Momoniat, E.
#### Journal:
International Journal of Heat and Mass Transfer
2017
|
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|
https://artofproblemsolving.com/wiki/index.php/2004_AMC_12A_Problems/Problem_25
|
# 2004 AMC 12A Problems/Problem 25
## Problem
For each integer , let denote the base- number . The product can be expressed as , where and are positive integers and is as small as possible. What is ?
## Solution
This is an infinite geometric series with common ratio and initial term , so .
Alternatively, we could have used the algebraic manipulation for repeating decimals,
Some factors cancel, (after all, isn't one of the answer choices)
Since the only factor in the numerator that goes into is , is minimized. Therefore the answer is .
## Solution 2
Note thatby geometric series. Thus, we're aiming to find the value ofExpanding the product out, this is equivalent to Note that the numerator of the th fraction and the denominator of the th fraction for cancel out to be sinceby the binomial theorem on the the denominator of the aforementioned. Since this forms a telescoping series, our product is now equivalent towhich, after simplification gives giving an answer of
-fidgetboss_4000
|
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|
https://homework.cpm.org/category/CON_FOUND/textbook/a2c/chapter/12/lesson/12.5.2/problem/12-210
|
Home > A2C > Chapter 12 > Lesson 12.5.2 > Problem12-210
12-210.
Omar was $8$ years old when he received $25{,}000$ dollars from his grandmother’s will. His father invested it for him in a fund that earned $6\%$ annual interest compounded quarterly. He was hoping to see the investment double by the time Omar was ready for college. Another fund offered the same interest rate but the interest would compound continuously. This second fund was a little riskier, however.
1. Write an equation to represent each situation.
$2 = (1.015)^{4t}, 2 = e^{0.06t}$
2. Which method of compounding the interest will double his money faster?
Solve both equations for $t$.
3. Is the difference in doubling time worth the extra risk?
What is the difference in doubling time?
|
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|
https://mathzsolution.com/graph-theoretic-proof-for-six-irrational-numbers-there-are-three-among-them-such-that-the-sum-of-any-two-of-them-is-irrational/
|
# Graph theoretic proof: For six irrational numbers, there are three among them such that the sum of any two of them is irrational.
Problem. Let there be six irrational numbers. Prove that there exists three irrational numbers among them such that the sum of any two of those irrational numbers is also irrational.
I have tried to prove it in the following way, but I am not sure whether it is watertight or not as I have just started learning graph theory.
Let there be a graph with $$66$$ vertices. We assign a weight equal to those six irrational numbers to each of the vertices. We join all the vertices with edges and color the edges in the following way:
• Edge is colored red if the sum of the weights of its end points is irrational.
• Edge is colored blue if the sum of the weights of its end points is rational.
We know that when we color a $$66$$-vertex graph with $$22$$ colors then there must be a monochromatic triangle.
• If the triangle is red then we are done.
• If it is blue, then let the irrational numbers be $$aa$$, $$bb$$ and $$cc$$. Therefore $$a+ba+b$$, $$b+cb+c$$ and $$c+ac+a$$ are all rational. Which implies $$2(a+b+c)2(a+b+c)$$ and $$a+b+ca+b+c$$ is rational. As $$a+ba+b$$ is rational and hence $$cc$$ is also rational. But this is a contradiction.
Hence, our original statement is proved.
## Answer
Your proof is OK.
But more easily we can prove more strong and general claim. Assume we have a collection of $n$ irrational numbers. We shall call numbers $a$ and $b$ equivalent if the difference $a-b$ is rational. So we can partition our collection into equivalence classes. We shall call classes $C$ and $C’$ complementary if $c+c’$ is rational for any $c\in C$ and $c’\in C’$. From our partition we can choose such classes which contain in total at least $n/2$ elements and no two complementary classes are chosen. It remains to remark that a sum of any two chosen elements is irrational. In particular, among $5$ irrational numbers we can choose $3$ with all mutual sums are irrational. From the other hand, a collection consisting of $n/2$ numbers $\sqrt{2}$ and $n/2$ numbers $2-\sqrt{2}$ witnesses that the bound $n/2$ is strict.
Attribution
Source : Link , Question Author : Arpon Basu , Answer Author : Alex Ravsky
|
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|
https://asciidoc.org/latex-bugs.html
|
AsciiDoc
Text based document generation
Benjamin Klum was unable to maintain the LaTeX backend beyond version 8.2.7, and as a consequence the latex.conf file ceased to work with asciidoc sometime after this. For version 8.4.3 I made some changes to the file to get it working again. This document summarises the remaining issues which I have found with generating LaTeX and thence PDF output with asciidoc, which is done as follows:
• asciidoc --backend=latex --unsafe FILE.txt
• latex FILE.tex
• kpdf FILE.pdf
Many of these were found by processing the asciidoc.txt file and comparing the HTML output with the PDF.
## Footnotes
Priority
Low.
Problem
References to footnotes, and a sensible value for the [footnoteref-inlinemacro] section, don’t seem to be possible.
Cause
LaTeX doesn’t support footnoting much beyond creating a footnote at a certain point in text and displaying the footnote itself.
Solution
Unclear. How important or necessary is this, anyway?
## Spurious text at starts of paragraphs
Priority
Medium
Problem
It is necessary to insert spurious text in paragraphs.
Cause
This asciidoc input:
-------------------------------------------------------------------
Text
-------------------------------------------------------------------
generates this LaTeX code:
\begin{lstlisting}
SPURIOUS TEXTText\end{lstlisting}
which should be:
\begin{lstlisting}[]
Text\end{lstlisting}
Solution
Find out a way to generate the correct LaTeX output as above. The obvious solution, as explained in latet.conf, doesn’t work.
## Tables
Priority
Rather high.
Problem
Not all of the table configuration options can be passed through to the LaTeX backend. In particular, I’ve had to assume that all tables will be fifteen or fewer left-justified columns wide.
Cause
The table models in LaTeX and HTML are too dissimilar for one asciidoc specification to generate valid output in both formats by simple regexp replacement. Related to this is the unfortunate fact that <COLGROUP> and related tags aren’t a required part of HTML4, and some broswers (at least Firefox and Konqueror) don’t implement them.
Solution
Perhaps table processing could be handled by a Python plugin, which would read in a table spec and generate the appropriate text?
## Unicode escaping
Priority
Rather high, to me at least.
Problem
The commented-out section in latex.conf, if uncommented, converts π to \unichar{960}, which then causes LaTeX to complain that the resulting command is unavailable in encoding T1. The more common non-ASCII characters, such as those in félicité and świeca, are handled properly, but some - such as the IPA characters in the tipa package - are not.
Cause
The encodings in the LaTeX output are wrong.
Solution
Correct the encodings.
## Text colours
Priority
Probably low
Problem
The text colour options are not processed by LaTeX; for example [#ff0000]#Red text# is not rendered in red.
Cause
LaTeX and HTML represent RGB triads differently: HTML is happy with #ff8000, but LaTeX needs [rgb]{1,0.5,0}.
Solution
Provide some sort of internal RGB conversion mechanism which can convert RGB triads to different representations.
## Text sizes
Priority
Probably low
Problem
The text size options are not processed by LaTeX: [,,1]#text# is rendered in the same size as normal text.
Cause
HTML size tags - h1 through h7 - are directly derivable from the size number, whereas LaTeX has a series of descriptive words (HUGE through normalsize to scriptsize).
Solution
Provide a way to treat the number as an index into an array.
## Background colour in paragraphs
Priority
Medium
Problem
If the backgroundcolor attribute is specified in the lstset command, all paragraphs are displayed as black rectangles by kpdf, xpdf, and evince, although kdvi has no problems. I’ve had to remove the attribute, and so paragraphs all appear on white backgrounds. The PDF viewers also complain:
Error (NNNN): Unknown operator 'rgb'
Cause
Apparently a known bug in the output of pdflatex. Not a bug in asciidoc.
Solution
Wait until this bug is fixed?
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http://bib-pubdb1.desy.de/collection/PUB_PETRA_III-20150811?ln=en
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# PETRA III
2018-09-0313:48 [PUBDB-2018-03341] Conference Presentation et al Retention of Particle Associated Radionuclides in Biota 2nd International Conference on Radioecological Concentration Processes, SevilleSeville, Spain, 6 Nov 2016 - 9 Nov 2016 2018-09-0311:42 [PUBDB-2018-03333] Contribution to a conference proceedings et al State-of-the-art tools for characterisation of particle exposure 4th International Conference on Radioecology and Environmental Radioactivity (ICRER), ICRER 2017, BerlinBerlin, Germany, 3 Sep 2017 - 8 Sep 2017 not applicable (2017) Methods for high-resolution non-invasive image analysis of the internal distribution of radionuclides s as well as toxic metals in intact animals or organs have been demonstrated. The retention of radioactive particles observed for environmental samples as well as in laboratory experiments calls for better exposure characterization in impact assessments of particle contaminated areas, in particular when the biota is of relevance for the human food pathway.. 2015-09-0311:30 [PUBDB-2015-03418] Journal Article et al Single Shot Polarization Characterization of XUV FEL Pulses from Crossed Polarized Undulators Scientific reports 5, 13531 (2015) [10.1038/srep13531] Polarization control is a key feature of light generated by short-wavelength free-electron lasers.In this work, we report the first experimental characterization of the polarization properties of anextreme ultraviolet high gain free-electron laser operated with crossed polarized undulators. Weinvestigate the average degree of polarization and the shot-to-shot stability and we analyze aspectssuch as existing possibilities for controlling and switching the polarization state of the emitted light.The results are in agreement with predictions based on Gaussian beams propagation.. OpenAccess: PDF PDF (PDFA); 2015-08-2708:58 [PUBDB-2015-03292] Journal Article et al Static Magnetic Proximity Effect in $\mathrm{Pt/NiFe_2O_4}$ and Pt/Fe Bilayers Investigated by X-Ray Resonant Magnetic Reflectivity Physical review letters 115(9), 097401 (2015) [10.1103/PhysRevLett.115.097401] The spin polarization of Pt in Pt/NiFe2O4 and Pt/Fe bilayers is studied by interface-sensitive x-ray resonant magnetic reflectivity to investigate static magnetic proximity effects. The asymmetry ratio of the reflectivity is measured at the Pt L3 absorption edge using circular polarized x-rays for opposite directions of the magnetization at room temperature. [...] OpenAccess: PDF PDF (PDFA);
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https://mathhelpboards.com/threads/arundevs-question-at-yahoo-answers-a-triangle-inscribed-in-a-semicircle-is-a-right-triangle.8154/
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# Arundev's question at Yahoo! Answers: a triangle inscribed in a semicircle is a right triangle
• #1
#### MarkFL
Staff member
Feb 24, 2012
13,775
Here is the question:
Using coordinate geometry prove that angle in a semicircle is a right angle?
I have posted a link there to this thread so the OP can view my work.
• #2
#### MarkFL
Staff member
Feb 24, 2012
13,775
Hello Arundev,
Consider the following diagram:
Without loss of generality, I have chosen a unit semicircle whose center is at the origin.
Point $P$ is $$\displaystyle (x,y)=\left(x,\sqrt{1-x^2} \right)$$.
The slope of line segment $A$ is:
$$\displaystyle m_A=\frac{\sqrt{1-x^2}-0}{x-(-1)}=\frac{\sqrt{1-x^2}}{1+x}=\sqrt{\frac{1-x}{1+x}}$$
The slope of line segment $B$ is:
$$\displaystyle m_B=\frac{\sqrt{1-x^2}-0}{x-1}=-\frac{\sqrt{1-x^2}}{1-x}=-\sqrt{\frac{1+x}{1-x}}$$
As proven >>>here<<<, two lines are perpendicular if the prodict of their slopes is $-1$.
$$\displaystyle m_Am_B=\left(\sqrt{\frac{1-x}{1+x}} \right)\left(-\sqrt{\frac{1+x}{1-x}} \right)=-1$$
Thus, we know line segments $A$ and $B$ are perpendicular, and so the triangle is a right triangle.
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http://simbad.cds.unistra.fr/simbad/sim-ref?bibcode=2017A%26A...598A..82G
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other querymodes : Identifierquery Coordinatequery Criteriaquery Referencequery Basicquery Scriptsubmission TAP Outputoptions Help
2017A&A...598A..82G - Astronomy and Astrophysics, volume 598A, 82-82 (2017/2-1)
TYC 8241 2652 1 and the case of the disappearing disk: No smoking gun yet.
GUNTHER H.M., KRAUS S., MELIS C., CURE M., HARRIES T., IRELAND M., KANAAN S., POPPENHAEGER K., RIZZUTO A., RODRIGUEZ D., SCHNEIDER C.P., SITKO M., WEIGELT G., WILLSON M. and WOLK S.
Abstract (from CDS):
Context. TYC 8241 2652 1 is a young star that showed a strong mid-infrared (mid-IR, 8-25µm) excess in all observations before 2008, which is consistent with a dusty disk. Between 2008 and 2010 the mid-IR luminosity of this system dropped dramatically by at least a factor of 30 suggesting a loss of dust mass of an order of magnitude or more.
Aims. We aim to constrain possible models including the removal of disk material by stellar activity processes, the presence of a binary companion, or other explanations suggested in the literature.
Methods. We present new X-ray observations, optical spectroscopy, near-IR interferometry, and mid-IR photometry of this system to constrain its parameters and further explore the cause of the dust mass loss.
Results. In X-rays TYC 8241 2652 1 has all the properties expected from a young star: Its luminosity is in the saturation regime and the abundance pattern shows enhancement of O/Fe. The photospheric Hα line is filled with a weak emission feature, indicating chromospheric activity that is consistent with the observed level of coronal emission. Interferometry does not detect a companion and sets upper limits on the companion mass of 0.2, 0.35, 0.1, and 0.05M at projected physical separations of 0.1-4AU, 4-5AU, 5-10AU, and 10-30AU, respectively (assuming a distance of 120.9pc). Our mid-IR measurements, the first of the system since 2012, are consistent with the depleted dust level seen after 2009.
Conclusions. The new data confirm that stellar activity is unlikely to destroy the dust in the disk and shows that scenarios, in which either TYC 8241 2652 1 heats the disk of a binary companion or a potential companion heats the disk of TYC 8241 2652 1, are unlikely.
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http://www.math.stonybrook.edu/~oleg/Rokhlin/RokhlinInErgodic.html
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Leningrad Math. J. Vol. 2 (1991), No. 2
On the work of V. A. Rokhlin in ergodic theory
by A. M. Vershik
The scientific heritage of Vladimir Abramovich Rokhlin consists of about sixty publications and several unfinished manuscripts from the 1950's and 60's, and can be conditionally split into four parts: topology - mainly four-dimensional topology and the algebraic apparatus of topology; real algebraic geometry (the last years); ergodic theory; and, finally, work on the history, teaching methods, and methodology of mathematics. The last group, unfortunately, was not reflected sufficiently in his publications, though it occupied Rokhlin constantly, and his ideas, presented often in reports and public lectures, are widely enough known and have had an influence on those around him.
Here we touch briefly on his work in ergodic theory; a detailed analysis of his work in topology and real algebraic geometry is contained in the paper of Viro and Kharlamov. Twenty-four publications were devoted to ergodic theory, along with several unpublished manuscripts which were not finished, unfortunately, and are among his unrealized plans. He returned more than once to the idea of writing a book on the metric theory of dynamical systems, including a large section on general measure theory in his own spirit; as far back as the 1940s he wrote several chapters and proposed continuing the work later with young coauthors, but after ceasing to study ergodic theory, he cooled somewhat to the idea. It should be remarked that some traces of his plans were realized in surveys and books that came out later.
In ergodic theory Vladimir Abramovich introduced a geometric and algebraic culture that it lacked by origin, which was rather analytic in the spirit of the traditions of the theory of dynamical systems of Poincare and, on the other hand, Boltzmann. In this he was continuing the tradition of von Neumann. In Rokhlin's work the geometric side of things (partitions, dynamics, etc.) pre-dominated over the analytic aspects. He proposed that systems of algebraic, analytic, probabilistic, number-theoretic, and other origins should be considered simultaneously. This tradition became established and yielded excellent results in his work and later in the work of his students. On the other hand, he strictly followed axiomatic constructions of measure theory, also affected by the influence of Kolmogorov and von Neumann.
Lebesgue spaces, introduced by Rokhlin in his undergraduate work and thoroughly investigated in the subsequent dissertation and paper 0n the fundamental concepts of measure theory'', have turned out to be a very successful concept, and his axiomatics an exceptionally convenient refinement of the axiomatizations used previously. It can be said without doubt that, after the axiomatics of Kolmogorov and von Neumann, Rokhlin made the most important step for distinguishing the proper category of measure spaces. Unfortunately, the convenience and importance of the theory of Lebesgue spaces were not realized for some time. It was perhaps for this reason that investigators resorted for a long time to topological concepts for constructions that are in essence purely metric. At present there is no doubt that the category of Lebesgue spaces is a fundamental construction in ergodic theory, measure theory, and other theories. In passing it should be mentioned that Rokhlin also made the important observation that a system of conditional measures, or, as he said, a canonical system of measures, exists only for measurable partitions of Lebesgue spaces, and attempts to introduce them in other categories were incorrect.
If one now asks any specialist in ergodic theory what the two most fundamental results at the basis of the theory are, the answer will be:
1. the Birkhoff-von Neumann ergodic theorem;
2. the Rokhlin-Halmos lemma.
This lemma, which is the starting point of all approximation constructions, was proved by Rokhlin at the end of the 1940s, and independently by Halmos in a weaker formulation. It states that, for every aperiodic transformation $T$ of a Lebesgue space $X$ with a finite invariant measure $\mu$, every integer $n$, and every positive number $\varepsilon$, there exists a periodic transformation $T_n$ with period $n$ such that $$\mu\{x\in X\mid T_nx\ne Tx\}<\frac1n+\varepsilon.$$ This lemma on periodic approximation has been generalized many times; it is the basis for category theorems, approximation theorems, entropy theorems, and so on.
Further, in early work on decomposition of automorphisms into ergodic components, Rokhlin actually proved a variant of a measurable selection theorem now called the Rokhlin-Kuratowski-Ryll-Nardzewski theorem. Influenced by the Gel'fand-Naimark-Raikov-Shilov theory of normed rings, Rokhlin made an (incomplete) attempt to construct a theory of so-called unitary rings. This theory is dual to the theory of Lebesgue spaces, which is a function-analytic version of it.
The first period of development of ergodic theory (the 1930's and 40's) concerned, for the most part, spectral theory. Here Vladimir Abramovich was the author of a number of the results included in his surveys of 1949 and 1958. Widely known are his categorical mixing estimates, the first investigations of automorphisms of compact Abelian groups as dynamical systems, and work on measurable flows.
Many papers, ideas, and initiatives of Vladimir Abramovich were completed or developed in investigations of his students and subsequent authors. These include, for example, the proposal to develop a trajectory theory (R. E. Belinskaya, A. M. Vershik), realization theorems and systems over systems'' (we would now say quantization dynamical systems), Gaussian systems (Vershik), the mixed spectrum, fiber bundles (L. M. Abramov), mixing (Ya. G. Sinai), and others.
We should dwell especially on his favorite topic of study in later years (and most important in the 1960's and 7O's) - entropy theory. Kolmogorov's discovery of entropy made a strong impression on Rokhlin. The language of this theory was the language of measurable partitions worked out earlier by Rokhlin and used by Kolmogorov in his work on entropy.
The precise analysis of the concept of the entropy of dynamical systems carried out in a cycle of papers by Kolmogorov and Sinai and then by Rokhlin, Abramov, Pinsker, and others, was simply not possible without the theory of measurable partitions, especially the part of it relating to decreasing sequences. A small and insignificant error in Kolmogorov's first paper, which was discovered by Vladimir Abramovich and made it necessary to give a somewhat different definition of the entropy in the Sinai sense, involved certain subtleties of the theory (see the remark in Kolmogorov's second paper). The unity of the two definitions was finally reestablished considerably later after Rokhlin proved a theorem on generators for aperiodic automorphisms. The concluding results on generators are due here to Krieger.
Vladimir Abramovich's two survey papers in Uspekhi Matematicheskikh Nauk (1960 and 1967) played an enormous role in the development of entropy theory in our country and abroad. The second paper summarizes the development of the concept of entropy and its applications to the theory of transformations with invariant measure.
The theory of invariant partitions for automorphisms especially interested Rokhlin, and he returned to it in later years, in the period when he finished his work on ergodic theory (this was the topic of several unpublished sketches). The start of this theory was the classical joint work of Rokhlin and Sinai in which it was proved, in particular, that the class of $K$-automorphisms coincides with the class of automorphisms with completely positive entropy (this was proved earlier in one direction by M. S. Pinsker). The very first formulas in entropy theory were the Abramov formulas for the derived automorphism and flow; formulas for the entropy of automorphisms of compact groups (Sinai, Arov, Yuzvinskii, and others) were a development of ideas and suggestions of Vladimir Abramovich. Also, the metric properties of automorphisms of compact Abelian groups were investigated (Rokhlin, Sinai, Yuzvinskii) on his initiative.
Rokhlin's interest in ergodic theory gradually began to fall, after the appearance of new post-entropy ideas - approximation and, especially, the fireworks of Ornstein's contributions and that of his successors. Vladimir Abramovich was undoubtedly interested in the course of events, but he did not take part, all the more so because his algebro-topological interests had prevailed by this time.
We mention two more circumstances. For a long time Rokhlin has been interested in number theory and the possibility of applying ergodic theory to it. Although he had only one paper on this topic, and that devoted mainly to the theory of exact endomorphisms (namely, the paper on continued fractions and the Gauss endomorphism), he thought (and this opinion had an indirect confirmation, for example, in the work of Linnik on the ergodic method in number theory) that the possibilities of metric theory in number theory were far from exhausted. Incidentally, Vladimir Abramovich always had an intense interest in the theory of endomorphisms (or semigroups of endomorphisms), and the paper mentioned is a vault of metric concepts and theorems relating precisely to this case. Especially important is the concept of a natural extension; this concept provides an invariant formulation of the immersion of a one-sided process in a two-sided process (metric dilatation). The other circumstance had to do with the interrelations with smooth and classical dynamics. It may seem strange that he, an outstanding specialist in the area of smooth manifolds who had a good knowledge of classical dynamics and physics, did not try to connect ergodic theory with smooth dynamics, all the more so because many of his students, and those who were close to him or felt his influence, studied this topic actively (Sinai, Arnol'd, Anosov, and others). Moreover, communications about the work of Smale, Anosov, and others were heard repeatedly in the seminar. Vladimir Abramovich himself said that here he was an advocate of purely'' posed problems not involving a mixture of categories completely unlike each other. In other words, he regarded smooth and metric dynamics as immiscible areas. This point of view was perhaps affected by an echo of axiomatic rigorism, which is now certainly not popular, but one cannot say that it is inconsistent.
At the sources of ergodic theory as a mathematical discipline stand the names of von Neumann and Kolmogorov; after them can be named a few others who shaped this theory from the 1930's to the 1950's and gave it its modern form - G. Birkhoff, S. Ya. Khinchin, E. Hopf, S. Kakutani, P. Halmos, and Vladimir Abramovich Rokhlin.
Work of Vladimir Abramovich Rokhlin on measure theory and ergodic theory
1. 0n classification of measurable partitions, Dokl. Akad. Nauk SSSR 58 (1947), 29 - 32. (Russian)
2. 0n the problem of classification of automorphisms of Lebesgue spaces, Dokl. Akad. Nauk SSSR 58:2 (1947), 189 - 191. (Russian)
3. Unitary rings, Dokl. Akad. Nauk SSSR 59 (1948), 643 - 646. (Russian)
4. A general transformation with invariant measure is not mixing, Dokl. Akad. Nauk SSSR 60 (1948), 349 - 351. (Russian)
5. 0n the fundamental concepts of measure theory, Mat. Sb. 25 (67) (1949), 107 - 150; English transl., Amer. Math. Soc. Transl. (1) 10 (1962).
6. 0n decomposition of a dynamical system into transitive components, Mat. Sb. 25 (67) (1949), 235 - 249. (Russian)
7. On dynamical systems whose irreducible components have purely point spectrum, Dokl. Akad. Nauk SSSR 64 (1949), 167 - 169. (Russian)
8. with A. A. Gurevich, 0n approximation of nonperiodic flows by periodic flows, Dokl. Akad. Nauk SSSR 64 (1949), 619-620. (Russian)
9. 0n endomorphisms of compact Abelian groups, Izv. Akad. Nauk SSSR Ser. Mat. 13 (1949), 329-340. (Russian)
10. Selected topics in the metric theory of dynamical systems, Uspekhi Mat. Nauk 4 (1949), no. 2 (30), 57 - 123. (Russian)
11. with A. A. Gurevich, Approximation theorems for measurable flows, Izv. Akad. Nauk SSSR, Ser. Mat. 14 (1950), no. 6 (40), 537 - 548. (Russian)
12. Metric classification of measurable functions, Uspekhi Mat. Nauk 12 (1957), no. 2 (74), 169 - 174. (Russian)
13. with S. V. Fomin, Spectral theory of dynamical systems, Proc. Third All-Union Math. Congress (1956), Vol. 3, 1958, p. 284. (Russian)
14. On the entropy of a metric automorphism, Dokl. Akad. Nauk SSSR 124 (1959), 980 - 982. (Russian)
15. New progress in the theory of transformations with invariant measure, Uspekhi Mat. Nauk 15 (1960), no. 4 (94), 3 - 26; English transl. in Russian Math. Surveys 15 (1960).
16. Structure and properties of invariant measurable partitions, Dokl. Akad. Nauk SSSR 141 (1961), 1038-1041; English transl. in Soviet Math. Dokl. 2 (1961).
17. with Ya. G. Sinai, 0n the entropy of an automorphism of a compact Abelian group, Teor. Veroyatnost. i Primenen. 6 (1961), 351 - 352; English transl. in Theory Probab. Appl. 6 (1961).
18. Exact endomorphisms ofa Lebesgue space, Izv. Akad. Nauk SSSR Ser. Mat. 25 (1961), 499-5 30; English transl. in Amer. Math. Soc. Transl. (2) 39 (1964).
19. with L. M. Abramov, The entropy of a fiber bundle of transformations with invariant measure, Vestnik Leningrad. Univ. 1962, no. 7 (Ser. Mat. Mekh. Astr. vyp. 2), 5 - 13. (Russian)
20. An axiomatic definition of the entropy of transformations with invariant measure, Dokl. Akad. Nauk SSSR 148 (1963), 779 - 781; English transl. in Soviet Math. Dokl. 4 (1963).
21. Generators in ergodic theory, Vestnik Leningrad. Univ. 1963, no. 1 (Ser. Mat. Mekh. Astr. vyp. 1), 26 - 32. (Russian)
22. Metric properties of endomorphisms of compact Abelian groups, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 867 - 874; English transl. in Amer. Math. Soc. Transl. (2) 64 (1967).
23. Generators in ergodic theory. II, Vestnik Leningrad. Univ. 1965, no. 13 (Ser. Mat. Mekh. Astr. vyp. 3), 68 - 72. (Russian)
24. Lectures on entropy theory of transformations with invariant measure, Uspekhi Mat. Nauk 22 (1967), no. 5 (137), 4 - 56; English transl. in Russian Math. Surveys 22 (1967)
List of manuscript material of Vladimir Abramovich Rokhlin on ergodic theory
1. Notebook of small format in black binding without heading, about 80 pages, materials for a book (apparently from the 1940's), Table of contents: Part I. Lebesgue spaces, Chapters 1 - 13.
2. Sketch: Foreword''. Organization of the book. History of the theory of transformations with invariant measure, its connections and applications. Measure theory as an independent science, and the true place of the theory of transformations with invariant measure. What is usually understood by measure theory; purpose of the first chapter, what is assumed known. Main goal of the book - new things. Begin with this. Characteristics of the old parts. Selection of materials. Degree of generality - Lebesgue spaces.
3. Manuscript, Transformations with invariant measure''. Written parenthetically: book'', 69 pages + 29 (apparently later) - probably relates to the 1960's.
4. Manuscript, Unitary rings'', 18 pages (apparently from the 1950s).
5. Ergodic theory 1966 - 1967. Lectures (plans), 4 pages.
6. Invariant partitions, June 1967, 2 pages; additions - July 1967, September 1967.
7. Closed partitions. Report October 1, 1968'', 1 page; additions - October 11 and 21, 1968.
8. Saturated partitions. December 1969'', 2 pages, 24 items.
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https://www.nalgebra.org/vectors_and_matrices/
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Vectors and matrices§
Vector and matrices are the fundamental building blocks of any linear algebra library. Their sizes can either be known at compile-time or only at run-time. In either case, they allow common operations (additions, multiplications, etc.) to be used through operator overloading.
The generic Matrix type§
We first give a short description of the generic Matrix type. Readers interested in the implementation details are referred to the section about implementation internals. In practice, most use-cases are covered by type aliases that hide the most complicated type parameters.
The Matrix<N, R, C, S> type is a column-major matrix with a shape that may or may not be known at compile-time. It takes four type parameters:
• N: the scalar type, i.e., the type of the matrix components. Typical values are f32 or f64.
• R: a type characterizing the number of rows on this matrix.
• C: a type characterizing the number of columns on this matrix.
• S: the buffer that contains all the matrix components and (if necessary) metadata about its shape at run-time. Of all the type parameters, this is the only element actually instantiated by a Matrix.
The type parameters R and C completely determine whether or not the matrix shape is known at compile-time or only at run-time. They can have two kinds of values:
1. Type-level integers: because the Rust programming language does not support parametrization over integer values (yet), we have to simulate this feature using types instead of literals. For example, instead of writing Matrix<N, 2, 4, S> for a 2x4 matrix, we have to write Matrix<N, U2, U4, S>, where U2 and U4 are types exported by the root module of nalgebra, e.g., use nalgebra::U2;. Note that nalgebra only defines types from U1 to U127. If you need type-level integers greater than 127, you have to grab them from the typenum crate instead, e.g. typenum::U1000. Redefining U1 to U127 instead of using types from typenum right away was necessary to improve significantly the quality of error messages when matrices with incompatible dimensions are, say, added or multiplied.
2. The special Dynamic type: using this instead of a type-level integer indicates that the corresponding matrix dimension is not known at compile-time. For example, Matrix<N, Dynamic, Dynamic, S> has a number of rows and number of columns that can only be known at runtime. Another typical example is a dynamically-sized column vector: Matrix<N, Dynamic, U1, S>.
use na::{U2, U3, Dynamic, MatrixArray, MatrixVec};
use typenum::U1000;
// Statically sized and statically allocated 2x3 matrix using 32-bit floats.
type Matrix2x3f = Matrix<f32, U2, U3, MatrixArray<f32, U2, U3>>;
// Half-dynamically sized and dynamically allocated matrix with
// two rows using 64-bit floats.
type Matrix2xXf64 = Matrix<f64, U2, Dynamic, MatrixVec<f64, U2, Dynamic>>;
// Dynamically sized and dynamically allocated matrix with
// two rows and using 32-bit signed integers.
type DMatrixi32 = Matrix<i32, Dynamic, Dynamic, MatrixVec<i32, Dynamic, Dynamic>>;
// Statically sized and statically allocated 1000x3 matrix using 32-bit floats.
// Note that U1000 is imported from typenum while U3 comes from nalgebra.
type Matrix1000x3f = Matrix<f32, U1000, U3, MatrixArray<f32, U1000, U3>>;
Note that vectors are just type aliases for matrices. For a column vector (resp. row vector), we simply use a matrix with C set to U1 (resp. R set to U1). Common low-dimensional matrices and vectors are exposed as type aliases so that the user does not have to deal with anything but the scalar type parameter N:
• Vector1<N> .. Vector6<N>: are column vectors of dimension 1 to 6.
• Matrix1<N> .. Matrix6<N>: are square matrices of dimension 1x1 to 6x6.
• Rectangular matrices have the form MatrixIxJ<N> where I and J are any value from 1 to 6, e.g., Matrix4x5<N>.
• DVector<N> and DMatrix<N>: are respectively a dynamically-sized column vector and a dynamically-sized matrix.
Internally, dynamically- and statically-sized matrices do not use the same data storage type. While the former is always allocated on the heap using a Vec, the latter prefers static allocation indirectly using a GenericArray from the generic-array crate. This distinction is made possible by using different concrete types for the S type parameter of the Matrix structure, depending on the values of the R and C parameters for the matrix shape. See the section dedicated to storage buffers for more details.
Matrix construction§
All matrices and vectors with shapes known at compile-time can be created from the values of their components given in conventional mathematical notation, i.e., row-by-rows, using the usual ::new method:
// A vector with three components.
let v = Vector3::new(1, 2, 3);
// A matrix with three lines and four columns.
// We chose values such that, for example, 23 is at the row 2 and column 3.
let m = Matrix3x4::new(11, 12, 13, 14,
21, 22, 23, 24,
31, 32, 33, 34);
Depending on the values of the R and C type parameters for the matrix shape, the matrix construction methods listed below may have different signatures. In particular, each constructor takes one usize parameter for each matrix dimension that is set to Dynamic. Specifically:
• If R and C are both type-level integers, ::from_element(e) takes only one parameter which is the element to fill the matrix with.
• If R is Dynamic and C a type-level integer, ::from_element(nrows, e) takes two parameters: one for the number of matrix rows and one for the element to fill the matrix with.
• If R is a type-level integer and C is Dynamic, ::from_element(ncols, e) takes two parameters: one for the number of matrix columns and one for the element to fill the matrix with.
• If both R and C are equal to Dynamic, then ::from_element(nrows, ncols, e) takes three parameters: one for the number of matrix rows, one for the number of columns, and the last one for the element to fill the matrix with.
Method Description
::from_rows(...) Creates a matrix filled with the given array of rows. Panics if any two rows provided do not have the same size.
::from_columns(...) Creates a matrix filled with the given array of columns. Panics if any two columns provided do not have the same size.
::from_diagonal(...) Creates a diagonal matrix with its diagonal equal to the provided vector. All off-diagonal elements are set to 0.
::repeat(...) Creates a matrix filled with the given element (same as ::from_element(...)).
::from_element(...) Creates a matrix filled with the given element (same as ::repeat(...)).
::from_iterator(...) Creates a matrix filled with the content of the given iterator. The iterator must provide the matrix components in column-major order.
::from_row_slice(...) Creates a matrix filled with the content of the given slice. Elements of the slice are provided in row-major order (which is the usual mathematical notation.)
::from_column_slice(...) Creates a matrix filled with the content of the given slice. Elements of the slice are provided in column-major order.
::from_vec(...) Creates a matrix filled with the content of the given Vec. Elements of the vec are provided in column-major order. Constructing a dynamically-sized matrix this way consumes the vec to avoid allocations.
::from_fn(...) Creates a matrix filled with the values returned by the given closure of type FnMut(usize, usize) -> N. This closure is called exactly once per matrix component and is given as parameter each matrix component’s 0-based indices.
::identity(...) Creates a matrix with 1 on its diagonal and 0 elsewhere. If the matrix to be constructed is not square, only the largest square submatrix formed by its first rows and columns is set to the identity matrix. All the other components are 0.
::from_diagonal_element(...) Creates a matrix with its diagonal filled with the given element and 0 elsewhere. If the matrix to be constructed is not square, only the largest square submatrix formed by its first rows and columns is set to the identity matrix. All the other components are set to 0.
::new_random(...) Creates a matrix with all its components initialized at random using the default random generator of the rand crate, i.e., the rand::random() function.
// All the following matrices are equal but constructed in different ways.
let m = Matrix2x3::new(1.1, 1.2, 1.3,
2.1, 2.2, 2.3);
let m1 = Matrix2x3::from_rows(&[
RowVector3::new(1.1, 1.2, 1.3),
RowVector3::new(2.1, 2.2, 2.3)
]);
let m2 = Matrix2x3::from_columns(&[
Vector2::new(1.1, 2.1),
Vector2::new(1.2, 2.2),
Vector2::new(1.3, 2.3)
]);
let m3 = Matrix2x3::from_row_slice(&[
1.1, 1.2, 1.3,
2.1, 2.2, 2.3
]);
let m4 = Matrix2x3::from_column_slice(&[
1.1, 2.1,
1.2, 2.2,
1.3, 2.3
]);
let m5 = Matrix2x3::from_fn(|r, c| (r + 1) as f32 + (c + 1) as f32 / 10.0);
let m6 = Matrix2x3::from_iterator([ 1.1f32, 2.1, 1.2, 2.2, 1.3, 2.3 ].iter().cloned());
assert_eq!(m, m1); assert_eq!(m, m2); assert_eq!(m, m3);
assert_eq!(m, m4); assert_eq!(m, m5); assert_eq!(m, m6);
// All the following matrices are equal but constructed in different ways.
// This time, we used a dynamically-sized matrix to show the extra arguments
// for the matrix shape.
let dm = DMatrix::from_row_slice(4, 3, &[
1.0, 0.0, 0.0,
0.0, 1.0, 0.0,
0.0, 0.0, 1.0,
0.0, 0.0, 0.0
]);
let dm1 = DMatrix::from_vec(4, 3, vec![1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0]);
let dm2 = DMatrix::from_diagonal_element(4, 3, 1.0);
let dm3 = DMatrix::identity(4, 3);
let dm4 = DMatrix::from_fn(4, 3, |r, c| if r == c { 1.0 } else { 0.0 });
let dm5 = DMatrix::from_iterator(4, 3, [
// Components listed column-by-column.
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0
].iter().cloned());
assert_eq!(dm, dm1); assert_eq!(dm, dm2);
assert_eq!(dm, dm3); assert_eq!(dm, dm4);
assert_eq!(dm, dm5);
Matrices with sizes known at compile-time also implement some construction traits from the num crate at well:
Trait method Description
Zero::zero() Creates a matrix filled with zeros.
One::one() Creates a matrix with a diagonal set to 1 and off-diagonal elements set to 0.
Bounded::min_value() Creates a matrix filled with the minimal value of the matrix scalar type.
Bounded::max_value() Creates a matrix filled with the maximal value of the matrix scalar type.
Column vectors (which are just Matrix with C set to U1) with low dimensions from 1 to 6 have additional constructors:
• ::x(), ::y(), and ::z() create a vector with, respectively, the first, second, or third coordinate set to 1 and all others to 0.
• ::a(), ::b(), and ::c() create a vector with, respectively, the fourth, fifth, or sixth coordinate set to 1 and all others to 0.
assert_eq!(Vector3::x(), Vector3::new(1.0, 0.0, 0.0));
assert_eq!(Vector3::y(), Vector3::new(0.0, 1.0, 0.0));
assert_eq!(Vector3::z(), Vector3::new(0.0, 0.0, 1.0));
assert_eq!(Vector6::a(), Vector6::new(0.0, 0.0, 0.0, 1.0, 0.0, 0.0));
assert_eq!(Vector6::b(), Vector6::new(0.0, 0.0, 0.0, 0.0, 1.0, 0.0));
assert_eq!(Vector6::c(), Vector6::new(0.0, 0.0, 0.0, 0.0, 0.0, 1.0));
Adding a _axis suffix to those constructors, e.g., ::y_axis(), will create a unit vector wrapped into the Unit structure. For example, Vector2::y_axis() will create a Unit<Vector2<N>> with its the second component of the underlying vector set to 1.
assert_eq!(Vector4::x_axis().unwrap(), Vector4::x());
assert_eq!(Vector4::y_axis().unwrap(), Vector4::y());
assert_eq!(Vector4::z_axis().unwrap(), Vector4::z());
assert_eq!(Vector5::a_axis().unwrap(), Vector5::a());
assert_eq!(Vector5::b_axis().unwrap(), Vector5::b());
Matrix operations§
Operations between two matrices like addition, division, and multiplication, require both matrices to have compatible shapes. In particular:
• Addition require both matrices to have the same number of rows and the same number of columns.
• Multiplication and division requires the matrix on the left-hand-side to have as many columns as the number of rows of the matrix on the right-hand-side.
Those restrictions are either checked at compile-time or at runtime, depending on the inputs types. In particular, if the matrix dimensions to be checked are type-level integers then the check is performed at compile-time. The following shows an example of compilation error for attempting to multiply a 2x3 matrix with a 4x4 matrix:
let a = Matrix2x3::zero();
let b = Matrix4::zero();
let _ = a * b; // Compile-time error here.
error[E0277]: the trait bound na::constraint::ShapeConstraint: na::constraint::DimEq<na::U3, na::U4> is not satisfied
--> tests/matrix.rs:27:13
|
27 | let _ = a * b;
| ^^^^^ the trait na::constraint::DimEq<na::U3, na::U4> is not implemented for na::constraint::ShapeConstraint
|
= help: the following implementations were found:
= help: <na::constraint::ShapeConstraint as na::constraint::DimEq<D, D>>
= help: <na::constraint::ShapeConstraint as na::constraint::DimEq<D, na::Dynamic>>
= help: <na::constraint::ShapeConstraint as na::constraint::DimEq<na::Dynamic, D>>
= note: required because of the requirements on the impl of na::constraint::AreMultipliable<na::U2, na::U3, na::U4, na::U4> for na::constraint::ShapeConstraint
= note: required because of the requirements on the impl of std::ops::Mul<na::Matrix<{float}, na::U4, na::U4, na::MatrixArray<{float}, na::U4, na::U4>>> for na::Matrix<{float}, na::U2, na::U3, na::MatrixArray<{float}, na::U2, na::U3>>
If at least one matrix dimension to be checked is Dynamic then the check is performed at run-time and panics in case of mismatch. The following example shows the run-time error for attempting to multiply a statically-sized 2x3 matrix with a dynamically-sized 4x4 matrix:
let a = Matrix2x3::zero();
let b = DMatrix::from_element(4, 4, 0.0);
let _ = a * b; // Compiles fine but panics here.
thread 'main' panicked at 'Matrix multiplication dimensions mismatch.', [...]/nalgebra/src/core/ops.rs:328
note: Run with RUST_BACKTRACE=1 for a backtrace
The return type of a matrix operation is automatically deduced from the matrix dimensions:
• If both matrices have dimensions known at compile-time then the result also has dimensions known at compile-time.
• If both matrices have dimensions known at run-time only then the result also has dimensions known at run-time.
• If one matrix has dimensions known at run-time and the other has dimensions known at compile-time then the result will have dimensions known at compile-time if they can be statically deduced from the arguments. For example, adding a Matrix2x3 to a DMatrix will return a Matrix2x3. However, multiplying a Matrix2x3 to a DMatrix will return a matrix with one dimension known at compile-time, and a second one known at run-time, i.e., Matrix<N, U2, Dynamic, S> (where N and S are some types not detailed here). Indeed, the number of rows can be deduced from the first argument but the number of columns depends on the run-time value stored by the second argument.
let static_m = Matrix2::zero();
let dynamic_m = DMatrix::from_element(2, 2, 0.0);
let static_v = Vector2::zero();
let dynamic_v = DVector::from_element(2, 0.0);
// We know at compile-time that the sum will be a 2x2 matrix
// because of the first argument. The result is thus a Matrix2.
let static_plus_dynamic: Matrix2<_> = static_m + dynamic_m;
// We don't know anything about the matrix dimensions at
// compile-time. The result is thus a DMatrix.
let dynamic_plus_dynamic: DMatrix<_> = dynamic_m + dynamic_m;
// The result is a static vector (even if the second argument
// has a dynamic size) because we know at compile-time that
// static_m has two rows and that dynamic_v has one column.
let static_times_dynamic: Vector2<_> = static_m * dynamic_v;
// The result is a dynamic vector because we do not know at
// compile-time its number of rows.
let dynamic_times_static: DVector<_> = dynamic_m * static_v;
Matrix slicing§
Matrix (and vector) slicing allows you to take a reference to a part of any matrix. Slicing a matrix does not perform any copy, move, or allocation of the original matrix data. Instead, it stores a pointer to that data together with some metadata about the slice size and strides. Note that taking a slice of a matrix slice is allowed!
Because a matrix slice also has a type like Matrix<N, R, C, S> (with some special value for the buffer S) it can usually be used just like a plain, non-slice matrix besides three exceptions:
1. Methods that require a &mut self cannot be called on non-mutable slices.
2. Matrix slices cannot be created out of thin air using the methods shown in the Matrix construction section. One must already have an allocated matrix or another slice and use one of the dedicated methods shown thereafter.
3. Assignment operators do not work on any kind of slice, i.e., one cannot write a *= b if a even if a is a mutable matrix slice. This is actually a limitation of the current design of nalgebra that will be fixed in the future. Use a.copy_from(&(a * b)) as a workaround.
There are three variations of matrix slicing methods. Mutable slices follow the same semantics, except that the method names end with _mut:
• “Fixed” slices: slices with numbers of rows and columns known at compile-time. The name of the corresponding slicing methods usually start with the prefix fixed_.
Method Description
.row(i) Reference to the i-th row of self.
.column(i) Reference to the i-th column of self.
.fixed_rows::<D>(i) Reference to the submatrix with D consecutive rows of self, starting with the i-th. D must be a type-level integer.
.fixed_columns::<D>(i) Reference to the submatrix with D consecutive columns of self, starting with the i-th. D must be a type-level integer.
.fixed_slice::<R, C>(irow, icol) Reference to the submatrix with R consecutive rows and C consecutive columns, starting with the irow-th row and icol-th column. R and C are type-level integers.
• “Dynamic” slices: slices with numbers of rows and columns known at run-time only.
Method Description
.rows(i, size) Reference to size rows of self, starting with the i-th.
.columns(i, size) Reference to size columns of self, starting with the i-th.
.slice(start, shape) Reference to the submatrix with shape.0 rows and shape.1 columns, starting with the start.0-th row and start.1-th column. start and shape are both tuples.
• Slices with strides: fixed or dynamic slices that reference non-consecutive (but regularly spaced) rows and columns of the original matrix. The name of the corresponding slicing methods end with _with_step.
Method Description
.fixed_rows_with_step::<D>(i, step) Reference to D non-consecutive rows of self, starting with the i-th. step rows of self are skipped between each referenced row.
.fixed_columns_with_step::<D>(i, step) Reference to D non-consecutive columns of self, starting with the i-th. step columns of self are skipped between each referenced column.
.fixed_slice_with_steps::<R, C>(start, step) Reference to R and C non-consecutive rows and columns, starting with the component (start.0, start.1). step.0 (resp. step.1) rows (resp. columns) are skipped between each referenced row (resp. column).
.rows_with_step(i, size, step) Reference to size rows of self, starting with the i-th. step rows are skipped between each referenced row.
.columns_with_step(i, size, step) Reference to size columns of self, starting with the i-th. step columns are skipped between each reference column.
.slice_with_steps(start, shape, steps) Reference to shape.0 rows and shape.1 columns, starting with the (start.0, start.1)-th component. step.0 (resp. step.1) rows (resp. columns) are skipped between each referenced row (resp. column).
Note that the method .clone_owned() may be used to create a plain matrix from a slice, i.e., actually copying the referenced components into a new matrix structure that owns its data. Whether or not the result of this cloning is a dynamically- or statically-sized matrix depends on the kind of slice. Fixed slices will yield a statically-sized matrix while dynamic slices yield a dynamically-sized matrix.
Matrix resizing§
The number of rows or columns of a matrix can be modified by adding or removing some of them. Similarly to slicing, two variants exist:
• “Fixed resizing” where the number of rows or columns to be removed or inserted are known at compile-time. This allows the compiler to output a statically-sized matrix when the input is also statically-sized.
Method Description
.remove_row(i) Removes the i-th row.
.remove_column(i) Removes the i-th column.
.remove_fixed_rows::<D>(i) Removes D consecutive rows, starting with the i-th.
.remove_fixed_columns::<D>(i) Removes D consecutive columns, starting with the i-th.
.insert_row(i, val) Adds one row filled with val at the i-th row position.
.insert_column(i, val) Adds one column filled with val at the i-th row position.
.insert_fixed_rows::<D>(i, val) Adds D consecutive rows filled with val starting at the i-th row position.
.insert_fixed_columns::<D>(i, val) Adds D consecutive columns filled with val starting at the i-th column position.
.fixed_resize::<R2, C2>(val) Resizes the matrix so that it contains R2 rows and C2 columns. Components are copied such that result[(i, j)] == input[(i, j)]. If the result matrix has more rows or more columns, then the extra components are initialized to val.
• “Dynamic resizing” where the number of rows or columns to be removed or inserted are not known at compile-time. The result matrix will always be dynamically-sized (the affected dimension-related type parameter of Matrix<...> is set to Dynamic).
Method Description
.remove_rows(i, n) Removes n rows, starting with the i-th.
.remove_columns(i, n) Removes n columns, starting with the i-th.
.insert_rows(i, n, val) Inserts n rows filled with val starting at the i-th row position.
.insert_columns(i, n, val) Inserts n columns filled with val starting at the i-th row position.
.resize(new_nrows, new_ncols, val) Resizes the matrix so that it contains new_nrows rows and new_ncols columns. Components are copied such that result[(i, j)] == input[(i, j)]. If the result matrix has more rows or more columns, then the extra components are initialized to val.
The implicit self argument of those methods is always consumed in order to re-use the input data storage to construct the output. Fixed resizing should be preferred whenever the number of rows/columns to be inserted or removed is known at compile-time.
It is strongly recommended to use fixed resizing whenever possible, especially when the matrix being resize has a size known at compile-time (and is thus statically allocated). Indeed, dynamic resizing will produce heap-allocated results because the size of the output matrix cannot be deduced at compile-time.
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http://mathhelpforum.com/pre-calculus/22560-solved-conic-section-what-each-equation-represents.html
|
# Math Help - [SOLVED] Conic section what each equation represents
1. ## [SOLVED] Conic section what each equation represents
I am suppose to state which type of conic section is represented by each equation step by step if its possible
1. x^2-6x+y=8
2. 3x^2+5y^2+6x-10y=16
3. 2x^2+8x=2y^2-y+10
4. 3x^2+x-y^2+y=12
5. x^2+4y^2=8
2. Originally Posted by xterminal01
I am suppose to state which type of conic section is represented by each equation step by step if its possible
1. x^2-6x+y=8
2. 3x^2+5y^2+6x-10y=16
3. 2x^2+8x=2y^2-y+10
4. 3x^2+x-y^2+y=12
5. x^2+4y^2=8
Hello,
rearrange your equations until you can determine the type of conic. All of them have their axes parallel to the coordinate axes so completing the square will do:
to #1:
$x^2-6x+y = 8~\iff~(x^2-6x+9)+y=8+9~\iff~ y = -(x-3)^2+17$
That's a parabola opening down.
to #2:
$
3x^2+5y^2+6x-10y=16~\iff~3(x^2+2x+1) + 5(y^2-2y+1)=16+3+5~\iff~$
$3(x+1)^2+5(y-1)^2=24$ . Now divide by 24 and you'll get:
$\frac{(x+1)^2}{8}+\frac{(y-1)^2}{\frac{24}{5}}=1$ That's the equation of an ellipse.
The ##3 to 5 should be done similary.(H, H, E)
3. Thanks alot for the help can you please state the step by step for number 3,4,5
4. Originally Posted by xterminal01
Thanks alot for the help can you please state the step by step for number 3,4,5
Hi,
I was quite sure that you could do the last problems using the way I demonstrated to you, but .... I'll start the problems and I'll leave the final brush up to you:
to #3:
$2x^2+8x=2y^2-y+10~\iff~2x^2+8x-2y^2+y=10~\iff~$ $2(x^2+4x+4)-2(y^2+\frac12 y+\frac{1}{16})= 10+8-\frac{2}{16}$ . Simplify and you should come out with a hyperbola
to #4:
$3x^2+x-y^2+y=12~\iff~3(x^2+\frac13 x+\frac{1}{36})-(y^2-y+\frac14)=12 + \frac{3}{36} - \frac14$ Simplify. It's a hyperbola too.
to #5:
$x^2+4y^2=8$ Divide by 8. Then you get the equation of an ellipse.
5. Okey so i tried to finish number 3 and this is what i came up with please check if its right
3 i got stuck with this...
$2(x+2)^2 -2(x+1/4)^2 = 143/8$
4 i dont know how to finish
5 should be $x^2/8+y^2/2=1$
6. Hello, xterminal01!
State which type of conic section is represented by each equation.
$1)\;\;x^2-6x+y\:=\:8$
$2)\;\;3x^2+5y^2+6x-10y\:=\:16$
$3)\;\;2x^2+8x\:=\:2y^2-y+10\quad\Rightarrow\quad 2x^2+8x-2y^2+y\:=\:10$
$4)\;\;3x^2+x-y^2+y\:=\:12$
$5)\;\;x^2+4y^2\:=\:8$
If we are to identity the type of conic only , there is an "eyeball" method.
First, get all the variables on one side of the equation.
. . (As we did in #3.)
If it has either $x^2$ or $y^2$, but not both, it is a parabola. .(#1)
If $x^2$ and $y^2$ have the same coefficient, it is a circle. .(None listed)
If $x^2$ and $y^2$ have the same sign, it is an ellipse. .(#2 and 5)
If $x^2$ and $y^2$ have opposite signs, it is a hyperbola. .(#3 and 4)
7. Originally Posted by xterminal01
3 i got stuck with this...
$2(x+2)^2 -2(x+1/4)^2 = 143/8$
4 i dont know how to finish
5 should be $x^2/8+y^2/2=1$
Hello,
you've done #5 correctly. I would have written:
$\frac{x^2}{(2\sqrt{2})^2}+\frac{y^2}{(\sqrt{2})^2} =1$
#4: I'll continue:
$3(x^2+\frac13 x+\frac{1}{36})-(y^2-y+\frac14)= \frac{71}{6}~\iff~ 3\left(x+\frac16\right)^2-\left(y-\frac12\right)^2=\frac{71}{6}$ and now divide by $\frac{71}{6}$. That's all.
#3: Divide by $\frac{143}{8}$ to get a 1 at the RHS.
8. Yea but i cant solve the equation to the end ...
9. Originally Posted by xterminal01
Yea but i cant solve the equation to the end ...
You have all the steps and all but the last one, the division, is given to you. What more do you need?
-Dan
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http://unifraktur.sourceforge.net/letterspacing.html
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# Fraktur letterſpacing
## Fraktur Letterſpacing
In proper fraktur typography, the markup for emphatic text is not “italic” or “bold”, but “letterſpacing”.
There is a catch to fraktur letterſpacing: The fraktur ligatures ‹ch›, ‹ck›, ‹ſt›, ‹tz› are treated as ſingle letters with regard to letterſpacing. If you uſe letterſpacing on a word like “ſitzen” (‘to ſit’), for inſtance, then there muſt be no additional ſpacing between in the ‹ch› or the ‹tz›, as can be ſeen in the following image:
This image is really a ſcreenſhot from Firefox 16.0.1 on Mac OS X 3.5.8 – ſince the releaſe of Firefox 4.0, all Firefox builds are capable of correct fraktur letterſpacing. If you want to know whether your browſer is, compare the following text:
ſitzen – ſitzen
This text ſhould really look exactly like the above image (except for differences in font raſterization), ſince the image is a ſcreenſhot of that very text.
## Fraktur letterſpacing and ſmart font technologies
There are four ligatures that do not get letterſpacing: ‹ch›, ‹ck›, ‹ſt›, ‹tz›. However, moſt fraktur fonts will uſe other ligatures as well, for inſtance ligatures for ‹ſi› or ‹fl›. Theſe other ligatures get letterſpacing juſt like normal ſequences of letters. This means that a fraktur font needs a way of diſtinguishing between two types of ligatures, the required ligatures that do not get letterſpacing and the other ligatures that do get letterſpacing. The different ſmart font technologies provides different means for doing ſo:
OpenType
In OpenType, the required ligatures that do not get letterſpacing have to be defined in the feature ccmp („Glyph Compoſition/Decompoſition“), while the other ligatures that do get letterſpacing have to be defined in the feature liga (“Standard Ligatures”). Both features ought to be activated by default in all ſcripts (ſee Features: Standard OpenType ſpecification). The ſpecification of the feature ccmp does not explicitly mention fraktur typography, but it perfectly matches its requirements: „[I]t may be preferable to compose two characters into a ſingle glyph for better glyph proceſſing“ (ſee ccmp in the OpenType Layout tag registry). The required ligatures behave like ſingle glyphs with regard to letterſpacing. That is why it is deſirable to compoſe them into a ſingle glyph before further glyph proceſſing adds letterſpacing.
AAT
In AAT, the required ligatures that do not get letterſpacing have the Setting Required Ligatures and the Settingcode 0, while the other ligatures that do get letterſpacing have the Setting Common Ligatures and the Settingcode 2.
Graphite
As far as I know, Graphite cannot diſtinguiſh between required ligatures and other ligatures.
## Browſer teſt for different ſmart font technologies
### Browſer teſt
OpenType
beſitze/Zeitzone – beſitze/Zeitzone
AAT
beſitze/Zeitzone – beſitze/Zeitzone
Graphite
beſitze/Zeitzone – beſitze/Zeitzone
Reference image
The browſer teſt ſhould look exactly like the reference image (except for differences in font raſterization), a ſcreenſhot from Firefox 16.0.1 on Mac OS X 3.5.8.
### Explanation of the browſer teſt
In order to teſt what ſmart font technologies is diſplayed by which browſer, the browſer teſt uſes ſpecial builds of UniFraktur Maguntia that only uſe one ſmart font technology at a time, while the normal UniFraktur Maguntia releaſe combines them all.
The following features are teſted:
• Ligatures in normal Text. In the word “beſitze” (‘own’), you ſhould ſee both required ligatures (‹tz›) and other ligatures (‹ſi›).
• ZWNJ in normal Text. In the word “Zeitzone” (‘time zone’), the ‹tz› has no ligature becauſe of a ZWNJ. The ZWNJ ſhould not be viſible (no ſquares or vertical bars or queſtion ſigns), and there ſhould be no increaſed letterſpace.
• Ligatures in letterſpaced Text. When letterſpacing is increaſed, in the word “beſitze” you ſhould only ſee the required ligature for ‹tz›, while the other ligature for ‹ſi› ſhould be dropped. (Note that the Graphite font will neceſſarily fail at this – if a browſer manages to diſplay the Graphite ligatures, then it will diſplay the incorrect ‹ſi› ligature.)
• ZWNJ in letterſpaced Text. In the word “Zeitzone”, the letterſpace between the ‹t› and the ‹z› ſhould not be wider than between the other letters, and of courſe, the ZWNJ ſhould ſtill be inviſible.
## Support in miſcellaneous applications
As of 2012-10, ſupport for correct fraktur letterſpacing ſeems to be very poor. The following table gives ſome impreſſions. It does not claim to be a comprehenſive overview – and it is not even complete (pleaſe contact me if there are miſtakes or if you know other applications):
Windows Mac OS Linux full poor [1] N/A poor [2] no partial [3] N/A poor [4] ? full N/A ? no N/A ? no N/A partial [5] N/A partial [5] partial [5] full [6]
Notes:
1. Internet Explorer 9 does not diſplay any ligatures until they are manually triggered by layout control characters (ZWNJ or ZWJ). Of courſe, this pretty much defies the very purpoſe ſmart ligatures. Ligatures may be called for by uſing a ZWJ.
2. On Windows and Mac OS, Opera does not diſplay any ligatures until they are manually triggered by layout control characters (ZWNJ or ZWJ). Of courſe, this pretty much defies the very purpoſe ſmart ligatures. Ligatures may be called for by uſing a ZWJ.
Additionally, Opera will diſplay the ligatures in any word that has a layout control character (ZWNJ or ZWJ). When letterſpacing is increaſed, all ligatures are retained. This cannot be fixed with a ZWNJ, becauſe a ZWNJ will cauſe double letterſpace.
3. Safari does not diſplay any ligatures unleſs two requirements are met: (a) There muſt be an additional CSS definition; (b) there muſt be no intervening non-printing characters. Since theſe two requirements may be ſet globally, they allow for a workaround. However, even if both requirements are met, ligature diſplay in text with increaſed letterſpacing is ſtill not correct.
1. Safari requires the following additional non-ſtandard CSS definition:
text-rendering: optimizeLegibility;
Since this definition is non-ſtandard, your CSS will fail to validate when you uſe it.
2. Safari will fail to diſplay the ligatures if there are any non-printing characters ſuch as a ſoft hyphen or – ironcally! – a ZWJ.
4. Google Chrome will not diſplay any ligatures until three requirements are met: (a) There muſt be – like in Safari – an additional CSS definition; (b) there muſt be – like in Safari – no intervening non-printable characters; and (c) the font muſt be locally inſtalled. Of courſe, this pretty much defies the very purpoſe of font embedding. On Windows and Linux, there is at leaſt one additional requirement, but I have not been able to pin it down.
5. In TextEdit, LibreOffice and Gimp, ligatures are diſplayed, but when letterſpacing is increaſed, the required ligatures are not diſtinguiſhed from the other ligatures; inſtead, either kind of ligatures is retained. Additionally, the ZWNJ cauſes double letterſpace when letterſpacing is increaſed.
6. For letterſpacing in XeLaTeX to work correctly, I uſe the packages fontspec and xspace to renew the command \emph ſo it produces text with increaſed letterſpacing:
\usepackage{fontspec,xspace}
\renewcommand\emshape{\xspace\addfontfeature{LetterSpace=20.0,WordSpace=1.5,Ligatures={NoCommon}}}
### Different font formats
WOFF
beſchütze/Zeitzone – beſchütze/Zeitzone
TTF
beſchütze/Zeitzone – beſchütze/Zeitzone
EOT
beſchütze/Zeitzone – beſchütze/Zeitzone
SVG
beſchütze/Zeitzone – beſchütze/Zeitzone
Reference image (ſcreenſhot from Firefox 3.6.12 on Mac OS X):
### Different embedding codes
Paul Iriſh’s Bulletproof @font-face: Smiley variation
beſchütze/Zeitzone – beſchütze/Zeitzone
Richard Fink’s Mo’ Bulletproofer @Font-Face CSS Syntax
beſchütze/Zeitzone – beſchütze/Zeitzone
Conditional comment
beſchütze/Zeitzone – beſchütze/Zeitzone
beſchütze/Zeitzone – beſchütze/Zeitzone
Reference image (ſcreenſhot from Firefox 3.6.12 on Mac OS X):
### Different ways of CSS definition
The following all use a conditional comment CSS. They all uſe the font-family name “UnifrakturMaguntia“ that is defined by the Google Font API.
Selector from main ſtyle ſheet (body)
beſchütze/Zeitzone – beſchütze/Zeitzone
Special claſs from main ſtyleſheet
beſchütze/Zeitzone – beſchütze/Zeitzone
Selector from additional ſtyleſheet (dd i)
beſchütze/Zeitzone – beſchütze/Zeitzone
Selector from style tag (dd b)
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https://wiki.kidzsearch.com/wiki/Epsilon
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kidzsearch.com > wiki Explore:images videos games
# Epsilon
Jump to: navigation, search
Greek alphabet Other letters Αα Alpha Νν Nu Ββ Beta Ξξ Xi Γγ Gamma Οο Omicron Δδ Delta Ππ Pi Εε Epsilon Ρρ Rho Ζζ Zeta Σσς Sigma Ηη Eta Ττ Tau Θθ Theta Υυ Upsilon Ιι Iota Φφ Phi Κκ Kappa Χχ Chi Λλ Lambda Ψψ Psi Μμ Mu Ωω Omega Ϝϝ Digamma Ⱶⱶ Heta Ϻϻ San Ϙϙ Koppa Ϡϡ Sampi Ϛϛ Stigma Ϸϸ Sho
Epsilon (uppercase/lowercase Ε ε), is the letter of the Greek alphabet, used to represent the "e" sound in Ancient and Modern Greek. In the system of Greek numerals, it has a value of 5. Letters that came from it include the Roman E and Cyrillic Е. It is also used in calculus to represent a very small number. In set theory it can be used to represent the statement "x is a member of y." (A little 'know': The Ypsilon is the only letter of the alphabet that you can divide into syllables: Y-psi-lon)
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http://kevin.zielnicki.com/2014/11/24/comments/
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# Poem? I 'ardly know 'em!
### Or: Using Machine Learning to Identify Poetic Comments
#### This was originally posted in January, 2014 as a fun machine learning primer / example problem.
Sometimes when reading the New York Times comments—between disgruntled complaints, armchair economics, and political banter—one stumbles across that rare gem, the comment poem:
But why should we have to sort through hundreds of regular comments and wait for a poem to catch our eyes? In this age of text mining, big data, and information extraction, shouldn’t a computer be able to do this for us? Well, whether or not this strikes you as a reasonable question to ask, the answer turns out to be yes! I wrote some code to do just that, and to find out how, read on…
## First Steps
First we have to get the comments for analysis. Thanks to the NYT’s Times Developer Network API, this turns out to be pleasantly easy! With direct access to tens of thousands of comments, we can start to think about doing all kinds of interesting analysis, but today I’m just going to talk about finding poems. I chose to use Python for this task, because its overall flexibility and the availability of packages like numpy and scikit-learn makes an excellent tool for the kind of analysis I wanted to do.
It’s usually pretty easy (for a human) to tell if something is or isn’t a poem, but it’s difficult to quantify in a set of rules (this makes it a great task for machine learning, which I’ll talk about later on). I tried anyways though: for a simple first attempt, I just calculated the ratio of line breaks to other characters, on the theory that poems would have more line breaks than ordinary comments (most ordinary NYT comments contain one or a few relatively long lines, and few line breaks). This strategy turned up actual poems like this bizarre love note to Mark Bittman from our hero Larry Eisenberg:
But also strange rants like:
And long lists like:
The previous two comments are examples of false positives (comments that the rules indicate to be poems, but aren’t actually). There’s also a lot of false negatives (poems that aren’t detected by my rules). We’ll have to find a way to do better! But how?
## Rhymes with Poem
Lots of poems employ a rhyming structure, whereas ordinary comments usually don’t. Rhymes can also be somewhat difficult for a computer to recognize, and accurately calculating rhymes and near-rhymes would require more sophisticated linguistic processing than I wanted to do for this project. But a quick rule of thumb that nevertheless catches a reasonably high percentage of rhymes is to compare the endings of two words and see how many characters they share (this is a very rough and simple rule, which could definitely be improved). For this program, I declare two words to rhyme if they end in the same two letters, and then count the percentage of rhyming words at the end of comment lines. To evaluate the performance, I categorized hundreds of comments as either poems or non-poems:
Sometimes it's hard to tell
With this simple rhyme detection included, the algorithm performs much better than the line break detection alone, but the performance is still limited. It’s easy to pick out Larry Eisenberg’s limericks, but non-rhyming verse slips through the cracks. Also some long comments show up as false positives because they have lots of line ending words, giving more chances for accidental “rhymes” (specifically, word-pairs grow as the square of the number of lines in the comment).
So far, we haven’t done any machine learning, or really anything at all sophisticated. And that’s about as far I went in a first-principles poem model building sort of way. Now it’s time to break out the machine learning toolbox!
## Data Mining The Soul
The basic idea of teaching machines to learn has been around since Turing & co started thinking about computation. Today, machine learning refers to the practice of constructing systems that can learn from examples to make predictions on new, unseen data. Recently, with the increasing availability of all kinds of data and the computational power to process it, the field has exploded, with applications like self-driving cars, computer vision, and automated recommendations. In essentially any problem where a human could look at an example and make a decision about it, a computer can do it with a machine learning algorithm, enough data, and enough time. So poetry classification should fit right in (and indeed researchers have worked on similar problems).
I manually classified thousands more comments so that I could start training a learning model. The model was trained on the following features: number of lines, average line length, standard deviation of line lengths (a measure of how uniform the lines are), and amount of rhyming. I also added features for two things I thought would be unlikely to show up in poems: number of numeric characters, and number of “special” characters (eg, \$%#^*). These are all very simple to compute, and between them capture most of the structure of a comment, so the learning model should be able to figure out how to use these to classify poems.
Before training the model, we should have an idea of how to evaluate how well it’s doing. Because only something like one out of a thousand comments are poems, measuring prediction accuracy would be very misleading, since predicting that every comment is not a poem would be 99.9% accurate. So instead we use the F1 score, which ranges from 0 (poor) to 1(ideal) and penalizes for false positives and false negatives.
Scikit-learn has an excellent array of learning algorithms to choose from. I decided to use logistic regression, which is a simple and straightforward supervised learning classifier (though there are many other options, some of which I might explore later). Logistic regression also allows us to trade off between false positives (precision) and false negatives (recall), by adjusting the threshold of probability at which we declare a comment to be a poem. So we can set a low threshold to be confident of catching all the poems, at the cost of having a lot of false positives. Or we can have a high threshold to make sure that almost everything we flag is actually a poem, but we will miss a lot of other poems.
Precision-recall tradeoff and F1 score for the final trained model
Although this was a big improvement over the simple classification strategy described earlier, it still has a lot of false negatives and false positives, with an $F_1$ score of about 0.5. One of the most interesting results of this model is that we can use it to get the relative importance of the different features of a poem:
Theta =
[ (-7.2096537078283305, ['aveLen']),
(-4.8577423788414134, ['stdev']),
(0.65553309239833091, ['rhymeQ']),
(0.41211121618657875, ['lines']),
(-0.39794436586003662, ["#'s"]),
(-0.25102236756414537, ['sChar'])]
What this tells us is that poems are especially likely to have short lines compared to other comments, and also quite likely to have lines of relatively uniform length. Also, they are somewhat more likely to have lines that end in rhymes, and have more line breaks. Containing numeric characters and other special characters makes a comment less likely to be a poem as I suspected, but the learning model tell us that these aren’t very important features. Average line length and line length uniformity appear to be by far the two most important distinguishing features of a poem.
## Scotty, We Need More Power(s)
A two-parameter model with two categories separated by a linear boundary (left) and a nonlinear boundary (right).
Since logistic regression is a linear classifier, it can only make distinctions between poems and non-poems that look like straight lines (planes / hyperplanes) in parameter space. But in general, poems might not be linearly separable in the features we have chosen. For example, maybe comments with a moderate number of lines are likely to be poems, but comments with both very few and very many lines are not: there is no good way to pick a value and say comments longer than this are probably poems and comments shorter are probably not. To allow for more sophisticated learning, I generalize the model to make curved rather than straight boundaries. (Specifically, I used polynomial feature mapping to map the existing features onto arbitrary polynomial products of features. For practicality, I limit this to 3rd degree polynomials, as feature number grows exponentially with polynomial degree.)
Diagram showing underfitting on the left and overfitting on the right. The center shows appropriate fitting. With the right amount of regularization, we can get a good fit despite having many parameters.
With additional features comes the problem of overfitting (aka high variance). With enough features, you can fit any data set with perfect accuracy, but the model would be meaningless: it wouldn’t generalize to comments it hasn’t seen. We can combat this using regularization. This penalizes the model for using large coefficients, so rather than trying to fit the data exactly, the model will try to produce a “smooth” prediction (with smoothness controlled by the size of the regularization coefficient), while still fitting the data approximately. Appropriately choosing the regularization coefficient will optimize the model’s ability to fit new data correctly.
This introduces one more problem: how can we choose the right regularization coefficient? The answer is to break the training data up into two sets, a training set and a test set. Now we can train the model with many different regularization coefficients, and choose the best one based on how the model performs on the test set.
The final model, trained on ~25,000 comments posted over a week, performs impressively well, identifying not just limericks, but also haikus, free-verse, and interesting “found poems” as well (see this post for more on the interesting poems of the week!).
## Here There Be Details…
In the final model, the F1 score on the test set is about 0.83. As another point of reference, with a prediction threshold of 20%, the model is expected to miss about 5% of comments that could be classified as poetry, and incorrectly identify about 30% of responses as false positives (at a 50% threshold, we would miss 20% of poems, but only incorrectly identify about 10%). The parameters for the final trained model are:
Theta =
[ (-4.4286398462753569, ['stdev', 'INV_aveLen']),
(-2.6152500876025178, ['INV_aveLen', 'INV_aveLen']),
(-2.1601108718169186, ['INV_lines', 'INV_aveLen']),
(-1.5661835626301197, ['aveLen', 'INV_aveLen']),
(-1.4763161231121018, ['INV_lines', 'INV_rhymeQ']),
(1.4050428584597547, ['INV_aveLen']),
(1.2017039641098926, ['lines']),
(0.81023821647484218, ['rhymeQ']),
(-0.78775350480991047, ["#'s", 'INV_sChar']),
(-0.76201605500088798, ['lines', 'lines']),
(-0.76028261886262782, ['lines', 'aveLen']),
(0.63474128816594866, ['INV_aveLen', 'INV_sChar']),
(-0.59726188490530607, ['aveLen', 'rhymeQ']),
(0.54676271186435077, ['lines', 'rhymeQ']),
(0.50811316869729972, ['lines', 'stdev']),
(-0.36339272447523757, ["#'s", 'INV_aveLen']),
(0.28263804343744037, ['lines', 'INV_rhymeQ']),
(-0.21376816680099142, ['rhymeQ', 'rhymeQ']),
(-0.18725536650062383, ['lines', "INV_#'s"]),
(-0.18436001068148844, ['rhymeQ', 'INV_lines']),
(0.097228828727091557, ['rhymeQ', 'INV_sChar']),
(0.082100023517069104, ['rhymeQ', "INV_#'s"]),
(0.074220229682818925, ['INV_aveLen', 'INV_rhymeQ']),
(-0.070214398383472529, ["#'s", "INV_#'s"]),
(-0.03687714292671937, ['rhymeQ', 'INV_stdev']),
(0.022787901290648147, ["INV_#'s", "INV_#'s"]),
(-0.0091864125942432914, ['lines', 'INV_sChar']),
...
All the remaining parameters are set to zero, a property of l1 regularization, which tends to produce sparse models. This model includes inverse features (defined as $1/X$ for each original feature $X$), and degree 2 polynomial products of features. The most significant feature in the final model is $\sigma_L/\mu_L$, which interestingly is the coefficient of variation of line length (where $\mu_L$, is the average line length, $\sigma_L$ is the standard deviation of line length). Comments with a high coefficient of variation turn out to be especially unlikely to be poems. The second most significant is $1/\mu_L^2$, which penalizes comments with both very short and very long line lengths. Third is $1/(\textrm{Lines}*\mu_L)$, which is the number of characters in a comment: posts with small numbers of characters are not likely to be poems (the benefit of using the inverse here is that it strongly penalizes posts with very few characters, but makes little distinction between posts with moderate and large character counts). Somewhat puzzling is the next feature, $\mu_L/\mu_L$, which at first glance appears to be just a constant, but because of the way the code computes the inverse and then scales features to be of uniform mean and standard deviation, this is an “accidental” feature that penalizes only comments with very short lines. Together with other features, this is selecting for average line length in a complicated, nonlinear way, which is exactly what we were looking for this model to do!
For the brave, visit my GitHub page to try the code out for yourself!
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https://nus.kattis.com/courses/CS3233/CS3233_S2_AY2223/assignments/nkzny5/problems/sudokunique
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Hide
# Problem BSudokunique
The popular game of Sudoku requires the player to fill in a $9$-by-$9$ board using the digits $1$ through $9$, such that no row, column, or $3$-by-$3$ square (see diagram) has more than one copy of each digit. The player is given a partially completed board and must fill in the blank squares. Designing a Sudoku puzzle appears easy – just start with a solved, valid puzzle, and erase the digits in some of the squares. However, if the designer erases too many squares, then there might be multiple solutions. This can make solving the puzzle more difficult, and potentially less fun. Thus, you should write a program to help a designer find out if their puzzle has exactly one solution.
3 5 7 4 9 1 6 2 8 9 2 4 8 6 7 3 5 1 6 1 8 5 2 3 4 7 9 1 6 9 2 7 5 8 3 4 7 4 5 9 3 8 1 6 2 8 3 2 6 1 4 7 9 5 2 9 1 3 8 6 5 4 7 5 7 6 1 4 2 9 8 3 4 8 3 7 5 9 2 1 6
## Input
Input consists of up to $100$ Sudoku boards. Each board is given as a $9$-by-$9$ matrix using digits $0$ through $9$, one matrix row per line. If a board square contains $0$, that means it’s been erased. There is a blank line between pairs of boards. Input ends at end of file.
## Output
For each board, if there is a unique solution, print the solution using the same format as the input. If there are multiple solutions, print “Non-unique”. If the designer has made a terrible mistake and there is no solution, print “Find another job”. Separate the outputs for adjacent cases with a blank line.
Sample Input 1 Sample Output 1
3 0 7 4 0 0 0 0 8
0 0 4 0 0 7 3 5 0
0 1 0 0 2 0 0 0 9
0 6 9 2 7 0 8 3 0
0 0 0 0 0 0 0 0 0
0 3 2 0 1 4 7 9 0
2 0 0 0 8 0 0 4 0
0 7 6 1 0 0 9 0 0
4 0 0 0 0 9 2 0 6
0 4 8 3 9 0 7 1 6
7 7 1 6 0 8 3 4 9
9 3 6 7 4 1 0 8 0
6 8 0 0 3 9 1 7 4
3 0 9 1 7 4 6 0 8
7 1 4 8 6 0 9 0 3
8 6 3 4 1 7 0 9 0
1 9 0 0 8 6 4 3 7
4 0 7 9 0 3 8 6 1
0 4 8 3 9 0 7 1 6
0 7 1 6 0 8 3 4 9
9 3 6 7 4 1 0 8 0
6 8 0 0 3 9 1 7 4
3 0 9 1 7 4 6 0 8
7 1 4 8 6 0 9 0 3
8 6 3 4 1 7 0 9 0
1 9 0 0 8 6 4 3 7
4 0 7 9 0 3 8 6 1
3 5 7 4 9 1 6 2 8
9 2 4 8 6 7 3 5 1
6 1 8 5 2 3 4 7 9
1 6 9 2 7 5 8 3 4
7 4 5 9 3 8 1 6 2
8 3 2 6 1 4 7 9 5
2 9 1 3 8 6 5 4 7
5 7 6 1 4 2 9 8 3
4 8 3 7 5 9 2 1 6
Find another job
Non-unique
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http://www.marinebiotech.eu/c/index.php?title=Wave_run-up&oldid=76391
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# Wave run-up
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Definition of Wave run-up: Landward incursion of a wave. Wave run-up is usually expressed as the maximum onshore elevation reached by a wave, relative to the wave-averaged shoreline position. This is the common definition for Wave run-up, other definitions can be discussed in the article
Wave run-up is an important parameter for assessing the safety of sea dikes or coastal settlements. Wave run-up is the sum of wave set-up and swash uprush (see Swash zone dynamics) and must be added to the water level reached as a result of tides and storm setup.
By waves is meant: waves generated by wind (locally or on the ocean) or waves generated by incidental disturbances of the sea surface such as tsunamis, seiches or ship waves. Wave run-up is often indicated with the sympol $R$.
For waves collapsing on the beach, the wave run-up can be estimated in first approach with the formula of Hunt (1959) [1],
$R = H \xi ,$
where $H$ is the offshore wave height and $\xi$ is the wave similarity parameter,
$\xi = \Large\frac{S}{\sqrt{H/L}}\normalsize = S \, T \Large\sqrt{\frac{g}{4\pi H}}\normalsize ,$
where $L = g T^2/(2 \pi)$ is the offshore wave length, $S$ is the beach slope and $T$ is the wave period. The horizontal wave incursion is approximately given by $R / S$.
For more precise estimates of wave run-up see:
Swash zone dynamics
Tsunami
## References
1. Hunt, I.A. 1959. Design of seawalls and breakwaters. J. Waterw. Harbors Division ASCE 85: 123–152
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https://www.physicsforums.com/threads/statistic-problems-with-quartiles-and-standard-deviations.196301/
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# Statistic Problems With Quartiles and Standard Deviations
1. Nov 5, 2007
### Rawr
There are two different problems that I am confused with:
1) The taste of mature cheese is related to the concentration of lactic acid in cheese. Use the concentrations of lactic acid in 30 samples of cheddar cheese on page 15.
Well, what's important is that using all the numbers it gave me, the mean is 1.44, the median is 1.45 and the standard deviation is .3035.
Then it asks, "Calculate the percent of data that lie within one, two and three standard deviations. I attempted to work with one standard deviation, but I can't seem to get the right answer, which is 66% (or something close).
What I did was... one standard deviation is 1.45 +/- .3035, which gets 1.15 and 1.75. Then you need to calculate the percentage of numbers that fall within that range.
So, I take the z-score of each number: (1.15 - 1.45)/1.44 = -0.21 and it's the same for the other, except it comes out a positive 0.21 using 1.75 instead of 1.15. Using the A chart.. I get numbers of .4168 and .5832 respectively. Subtracting them gives me something like.. 12%. What am I doing wrong? Am I even in the right direction?
The second question..is "How many standard deviations away from the mean do the quartiles lie in any normal distribution? What are the quartile for the lengths of human pregnancies? (which says that... for human pregnancies, the mean is 266 days and the Standard deviation is 16 days)
Frankly, I have no idea how to start and I was hoping I would get a little push in the right direction.
2. Nov 5, 2007
### EnumaElish
z_ = 0 - 1 = -1 is the standard z score for "one std below" and z+ = 0 + 1 = +1 is for "one std above."
Similar Discussions: Statistic Problems With Quartiles and Standard Deviations
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http://mathhelpforum.com/discrete-math/169973-compactness-theorem-partial-orderings-print.html
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# Compactness Theorem and partial orderings
• Feb 1st 2011, 07:44 PM
Compactness Theorem and partial orderings
Hello folks,
I've been asked 'If P is a partial ordering, how do I use the compactness theorem to show that P is the union of k chains iff each finite subset on P is the union of k chains?'
But, I have absolutely no idea what this question is even driving at. Set theory and logic is easily my weakest area of maths and any help would be much appreciated (I will attempt to reciprocate in differenctial equations or algebra - things I can actually do!)
• Feb 2nd 2011, 12:35 PM
emakarov
A chain is a totally ordered subset.
There is a question what a subset of P is. Let's say P is an order on a set A, i.e., $P\subseteq A\times A$. Then a subset of P could mean a subrelation on the same set A. However, if A is infinite, the premise of the statement is trivially false and so the statement is trivially true. Indeed, each finite subrelation has infinitely many isolated points, and each of them is a degenerate chain. So I think the problem is talking about finite subsets of A and restrictions of P on these subsets.
I have not worked out all details, but the idea may be as follows. Let C be a formula saying that for any k + 1 elements, some pair of them are comparable. We can prove that C holds for P.
Let A_n be a subset of A with n elements and let P_n be the restriction of P to A_n. By [P_n] I will denote a single formula that records the structure of P_n. It has constants c_1, ..., c_n and is a big conjunction of inequalities between these constants. If constants' names are chosen consistently, then [P_n] implies [P_k] for k < n. The problem statement implies that for each n, the set {[P_1], ..., [P_n], C} is consistent since P_n is its model. Therefore, the union of these sets is consistent by compactness theorem. A model of this union must include P as a substructure and so C is true on P.
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https://worldwidescience.org/topicpages/v/vlasov+ions+cold.html
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#### Sample records for vlasov ions cold
1. Hybrid (Vlasov-Fluid) simulation of ion-acoustic soliton chain formation and validity of Korteweg de-Vries model
Science.gov (United States)
Aminmansoor, F.; Abbasi, H.
2015-08-01
The present paper is devoted to simulation of nonlinear disintegration of a localized perturbation into ion-acoustic solitons train in a plasma with hot electrons and cold ions. A Gaussian initial perturbation is used to model the localized perturbation. For this purpose, first, we reduce fluid system of equations to a Korteweg de-Vries equation by the following well-known assumptions. (i) On the ion-acoustic evolution time-scale, the electron velocity distribution function (EVDF) is assumed to be stationary. (ii) The calculation is restricted to small amplitude cases. Next, in order to generalize the model to finite amplitudes cases, the evolution of EVDF is included. To this end, a hybrid code is designed to simulate the case, in which electrons dynamics is governed by Vlasov equation, while cold ions dynamics is, like before, studied by the fluid equations. A comparison between the two models shows that although the fluid model is capable of demonstrating the general features of the process, to have a better insight into the relevant physics resulting from the evolution of EVDF, the use of kinetic treatment is of great importance.
2. Vlasov simulations of multi-ion plasma turbulence in the solar wind
CERN Document Server
Perrone, Denise; Servidio, Sergio; Dalena, Serena; Veltri, Pierluigi
2012-01-01
Hybrid Vlasov-Maxwell simulations are employed to investigate the role of kinetic effects in a two-dimensional turbulent multi-ion plasma, composed of protons, alpha particles and fluid electrons. In the typical conditions of the solar-wind environment, and in situations of decaying turbulence, the numerical results show that the velocity distribution functions of both ion species depart from the typical configuration of thermal equilibrium. These non-Maxwellian features are quantified through the statistical analysis of the temperature anisotropy, for both protons and alpha particles, in the reference frame given by the local magnetic field. Anisotropy is found to be higher in regions of high magnetic stress. Both ion species manifest a preferentially perpendicular heating, although the anisotropy is more pronounced for the alpha particles, according with solar wind observations. Anisotropy of the alpha particle, moreover, is correlated to the proton anisotropy, and also depends on the local differential flo...
3. Vlasov Simulations of Electron-Ion Collision Effects on Damping of Electron Plasma Waves
CERN Document Server
Banks, J W; Berger, R L; Tran, T M
2016-01-01
Collisional effects can play an essential role in the dynamics of plasma waves by setting a minimum damping rate and by interfering with wave-particle resonances. Kinetic simulations of the effects of electron-ion pitch angle scattering on Electron Plasma Waves (EPWs) are presented here. In particular, the effects of such collisions on the frequency and damping of small-amplitude EPWs for a range of collision rates and wave phase velocities are computed and compared with theory. Both the Vlasov simulations and linear kinetic theory find the direct contribution of electron-ion collisions to wave damping is about a factor of two smaller than is obtained from linearized fluid theory. To our knowledge, this simple result has not been published before. Simulations have been carried out using a grid-based (Vlasov) approach, based on a high-order conservative finite difference method for discretizing the Fokker-Planck equation describing the evolution of the electron distribution function. Details of the implementat...
4. Vlasov simulations of electron-ion collision effects on damping of electron plasma waves
Energy Technology Data Exchange (ETDEWEB)
Banks, J. W., E-mail: [email protected] [Rensselaer Polytechnic Institute, Department of Mathematical Sciences, Troy, New York 12180 (United States); Brunner, S.; Tran, T. M. [Ecole Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne (Switzerland); Berger, R. L. [Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, California 94551 (United States)
2016-03-15
Collisional effects can play an essential role in the dynamics of plasma waves by setting a minimum damping rate and by interfering with wave-particle resonances. Kinetic simulations of the effects of electron-ion pitch angle scattering on Electron Plasma Waves (EPWs) are presented here. In particular, the effects of such collisions on the frequency and damping of small-amplitude EPWs for a range of collision rates and wave phase velocities are computed and compared with theory. Both the Vlasov simulations and linear kinetic theory find the direct contribution of electron-ion collisions to wave damping significantly reduced from that obtained through linearized fluid theory. To our knowledge, this simple result has not been published before. Simulations have been carried out using a grid-based (Vlasov) approach, based on a high-order conservative finite difference method for discretizing the Fokker-Planck equation describing the evolution of the electron distribution function. Details of the implementation of the collision operator within this framework are presented. Such a grid-based approach, which is not subject to numerical noise, is of particular interest for the accurate measurements of the wave damping rates.
5. Nanofriction in cold ion traps.
Science.gov (United States)
Benassi, A; Vanossi, A; Tosatti, E
2011-01-01
Sliding friction between crystal lattices and the physics of cold ion traps are so far non-overlapping fields. Two sliding lattices may either stick and show static friction or slip with dynamic friction; cold ions are known to form static chains, helices or clusters, depending on the trapping conditions. Here we show, based on simulations, that much could be learnt about friction by sliding, through, for example, an electric field, the trapped ion chains over a corrugated potential. Unlike infinite chains, in which the theoretically predicted Aubry transition to free sliding may take place, trapped chains are always pinned. Yet, a properly defined static friction still vanishes Aubry-like at a symmetric-asymmetric structural transition, found for decreasing corrugation in both straight and zig-zag trapped chains. Dynamic friction is also accessible in ringdown oscillations of the ion trap. Long theorized static and dynamic one-dimensional friction phenomena could thus become accessible in future cold ion tribology.
6. Cold Ion Escape from Mars
Science.gov (United States)
Fränz, M.; Dubinin, E.; Wei, Y.; Morgan, D.; Andrews, D.; Barabash, S.; Lundin, R.; Fedorov, A.
2013-09-01
It has always been challenging to observe the flux of ions with energies of less than 10eV escaping from the planetary ionospheres. We here report on new measurements of the ionospheric ion flows at Mars by the ASPERA-3 experiment on board Mars Express in combination with the MARSIS radar experiment. We first compare calculations of the mean ion flux observed by ASPERA-3 alone with previously published results. We then combine observations of the cold ion velocity by ASPERA-3 with observations of the cold plasma density by MARSIS since ASPERA-3 misses the cold core of the ion distribution. We show that the mean density of the nightside plasma observed by MARSIS is about two orders higher than observed by ASPERA-3 (Fig.1). Combining both datasets we show that the main escape channel is along the shadow boundary on the tailside of Mars (Fig. 2). At a distance of about 0.5 R_M the flux settles at a constant value (Fig. 3) which indicates that about half of the transterminator ionospheric flow escapes from the planet. Possible mechanism to generate this flux can be the ionospheric pressure gradient between dayside and nightside or momentum transfer from the solar wind via the induced magnetic field since the flow velocity is in the Alfvénic regime.
7. Cold Strontium Ion Source for Ion Interferometry
Science.gov (United States)
Jackson, Jarom; Durfee, Dallin
2015-05-01
We are working on a cold source of Sr Ions to be used in an ion interferometer. The beam will be generated from a magneto-optical trap (MOT) of Sr atoms by optically ionizing atoms leaking out a carefully prepared hole in the MOT. A single laser cooling on the resonant transition (461 nm) in Sr should be sufficient for trapping, as we've calculated that losses to the atom beam will outweigh losses to dark states. Another laser (405 nm), together with light from the trapping laser, will drive a two photon transition in the atom beam to an autoionizing state. Supported by NSF Award No. 1205736.
8. Vlasov-Poisson in 1D for initially cold systems: post-collapse Lagrangian perturbation theory
CERN Document Server
Colombi, Stephane
2014-01-01
We study analytically the collapse of an initially smooth, cold, self-gravitating collisionless system in one dimension. The system is described as a central "S" shape in phase-space surrounded by a nearly stationary halo acting locally like a harmonic background on the S. To resolve the dynamics of the S under its self-gravity and under the influence of the halo, we introduce a novel approach using post-collapse Lagrangian perturbation theory. This approach allows us to follow the evolution of the system between successive crossing times and to describe in an iterative way the interplay between the central S and the halo. Our theoretical predictions are checked against measurements in entropy conserving numerical simulations based on the waterbag method. While our post-collapse Lagrangian approach does not allow us to compute rigorously the long term behavior of the system, i.e. after many crossing times, it explains the close to power-law behavior of the projected density observed in numerical simulations. ...
9. 3D Maxwell-Vlasov boundary value problem solution in stellarator geometry in ion cyclotron frequency range. Final report
Energy Technology Data Exchange (ETDEWEB)
Vdovin, V.; Watari, T.; Fukuyama, A.
1996-12-01
We develop the theory for the wave excitation, propagation and absorption in 3-dimensional (3D) stellarator equilibrium high beta plasma in ion cyclotron frequency range (ICRF). This theory forms a basis for a 3D code creation, urgently needed for the ICRF heating scenarios development for the constructed LHD and projected W7-X stellarators and for the stellarators being at operation (like CHS, W7-AS, etc.). The theory solves the 3D Maxwell-Vlasov antenna-plasma-conducting shell boundary value problem in the non - orthogonal flux coordinates ({psi}, {theta}, {phi}), {psi} being magnetic flux function, {theta} and {phi} being the poloidal and toroidal angles, respectively. All basic physics, like wave refraction, reflection and diffraction are firstly self consistently included, along with the fundamental ion and ion minority cyclotron resonances, two ion hybrid resonance, electron Landau and TTMP absorption. Antenna reactive impedance and loading resistance are also calculated and urgently needed for an antenna -generator matching. This is accomplished in a real confining magnetic field being varying in a plasma major radius direction, in toroidal and poloidal directions, through making use of the hot dense plasma dielectric kinetic tensor. The theory is developed in a manner that includes tokamaks and magnetic mirrors as the particular cases through general metric tensor (provided by an equilibrium solver) treatment of the wave equations. We describe the structure of newly developed stellarator ICRF 3D full wave code STELION, based on theory described in this report. (J.P.N.)
10. Study of the heavy ions (Au+Au at 150 AMeV) collisions with the FOPI detector. Comparison with the Landau-Vlasov model; Etude des collisions dions lourds AU+AU a 150 A.MeV avec le detecteur FOPI. Comparaison avec le modele de Landau-Vlasov
Energy Technology Data Exchange (ETDEWEB)
Boussange, S.
1995-09-15
In this thesis, heavy ions (Au+Au) collisions experiments are made at 150 AMeV.In the first part, a general study of the nuclear matter equation is presented. Then the used Landau-Vlasov theoretical model is describe. The third part presents the FOPI experience and the details of how to obtain this theoretical predictions (filter, cuts, corrections, possible centrality selections).At the end, experimental results and comparisons with the Landau-Vlasov model are presented. (TEC). 105 refs., 96 figs., 14 tabs.
11. Cold molecular ions on a chip
CERN Document Server
Mokhberi, A
2014-01-01
We report the sympathetic cooling and Coulomb crystallization of molecular ions above the surface of an ion-trap chip. N$_2^+$ and CaH$^+$ ions were confined in a surface-electrode radiofrequency ion trap and cooled by the interaction with laser-cooled Ca$^{+}$ ions to secular translational temperatures in the millikelvin range. The configuration of trapping potentials generated by the surface electrodes enabled the formation of planar bicomponent Coulomb crystals and the spatial separation of the molecular from the atomic ions on the chip. The structural and thermal properties of the Coulomb crystals were characterized using molecular dynamics simulations. The present study extends chip-based trapping techniques to Coulomb-crystallized molecular ions with potential applications in mass spectrometry, cold chemistry, quantum information science and spectroscopy.
12. Cold heteronuclear atom-ion collisions
CERN Document Server
Zipkes, Christoph; Ratschbacher, Lothar; Sias, Carlo; Köhl, Michael
2010-01-01
We study cold heteronuclear atom ion collisions by immersing a trapped single ion into an ultracold atomic cloud. Using ultracold atoms as reaction targets, our measurement is sensitive to elastic collisions with extremely small energy transfer. The observed energy-dependent elastic atom-ion scattering rate deviates significantly from the prediction of Langevin but is in full agreement with the quantum mechanical cross section. Additionally, we characterize inelastic collisions leading to chemical reactions at the single particle level and measure the energy-dependent reaction rate constants. The reaction products are identified by in-trap mass spectrometry, revealing the branching ratio between radiative and non-radiative charge exchange processes.
13. Cold Trapped Ions as Quantum Information Processors
CERN Document Server
Sasura, M; Sasura, Marek; Buzek, Vladimir
2002-01-01
In this tutorial we review physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travelling-wave and standing-wave configuration for dipole and quadrupole transitions. We review different types of laser cooling techniques associated with trapped ions. We address Doppler cooling, sideband cooling in and beyond the Lamb-Dicke limit, sympathetic cooling and laser cooling using electromagnetically induced transparency. After that we discuss the problem of state detection using the electron shelving method. Then quantum gates are described. We introduce single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT gates. We also comment on...
14. Cold fission as heavy ion emission
Energy Technology Data Exchange (ETDEWEB)
Poenaru, D.N.; Maruhn, J.A.; Greiner, W.; Ivascu, M.; Mazilu, D.; Gherghescu, R.
1987-11-01
The last version of the analytical superasymmetric fission model is applied to study cold fission processes. Strong shell effects are present either in one or both fission fragments. A smooth behaviour is observed when the proton or the neutron numbers are changed by four units. Increasing Z and N, in the transuranium region, a sharp transition from asymmetry with a large peak-to-valley ratio to symmetry at Z=100 and/or N=164 is obtained. The transition toward asymmetry at higher Z and N is much smoother. The most probable cold fission light fragments from /sup 234/U, /sup 236/U, /sup 239/Np and /sup 240/Pu are /sup 100/Zr, /sup 104/Mo, /sup 106/Mo and /sup 106/Mo, respectively, in good agreement with experimental data. The unified treatment of alpha decay, heavy ion radioactivities and cold fission is illustrated for /sup 234/U - the first nucleus in which all three groups have been already observed.
15. Numerical solution of the Maxwell-Vlasov equations in the periodic regime. Application to the study of isotope separation by ion cyclotron resonance; Resolution numerique des equations de Maxwell-Vlasov en regime periodique. Application a l'etude de la separation isotopique par resonance cyclotron ionique
Energy Technology Data Exchange (ETDEWEB)
Omnes, P
1999-01-25
This work is dedicated to the study of the behaviour of a magnetic confined plasma that is excited by a purely sinusoidal electric current delivered by an antenna. The response of the electrons to the electromagnetic field is considered as linear,whereas the ions of the plasma are represented by a non-relativistic Vlasov equation. In order to avoid transients, the coupled Maxwell-Vlasov equations are solved in a periodic mode and in a bounded domain. An equivalent electric conductivity tensor has been defined, this tensor is a linear operator that links the electric current generated by the movement of the particles to the electromagnetic field. Theoretical considerations can assure the existence and uniqueness of a periodical solution to Vlasov equations and of a solution to Maxwell equations in harmonic mode. The system of equations is periodical and has been solved by using an iterative method. The application of this method to the simulation of a isotopic separation device based on ionic cyclotron resonance has shown that the convergence is reached in a few iterations and that the solution is valid. Furthermore a method based on a finite-volume formulation of Maxwell equations in the time domain is presented. 2 new variables are defined in order to better take into account the Gauss' law and the conservation of the magnetic flux, the new system is still hyperbolic. The parallelization of the process has been successfully realized. (A.C.)
16. The whistler mode in a Vlasov plasma
Science.gov (United States)
Tokar, R. L.; Gary, S. P.
1985-01-01
In this study, properties of small-amplitude parallel and oblique whistler-mode waves are investigated for a wide range of plasma parameters by numerically solving the full electromagnetic Vlasov-dispersion equation. To investigate the cold-plasma and electrostatic approximations for the whistler mode, the results are compared with results obtained using these descriptions. For large wavelengths, the cold-plasma description is often accurate, while for short wavelengths and sufficiently oblique propagation, the electrostatic description is often accurate. The study demonstrates that in a Vlasov plasma the whistler mode near resonance has a group velocity more nearly parallel to the magnetic field than that predicted by cold-plasma theory.
17. Tokamak-like Vlasov equilibria
CERN Document Server
Tasso, H
2014-01-01
Vlasov equilibria of axisymmetric plasmas with vacuum toroidal magnetic field can be reduced, up to a selection of ions and electrons distributions functions, to a Grad-Shafranov-like equation. Quasineutrality narrow the choice of the distributions functions. In contrast to two-dimensional translationally symmetric equilibria whose electron distribution function consists of a displaced Maxwellian, the toroidal equilibria need deformed Maxwellians. In order to be able to carry through the calculations, this deformation is produced by means of either a Heaviside step function or an exponential function. The resulting Grad-Shafranov-like equations are established explicitly.
18. Quasineutral limit of the Vlasov-Poisson system with massless electrons
CERN Document Server
Han-Kwan, Daniel
2010-01-01
In this paper, we study the quasineutral limit (in other words the limit when the Debye length tends to zero) of Vlasov-Poisson like equations describing the behaviour of ions in a plasma. We consider massless electrons, with a charge density following a Maxwell-Boltzmann law. For cold ions, using the relative entropy method, we derive the classical Isothermal Euler or the (inviscid) Shallow Water systems from fluid mechanics. In a second time, we study the combined quasineutral and strong magnetic field regime for such plasmas.
19. Solving the Vlasov equation in complex geometries
Directory of Open Access Journals (Sweden)
Sonnendrücker E.
2011-11-01
Full Text Available This paper introduces an isoparametric analysis to solve the Vlasov equation with a semi-Lagrangian scheme. A Vlasov-Poisson problem modeling a heavy ion beam in an axisymmetric configuration is considered. Numerical experiments are conducted on computational meshes targeting different geometries. The impact of the computational grid on the accuracy and the computational cost are shown. The use of analytical mapping or Bézier patches does not induce a too large computational overhead and is quite accurate. This approach successfully couples an isoparametric analysis with a semi-Lagrangian scheme, and we expect to apply it to a gyrokinetic Vlasov solver. Nous présentons ici une analyse isoparamétrique pour résoudre l’équation de Vlasov à l’aide d’un schéma Semi-Lagrangien. Le cas test d’un faisceau axisymétrique d’ions lourds est étudié dans le cadre du système Vlasov-Poisson. Des tests numériques sont effectués sur différents maillages a fin d’étudier diverses géométries. L’impact du choix de maillage sur la précision numérique et le coût de calcul est quantifié. L’utilisation de mapping analytique ou de patches de Bézier ne semble pas trop coûteux et permet une précision numérique suffisante. Le couplage de l’analyse isoparamétrique au schéma Semi-Lagrangien est donc réeussi, nous espérons pouvoir appliquer cette méthode à des solveurs de l’équation de Vlasov gyrocinétique.
20. Verification of high efficient broad beam cold cathode ion source
Science.gov (United States)
Abdel Reheem, A. M.; Ahmed, M. M.; Abdelhamid, M. M.; Ashour, A. H.
2016-08-01
An improved form of cold cathode ion source has been designed and constructed. It consists of stainless steel hollow cylinder anode and stainless steel cathode disc, which are separated by a Teflon flange. The electrical discharge and output characteristics have been measured at different pressures using argon, nitrogen, and oxygen gases. The ion exit aperture shape and optimum distance between ion collector plate and cathode disc are studied. The stable discharge current and maximum output ion beam current have been obtained using grid exit aperture. It was found that the optimum distance between ion collector plate and ion exit aperture is equal to 6.25 cm. The cold cathode ion source is used to deposit aluminum coating layer on AZ31 magnesium alloy using argon ion beam current which equals 600 μA. Scanning electron microscope and X-ray diffraction techniques used for characterizing samples before and after aluminum deposition.
1. Cold atom-ion experiments in hybrid traps
CERN Document Server
Härter, Arne
2013-01-01
In the last 5 years, a novel field of physics and chemistry has developed in which cold trapped ions and ultracold atomic gases are brought into contact with each other. Combining ion traps with traps for neutral atoms yields a variety of new possibilities for research and experiments. These range from studies of cold atom-ion collisions and atom-ion chemistry to applications in quantum information science and condensed matter related research. In this article we give a brief introduction into this new field and describe some of the perspectives for its future development.
2. a Continuous Supersonic Expansion Discharge Nozzle for Rotationally Cold Ions
Science.gov (United States)
Kauffman, Carrie A.; Crabtree, Kyle N.; McCall, Benjamin J.
2009-06-01
Molecular ions play an important role in chemistry and astronomy. In particular, molecular ions are key reaction intermediates, and in the interstellar medium, where temperatures and densities are low, they dominate the chemistry. Studying these ions spectroscopically in the laboratory poses a difficult challenge due to their reactivity. In our effort to study molecular ions, our research group is building SCRIBES (Sensitive Cooled Resolved Ion BEam Spectroscopy), which combines a cold ion source, mass spectrometry, and cavity ring-down spectroscopy. With this apparatus, we will be able to record rotationally-resolved gas-phase spectra, enabling interstellar searches for these species. The SCRIBES instrument requires a source of rotationally cold ions, and this has been accomplished by coupling a supersonic expansion with an electric discharge. Other groups (e.g. Thaddeus and McCarthy at Harvard, Salama et. al at NASA-Ames) have produced cold ions in a similar fashion, but always with a pulsed discharge source. Due to our need for a continuous ion source for SCRIBES, we have designed a continuous supersonic expansion discharge nozzle. We will discuss the various design factors considered during the construction of our continuous self-aligning cold ion source.
3. Production of translationally cold barium monohalide ions
CERN Document Server
DePalatis, M V
2013-01-01
We have produced sympathetically cooled barium monohalide ions BaX$^+$ (X = F, Cl, Br) by reacting trapped, laser cooled Ba$^+$ ions with room temperature gas phase neutral halogen-containing molecules. Reaction rates for two of these (SF$_6$ and CH$_3$Cl) have been measured and are in agreement with classical models. BaX$^+$ ions are promising candidates for cooling to the rovibrational ground state, and our method presents a straightforward way to produce these polar molecular ions.
4. Rotational Laser Cooling of Vibrationally and Translationally Cold Molecular Ions
DEFF Research Database (Denmark)
Drewsen, Michael
2011-01-01
[7,8,9]. Furthermore, in order to learn more about the chemistry in interstellar clouds, astrochemists can benefit greatly from direct measurements on cold reactions in laboratories [9]. Working with MgH+ molecular ions in a linear Paul trap, we routinely cool their translational degree of freedom...... of a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ ions [10]. The scheme is based on excitation of a single rovibrational transition [11], and it should be generalizable to any diatomic polar molecular ion, given appropriate mid...
5. Reduced Vlasov-Maxwell simulations
Science.gov (United States)
Helluy, Philippe; Navoret, Laurent; Pham, Nhung; Crestetto, Anaïs
2014-10-01
In this paper we review two different numerical methods for Vlasov-Maxwell simulations. The first method is based on a coupling between a Discontinuous Galerkin (DG) Maxwell solver and a Particle-In-Cell (PIC) Vlasov solver. The second method only uses a DG approach for the Vlasov and Maxwell equations. The Vlasov equation is first reduced to a space-only hyperbolic system thanks to the finite-element method. The two numerical methods are implemented using OpenCL in order to achieve high performance on recent Graphic Processing Units (GPU).
6. Controlling fast transport of cold trapped ions
CERN Document Server
Walther, Andreas; Ruster, Thomas; Dawkins, Sam T; Ott, Konstantin; Hettrich, Max; Singer, Kilian; Schmidt-Kaler, Ferdinand; Poschinger, Ulrich
2012-01-01
We realize fast transport of ions in a segmented micro-structured Paul trap. The ion is shuttled over a distance of more than 10^4 times its groundstate wavefunction size during only 5 motional cycles of the trap (280 micro meter in 3.6 micro seconds). Starting from a ground-state-cooled ion, we find an optimized transport such that the energy increase is as low as 0.10 $\\pm$ 0.01 motional quanta. In addition, we demonstrate that quantum information stored in a spin-motion entangled state is preserved throughout the transport. Shuttling operations are concatenated, as a proof-of-principle for the shuttling-based architecture to scalable ion trap quantum computing.
7. Exact Quantum Logic Gates with a Single Trapped Cold Ion
Institute of Scientific and Technical Information of China (English)
韦联福; 刘世勇; 雷啸霖
2001-01-01
We present an alternative scheme to exactly implement one-qubit and two-qubit quantum gates with a single trapped cold ion driven by a travelling laser field. The internal degree of freedom of the ion acts as the target qubit and the control qubit is encoded by two Fock states of the external vibration of the ion. The conditions to realize these operations, including the duration of each applied laser pulse and Lamb-Dicke parameter, are derived. In our scheme neither the auxiliary atomic level nor the Lamb-Dicke approximation is required. The multiquantum transition between the internal and external degrees of freedom of the ion is considered.
8. A proposal for sympathetically cooling neutral molecules using cold ions
CERN Document Server
Robicheaux, F
2014-01-01
We describe a method for cooling neutral molecules that have magnetic and electric dipole moments using collisions with cold ions. An external magnetic field is used to split the ground rovibrational energy levels of the molecule. The highest energy state within the ground rovibrational manifold increases in energy as the distance to the ion decreases leading to a repelling potential. At low energy, inelastic collisions are strongly suppressed due to the large distance of closest approach. Thus, a collision between a neutral molecule and a cold ion will lead to a decrease in the molecule's kinetic energy with no change in internal energy. We present results for the specific case of OH molecules cooled by Be$^+$, Mg$^+$, or Ca$^+$ ions.
9. DESIREE: Physics with cold stored ion beams
Directory of Open Access Journals (Sweden)
Thomas R.D.
2015-01-01
Full Text Available Here we will briefly describe the commissioning of the Double ElectroStatic Ion Ring ExpEriment (DESIREE facility at Stockholm University, Sweden. This device uses purely electrostatic focussing and deflection elements and allows ion beams of opposite charge to be confined under extreme high vacuum and cryogenic conditions in separate “rings” and then merged over a common straight section. This apparatus allows for studies of interactions between cations and anions at very low and well-defined centre-of-mass energies (down to a few meV and at very low internal temperatures (down to a few K.
10. Cryogenic linear Paul trap for cold highly charged ion experiments.
Science.gov (United States)
Schwarz, M; Versolato, O O; Windberger, A; Brunner, F R; Ballance, T; Eberle, S N; Ullrich, J; Schmidt, P O; Hansen, A K; Gingell, A D; Drewsen, M; López-Urrutia, J R Crespo
2012-08-01
Storage and cooling of highly charged ions require ultra-high vacuum levels obtainable by means of cryogenic methods. We have developed a linear Paul trap operating at 4 K capable of very long ion storage times of about 30 h. A conservative upper bound of the H(2) partial pressure of about 10(-15) mbar (at 4 K) is obtained from this. External ion injection is possible and optimized optical access for lasers is provided, while exposure to black body radiation is minimized. First results of its operation with atomic and molecular ions are presented. An all-solid state laser system at 313 nm has been set up to provide cold Be(+) ions for sympathetic cooling of highly charged ions.
11. Cryogenic linear Paul trap for cold highly charged ion experiments
DEFF Research Database (Denmark)
Schwarz, Maria; Versolato, Oscar; Windberger, Alexander
2012-01-01
Storage and cooling of highly charged ions require ultra-high vacuum levels obtainable by means of cryogenic methods. We have developed a linear Paul trap operating at 4 K capable of very long ion storage times of about 30 h. A conservative upper bound of the H2 partial pressure of about 10−15 mbar...... (at 4 K) is obtained from this. External ion injection is possible and optimized optical access for lasers is provided, while exposure to black body radiation is minimized. First results of its operation with atomic and molecular ions are presented. An all-solid state laser system at 313 nm has been...... set up to provide cold Be+ ions for sympathetic cooling of highly charged ions....
12. Disordered complex systems using cold gases and trapped ions
CERN Document Server
De, A S; Lewenstein, M; Ahufinger, V; Pons, M L; Sanpera, A; De, Aditi Sen; Sen, Ujjwal; Lewenstein, Maciej; Ahufinger, Veronica; Pons, Marisa Ll.; Sanpera, Anna
2005-01-01
We report our research on disordered complex systems using cold gases and trapped ions, and address the possibility of using complex systems for quantum information processing. Two simple paradigmatic models of disordered complex systems are revisited here. The first one corresponds to a short range disordered Ising Hamiltonian (spin glasses), which can be implemented with a Bose-Fermi (Bose-Bose) mixture in a disordered optical lattice. The second model we address here is a long range disordered Hamiltonian, characteristic of neural networks (Hopfield model), which can be implemented in a chain of trapped ions with appropriately designed interactions.
13. Rotational Laser Cooling of Vibrationally and Translationally Cold Molecular Ions
DEFF Research Database (Denmark)
Drewsen, Michael
2011-01-01
by sympathetic cooling with Doppler laser cooled Mg+ ions. Giving the time for the molecules to equilibrate internally to the room temperature blackbody radiation, the vibrational degree of freedom will freeze out, leaving only the rotational degree of freedom to be cooled. We report here on the implementation...... of a new technique for laser-induced rotational ground-state cooling of vibrationally and translationally cold MgH+ ions [10]. The scheme is based on excitation of a single rovibrational transition [11], and it should be generalizable to any diatomic polar molecular ion, given appropriate mid......-infrared laser sources such as a quantum cascade laser are available. In recent experiments, a nearly 15-fold increase in the rotational ground-state population was obtained, with the resulting ground-state population of 36,7±1,2 %, equivalent to that of a thermal distribution at about 20 K. The obtained cooling...
14. A cloudy Vlasov solution
CERN Document Server
Alard, C
2004-01-01
We propose to integrate the Vlasov-Poisson equations giving the evolution of a dynamical system in phase-space using a continuous set of local basis functions. In practice, the method decomposes the density in phase-space into small smooth units having compact support. We call these small units clouds'' and choose them to be Gaussians of elliptical support. Fortunately, the evolution of these clouds in the local potential has an analytical solution, that can be used to evolve the whole system during a significant fraction of dynamical time. In the process, the clouds, initially round, change shape and get elongated. At some point, the system needs to be remapped on round clouds once again. This remapping can be performed optimally using a small number of Lucy iterations. The remapped solution can be evolved again with the cloud method, and the process can be iterated a large number of times without showing significant diffusion. Our numerical experiments show that it is possible to follow the 2 dimensional ...
15. Small amplitude ion-acoustic double layers with cold electron beam and q-nonextensive electrons
Energy Technology Data Exchange (ETDEWEB)
Ali Shan, S., E-mail: [email protected] [Theoretical Plasma Physics Division, PINSTECH, Nilore, 44000 Islamabad (Pakistan); National Centre for Physics (NCP), Shahdra Valley Road, 44000 Islamabad (Pakistan); Department of Mathematics and Applied Physics (DPAM), PIEAS, Islamabad (Pakistan); Saleem, H., E-mail: [email protected] [National Centre for Physics (NCP), Shahdra Valley Road, 44000 Islamabad (Pakistan); Department of Mathematics and Applied Physics (DPAM), PIEAS, Islamabad (Pakistan)
2014-02-01
Small amplitude ion-acoustic double layers in an unmagnetized and collisionless plasma consisting of cold positive ions, q-nonextensive electrons, and a cold electron beam are investigated. Small amplitude double layer solution is obtained by expanding the Sagdeev potential truncated method. The effects of entropic index q, speed and density of cold electron beam on double layer structures are discussed.
16. Spectra of Cold Molecular Ions from Hot Helium Nanodroplets
Science.gov (United States)
Drabbels, Marcel
2012-06-01
The function of a molecule is intimately related to its structure. Accordingly, in the quest for a better understanding of molecular function, the development of spectroscopic methods to elucidate molecular structures increasingly takes central stage. The amount of detail that can be derived from spectra depends on the experimental conditions, most notably on the temperature of the sample and the intermolecular interactions a molecule experiences. Helium nanodroplets provide in this respect an almost ideal matrix [1, 2]. For neutral molecules, helium nanodroplet spectroscopy thus has led to important discoveries related to the structure of key molecular systems and has provided insight into the mechanisms underlying chemical reactions. Compared to the level of sophistication that has been reached for neutrals, the spectroscopic exploration of ions is still in its infancy. The use of helium droplets as a cryogenic matrix could potentially solve many of the technical challenges associated with recording high-resolution spectra of cold molecular ions. Here, we will present a method to record spectra of ion containing helium nanodroplets that finds its roots in the nonthermal cooling dynamics of excited molecular ions. In addition, spectra of several molecular ions will be present and the influence of the helium environment on these spectra will be discussed. [1] G. Scoles, and K. K. Lehmann, Science 287, 2429 (2000). [2] J. P. Toennies, and A. F. Vilesov, Angew. Chem. Int. Ed. 43, 2622 (2004).
17. Precision Spectroscopy on Single Cold Trapped Molecular Nitrogen Ions
Science.gov (United States)
Hegi, Gregor; Najafian, Kaveh; Germann, Matthias; Sergachev, Ilia; Willitsch, Stefan
2016-06-01
The ability to precisely control and manipulate single cold trapped particles has enabled spectroscopic studies on narrow transitions of ions at unprecedented levels of precision. This has opened up a wide range of applications, from tests of fundamental physical concepts, e.g., possible time-variations of fundamental constants, to new and improved frequency standards. So far most of these experiments have concentrated on atomic ions. Recently, however, attention has also been focused on molecular species, and molecular nitrogen ions have been identified as promising candidates for testing a possible time-variation of the proton/electron mass ratio. Here, we report progress towards precision-spectroscopic studies on dipole-forbidden vibrational transitions in single trapped N2+ ions. Our approach relies on the state-selective generation of single N2+ ions, subsequent infrared excitation using high intensity, narrow-band quantum-cascade lasers and a quantum-logic scheme for non-destructive state readout. We also characterize processes limiting the state lifetimes in our experiment, which impair the measurement fidelity. P. O. Schmidt et. al., Science 309 (2005), 749. M. Kajita et. al., Phys. Rev. A 89 (2014), 032509 M. Germann , X. Tong, S. Willitsch, Nature Physics 10 (2014), 820. X. Tong, A. Winney, S. Willitsch, Phys. Rev. Lett. 105 (2010), 143001
18. Wave dispersion in the hybrid-Vlasov model: Verification of Vlasiator
OpenAIRE
Kempf, Yann; Pokhotelov, Dimitry; von Alfthan, Sebastian; Vaivads, Andris; Palmroth, Minna; Koskinen, Hannu E. J.
2013-01-01
Vlasiator is a new hybrid-Vlasov plasma simulation code aimed at simulating the entire magnetosphere of the Earth. The code treats ions (protons) kinetically through Vlasov's equation in the six-dimensional phase space while electrons are a massless charge-neutralizing fluid [M. Palmroth et al., Journal of Atmospheric and Solar-Terrestrial Physics 99, 41 (2013); A. Sandroos et al., Parallel Computing 39, 306 (2013)]. For first global simulations of the magnetosphere, it is critical to verify ...
19. Relativistic simulation of the Vlasov equation for plasma expansion into vacuum
OpenAIRE
H ABBASI; R Shokoohi; Moridi, M.
2012-01-01
In this study, relativistic Vlasov simulation of plasma for expansion of collisionless plasma for into vacuum is presented. The model is based on 1+1 dimensional phase space and electrostatic approximation. For this purpose, the electron dynamics is studied by the relativistic Vlasov equation. Regardless of the ions temperature, fluid equations are used for their dynamics. The initial electrons distribution function is the relativistic Maxwellian. The results show that due to the electrons ...
20. Spectroscopic studies of cold, gas-phase biomolecular ions
Science.gov (United States)
Rizzo, Thomas R.; Stearns, Jaime A.; Boyarkin, Oleg V.
While the marriage of mass spectrometry and laser spectroscopy is not new, developments over the last few years in this relationship have opened up new horizons for the spectroscopic study of biological molecules. The combination of electrospray ionisation for producing large biological molecules in the gas phase together with cooled ion traps and multiple-resonance laser schemes are allowing spectroscopic investigation of individual conformations of peptides with more than a dozen amino acids. Highly resolved infrared spectra of single conformations of such species provide important benchmarks for testing the accuracy of theoretical calculations. This review presents a number of techniques employed in our laboratory and in others for measuring the spectroscopy of cold, gas-phase protonated peptides. We show examples that demonstrate the power of these techniques and evaluate their extension to still larger biological molecules.
1. Rotational laser cooling of vibrationally and translationally cold molecular ions
DEFF Research Database (Denmark)
Staanum, Peter; Højbjerre, Klaus; Skyt, Peter Sandegaard
2010-01-01
-molecular reactions with coherent light fields 8, 9 , for quantum-state-selected bi-molecular reactions 10, 11, 12 and for astrochemistry 12 . Here, we demonstrate rotational ground-state cooling of vibrationally and translationally cold MgH+ ions, using a laser-cooling scheme based on excitation of a single...... rovibrational transition 13, 14 . A nearly 15-fold increase in the rotational ground-state population of the X 1Σ+ electronic ground-state potential has been obtained. The resulting ground-state population of 36.7±1.2% is equivalent to that of a thermal distribution at about 20 K. The obtained cooling results...
2. Formation of molecular ions by radiative association of cold trapped atoms and ions
CERN Document Server
Silva, Humberto Da; Aymar, Mireille; Dulieu, Olivier
2015-01-01
Radiative emission during cold collisions between trapped laser-cooled Rb atoms and alkaline-earth ions (Ca + , Sr + , Ba +) and Yb + are studied theoretically, using accurate effective-core-potential based quantum chemistry calculations of potential energy curves and transition dipole moments of the related molecular ions. Radiative association of molecular ions is predicted to occur for all systems with a cross section two to ten times larger than the radiative charge transfer one. Partial and total rate constants are also calculated and compared to available experiments. Narrow shape resonances are expected, which could be detectable at low temperature with an experimental resolution at the limit of the present standards. Vibrational distributions are also calculated, showing that the final molecular ions are not created in their ground state level.
3. Stick-slip nanofriction in cold-ion traps
Science.gov (United States)
Mandelli, Davide; Vanossi, Andrea; Tosatti, Erio
2013-03-01
Trapped cold ions are known to form linear or planar zigzag chains, helices or clusters depending on trapping conditions. They may be forced to slide over a laser induced corrugated potential, a mimick of sliding friction. We present MD simulations of an incommensurate 101 ions chain sliding subject to an external electric field. As expected with increasing corrugation, we observe the transition from a smooth-sliding, highly lubric regime to a strongly dissipative stick-slip regime. Owing to inhomogeneity the dynamics shows features reminiscent of macroscopic frictional behaviors. While the chain extremities are pinned, the incommensurate central part is initially free to slide. The onset of global sliding is preceded by precursor events consisting of partial slips of chain portions further from the center. We also look for frictional anomalies expected for the chain sliding across the linear-zigzag structural phase transition. Although the chain is too short for a proper critical behavior, the sliding friction displays a frank rise near the transition, due to opening of a new dissipative channel via excitations of transverse modes. Research partly sponsored by Sinergia Project CRSII2 136287/1.
4. Vlasov Analysis of Microbunching Gain for Magnetized Beams
Energy Technology Data Exchange (ETDEWEB)
Tsai, Cheng Ying [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Derbenev, Yaroslav [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Douglas, David R. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Li, Rui [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Tennant, Christopher D. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2016-10-01
For a high-brightness electron beam with low energy and high bunch charge traversing a recirculation beamline, coherent synchrotron radiation and space charge effect may result in the microbunching instability (MBI). Both tracking simulation and Vlasov analysis for an early design of Circulator Cooler Ring for the Jefferson Lab Electron Ion Collider reveal significant MBI. It is envisioned these could be substantially suppressed by using a magnetized beam. In this work, we extend the existing Vlasov analysis, originally developed for a non-magnetized beam, to the description of transport of a magnetized beam including relevant collective effects. The new formulation will be further employed to confirm prediction of microbunching suppression for a magnetized beam transport in a recirculating machine design.
5. Vlasov simulations of parallel potential drops
Directory of Open Access Journals (Sweden)
H. Gunell
2013-07-01
Full Text Available An auroral flux tube is modelled from the magnetospheric equator to the ionosphere using Vlasov simulations. Starting from an initial state, the evolution of the plasma on the flux tube is followed in time. It is found that when applying a voltage between the ends of the flux tube, about two thirds of the potential drop is concentrated in a thin double layer at approximately one Earth radius altitude. The remaining part is situated in an extended region 1–2 Earth radii above the double layer. Waves on the ion timescale develop above the double layer, and they move toward higher altitude at approximately the ion acoustic speed. These waves are seen both in the electric field and as perturbations of the ion and electron distributions, indicative of an instability. Electrons of magnetospheric origin become trapped between the magnetic mirror and the double layer during its formation. At low altitude, waves on electron timescales appear and are seen to be non-uniformly distributed in space. The temporal evolution of the potential profile and the total voltage affect the double layer altitude, which decreases with an increasing field aligned potential drop. A current–voltage relationship is found by running several simulations with different voltages over the system, and it agrees with the Knight relation reasonably well.
6. Lagrangian formulation of the one-dimensional Vlasov equation. [in plasma physics
Science.gov (United States)
Lewak, G. J.
1974-01-01
A new formulation of the one-dimensional Vlasov equation is derived which is analogous to the Kalman-transformed cold-plasma equations. The equations are shown to yield nonsecular, nonlinear approximations to a source or boundary-value problem. It is suggested that the formulation may have other applications in nonlinear plasma theory.
7. Vlasov on GPU (VOG Project)
CERN Document Server
Mehrenberger, M; Marradi, L; Crouseilles, N; Sonnendrucker, E; Afeyan, B
2013-01-01
This work concerns the numerical simulation of the Vlasov-Poisson set of equations using semi- Lagrangian methods on Graphical Processing Units (GPU). To accomplish this goal, modifications to traditional methods had to be implemented. First and foremost, a reformulation of semi-Lagrangian methods is performed, which enables us to rewrite the governing equations as a circulant matrix operating on the vector of unknowns. This product calculation can be performed efficiently using FFT routines. Second, to overcome the limitation of single precision inherent in GPU, a {\\delta}f type method is adopted which only needs refinement in specialized areas of phase space but not throughout. Thus, a GPU Vlasov-Poisson solver can indeed perform high precision simulations (since it uses very high order reconstruction methods and a large number of grid points in phase space). We show results for rather academic test cases on Landau damping and also for physically relevant phenomena such as the bump on tail instability and t...
8. Vlasov-Poisson in 1D: waterbags
CERN Document Server
Colombi, Stéphane
2014-01-01
We revisit in one dimension the waterbag method to solve numerically Vlasov-Poisson equations. In this approach, the phase-space distribution function $f(x,v)$ is initially sampled by an ensemble of patches, the waterbags, where $f$ is assumed to be constant. As a consequence of Liouville theorem it is only needed to follow the evolution of the border of these waterbags, which can be done by employing an orientated, self-adaptive polygon tracing isocontours of $f$. This method, which is entropy conserving in essence, is very accurate and can trace very well non linear instabilities as illustrated by specific examples. As an application of the method, we generate an ensemble of single waterbag simulations with decreasing thickness, to perform a convergence study to the cold case. Our measurements show that the system relaxes to a steady state where the gravitational potential profile is a power-law of slowly varying index $\\beta$, with $\\beta$ close to $3/2$ as found in the literature. However, detailed analys...
9. Relativistic simulation of the Vlasov equation for plasma expansion into vacuum
Directory of Open Access Journals (Sweden)
H Abbasi
2012-12-01
Full Text Available In this study, relativistic Vlasov simulation of plasma for expansion of collisionless plasma for into vacuum is presented. The model is based on 1+1 dimensional phase space and electrostatic approximation. For this purpose, the electron dynamics is studied by the relativistic Vlasov equation. Regardless of the ions temperature, fluid equations are used for their dynamics. The initial electrons distribution function is the relativistic Maxwellian. The results show that due to the electrons relativistic temperature, the process of the plasma expansion takes place faster, the resulting electric field is stronger and the ions are accelerated to higher velocities, in comparison to the non-relativistic case.
10. Range of plasma ions in cold cluster gases near the critical point
Energy Technology Data Exchange (ETDEWEB)
Zhang, G. [Cyclotron Institute, Texas A& M University, 77843 College Station, TX (United States); Quevedo, H.J. [Center for High Energy Density Science, C1510, University of Texas at Austin, Austin, TX 78712 (United States); Bonasera, A., E-mail: [email protected] [Cyclotron Institute, Texas A& M University, 77843 College Station, TX (United States); Laboratori Nazionali del Sud-INFN, via S. Sofia 64, 95123 Catania (Italy); Donovan, M.; Dyer, G.; Gaul, E. [Center for High Energy Density Science, C1510, University of Texas at Austin, Austin, TX 78712 (United States); Guardo, G.L. [Laboratori Nazionali del Sud-INFN, via S. Sofia 64, 95123 Catania (Italy); Gulino, M. [Laboratori Nazionali del Sud-INFN, via S. Sofia 64, 95123 Catania (Italy); Libera Universita' Kore, 94100 Enna (Italy); La Cognata, M.; Lattuada, D. [Laboratori Nazionali del Sud-INFN, via S. Sofia 64, 95123 Catania (Italy); Palmerini, S. [Department of Physics and Geology, University of Perugia, Via A. Pascoli, 06123 Perugia (Italy); Istituto Nazionale di Fisica Nucleare, Section of Perugia, Via A. Pascoli, 06123 Perugia (Italy); Pizzone, R.G.; Romano, S. [Laboratori Nazionali del Sud-INFN, via S. Sofia 64, 95123 Catania (Italy); Smith, H. [Center for High Energy Density Science, C1510, University of Texas at Austin, Austin, TX 78712 (United States); Trippella, O. [Department of Physics and Geology, University of Perugia, Via A. Pascoli, 06123 Perugia (Italy); Istituto Nazionale di Fisica Nucleare, Section of Perugia, Via A. Pascoli, 06123 Perugia (Italy); Anzalone, A.; Spitaleri, C. [Laboratori Nazionali del Sud-INFN, via S. Sofia 64, 95123 Catania (Italy); Ditmire, T. [Center for High Energy Density Science, C1510, University of Texas at Austin, Austin, TX 78712 (United States)
2017-05-18
We measure the range of plasma ions in cold cluster gases by using the Petawatt laser at the University of Texas-Austin. The produced plasma propagated in all directions some hitting the cold cluster gas not illuminated by the laser. From the ratio of the measured ion distributions at different angles we can estimate the range of the ions in the cold cluster gas. It is much smaller than estimated using popular models, which take only into account the slowing down of charged particles in uniform matter. We discuss the ion range in systems prepared near a liquid–gas phase transition. - Highlights: • We present experimental results obtained at the UT Petawatt laser facility, Austin, TX. • The ion range is strongly modified for cluster gases as compared to its value in a homogeneous system. • Large fluctuations are found if the cluster gas is prepared near the liquid–gas phase transition region.
11. Stability analysis of cylindrical Vlasov equilibria
Energy Technology Data Exchange (ETDEWEB)
Short, R.W.
1979-01-01
A general method of stability analysis is described which may be applied to a large class of such problems, namely those which are described dynamically by the Vlasov equation, and geometrically by cylindrical symmetry. The method is presented for the simple case of the Vlasov-Poisson (electrostatic) equations, and the results are applied to a calculation of the lower-hybrid-drift instability in a plasma with a rigid rotor distribution function. The method is extended to the full Vlasov-Maxwell (electromagnetic) equations. These results are applied to a calculation of the instability of the extraordinary electromagnetic mode in a relativistic E-layer interacting with a background plasma.
12. Superstatistical velocity distributions of cold trapped ions in molecular dynamics simulations
CERN Document Server
Rouse, I
2015-01-01
We present a realistic molecular-dynamics treatment of laser-cooled ions in radiofrequency ion traps which avoids previously made simplifications such as modeling laser cooling as a friction force and combining individual heating mechanisms into a single effective heating force. Based on this implementation, we show that infrequent energetic collisions of single ions with background gas molecules lead to pronounced heating of the entire ion ensemble and a time-varying secular ensemble temperature which manifests itself in a superstatistical time-averaged velocity distribution of the ions. The effect of this finding on the experimental determination of ion temperatures and rate constants for cold chemical reactions is discussed.
13. Vlasov moments, integrable systems and singular solutions
Energy Technology Data Exchange (ETDEWEB)
Gibbons, John [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); Holm, Darryl D. [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); Computer and Computational Science Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)], E-mail: [email protected]; Tronci, Cesare [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); TERA Foundation for Oncological Hadrontherapy, 11 V. Puccini, Novara 28100 (Italy)
2008-02-11
The Vlasov equation governs the evolution of the single-particle probability distribution function (PDF) for a system of particles interacting without dissipation. Its singular solutions correspond to the individual particle motions. The operation of taking the moments of the Vlasov equation is a Poisson map. The resulting Lie-Poisson Hamiltonian dynamics of the Vlasov moments is found to be integrable is several cases. For example, the dynamics for coasting beams in particle accelerators is associated by a hodograph transformation to the known integrable Benney shallow-water equation. After setting the context, the Letter focuses on geodesic Vlasov moment equations. Continuum closures of these equations at two different orders are found to be integrable systems whose singular solutions characterize the geodesic motion of the individual particles.
14. Deterministic delivery of externally cold and precisely positioned single molecular ions
CERN Document Server
Leschhorn, G; Schaetz, T
2011-01-01
We present the preparation and deterministic delivery of a selectable number of externally cold molecular ions. A laser cooled ensemble of Mg^+ ions subsequently confined in several linear Paul traps inter-connected via a quadrupole guide serves as a cold bath for a single or up to a few hundred molecular ions. Sympathetic cooling embeds the molecular ions in the crystalline structure. MgH^+ ions, that serve as a model system for a large variety of other possible molecular ions, are cooled down close to the Doppler limit and are positioned with an accuracy of one micrometer. After the production process, severely compromising the vacuum conditions, the molecular ion is efficiently transfered into nearly background-free environment. The transfer of a molecular ion between different traps as well as the control of the molecular ions in the traps is demonstrated. Schemes, optimized for the transfer of a specific number of ions, are realized and their efficiencies are evaluated. This versatile source applicable f...
15. Decoherence bounds on the capabilities of cold trapped ion quantum computers
Energy Technology Data Exchange (ETDEWEB)
James, D.F.V.; Hughes, R.J.; Knill, E.H. [and others
1997-05-01
Using simple physical arguments we investigate the capabilities of a quantum computer based on cold trapped ions of the type recently proposed by Cirac and Zoller. From the limitations imposed on such a device by decoherence due to spontaneous decay, laser phase coherence times, ion heating and other possible sources of error, we derive bounds on the number of laser interactions and on the number of ions that may be used. As a quantitative measure of the possible performance of these devices, the largest number which may be factored using Shors quantum factoring algorithm is determined for a variety of species of ion.
16. Rotational state-changing cold collisions of hydroxyl ions with helium
CERN Document Server
Hauser, Daniel; Carelli, Fabio; Spieler, Steffen; Lakhmanskaya, Olga; Endres, Eric S; Kumar, Sunil S; Gianturco, Franco; Wester, Roland
2015-01-01
Cold molecules are important for many applications, from fundamental precision measurements, quantum information processing, quantum-controlled chemistry, to understanding the cold interstellar medium. Molecular ions are known to be cooled efficiently in sympathetic collisions with cold atoms or ions. However, little knowledge is available on the elementary cooling steps, because the determination of quantum state-to-state collision rates at low temperature is prohibitively challenging for both experiment and theory. Here we present a method to manipulate molecular quantum states by non-resonant photodetachment. Based on this we provide absolute quantum scattering rate coefficients under full quantum state control for the rotationally inelastic collision of hydroxyl anions with helium. Experiment and quantum scattering theory show excellent agreement without adjustable parameters. Very similar rate coefficients are obtained for two different isotopes, which is linked to several quantum scattering resonances a...
17. Kinetic Boltzmann, Vlasov and Related Equations
CERN Document Server
Sinitsyn, Alexander; Vedenyapin, Victor
2011-01-01
Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in
18. Achieving translational symmetry in trapped cold ion rings
CERN Document Server
Li, Hao-Kun; Noel, Crystal; Chuang, Alexander; Xia, Yang; Ransford, Anthony; Hemmerling, Boerge; Wang, Yuan; Li, Tongcang; Haeffner, Hartmut; Zhang, Xiang
2016-01-01
Spontaneous symmetry breaking is a universal concept throughout science. For instance, the Landau-Ginzburg paradigm of translational symmetry breaking underlies the classification of nearly all quantum phases of matter and explains the emergence of crystals, insulators, and superconductors. Usually, the consequences of translational invariance are studied in large systems to suppress edge effects which cause undesired symmetry breaking. While this approach works for investigating global properties, studies of local observables and their correlations require access and control of the individual constituents. Periodic boundary conditions, on the other hand, could allow for translational symmetry in small systems where single particle control is achievable. Here, we crystallize up to fifteen 40Ca+ ions in a microscopic ring with inherent periodic boundary conditions. We show the ring's translational symmetry is preserved at millikelvin temperatures by delocalizing the Doppler laser cooled ions. This establishes ...
19. Cold highly charged ions in a cryogenic Paul trap
DEFF Research Database (Denmark)
Versolato, O.O.; Schwarz, M.; Windberger, A.
2013-01-01
17 + . However, lasers pectroscopy of HCIs is hindered by the large (∼ 106 K) temperatures at which they are produced and trapped. An unprecedented improvement in such laser spectroscopy can be obtained when HCIs are cooled down to the mK range in a linear Paul trap. We have developed a cryogenic...... linear Paul trap in which HCIs will be sympathetically cooled by 9Be + ions. Optimized optical access for laser light is provided while maintaining excellent UHV conditions. The Paul trap will be connected to an electron beam ion trap (EBIT) which is able to produce a wide range of HCIs. This EBIT...... will also provide the first experimental input needed for the determination of the transition energies inIr 17+ , enabling further laser-spectroscopic investigations of this promising HCI....
20. Low-energy, high-current, ion source with cold electron emitter
Energy Technology Data Exchange (ETDEWEB)
Vizir, A. V.; Oks, E. M. [High Current Electronics Institute, Russian Academy of Sciences, Tomsk 634055 (Russian Federation); State University of Control Systems and Radioelectronics, Tomsk 634050 (Russian Federation); Shandrikov, M. V.; Yushkov, G. Yu. [High Current Electronics Institute, Russian Academy of Sciences, Tomsk 634055 (Russian Federation)
2012-02-15
An ion source based on a two-stage discharge with electron injection from a cold emitter is presented. The first stage is the emitter itself, and the second stage provides acceleration of injected electrons for gas ionization and formation of ion flow (<20 eV, 5 A dc). The ion accelerating system is gridless; acceleration is accomplished by an electric field in the discharge plasma within an axially symmetric, diverging, magnetic field. The hollow cathode electron emitter utilizes an arc discharge with cathode spots hidden inside the cathode cavity. Selection of the appropriate emitter material provides a very low erosion rate and long lifetime.
1. Vlasov tokamak equilibria with shearad toroidal flow and anisotropic pressure
CERN Document Server
Kuiroukidis, Ap; Tasso, H
2015-01-01
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e. the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis.
2. Rotational state resolved photodissociation spectroscopy of translationally and vibrationally cold MgH+ ions: toward rotational cooling of molecular ions
DEFF Research Database (Denmark)
Højbjerre, Klaus; Hansen, Anders Kragh; Skyt, Peter Sandegaard
2009-01-01
and vibrationally cold MgH+ ions are presented, with and without the optical pumping laser being present. While rotational cooling is as yet not evident, first results showed evidence of a change in the rotational distribution in the presence of the optical pumping laser.......The first steps toward the implementation of a simple scheme for rotational cooling of MgH+ ions based on rotational state optical pumping is considered. The various aspects of such an experiment are described in detail, and the rotational state-selective dissociation spectra of translationally...
3. Solar Illumination of the Polar Ionosphere and Its Effects on Cold Ion Outflow.
Science.gov (United States)
Maes, L.; Maggiolo, R.; Haaland, S.; Li, K.; Andre, M.; Eriksson, A. I.
2015-12-01
Solar illumination is the most important form of energy driving the outflow of cold ionospheric ions in the polar regions, called the polar wind. Due to the offset of the magnetic poles from the rotation axis and Earth's rotational and orbital motion, the part of the magnetic polar cap being illuminated and the part being in the dark, will vary throughout the day and the seasons. Therefore the outflowing ion flux from the whole polar cap will vary accordingly. Moreover, the offset in the Northern hemisphere is different from the one in the Southern hemisphere. Thus the flux from both polar caps will also be different. With a very simple model we will explore the effects of this on the outflowing flux, which will affect the atmospheric erosion as well as the supply of ionospheric ions to the plasma sheet. In recent observations with the Cluster satellites, the heavier O⁺ ions have been shown to be affected more strongly by solar illumination than H⁺ ions. So this may lead to an alteration of the mass density in the plasma sheet on a periodic basis. This study will also look for signatures of the effects predicted by this model in data of cold ion outflow. The Cluster extensive data set from André et al. [2015] seems best suited for this. It uses the technique detecting the wake formed behind a charged spacecraft in a low density and low energy plasma environment. This technique will generally only observe ions with an energy too low to overcome the spacecraft potential (i.e. ~< 40 eV). The measurements are made in the magnetospheric lobes, up to altitudes of 20 RE, between 2001 and 2010. This long period of observations creates the possibility to study the seasonal variation of cold ion outflow from the polar ionosphere and look for possible differences between both hemispheres.
4. Vlasov analysis of microbunching instability for magnetized beams
Directory of Open Access Journals (Sweden)
C.-Y. Tsai
2017-05-01
Full Text Available For a high-brightness electron beam with high bunch charge traversing a recirculation beam line, coherent synchrotron radiation and space charge effects may result in microbunching instability (MBI. Both tracking simulation and Vlasov analysis for an early design of a circulator cooler ring (CCR for the Jefferson Lab Electron Ion Collider (JLEIC reveal significant MBI [Ya. Derbenev and Y. Zhang, Proceedings of the Workshop on Beam Cooling and Related Topics, COOL’09, Lanzhou, China, 2009 (2009, FRM2MCCO01]. It is envisioned that the MBI could be substantially suppressed by using a magnetized beam. In this paper we have generalized the existing Vlasov analysis, originally developed for a nonmagnetized beam (or transversely uncoupled beam, to the description of transport of a magnetized beam including relevant collective effects. The new formulation is then employed to confirm prediction of microbunching suppression for a magnetized beam transport in the recirculation arc of a recent JLEIC energy recovery linac (ERL based cooler design for electron cooling. It is found that the smearing effect in the longitudinal beam phase space originates from the large transverse beam size as a nature of the magnetized beams and becomes effective through the x-z correlation when the correlated distance is larger than the microbunched scale. As a comparison, MBI analysis of the early design of JLEIC CCR is also presented in this paper.
5. Hydrodynamic limits of the Vlasov equation
Energy Technology Data Exchange (ETDEWEB)
Caprino, S. (Universita' de L' Aquila Coppito (Italy)); Esposito, R.; Marra, R. (Universita' di Roma tor Vergata, Roma (Italy)); Pulvirenti, M. (Universita' di Roma la Sapienza, Roma (Italy))
1993-01-01
In the present work, the authors study the Vlasov equation for repulsive forces in the hydrodynamic regime. For initial distributions at zero temperature the limit equations turn out to be the compressible and incompressible Euler equations under suitable space-time scalings. 17 refs.
6. Irreversible energy flow in forced Vlasov dynamics
KAUST Repository
Plunk, Gabriel G.
2014-10-01
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag. The recent paper of Plunk [G.G. Plunk, Phys. Plasmas 20, 032304 (2013)] considered the forced linear Vlasov equation as a model for the quasi-steady state of a single stable plasma wavenumber interacting with a bath of turbulent fluctuations. This approach gives some insight into possible energy flows without solving for nonlinear dynamics. The central result of the present work is that the forced linear Vlasov equation exhibits asymptotically zero (irreversible) dissipation to all orders under a detuning of the forcing frequency and the characteristic frequency associated with particle streaming. We first prove this by direct calculation, tracking energy flow in terms of certain exact conservation laws of the linear (collisionless) Vlasov equation. Then we analyze the steady-state solutions in detail using a weakly collisional Hermite-moment formulation, and compare with numerical solution. This leads to a detailed description of the Hermite energy spectrum, and a proof of no dissipation at all orders, complementing the collisionless Vlasov result.
7. Dynamics of a ground-state cooled ion colliding with ultra-cold atoms
CERN Document Server
Meir, Ziv; Ben-shlomi, Ruti; Akerman, Nitzan; Dallal, Yehonatan; Ozeri, Roee
2016-01-01
Ultra-cold atom-ion mixtures are gaining increasing interest due to their potential applications in quantum chemistry, quantum computing and many-body physics. The polarization potential between atoms and ions scales as 1/r^4 and extends to 100's of nm. This long length-scale interaction can form macroscopic objects while exhibiting quantum features such as Feshbach and shape resonances at sufficiently low temperatures. So far, reaching the quantum regime of atom-ion interaction has been impeded by the ion's excess micromotion (EMM) which sets a scale for the steady-state energy. In this work, we studied the dynamics of a ground-state cooled ion with negligible EMM during few, to many, Langevin (spiraling) collisions with ultra-cold atoms. We measured the energy distribution of the ion using both coherent (Rabi) and non-coherent (photon scattering) spectroscopy. We observed a clear deviation from a Maxwell-Boltzmann thermal distribution to a Tsallis energy distribution characterized by a power-law tail of hig...
8. Cold ion UV photofragmentation spectroscopy and dynamics (Invited)
Energy Technology Data Exchange (ETDEWEB)
Feraud, Geraldine; Dedonder, Claude; Jouvet, Christophe [CNRS, Aix Marseille Université, laboratoire de Physique des Interactions Ioniques et Moléculaires (PIIM) UMR 7345, 13397 Marseille cedex 20 (France); Broquier, Michel [Université Paris Sud, CLUPS (Centre Laser de l' Université Paris Sud) LUMAT FR 2764, 91405 Orsay Cedex, France and CNRS, Université Paris Sud, Institut des Sciences Moléculaires d' Orsay (ISMO) UMR 8624, 91405 Orsay Cedex (France); Gregoire, Gilles [CNRS, Université Paris 13, Sorbonne Paris Cité, Laboratoire de Physique des Lasers, UMR 7538, 93430 Villetaneuse (France); Soorkia, Satchin [CNRS, Université Paris Sud, Institut des Sciences Moléculaires d' Orsay (ISMO) UMR 8624, 91405 Orsay Cedex (France)
2014-12-09
Up to ten years ago, very little was known about the excited states of protonated amino acids isolated in the gas phase. From the experimental point of view, the study was hampered by the lack of ease of production of such species in sufficient density to apply photon-based techniques. With the development and widespread use of electrospray ionization sources coupled with modified or homebuilt mass spectrometers, there has been significant research into the spectroscopy of biomimetic and biologically relevant molecules. Besides, these species are floppy such that an efficient cooling is required to record clear spectroscopy. Warm protonated species display congested spectra. To extract precise spectroscopic information and avoid spectral congestion, the species need to be cooled down to less than 50 K. We present our latest results on the electronic spectroscopy of protonated phenylalanine and tyrosine on a large spectral domain (225-290 nm). These species are studied in a new simplified apparatus combining an electrospray ionization source, a cryogenically cooled quadrupole ion trap (∼10 K) and time-of-flight mass spectrometry. The role of proton transfer from the NH{sub 3}{sup +} moiety to the p-ring or to CO of the carboxylic acid group is evidenced by UV photofragment spectroscopy. This first step controls the fragmentation pathways, which strongly depend on the nature of the electronic excited states, i.e. ππ*, ππ*{sub CO} and πσ{sub NH3}.
9. Cold ion UV photofragmentation spectroscopy and dynamics (Invited)
Science.gov (United States)
Feraud, Geraldine; Broquier, Michel; Dedonder, Claude; Jouvet, Christophe; Gregoire, Gilles; Soorkia, Satchin
2014-12-01
Up to ten years ago, very little was known about the excited states of protonated amino acids isolated in the gas phase. From the experimental point of view, the study was hampered by the lack of ease of production of such species in sufficient density to apply photon-based techniques. With the development and widespread use of electrospray ionization sources coupled with modified or homebuilt mass spectrometers, there has been significant research into the spectroscopy of biomimetic and biologically relevant molecules. Besides, these species are floppy such that an efficient cooling is required to record clear spectroscopy. Warm protonated species display congested spectra. To extract precise spectroscopic information and avoid spectral congestion, the species need to be cooled down to less than 50 K. We present our latest results on the electronic spectroscopy of protonated phenylalanine and tyrosine on a large spectral domain (225-290 nm). These species are studied in a new simplified apparatus combining an electrospray ionization source, a cryogenically cooled quadrupole ion trap (˜10 K) and time-of-flight mass spectrometry. The role of proton transfer from the NH3+ moiety to the p-ring or to CO of the carboxylic acid group is evidenced by UV photofragment spectroscopy. This first step controls the fragmentation pathways, which strongly depend on the nature of the electronic excited states, i.e. ππ*, ππ*CO and πσNH 3.
10. Noxious cold ion channel TRPA1 is activated by pungent compounds and bradykinin.
Science.gov (United States)
Bandell, Michael; Story, Gina M; Hwang, Sun Wook; Viswanath, Veena; Eid, Samer R; Petrus, Matt J; Earley, Taryn J; Patapoutian, Ardem
2004-03-25
Six members of the mammalian transient receptor potential (TRP) ion channels respond to varied temperature thresholds. The natural compounds capsaicin and menthol activate noxious heat-sensitive TRPV1 and cold-sensitive TRPM8, respectively. The burning and cooling perception of capsaicin and menthol demonstrate that these ion channels mediate thermosensation. We show that, in addition to noxious cold, pungent natural compounds present in cinnamon oil, wintergreen oil, clove oil, mustard oil, and ginger all activate TRPA1 (ANKTM1). Bradykinin, an inflammatory peptide acting through its G protein-coupled receptor, also activates TRPA1. We further show that phospholipase C is an important signaling component for TRPA1 activation. Cinnamaldehyde, the most specific TRPA1 activator, excites a subset of sensory neurons highly enriched in cold-sensitive neurons and elicits nociceptive behavior in mice. Collectively, these data demonstrate that TRPA1 activation elicits a painful sensation and provide a potential molecular model for why noxious cold can paradoxically be perceived as burning pain.
11. Stimulated Raman Adiabatic Passage for Improved Performance of a Cold Atom Electron and Ion Source
CERN Document Server
Sparkes, B M; Taylor, R J; Spiers, R W; McCulloch, A J; Scholten, R E
2016-01-01
We experimentally implement high-efficiency coherent excitation to a Rydberg state using stimulated Raman adiabatic passage in a cold atom electron and ion source, leading to a peak efficiency of 85%, a 1.7 times improvement in excitation probability relative to incoherent pulsed-laser excitation. Using streak measurements and pulsed electric field ionization of the Rydberg atoms we demonstrate electron bunches with duration of 250 ps. High-efficiency excitation will increase source brightness, crucial for ultrafast electron diffraction experiments, while using coherent excitation to high-lying Rydberg states could allow for the reduction of internal bunch heating and the creation of a high-speed single ion source.
12. Vlasov simulation in multiple spatial dimensions
CERN Document Server
Rose, Harvey A
2011-01-01
A long-standing challenge encountered in modeling plasma dynamics is achieving practical Vlasov equation simulation in multiple spatial dimensions over large length and time scales. While direct multi-dimension Vlasov simulation methods using adaptive mesh methods [J. W. Banks et al., Physics of Plasmas 18, no. 5 (2011): 052102; B. I. Cohen et al., November 10, 2010, http://meetings.aps.org/link/BAPS.2010.DPP.NP9.142] have recently shown promising results, in this paper we present an alternative, the Vlasov Multi Dimensional (VMD) model, that is specifically designed to take advantage of solution properties in regimes when plasma waves are confined to a narrow cone, as may be the case for stimulated Raman scatter in large optic f# laser beams. Perpendicular grid spacing large compared to a Debye length is then possible without instability, enabling an order 10 decrease in required computational resources compared to standard particle in cell (PIC) methods in 2D, with another reduction of that order in 3D. Fur...
13. Commissioning of the DESIREE storage rings - a new facility for cold ion-ion collisions
Science.gov (United States)
Gatchell, M.; Schmidt, H. T.; Thomas, R. D.; Rosén, S.; Reinhed, P.; Löfgren, P.; Brännholm, L.; Blom, M.; Björkhage, M.; Bäckström, E.; Alexander, J. D.; Leontein, S.; Hanstorp, D.; Zettergren, H.; Liljeby, L.; Källberg, A.; Simonsson, A.; Hellberg, F.; Mannervik, S.; Larsson, M.; Geppert, W. D.; Rensfelt, K. G.; Danared, H.; Paál, A.; Masuda, M.; Halldén, P.; Andler, G.; Stockett, M. H.; Chen, T.; Källersjö, G.; Weimer, J.; Hansen, K.; Hartman, H.; Cederquist, H.
2014-04-01
We report on the ongoing commissioning of the Double ElectroStatic Ion Ring ExpEriment, DESIREE, at Stockholm University. Beams of atomic carbon anions (C-) and smaller carbon anion molecules (C-2, C-3, C-4 etc.) have been produced in a sputter ion source, accelerated to 10 keV or 20 keV, and stored successfully in the two electrostatic rings. The rings are enclosed in a common vacuum chamber cooled to below 13 Kelvin. The DESIREE facility allows for studies of internally relaxed single isolated atomic, molecular and cluster ions and for collision experiments between cat- and anions down to very low center-of-mass collision energies (meV scale). The total thermal load of the vacuum chamber at this temperature is measured to be 32 W. The decay rates of stored ion beams have two components: a non-exponential component caused by the space charge of the beam itself which dominates at early times and an exponential term from the neutralization of the beam in collisions with residual gas at later times. The residual gas limited storage lifetime of carbon anions in the symmetric ring is over seven minutes while the 1/e lifetime in the asymmetric ring is measured to be about 30 seconds. Although we aim to improve the storage in the second ring, the number of stored ions are now sufficient for many merged beams experiments with positive and negative ions requiring milliseconds to seconds ion storage.
14. Mechanosensitive ion channel MscL controls ionic fluxes during cold and heat stress in Synechocystis.
Science.gov (United States)
Bachin, Dmitry; Nazarenko, Lyudmila V; Mironov, Kirill S; Pisareva, Tatiana; Allakhverdiev, Suleyman I; Los, Dmitry A
2015-06-01
Calcium plays an essential role in a variety of stress responses of eukaryotic cells; however, its function in prokaryotes is obscure. Bacterial ion channels that transport Ca(2+) are barely known. We investigated temperature-induced changes in intracellular concentration of Ca(2+), Na(+) and K(+) in the cyanobacterium Synechocystis sp. strain PCC 6803 and its mutant that is defective in mechanosensitive ion channel MscL. Concentration of cations rapidly and transiently increased in wild-type cells in response to cold and heat treatments. These changes in ionic concentrations correlated with the changes in cytoplasmic volume that transiently decreased in response to temperature treatments. However, no increase in ionic concentrations was observed in the MscL-mutant cells. It implies that MscL functions as a non-specific ion channel, and it participates in regulation of cell volume under temperature-stress conditions.
15. Energy and charge dependence of the rate of electron-ion recombination in cold magnetized plasmas
Energy Technology Data Exchange (ETDEWEB)
Gao, H.; Schuch, R.; Zong, W.; Justiniano, E.; DeWitt, D.R.; Lebius, H.; Spies, W. [Stockholm Univ., Atomic Physics Dept., Stockholm (Sweden)
1997-07-28
We have measured electron-ion recombination rates for bare ions of D{sup +}, He{sup 2+}, N{sup 7+}, Ne{sup 10+} and Si{sup 14+} in a storage ring. For the multi-charged ions an unexpected energy dependence was found, showing a strong increase of the measured rates over the calculated radiative recombination rate for electron beam detuning energies below the electron beam transverse temperature. The measured enhanced rates increase approximately as Z{sup 2.8} with the charge state Z. A comparison of these rates with theoretical predictions for collisional-radiative recombination in the cold magnetized electron plasma, in particular three-body recombination including radiative de-excitation of electrons in Rydberg levels, is made. (author).
16. Rotationally Cold OH^{-} Ions in the Cryogenic Electrostatic Ion-Beam Storage Ring DESIREE.
Science.gov (United States)
Schmidt, H T; Eklund, G; Chartkunchand, K C; Anderson, E K; Kamińska, M; de Ruette, N; Thomas, R D; Kristiansson, M K; Gatchell, M; Reinhed, P; Rosén, S; Simonsson, A; Källberg, A; Löfgren, P; Mannervik, S; Zettergren, H; Cederquist, H
2017-08-18
We apply near-threshold laser photodetachment to characterize the rotational quantum level distribution of OH^{-} ions stored in the cryogenic ion-beam storage ring DESIREE at Stockholm University. We find that the stored ions relax to a rotational temperature of 13.4±0.2 K with 94.9±0.3% of the ions in the rotational ground state. This is consistent with the storage ring temperature of 13.5±0.5 K as measured with eight silicon diodes but in contrast to all earlier studies in cryogenic traps and rings where the rotational temperatures were always much higher than those of the storage devices at their lowest temperatures. Furthermore, we actively modify the rotational distribution through selective photodetachment to produce an OH^{-} beam where 99.1±0.1% of approximately one million stored ions are in the J=0 rotational ground state. We measure the intrinsic lifetime of the J=1 rotational level to be 145±28 s.
17. Rotationally Cold OH- Ions in the Cryogenic Electrostatic Ion-Beam Storage Ring DESIREE
Science.gov (United States)
Schmidt, H. T.; Eklund, G.; Chartkunchand, K. C.; Anderson, E. K.; Kamińska, M.; de Ruette, N.; Thomas, R. D.; Kristiansson, M. K.; Gatchell, M.; Reinhed, P.; Rosén, S.; Simonsson, A.; Källberg, A.; Löfgren, P.; Mannervik, S.; Zettergren, H.; Cederquist, H.
2017-08-01
We apply near-threshold laser photodetachment to characterize the rotational quantum level distribution of OH- ions stored in the cryogenic ion-beam storage ring DESIREE at Stockholm University. We find that the stored ions relax to a rotational temperature of 13.4 ±0.2 K with 94.9 ±0.3 % of the ions in the rotational ground state. This is consistent with the storage ring temperature of 13.5 ±0.5 K as measured with eight silicon diodes but in contrast to all earlier studies in cryogenic traps and rings where the rotational temperatures were always much higher than those of the storage devices at their lowest temperatures. Furthermore, we actively modify the rotational distribution through selective photodetachment to produce an OH- beam where 99.1 ±0.1 % of approximately one million stored ions are in the J =0 rotational ground state. We measure the intrinsic lifetime of the J =1 rotational level to be 145 ±28 s .
18. Preparation of cold Mg{sup +}ion clouds for sympathetic cooling of highly charged ions at SPECTRAP
Energy Technology Data Exchange (ETDEWEB)
2012-02-15
The bound electrons in hydrogen-like or lithium-like heavy ions experience extremely strong electric and magnetic fields in the surrounding of the nucleus. Laser spectroscopy of the ground-state hyperfine splitting in the lead region provides a sensitive tool to test strong-field quantum electro dynamics (QED), especially in the magnetic sector. Previous measurements on hydrogen-like systems performed in an electron-beam ion trap (EBIT) or at the experimental storage ring (ESR) were experimentally limited in accuracy due to statistics, the large Doppler broadening and the ion energy. The full potential of the QED test can only be exploited if measurements for hydrogen- and lithium-like ions are performed with accuracy improved by 2-3 orders of magnitude. Therefore, the new Penning trap setup SPECTRAP - dedicated for laser spectroscopy on trapped and cooled highly charged ions - is currently commissioned at GSI Darmstadt. Heavy highly charged ions will be delivered to this trap by the HITRAP facility in the future. SPECTRAP is a cylindrical Penning trap with axial access for external ion injection and radial optical access mounted inside a cold-bore superconducting Helmholtz-type split-coil magnet. To reach the targeted accuracy in laser spectroscopy, an efficient and fast cooling process for the highly charged ions must be employed. This can be realized by sympathetic cooling with a cloud of laser-cooled light ions. Within this thesis work, a laser system and an ion source for the production of such a {sup 24}Mg{sup +} ion cloud was developed and commissioned at SPECTRAP. An all-solid-state laser system for the generation of 279.6 nm light was designed and built. It consists of a fiber laser at 1118.5 nm followed by frequency quadrupling using two successive second-harmonic generation stages with actively stabilized ring resonators and nonlinear crystals. The laser system can deliver more than 15 mW of UV laser power under optimal conditions and requires little
19. Ionization and fragmentation of cold clusters of PAH molecules - collisions with keV ions
Science.gov (United States)
Holm, A. I. S.; Zettergren, H.; Gatchell, M.; Johansson, H. A. B.; Seitz, F.; Schmidt, H. T.; Rousseau, P.; Ławicki, A.; Capron, M.; Domaracka, A.; Lattouf, E.; Maclot, S.; Maisonny, R.; Chesnel, J.-Y.; Manil, B.; Adoui, L.; Huber, B. A.; Cederquist, H.
2012-11-01
We discuss the ionization and fragmentation of isolated monomers and cold clusters of polycyclic aromatic hydrocarbon (PAH) molecules in collisions with keV ions in low or high charge states. With low charge state projectile ions, PAH cluster or monomer targets are thermally excited through electronic stopping processes directly in close peripheral or penetrating collisions while only single or few electrons are removed. With high charge state projectiles, electrons are very effectively removed from both the cluster and the monomer target already at very large distances with very little direct target heating. Singly charged and internally very hot PAH monomers are dominant fragmentation products following collisions between Xe20+ ions and PAH clusters. We suggest that this due to an unusually strong dominance of multiple-ionization over single ionization for PAH clusters interacting with highly charged ions. Here, charge and excitation energy is very rapidly redistributed within the clusters before they Coulomb explode and we suggest that these Coulomb explosions induce strong internal heating in the individual PAH molecules. We thus conclude that PAH cluster fragmentation always dominates strongly for all ionization processes regardless if these are due to interactions with ions in high or low charge states. These findings are discussed in view of simple models for cluster evaporation or single and multiple ionizations of PAH clusters.
20. Investigation of cold cathodes of plasma sources generating of hydrogen ion beams
CERN Document Server
Veresov, L P; Dzkuya, M I; Zhukov, Y N; Kuznetsov, G V; Tsekvava, I A
2001-01-01
Designs of a hollow cellular cathode (HCC) and of an inverse cylindrical multichamber magnetronic cathode (ICMMC), used as cold cathodes in duoplasmatron for hydrogen ion beam generation, are described. Their service characteristics are compared. It is ascertained that emission ability of both HCC and ICMMC is approximately the same. However, duoplasmatron with ICMMC features a three times higher gas effectiveness compared with HCC. Service life of duoplasmatron with both types of cathodes amounts to several thousand hours. On the basis of test results the choice is made in favour of ICMMC
1. Wave dispersion in the hybrid-Vlasov model: verification of Vlasiator
CERN Document Server
Kempf, Yann; von Alfthan, Sebastian; Vaivads, Andris; Palmroth, Minna; Koskinen, Hannu E J
2013-01-01
Vlasiator is a new hybrid-Vlasov plasma simulation code aimed at simulating the entire magnetosphere of the Earth. The code treats ions (protons) kinetically through Vlasov's equation in the six-dimensional phase space while electrons are a massless charge-neutralizing fluid [M. Palmroth et al., Journal of Atmospheric and Solar-Terrestrial Physics 99, 41 (2013); A. Sandroos et al., Parallel Computing 39, 306 (2013)]. For first global simulations of the magnetosphere, it is critical to verify and validate the model by established methods. Here, as part of the verification of Vlasiator, we characterize the low-\\beta\\ plasma wave modes described by this model and compare with the solution computed by the Waves in Homogeneous, Anisotropic Multicomponent Plasmas (WHAMP) code [K. R\\"onnmark, Kiruna Geophysical Institute Reports 179 (1982)], using dispersion curves and surfaces produced with both programs. The match between the two fundamentally different approaches is excellent in the low-frequency, long wavelength...
2. Comparison of free-streaming ELM formulae to a Vlasov simulation
Energy Technology Data Exchange (ETDEWEB)
Moulton, D., E-mail: [email protected] [CEA, IRFM, F-13108 Saint-Paul Lez Durance (France); Fundamenski, W. [Imperial College of Science, Technology and Medicine, London (United Kingdom); Manfredi, G. [Institut de Physique et Chimie des Matériaux, CNRS and Université de Strasbourg, BP 43, F-67034 Strasbourg (France); Hirstoaga, S. [INRIA Nancy Grand-Est and Institut de Recherche en Mathématiques Avancées, 7 rue René Descartes, F-67084 Strasbourg (France); Tskhakaya, D. [Association EURATOM-ÖAW, University of Innsbruck, A-6020 Innsbruck (Austria)
2013-07-15
The main drawbacks of the original free-streaming equations for edge localised mode transport in the scrape-off layer [W. Fundamenski, R.A. Pitts, Plasma Phys. Control Fusion 48 (2006) 109] are that the plasma potential is not accounted for and that only solutions for ion quantities are considered. In this work, the equations are modified and augmented in order to address these two issues. The new equations are benchmarked against (and justified by) a numerical simulation which solves the Vlasov equation in 1d1v. When the source function due to an edge localised mode is instantaneous, the modified free-streaming ‘impulse response’ equations agree closely with the Vlasov simulation results. When the source has a finite duration in time, the agreement worsens. However, in all cases the match is encouragingly good, thus justifying the applicability of the free-streaming approach.
3. Canonical derivation of the Vlasov-Coulomb noncanonical Poisson structure
Energy Technology Data Exchange (ETDEWEB)
Kaufman, A.N.; Dewar, R.L.
1983-09-01
Starting from a Lagrangian formulation of the Vlasov-Coulomb system, canonical methods are used to define a Poisson structure for this system. Successive changes of representation then lead systematically to the noncanonical Lie-Poisson structure for functionals of the Vlasov distribution.
4. Preparation of Schr\\"odinger cat states with cold ions in a cavity beyond the Lamb-Dicke limit
CERN Document Server
Freitas, Dagoberto S
2010-01-01
We investigate the dynamics of a cold trapped ion coupled to the quantized field inside a high-finesse cavity. We have used an approach for preparing the SC states of motion of ion. This approach, based on unitary transformating the Hamiltonian, allows its exact diagonalization without performing the Lamb-Dicke aproximation. We show that is possible to generate a SC states having rather simple initial state preparation, e.g., the vacuum sate for both cavity field and the ion motion.
5. Measurements of the ion velocity distribution in an ultracold neutral plasma derived from a cold, dense Rydberg gas
OpenAIRE
S. D. Bergeson; Lyon, M
2016-01-01
We report measurements of the ion velocity distribution in an ultracold neutral plasma derived from a dense, cold Rydberg gas in a MOT. The Rydberg atoms are excited using a resonant two-step excitation pathway with lasers of 4 ns duration. The plasma forms spontaneously and rapidly. The rms width of the ion velocity distribution is determined by measuring laser-induced fluorescence (LIF) of the ions. The measured excitation efficiency is compared with a Monte-Carlo wavefunction calculation, ...
6. Stimulated Raman adiabatic passage for improved performance of a cold-atom electron and ion source
Science.gov (United States)
Sparkes, B. M.; Murphy, D.; Taylor, R. J.; Speirs, R. W.; McCulloch, A. J.; Scholten, R. E.
2016-08-01
We implement high-efficiency coherent excitation to a Rydberg state using stimulated Raman adiabatic passage in a cold-atom electron and ion source. We achieve an efficiency of 60% averaged over the laser excitation volume with a peak efficiency of 82%, a 1.6 times improvement relative to incoherent pulsed-laser excitation. Using pulsed electric field ionization of the Rydberg atoms we create electron bunches with durations of 250 ps. High-efficiency excitation will increase source brightness, crucial for ultrafast electron diffraction experiments, and coherent excitation to high-lying Rydberg states could allow for the reduction of internal bunch heating and the creation of a high-speed single-ion source.
7. Diamond-Like Carbon Film Deposition Using DC Ion Source with Cold Hollow Cathode
Directory of Open Access Journals (Sweden)
E. F. Shevchenko
2014-01-01
Full Text Available Carbon diamond-like thin films on a silicon substrate were deposited by direct reactive ion beam method with an ion source based on Penning direct-current discharge system with cold hollow cathode. Deposition was performed under various conditions. The pressure (12–200 mPa and the plasma-forming gas composition consisting of different organic compounds and hydrogen (C3H8, CH4, Si(CH32Cl2, H2, the voltage of accelerating gap in the range 0.5–5 kV, and the substrate temperature in the range 20–850°C were varied. Synthesized films were researched using nanoindentation, Raman, and FTIR spectroscopy methods. Analysis of the experimental results was made in accordance with a developed model describing processes of growth of the amorphous and crystalline carbon materials.
8. Spin-orbit interactions and quantum spin dynamics in cold ion-atom collisions
CERN Document Server
Tscherbul, Timur V; Buchachenko, Alexei A
2015-01-01
We present accurate ab initio and quantum scattering calculations on a prototypical hybrid ion-atom system Yb$^+$-Rb, recently suggested as a promising candidate for the experimental study of open quantum systems, quantum information processing, and quantum simulation. We identify the second-oder spin-orbit (SO) interaction as the dominant source of hyperfine relaxation and decoherence in cold Yb$^+$-Rb collisions. Our results are in good agreement with recent experimental observations [L. Ratschbacher et al., Phys. Rev. Lett. 110, 160402 (2013)] of hyperfine relaxation rates of trapped Yb$^+$ immersed in an ultracold Rb gas. The calculated rates are 4 times smaller than predicted by the Langevin capture theory and display a weak $T^{-0.3}$ temperature dependence, indicating significant deviations from statistical behavior. Our analysis underscores the deleterious nature of the SO interaction and implies that light ion-atom combinations such as Yb$^+$-Li should be used to minimize hyperfine relaxation and dec...
9. UV and IR spectroscopy of cold 1,2-dimethoxybenzene complexes with alkali metal ions.
Science.gov (United States)
Inokuchi, Yoshiya; Boyarkin, Oleg V; Ebata, Takayuki; Rizzo, Thomas R
2012-04-01
We report UV photodissociation (UVPD) and IR-UV double-resonance spectra of 1,2-dimethoxybenzene (DMB) complexes with alkali metal ions, M(+)·DMB (M = Li, Na, K, Rb, and Cs), in a cold, 22-pole ion trap. The UVPD spectrum of the Li(+) complex shows a strong origin band. For the K(+)·DMB, Rb(+)·DMB, and Cs(+)·DMB complexes, the origin band is very weak and low-frequency progressions are much more extensive than that of the Li(+) ion. In the case of the Na(+)·DMB complex, spectral features are similar to those of the K(+), Rb(+), and Cs(+) complexes, but vibronic bands are not resolved. Geometry optimization with density functional theory indicates that the metal ions are bonded to the oxygen atoms in all the M(+)·DMB complexes. For the Li(+) complex in the S(0) state, the Li(+) ion is located in the same plane as the benzene ring, while the Na(+), K(+), Rb(+), and Cs(+) ions are located off the plane. In the S(1) state, the Li(+) complex has a structure similar to that in the S(0) state, providing the strong origin band in the UV spectrum. In contrast, the other complexes show a large structural change in the out-of-plane direction upon S(1)-S(0) excitation, which results in the extensive low-frequency progressions in the UVPD spectra. For the Na(+)·DMB complex, fast charge transfer occurs from Na(+) to DMB after the UV excitation, making the bandwidth of the UVPD spectrum much broader than that of the other complexes and producing the photofragment DMB(+) ion.
10. Geometry of Vlasov kinetic moments: A bosonic Fock space for the symmetric Schouten bracket
Energy Technology Data Exchange (ETDEWEB)
Gibbons, John [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); Holm, Darryl D. [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); Computer and Computational Science Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Tronci, Cesare [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom); TERA Foundation for Oncological Hadrontherapy, 11 V. Puccini, Novara 28100 (Italy)], E-mail: [email protected]
2008-06-02
The dynamics of Vlasov kinetic moments is shown to be Lie-Poisson on the dual Lie algebra of symmetric contravariant tensor fields. The corresponding Lie bracket is identified with the symmetric Schouten bracket and the moment Lie algebra is related with a bundle of bosonic Fock spaces, where creation and annihilation operators are used to construct the cold plasma closure. Kinetic moments are also shown to define a momentum map, which is infinitesimally equivariant. This momentum map is the dual of a Lie algebra homomorphism, defined through the Schouten bracket. Finally the moment Lie-Poisson bracket is extended to anisotropic interactions.
11. Numerical simulation of Vlasov equation with parallel tools; Simulations numeriques de l'equation de Vlasov a l'aide d'outils paralleles
Energy Technology Data Exchange (ETDEWEB)
Peyroux, J
2005-11-15
This project aims to make even more powerful the resolution of Vlasov codes through the various parallelization tools (MPI, OpenMP...). A simplified test case served as a base for constructing the parallel codes for obtaining a data-processing skeleton which, thereafter, could be re-used for increasingly complex models (more than four variables of phase space). This will thus make it possible to treat more realistic situations linked, for example, to the injection of ultra short and ultra intense impulses in inertial fusion plasmas, or the study of the instability of trapped ions now taken as being responsible for the generation of turbulence in tokamak plasmas. (author)
12. Equations of motion of test particles for solving the spin-dependent Boltzmann-Vlasov equation
CERN Document Server
Xia, Yin; Li, Bao-An; Shen, Wen-Qing
2016-01-01
A consistent derivation of the equations of motion (EOMs) of test particles for solving the spin-dependent Boltzmann-Vlasov equation is presented. Though the obtained EOMs are general, they are particularly useful in simulating nucleon spinor transport in heavy-ion collisions at intermediate energies. It is shown that the nucleon transverse flow in heavy-ion collisions especially those involving polarized projectile and/or target nuclei depends strongly on the spin-orbit coupling. Future comparisons of model simulations with experimental data will help constrain the poorly known in-medium nucleon spin-orbit coupling relevant for understanding properties of rare isotopes and their astrophysical impacts.
13. Transient Growth in a Magnetized Vlasov Plasma
Science.gov (United States)
Ratushnaya, Valeria; Samtaney, Ravi
2015-11-01
Collisionless plasmas, such as those encountered in tokamaks, exhibit a rich variety of instabilities. The physical origin, triggering mechanisms and fundamental understanding of many tokamak instabilities, however, is still an open problem. Aiming to gain a better insight into this question, we investigate the stability properties of a collisionless Vlasov plasma for the case of: (a) stationary homogeneous magnetic field, and (b) weakly non-stationary and non-homogeneous magnetic field. We narrow the scope of our investigation to the case of a Maxwellian plasma and examine its evolution with an electrostatic approximation. We show that the linearized Vlasov operator is non-normal, which leads to an algebraic growth of perturbations in a magnetized plasma followed by exponential decay, i.e., classical Landau damping behaviour. This is a so-called transient growth phenomenon, developed in the framework of non-modal stability theory in the context of hydrodynamics. In a homogeneous magnetic field the typical time scales of the transient growth are of the order of several plasma periods. The first-order distribution function and the corresponding electric field are calculated and the dependence on the initial conditions is studied. Supported by baseline research funds at KAUST.
14. Osmotic versus adrenergic control of ion transport by ionocytes of Fundulus heteroclitus in the cold
DEFF Research Database (Denmark)
Tait, Janet C; Mercer, Evan W; Gerber, Lucie;
2017-01-01
In eurythermic vertebrates, acclimation to the cold may produce changes in physiological control systems. We hypothesize that relatively direct osmosensitive control will operate better than adrenergic receptor mediated control of ion transport in cold vs. warm conditions. Fish were acclimated...... to full strength seawater (SW) at 21°C and 5°C for four weeks, gill samples and blood were taken and opercular epithelia mounted in Ussing style chambers. Short-circuit current Isc at 21°C and 5°C (measured at acclimation temperature), was significantly inhibited by the α2-adrenergic agonist clonidine...... inhibition of Isc, was higher in warm acclimated (-95%), compared to cold acclimated fish (-75%), while hypertonic stimulations were the same, indicating equal responsiveness to hyperosmotic stimuli. Plasma osmolality was significantly elevated in cold acclimated fish and, by TEM, gill ionocytes from cold...
15. Nonlinear evolution of parallel propagating Alfven waves: Vlasov - MHD simulation
CERN Document Server
Nariyuki, Y; Kumashiro, T; Hada, T
2009-01-01
Nonlinear evolution of circularly polarized Alfv\\'en waves are discussed by using the recently developed Vlasov-MHD code, which is a generalized Landau-fluid model. The numerical results indicate that as far as the nonlinearity in the system is not so large, the Vlasov-MHD model can validly solve time evolution of the Alfv\\'enic turbulence both in the linear and nonlinear stages. The present Vlasov-MHD model is proper to discuss the solar coronal heating and solar wind acceleration by Alfve\\'n waves propagating from the photosphere.
16. Rotation of cold molecular ions inside a Bose-Einstein condensate
CERN Document Server
Midya, Bikashkali; Schmidt, Richard; Lemeshko, Mikhail
2016-01-01
We use recently developed angulon theory [Phys. Rev. Lett. 114, 203001 (2015)] to study the rotational spectrum of a cyanide molecular anion immersed into Bose-Einstein condensates of rubidium and strontium. Based on $\\textit {ab initio}$ potential energy surfaces, we provide a detailed study of the rotational Lamb shift and many-body-induced fine structure which arise due to dressing of molecular rotation by a field of phonon excitations. We demonstrate that the magnitude of these effects is large enough in order to be observed in modern experiments on cold molecular ions. Furthermore, we introduce a novel method to construct pseudopotentials starting from the $\\textit {ab initio}$ potential energy surfaces, which provides a means to obtain effective coupling constants for low-energy polaron models.
17. Suppression of Emittance Growth Using a Shaped Cold Atom Electron and Ion Source
Science.gov (United States)
Thompson, D. J.; Murphy, D.; Speirs, R. W.; van Bijnen, R. M. W.; McCulloch, A. J.; Scholten, R. E.; Sparkes, B. M.
2016-11-01
We demonstrate precise control of charged particle bunch shape with a cold atom electron and ion source to create bunches with linear and, therefore, reversible Coulomb expansion. Using ultracold charged particles enables detailed observation of space-charge effects without loss of information from thermal diffusion, unambiguously demonstrating that shaping in three dimensions can result in a marked reduction of Coulomb-driven emittance growth. We show that the emittance growth suppression is accompanied by an increase in bunch focusability and brightness, improvements necessary for the development of sources capable of coherent single-shot ultrafast electron diffraction of noncrystalline objects, with applications ranging from femtosecond chemistry to materials science and rational drug design.
18. Bifurcation of BGK waves in a plasma of cold ions and electrons
Energy Technology Data Exchange (ETDEWEB)
Hannibal, L.; Rebhan, E.; Kielhorn, C. (Duesseldorf Univ. (Germany). Inst. fuer Theoretische Physik)
1994-08-01
For the simple model of cold electrons streaming against cold ions the complete set of nonlinear stationary waves is expressed in terms of elliptic functions. The conditions for their dynamical connection to a uniform neutral plasma state are taken into account, and the conditions for the neglect of the magnetic field are analysed. The range of existence of stationary waves is found to be confined to the stable regime of the two-stream instability, but covers only part of it. All nonlinear BGK waves that are found within the limits of the model can be shown to bifurcate from the two-stream instability, some of them also exhibiting secondary and further bifurcations. As an exceptional case, all bifurcations can be treated exactly. Close to the linear regime, all nonlinear modes turn out to be unstable. The corresponding instability is caused by a wave decay that transports energy from low to high wavenumbers of the Fourier modes constituting the wave. From the two-stream solutions four-stream solutions with exactly vanishing magnetic field are derived. (author).
19. Nonlinear dynamics of cold magnetized non-relativistic plasma in the presence of electron-ion collisions
Energy Technology Data Exchange (ETDEWEB)
Sahu, Biswajit, E-mail: [email protected] [Department of Mathematics, West Bengal State University, Barasat, Kolkata 700126 (India); Sinha, Anjana, E-mail: [email protected] [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India); Roychoudhury, Rajkumar, E-mail: [email protected] [Department of Mathematics, Visva-Bharati, Santiniketan - 731 204, India and Advanced Centre for Nonlinear and Complex Phenomena, 1175 Survey Park, Kolkata 700 075 (India)
2015-09-15
A numerical study is presented of the nonlinear dynamics of a magnetized, cold, non-relativistic plasma, in the presence of electron-ion collisions. The ions are considered to be immobile while the electrons move with non-relativistic velocities. The primary interest is to study the effects of the collision parameter, external magnetic field strength, and the initial electromagnetic polarization on the evolution of the plasma system.
20. One-dimensional Vlasov-Maxwell equilibria
Science.gov (United States)
Greene, John M.
1993-06-01
The purpose of this paper is to show that the Vlasov equilibrium of a plasma of charged particles in an electromagnetic field is closely related to a fluid equilibrium, where only a few moments of the velocity distribution of the plasma are considered. In this fluid equilibrium the electric field should be calculated from Ohm's law, rather than the Poisson equation. In practice, only one-dimensional equilibria are treated, because the symmetry makes this case tractable. The emphasis here is on gaining a better understanding of the subject, but an alternate way of doing the calculations is suggested. It is shown that particle distributions can be found that are consistent with any reasonable electromagnetic field profile.
1. Entropy production in coarse grained Vlasov equations
Energy Technology Data Exchange (ETDEWEB)
Morawetz, K. [Grand Accelerateur National d' Ions Lourds (GANIL), LPC-ISMRA, 14 - Caen (France); Walke, R. [Rostock Univ., Fachbereich Physick (Germany)
2000-07-01
The Vlasov equation is analyzed for coarse grained distributions. This coarse graining resembles a finite width of test-particles as used in numerical implementations. It is shown that this coarse grained distribution obeys a kinetic equation similar to the Vlasov equation, but with additional terms. These terms give rise to entropy production indicating dissipative features. The reason is a nonlinear mode coupling due to the finite width of the test-particles. The interchange of coarse graining and dynamical evolution is discussed with the help of an exactly solvable model and practical consequences are worked out. By calculating analytically the stationary solution we can show that a sum of modified Boltzmann-like distributions is approached dependent on the initial distribution. This behavior is independent of degeneracy and only controlled by the width of test-particles. The condition for approaching a stationary solution is derived in that the coarse graining energy given by momentum coarse graining should be smaller than a quarter of the kinetic energy. Observable consequences of this coarse graining are: (i) In the thermodynamics the coarse graining leads to spatial correlations in observables. (ii) Too large radii of nucleus in self-consistent treatments are observed and an explicit correction term appears in the Thomas Fermi equation. (iii) The momentum coarse graining translates into a structure term in the response function and resembles to a certain extent vertex correction correlations or internal structure effects. (iv) The coarse graining which is numerically unavoidable leads to a modified centroid energy and higher damping width of collective modes. The numerical codes should be revised in that a refolding is proposed. (author)
2. Diffusive Transport Particle Simulations of Cold and Hot Ions Under Northward Interplanetary Magnetic Field
Science.gov (United States)
Mata, W.; Wang, C.; Lemon, C. L.; Lyons, L. R.
2013-12-01
The main difference seen in the plasma sheet between northward interplanetary magnetic field (NIMF) and southward interplanetary magnetic field (SIMF) intervals is that the plasma sheet is colder and denser during NIMF [e.g., Terasawa et al., 1997]. The basic processes responsible for these changes in the plasma sheet during NIMF and SIMF are not fully understood. The plasma sheet densities increase gradually following a northward turning of the IMF [Wing et al., 2005], and the density change is associated with a < ~1 keV cold population near the flanks. Observations also show a large variation in density across the tail with higher densities near the flanks than at midnight [e.g., Wing and Newell.,2002; Wang et al., 2006], which suggests that there are transport processes that allow the cold particles access to the midnight sector from the flanks. It has been proposed [e.g., Terasawa et al., 1997; Antonova, 2006] that diffusion may transport cold particles from the flanks deep into the plasma sheet. Diffusive particle transport results from fluctuations in the plasma sheet flow in the presence of a spatial gradient in the particle number. In this study we add electric and magnetic field perturbations to the background Tsyganenko 2001 (T01) magnetic field and Weimer 2000 electric potential with the superposition of different waves to determine whether diffusive transport can account for the gradual cooling and densification of the plasma sheet during NIMF. We follow the guiding center drift and full particle drift, where appropriate, of over 20,000 protons with arbitrary pitch angles and energies from 32 eV-30 keV in the simulation region from X = -10 to -50 and |Y| < 20 RE .We then obtain particle distributions by mapping the phase space densities to realistic source distributions based on THEMIS and Geotail observations and compute the resulting plasma moments. We investigate if diffusion can transport colder ions more efficiently than the hotter ions from the
3. Positron-acoustic shock waves associated with cold viscous positron fluid in superthermal electron-positron-ion plasmas
Energy Technology Data Exchange (ETDEWEB)
Uddin, M. J., E-mail: [email protected]; Alam, M. S.; Mamun, A. A. [Department of Physics, Jahangirnagar University, Savar, Dhaka 1342 (Bangladesh)
2015-06-15
A theoretical investigation is made on the positron-acoustic (PA) shock waves (SHWs) in an unmagnetized electron-positron-ion plasma containing immobile positive ions, cold mobile positrons, and hot positrons and electrons following the kappa (κ) distribution. The cold positron kinematic viscosity is taken into account, and the reductive perturbation method is used to derive the Burgers equation. It is found that the viscous force acting on cold mobile positron fluid is a source of dissipation and is responsible for the formation of the PA SHWs. It is also observed that the fundamental properties of the PA SHWs are significantly modified by the effects of different parameters associated with superthermal (κ distributed) hot positrons and electrons.
4. Vlasov-Fokker-Planck modeling of magnetized plasma
Energy Technology Data Exchange (ETDEWEB)
Thomas, Alexander [Univ. of Michigan, Ann Arbor, MI (United States)
2016-08-01
Understanding the magnetic fields that can develop in high-power-laser interactions with solid-density plasma is important because such fields significantly modify both the magnitude and direction of electron heat fluxes. The dynamics of such fields evidently have consequences for inertial fusion energy applications, as the coupling of the laser beams with the walls or pellet and the development of temperature inhomogeneities are critical to the uniformity of the implosion and potentially the success of, for example, the National Ignition Facility. To study these effects, we used the code Impacta, a two-dimensional, fully implicit, Vlasov-Fokker-Planck code with self-consistent magnetic fields and a hydrodynamic ion model, designed for nanosecond time-scale laser-plasma interactions. Heat-flux effects in Ohm’s law under non-local conditions was investigated; physics that is not well captured by standard numerical models but is nevertheless important in fusion-related scenarios. Under such conditions there are numerous interesting physical effects, such as collisional magnetic instabilities, amplification of magnetic fields, re-emergence of non-locality through magnetic convection, and reconnection of magnetic field lines and redistribution of thermal energy. In this project highlights included the first full scale kinetic simulations of a magnetized hohlraum [Joglekar 2016] and the discovery of a new magnetic reconnection mechanism [Joglekar 2014] as well as a completed PhD thesis and the production of a new code for Inertial Fusion research.
5. Convergence analysis of Strang splitting for Vlasov-type equations
CERN Document Server
Einkemmer, Lukas
2012-01-01
A rigorous convergence analysis of the Strang splitting algorithm for Vlasov-type equations in the setting of abstract evolution equations is provided. It is shown that under suitable assumptions the convergence is of second order in the time step h. As an example, it is verified that the Vlasov-Poisson equation in 1+1 dimensions fits into the framework of this analysis. Also, numerical experiments for the latter case are presented.
6. The Hamiltonian Structure of the Maxwell-Vlasov Equations.
Science.gov (United States)
1981-02-01
principle of Percival [1979). 4. By using an appropriate Darboux theorem, (see Marsden [1981], lecture 1), one can show that Of admits canonically...get the Vlasov-Poisson equation. It would also be of interest to realize both the Vlasov-Maxwell and MHD equations as limiting cases of a grand...de Vries equation, Springer Lecture Notes, #755, 1-15 and Inv. Math. 50, 219-248. J. Arms (1979]. Linearization stability of gravitational and gauge
7. Explicit Solutions of the One-dimensional Vlasov-Poisson System with Infinite Mass and Energy
CERN Document Server
Pankavich, Stephen
2010-01-01
A collisionless plasma is modeled by the Vlasov-Poisson system in one-dimension. A fixed background of positive charge, dependent only upon velocity, is assumed and the situation in which the mobile negative ions balance the positive charge as x tends to positive or negative infinity. Thus, the total positive charge and the total negative charge are infinite. In this paper, the charge density of the system is shown to be compactly supported. More importantly, both the electric field and the number density are determined explicitly for large values of x.
8. Charge breeding investigation in EBIS/T and collision study of ions with cold atoms for HITRAP
Energy Technology Data Exchange (ETDEWEB)
Sokolov, Alexey
2010-01-29
Highly charged ions (HCI) at low velocities or at rest are interesting systems for various atomic physics experiments. For investigations on HCI of heavy stable or radioactive nuclides the HITRAP (Highly charged Ion TRAP) decelerator facility has been set up at GSI to deliver cooled beams of HCI at an energy of 5 keV/q. The HCI are produced in a stripper foil at relativistic energies and are decelerated in several steps at ESR storage ring and HITRAP before they are delivered to experimental setups. One of the experiments is the investigation of multi-electron charge exchange in collisions of heavy HCI with cold atoms using novel MOTRIMS technique. Collision experiments on light ions from an ECR ion source colliding with cold atoms in a MOT have been performed and the results are described. An electron beam ion trap (EBIT) has been tested and optimized for commissioning of the HITRAP physics experiments. The process of charge breeding in the EBIT has been successfully studied with gaseous elements and with an alkaline element injected from an external ion source. (orig.)
9. Integer lattice dynamics for Vlasov-Poisson
Science.gov (United States)
Mocz, Philip; Succi, Sauro
2017-03-01
We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving-mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N6, where N is the resolution per linear phase-space dimension). However, we describe a new technique for achieving N4 scaling. The method offers promise for investigating the full 6D phase-space of collisionless systems of stars and dark matter.
10. Integer Lattice Dynamics for Vlasov-Poisson
CERN Document Server
Mocz, Philip
2016-01-01
We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte-Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N^6, ...
11. NEW INSIGHT INTO SHORT-WAVELENGTH SOLAR WIND FLUCTUATIONS FROM VLASOV THEORY
Energy Technology Data Exchange (ETDEWEB)
Sahraoui, F.; Belmont, G. [Laboratoire de Physique des Plasmas, CNRS-Ecole Polytechnique-UPMC, Observatoire de Saint-Maur, 4 avenue de Neptune, 94107 Saint-Maur-des-Fosses (France); Goldstein, M. L., E-mail: [email protected] [NASA Goddard Space Flight Center, Code 673, Greenbelt, MD 20771 (United States)
2012-04-01
The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations gave evidence of the dominance of kinetic Alfven waves (KAWs) at sub-ion scales with {omega} < {omega}{sub ci}, other studies suggest that the KAW mode cannot carry the turbulence cascade down to electron scales and that the whistler mode (i.e., {omega} > {omega}{sub ci}) is more relevant. Here, we study key properties of the short-wavelength plasma modes under limited, but realistic, SW conditions, typically {beta}{sub i} {approx}> {beta}{sub e} {approx} 1 and for high oblique angles of propagation 80 Degree-Sign {<=} {Theta}{sub kB} < 90 Degree-Sign as observed from the Cluster spacecraft data. The linear properties of the plasma modes under these conditions are poorly known, which contrasts with the well-documented cold plasma limit and/or moderate oblique angles of propagation ({Theta}{sub kB} < 80 Degree-Sign ). Based on linear solutions of the Vlasov kinetic theory, we discuss the relevance of each plasma mode (fast, Bernstein, KAW, whistler) in carrying the energy cascade down to electron scales. We show, in particular, that the shear Alfven mode (known in the magnetohydrodynamic limit) extends at scales k{rho}{sub i} {approx}> 1 to frequencies either larger or smaller than {omega}{sub ci}, depending on the anisotropy k{sub ||}/k . This extension into small scales is more readily called whistler ({omega} > {omega}{sub ci}) or KAW ({omega} < {omega}{sub ci}), although the mode is essentially the same. This contrasts with the well-accepted idea that the whistler branch always develops as a continuation at high frequencies of the fast magnetosonic mode. We show, furthermore, that the whistler branch is more damped than the KAW one, which makes the latter the more relevant candidate to carry the energy cascade down to electron scales. We discuss how these new findings
12. Oblique propagation of solitary electrostatic waves in magnetized plasmas with cold ions and nonthermal electrons
Science.gov (United States)
Verheest, Frank; Hellberg, Manfred A.
2017-02-01
Oblique propagation of large amplitude electrostatic waves and solitary structures is investigated in magnetized plasmas, comprising cold fluid ions and Cairns nonthermally distributed electrons, by using a Sagdeev pseudopotential formalism. To perform the analysis, quasineutrality is assumed, so that in normalized variables the electrostatic potential and the occurrence of solitary structures are governed by three parameters: the Mach number M, the typical Cairns parameter β, and the angle ϑ between the directions of propagation and the static magnetic field. Below a critical β, only positive compressive solitons are possible, and their amplitudes increase with increasing β, M, and ϑ. Above the critical β, there is coexistence between negative rarefactive and positive compressive solitons, and the range of negative solitons, at increasing M, ends upon encountering a double layer or a singularity. The double layer amplitudes (in absolute value) increase with β but are independent of ϑ. Roots of the Sagdeev pseudopotential beyond the double layer are not accessible from the undisturbed conditions, because of an intervening singularity where the pseudopotential becomes infinite. Recent claims of finding supersolitons beyond a double layer appear to be based on a misinterpretation of the nature of the singularity.
13. Vlasov modelling of parallel transport in a tokamak scrape-off layer
Energy Technology Data Exchange (ETDEWEB)
Manfredi, G [Institut de Physique et Chimie des Materiaux, CNRS and Universite de Strasbourg, BP 43, F-67034 Strasbourg (France); Hirstoaga, S [INRIA Nancy Grand-Est and Institut de Recherche en Mathematiques Avancees, 7 rue Rene Descartes, F-67084 Strasbourg (France); Devaux, S, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [JET-EFDA, Culham Science Centre, Abingdon, OX14 3DB (United Kingdom)
2011-01-15
A one-dimensional Vlasov-Poisson model is used to describe the parallel transport in a tokamak scrape-off layer. Thanks to a recently developed 'asymptotic-preserving' numerical scheme, it is possible to lift numerical constraints on the time step and grid spacing, which are no longer limited by, respectively, the electron plasma period and Debye length. The Vlasov approach provides a good velocity-space resolution even in regions of low density. The model is applied to the study of parallel transport during edge-localized modes, with particular emphasis on the particles and energy fluxes on the divertor plates. The numerical results are compared with analytical estimates based on a free-streaming model, with good general agreement. An interesting feature is the observation of an early electron energy flux, due to suprathermal electrons escaping the ions' attraction. In contrast, the long-time evolution is essentially quasi-neutral and dominated by the ion dynamics.
14. Simple Approach to the Solution of a Trapped and Radiated Cold Ion Beyond the Lamb-Dicke Limit
Institute of Scientific and Technical Information of China (English)
FENG Mang; SHI Lei; GAO Ke-Lin; ZHU Xi-Wen
2002-01-01
Trapping ions outside the Lamb-Dicke limit have been proven to be useful for the laser-cooling and quantum computing.Under the supposition of the Rabi frequency much smaller than the Lamb Dicke parameter,we can use a simple method to analytically solve the system with a single cold ion trapped and radiated beyond the Lamb Dickc limit,in the absence of the rotating-wave approximation (RWA).Discussion has been made for the limitation of our approach and the comparison of our results with the solutions under the RWA.
15. The Einstein-Vlasov System/Kinetic Theory
Directory of Open Access Journals (Sweden)
Håkan Andréasson
2011-05-01
Full Text Available The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein’s equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein–Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.
16. Preparation of cold ions in strong magnetic field and its application to gas-phase NMR spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Fuke, K., E-mail: [email protected] [Institute for Molecular Science (Japan); Ohshima, Y. [Tokyo Institute of Technology, Department of Chemistry (Japan); Tona, M. [Ayabo Co. Fukukama (Japan)
2015-11-15
Nuclear Magnetic Resonance (NMR) technique is widely used as a powerful tool to study the physical and chemical properties of materials. However, this technique is limited to the materials in condensed phases. To extend this technique to the gas-phase molecular ions, we are developing a gas-phase NMR apparatus. In this note, we describe the basic principle of the NMR detection for molecular ions in the gas phase based on a Stern-Gerlach type experiment in a Penning trap and outline the apparatus under development. We also present the experimental procedures and the results on the formation and the manipulation of cold ions under a strong magnetic field, which are the key techniques to detect the NMR by the present method.
17. Preparation of cold ions in strong magnetic field and its application to gas-phase NMR spectroscopy
Science.gov (United States)
Fuke, K.; Ohshima, Y.; Tona, M.
2015-11-01
Nuclear Magnetic Resonance (NMR) technique is widely used as a powerful tool to study the physical and chemical properties of materials. However, this technique is limited to the materials in condensed phases. To extend this technique to the gas-phase molecular ions, we are developing a gas-phase NMR apparatus. In this note, we describe the basic principle of the NMR detection for molecular ions in the gas phase based on a Stern-Gerlach type experiment in a Penning trap and outline the apparatus under development. We also present the experimental procedures and the results on the formation and the manipulation of cold ions under a strong magnetic field, which are the key techniques to detect the NMR by the present method.
18. Measurements of the ion velocity distribution in an ultracold neutral plasma derived from a cold, dense Rydberg gas
Science.gov (United States)
Bergeson, Scott; Lyon, Mary
2016-05-01
We report measurements of the ion velocity distribution in an ultracold neutral plasma derived from a dense, cold Rydberg gas in a MOT. The Rydberg atoms are excited using a resonant two-step excitation pathway with lasers of 4 ns duration. The plasma forms spontaneously and rapidly. The rms width of the ion velocity distribution is determined by measuring laser-induced fluorescence (LIF) of the ions. The measured excitation efficiency is compared with a Monte-Carlo wavefunction calculation, and significant differences are observed. We discuss the conditions for blockaded Rydberg excitation and the subsequent spatial ordering of Rydberg atom domains. While the blockade interaction is greater than the Rabi frequency in portions of the atomic sample, no evidence for spatial ordering is observed. This research is supported in part by the Air Force Office of Scientific Research (Grant No. FA9950-12- 0308) and by the National Science Foundation (Grant No. PHY-1404488).
19. Measurements of the ion velocity distribution in an ultracold neutral plasma derived from a cold, dense Rydberg gas
CERN Document Server
Bergeson, S D
2016-01-01
We report measurements of the ion velocity distribution in an ultracold neutral plasma derived from a dense, cold Rydberg gas in a MOT. The Rydberg atoms are excited using a resonant two-step excitation pathway with lasers of 4 ns duration. The plasma forms spontaneously and rapidly. The rms width of the ion velocity distribution is determined by measuring laser-induced fluorescence (LIF) of the ions. The measured excitation efficiency is compared with a Monte-Carlo wavefunction calculation, and significant differences are observed. We discuss the conditions for blockaded Rydberg excitation and the subsequent spatial ordering of Rydberg atom domains. While the blockade interaction is greater than the Rabi frequency in portions of the atomic sample, no evidence for spatial ordering is observed.
20. Rapid cold hardening improves recovery of ion homeostasis and chill coma recovery time in the migratory locust, Locusta migratoria.
Science.gov (United States)
Findsen, Anders; Andersen, Jonas Lembcke; Calderon, Sofia; Overgaard, Johannes
2013-05-01
Chill tolerance of insects is defined as the ability to tolerate low temperature under circumstances not involving freezing of intracellular or extracellular fluids. For many insects chill tolerance is crucial for their ability to persist in cold environments and mounting evidence indicates that chill tolerance is associated with the ability to maintain ion and water homeostasis, thereby ensuring muscular function and preventing chill injury at low temperature. The present study describes the relationship between muscle and haemolymph ion homeostasis and time to regain posture following cold shock (CS, 2 h at -4°C) in the chill-susceptible locust Locusta migratoria. This relationship was examined in animals with and without a prior rapid cold-hardening treatment (RCH, 2 h at 0°C) to investigate the physiological underpinnings of RCH. CS elicited a doubling of haemolymph [K(+)] and this disturbance was greater in locusts pre-exposed to RCH. Recovery of ion homeostasis was, however, markedly faster in RCH-treated animals, which correlated well with whole-organism performance as hardened individuals regained posture faster than non-hardened individuals following CS. The present study indicates that loss and recovery of muscular function are associated with the resting membrane potential of excitable membranes as attested by the changes in the equilibrium potential for K(+) (EK) following CS. Both hardened and non-hardened animals regained movement once K(+) homeostasis had recovered to a fixed level (EK≈-41 mV). RCH is therefore not associated with altered sensitivity to ion disturbance but instead is correlated to a faster recovery of haemolymph [K(+)].
1. From the Hartree dynamics to the Vlasov equation
DEFF Research Database (Denmark)
Benedikter, Niels Patriz; Porta, Marcello; Saffirio, Chiara;
2016-01-01
We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large N, we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise...... bounds on the 0rate of convergence....
2. On global solutions for the Vlasov-Poisson system
Directory of Open Access Journals (Sweden)
Peter E. Zhidkov
2004-04-01
Full Text Available In this article we show that the Vlasov-Poisson system has a unique weak solution in the space $L_1cap L_infty$. For this purpose, we use the method of characteristics, unlike the approach in [12].
3. The Einstein-Vlasov System/Kinetic Theory
Directory of Open Access Journals (Sweden)
Andréasson Håkan
2005-01-01
Full Text Available The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einsteins equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special relativistic physics, i.e. to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically, and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (i.e. fluid models. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to good comprehension of kinetic theory in general relativity.
4. A new explanation to the cold nuclear matter effects in heavy ion collisions
CERN Document Server
Liu, Zhi-Feng
2014-01-01
The J/Psi cross section ratios of p-A/p-p under different collision energy is calculated with cold nuclear matter effects redefined in this paper. The advantage of these new definitions is that all cold nuclear matter effects have clear physical origins.The radios are compared with the corresponding experiment data and that calculated with classic nuclear effects. The ratios calculated with new definitions can reproduce almost all existing J/Psi measurements in p-A collisions more accuratly than that calculated with classic nuclear effects. Hence, this paper presents a new approach to explain cold nuclear effects in the hardproduction of quarkonium.
5. MICRO-MOTION EFFECT OF A TRAPPED ULTRA-COLD ION IN A STANDING-WAVE LASER
Institute of Scientific and Technical Information of China (English)
JIANG YU-RONG; FENG MANG; GAO KE-LIN; ZHU XI-WEN
2001-01-01
In the absence of the requirements of the Lamb-Dicke limit and rotating wave approximation, we semi-classically investigate the dynamics of a trapped ultra-cold ion in the standing-wave laser, with the consideration of the time- dependent potential and pseudo-potential of the Paul trap. The specific calculations show that the larger the Lamb-Dicke parameter η and the Rabi frequency Ω, the greater the difference between the dynamics in the time-dependent potential and the pseudo-potential.
6. Exact nonlinear analytic Vlasov-Maxwell tangential equilibria with arbitrary density and temperature profiles
CERN Document Server
Mottez, F
2003-01-01
The tangential layers are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. They have been extensively described in the frame of the Magneto-Hydro-Dynamic (MHD) theory. But the MHD theory does not look inside the transition region if the transition has a size of a few ion gyroradii. A series of kinetic tangential equilibria, valid for a collisionless plasma is presented. These equilibria are exact analytical solutions of the Maxwell-Vlasov equations. The particle distribution functions are sums of an infinite number of elementary functions parametrized by a vector potential. Examples of equilibria relevant to space plasmas are shown. A model for the deep and sharp density depletions observed in the auroral zone of the Earth is proposed. Tangential equilibria are also relevant for the study of planetary environments and of remote astrophysical plasmas.
7. Landau damping of Gardner solitons in a dusty bi-ion plasma
CERN Document Server
Misra, A P
2015-01-01
The effects of linear Landau damping on the nonlinear propagation of dust-acoustic solitary waves (DASWs) are studied in a collisionless unmagnetized dusty plasma with two species of positive ions. The extremely massive, micron-seized, cold and negatively charged dust particles are described by fluid equations, whereas the two species of positive ions, namely the cold (heavy) and hot (light) ions are described by the kinetic Vlasov equations. Following Ott and Sudan [Phys. Fluids {\\bf 12}, 2388 (1969)], and by considering lower and higher-order perturbations, the evolution of DASWs with Landau damping is shown to be governed by Korteweg-de Vries (KdV), modified KdV (mKdV) or Gardner (KdV-mKdV)-like equations. The properties of the phase velocity and the Landau damping rate of DASWs are studied for different values of the ratios of the temperatures $(\\sigma)$ and the number densities $(\\mu)$ of hot and cold ions as well the cold to hot ion mass ratio $m$. The distinctive features of the decay rates of the ampl...
8. Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Science.gov (United States)
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
9. Linear Vlasov analysis for stability of a bunched beam
Energy Technology Data Exchange (ETDEWEB)
Warnock, Robert; Stupakov, Gennady; Venturini, Marco; Ellison, James A.
2004-06-30
We study the linearized Vlasov equation for a bunched beam subject to an arbitrary wake function. Following Oide and Yokoya, the equation is reduced to an integral equation expressed in angle-action coordinates of the distorted potential well. Numerical solution of the equation as a formal eigenvalue problem leads to difficulties, because of singular eigenmodes from the incoherent spectrum. We rephrase the equation so that it becomes non-singular in the sense of operator theory, and has only regular solutions for coherent modes. We report on a code that finds thresholds of instability by detecting zeros of the determinant of the system as they enter the upper-half frequency plane, upon increase of current. Results are compared with a time-domain integration of the nonlinear Vlasov equation with a realistic wake function for the SLC damping rings. There is close agreement between the two calculations.
10. Linear Vlasov Analysis for Stability of a Bunched Beam
Energy Technology Data Exchange (ETDEWEB)
Warnock, R
2004-08-12
The authors study the linearized Vlasov equation for a bunched beam subject to an arbitrary wake function. Following Oide and Yokoya, the equation is reduced to an integral equation expressed in angle-action coordinates of the distorted potential well. Numerical solution of the equation as a formal eigenvalue problem leads to difficulties, because of singular eigenmodes from the incoherent spectrum. The authors rephrase the equation so that it becomes non-singular in the sense of operatory theory, and has only regular solutions for coherent modes. They report on a code that finds thresholds of instability by detecting zeros of the determinant of the system as they enter the upper-half frequency plane, upon increase of current. Results are compared with a time-domain integration of the nonlinear Vlasov equation with a realistic wake function for the SLC damping rings. There is close agreement between the two calculations.
11. Block-Structured Adaptive Mesh Refinement Algorithms for Vlasov Simulation
CERN Document Server
Hittinger, J A F
2012-01-01
Direct discretization of continuum kinetic equations, like the Vlasov equation, are under-utilized because the distribution function generally exists in a high-dimensional (>3D) space and computational cost increases geometrically with dimension. We propose to use high-order finite-volume techniques with block-structured adaptive mesh refinement (AMR) to reduce the computational cost. The primary complication comes from a solution state comprised of variables of different dimensions. We develop the algorithms required to extend standard single-dimension block structured AMR to the multi-dimension case. Specifically, algorithms for reduction and injection operations that transfer data between mesh hierarchies of different dimensions are explained in detail. In addition, modifications to the basic AMR algorithm that enable the use of high-order spatial and temporal discretizations are discussed. Preliminary results for a standard 1D+1V Vlasov-Poisson test problem are presented. Results indicate that there is po...
12. Variational formulations of guiding-center Vlasov-Maxwell theory
Science.gov (United States)
Brizard, Alain J.; Tronci, Cesare
2016-06-01
The variational formulations of guiding-center Vlasov-Maxwell theory based on Lagrange, Euler, and Euler-Poincaré variational principles are presented. Each variational principle yields a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. The conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric.
13. Coupled Vlasov and two-fluid codes on GPUs
CERN Document Server
Rieke, M; Grauer, R
2014-01-01
We present a way to combine Vlasov and two-fluid codes for the simulation of a collisionless plasma in large domains while keeping full information of the velocity distribution in localized areas of interest. This is made possible by solving the full Vlasov equation in one region while the remaining area is treated by a 5-moment two-fluid code. In such a treatment, the main challenge of coupling kinetic and fluid descriptions is the interchange of physically correct boundary conditions between the different plasma models. In contrast to other treatments, we do not rely on any specific form of the distribution function, e.g. a Maxwellian type. Instead, we combine an extrapolation of the distribution function and a correction of the moments based on the fluid data. Thus, throughout the simulation both codes provide the necessary boundary conditions for each other. A speed-up factor of around 20 is achieved by using GPUs for the computationally expensive solution of the Vlasov equation and an overall factor of a...
14. Vlasov versus N-body: the H\\'enon sphere
CERN Document Server
Colombi, S; Peirani, S; Plum, G; Suto, Y
2015-01-01
We perform a detailed comparison of the phase-space density traced by the particle distribution in Gadget simulations to the result obtained with a spherical Vlasov solver using the splitting algorithm. The systems considered are apodized H\\'enon spheres with two values of the virial ratio, R ~ 0.1 and 0.5. After checking that spherical symmetry is well preserved by the N-body simulations, visual and quantitative comparisons are performed. In particular we introduce new statistics, correlators and entropic estimators, based on the likelihood of whether N-body simulations actually trace randomly the Vlasov phase-space density. When taking into account the limits of both the N-body and the Vlasov codes, namely collective effects due to the particle shot noise in the first case and diffusion and possible nonlinear instabilities due to finite resolution of the phase-space grid in the second case, we find a spectacular agreement between both methods, even in regions of phase-space where nontrivial physical instabi...
15. Vlasov models for kinetic Weibel-type instabilities
Science.gov (United States)
Ghizzo, A.; Sarrat, M.; Del Sarto, D.
2017-02-01
The Weibel instability, driven by a temperature anisotropy, is investigated within different kinetic descriptions based on the semi-Lagrangian full kinetic and relativistic Vlasov-Maxwell model, on the multi-stream approach, which is based on a Hamiltonian reduction technique, and finally, with the full pressure tensor fluid-type description. Dispersion relations of the Weibel instability are derived using the three different models. A qualitatively different regime is observed in Vlasov numerical experiments depending on the excitation of a longitudinal plasma electric field driven initially by the combined action of the stream symmetry breaking and weak relativistic effects, in contrast with the existing theories of the Weibel instability based on their purely transverse characters. The multi-stream model offers an alternate way to simulate easily the coupling with the longitudinal electric field and particularly the nonlinear regime of saturation, making numerical experiments more tractable, when only a few moments of the distribution are considered. Thus a numerical comparison between the reduced Hamiltonian model (the multi-stream model) and full kinetic (relativistic) Vlasov simulations has been investigated in that regime. Although nonlinear simulations of the fluid model, including the dynamics of the pressure tensor, have not been carried out here, the model is strongly relevant even in the three-dimensional case.
16. Sympathetic cooling and detection of a hot trapped ion by a cold one
CERN Document Server
Guggemos, M; Herrera-Sancho, O A; Blatt, R; Roos, C F
2015-01-01
We investigate the dynamics of an ion sympathetically cooled by another laser-cooled ion or small ion crystal. To this end, we develop simple models of the cooling dynamics in the limit of weak Coulomb interactions. Experimentally, we create a two-ion crystal of Ca$^+$ and Al$^+$ by photo-ionization of neutral atoms produced by laser ablation. We characterize the velocity distribution of the laser-ablated atoms crossing the trap by time-resolved fluorescence spectroscopy. We observe neutral atom velocities much higher than the ones of thermally heated samples and find as a consequence long sympathethic cooling times before crystallization occurs. Our key result is a new technique for detecting the loading of an initially hot ion with energy in the eV range by monitoring the motional state of a Doppler-cooled ion already present in the trap. This technique not only detects the ion but also provides information about dynamics of the sympathetic cooling process.
17. Properties of cold ions produced by synchrotron radiation and by charged particle impact
Science.gov (United States)
Levin, J. C.; Biedermann, C.; Cederquist, H.; O, C.-S.; Short, R. T.; Sellin, I. A.
1989-04-01
Argon recoil ions produced by beams of 0.8 MeV/u Cl 5+ have been detected by time-of-flight (TOF) techniques in coincidence with the loss of from one to five projectile electrons. Recoil-ion energies have been determined to be more than an order of magnitude higher than those of highly charged ions produced by unmonochromatized synchrotron radiation. Charge-state distributions, however, show similarities, suggesting that loss of projectile electrons corresponds, in some cases, to inner-shell target ionization producing vacancy cascades. In an essential improvement to the usual multinomial description of ionization in the independent-electron-ejection model, we find the inclusion of Auger vacancy cascades significantly alters the description of the recoil ion spectra corresponding to the projectile-electron loss. These conclusions are consistent with impact parameters inferred from determination of mean recoil energy.
18. Energy scaling of cold atom-atom-ion three-body recombination
CERN Document Server
Krükow, Artjom; Härter, Arne; Denschlag, Johannes Hecker; Pérez-Ríos, Jesús; Greene, Chris H
2015-01-01
We study three-body recombination of Ba$^+$ + Rb + Rb in the mK regime where a single $^{138}$Ba$^{+}$ ion in a Paul trap is immersed into a cloud of ultracold $^{87}$Rb atoms. We measure the energy dependence of the three-body rate coefficient $k_3$ and compare the results to the theoretical prediction, $k_3 \\propto E_{\\textrm{col}}^{-3/4}$ where $E_{\\textrm{col}}$ is the collision energy. We find agreement if we assume that the non-thermal ion energy distribution is determined by at least two different micro-motion induced energy scales. Furthermore, using classical trajectory calculations we predict how the median binding energy of the formed molecules scales with the collision energy. Our studies give new insights into the kinetics of an ion immersed into an ultracold atom cloud and yield important prospects for atom-ion experiments targeting the s-wave regime.
19. Yang-Mills-Vlasov system in the temporal gauge. Systeme de Yang-Mills-Vlasov en jauge temporelle
Energy Technology Data Exchange (ETDEWEB)
Choquet-Bruhat, Y.; Noutchegueme, N. (Paris-6 Univ., 75 (FR))
1991-01-01
We prove a local in time existence theorem of a solution of the Cauchy problem for the Yang-Mills-Vlasov integrodifferential system. Such equations govern the evolution of plasmas, for instance of quarks and gluons (quagmas), where non abelian gauge fields and Yang-Mills charges replace the usual electromagnetic field and electric charge. We work with the temporal gauge and use functional spaces with appropriate weight on the momenta, but no fall off is required in the space direction.
20. Forbidden Vibrational Transitions in Cold Molecular Ions: Experimental Observation and Potential Applications.
Science.gov (United States)
Germann, Matthias; Tonga, Xin; Willitsch, Stefan
2015-01-01
A range of interesting fundamental scientific questions can be addressed by high-precision molecular spectroscopy. A promising way towards this goal is the measurement of dipole-forbidden vibrational transitions in molecular ions. We have recently reported the first such observation in a molecular ion. Here, we give an overview of our method and our results as well as an outlook on potential future applications.
1. Non-Linear Excitation of Ion Acoustic Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Hirsfield, J. L.
1974-01-01
The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....
2. Light-Assisted Cold Chemical Reactions of Barium Ions with Rubidium Atoms
CERN Document Server
Hall, Felix H J; Raoult, Maurice; Dulieu, Olivier; Willitsch, Stefan
2013-01-01
Light-assisted reactive collisions between laser-cooled Ba+ ions and Rb atoms were studied in an ion-atom hybrid trap. The reaction rate was found to strongly depend on the electronic state of the reaction partners with the largest rate constant (7(2) x 10^-11 cm^3 s^-1) obtained for the excited Ba+(6s)+Rb(5p) reaction channel. Similar to the previously studied Ca+ + Rb system, charge transfer and radiative association were found to be the dominant reactive processes. The generation of molecular ions by radiative association could directly be observed by their sympathetic cooling into a Coulomb crystal. Potential energy curves up to the Ba+(6s)+Rb(5p) asymptote and reactive-scattering cross sections for the radiative processes were calculated. The theoretical rate constant obtained for the lowest reaction channel Ba+(6s)+Rb(5s) is compatible with the experimental estimates obtained thus far.
3. Model and observations of Schottky-noise suppression in a cold heavy-ion beam.
Science.gov (United States)
Danared, H; Källberg, A; Rensfelt, K-G; Simonsson, A
2002-04-29
Some years ago it was found at GSI in Darmstadt that the momentum spread of electron-cooled beams of highly charged ions dropped abruptly to very low values when the particle number decreased to 10 000 or less. This has been interpreted as an ordering of the ions, such that they line up after one another in the ring. We report observations of similar transitions at CRYRING, including an accompanying drop in Schottky-noise power. We also introduce a model of the ordered beam from which the Schottky-noise power can be calculated numerically. The good agreement between the model calculation and the experimental data is seen as evidence for a spatial ordering of the ions.
4. Generation of Schr(o)dinger cat state of a single trapped cold ion
Institute of Scientific and Technical Information of China (English)
Zhang Miao; Jia Huan-Yu; Ji Xiao-Hui; Si Kun
2009-01-01
The fidelity of the generated Schr(o)dinger Cat state (SCS) of a single trapped ion in the Lamb-Dicke approximation is discussed. The results show that the fidelity significantly decreases with the values of Lamb-Dicke parameter η and coherent state amplitude α increasing. For η = 0.20 and α = 3, the typical values of experimental parameters, the fidelity is rather low (30%). A scheme for generating the SCS is proposed without making the Lamb-Dike approximation in laser-ion interaction, and the fidelity of the generated SCS is about 99% for the typical values of experimental Lamb-Dicke parameters.
5. Adaptive multiresolution semi-Lagrangian discontinuous Galerkin methods for the Vlasov equations
Science.gov (United States)
Besse, N.; Deriaz, E.; Madaule, É.
2017-03-01
We develop adaptive numerical schemes for the Vlasov equation by combining discontinuous Galerkin discretisation, multiresolution analysis and semi-Lagrangian time integration. We implement a tree based structure in order to achieve adaptivity. Both multi-wavelets and discontinuous Galerkin rely on a local polynomial basis. The schemes are tested and validated using Vlasov-Poisson equations for plasma physics and astrophysics.
6. A simple class of singular, two species Vlasov equilibria sustaining nonmonotonic potential distributions
Energy Technology Data Exchange (ETDEWEB)
Nocera, L.; Palumbo, L. J. [CNR-IPCF, Theoretical Plasma Physics, Via Moruzzi 1, I-56124 Pisa (Italy)
2013-01-15
We present new elementary, exact weak singular solutions of the steady state, two species, electrostatic, one dimensional Vlasov-Poisson equations. The distribution of the hot, finite mass, mobile ions is assumed to be log singular at the position of the electric potential's minimum. We show that the electron energy distributions on opposite sides of this minimum are not equal. This leads to a jump discontinuity of the electron distribution across its separatrix. A simple relation exists between the difference of these two electron distributions and that of the ions. The velocity Fourier transform of the electron singular distribution is smooth and appears as a simple Neumann series. Elementary, finite amplitude profiles of the electric potential result from Poisson equation, which are smoothly, but nonmonotonically and asymmetrically distributed in space. Two such profiles are given explicitly as appropriate for a nonmonotonic double layer and for a plasma bounded by a surface. The distributions of both electrons and ions supporting such potential meet smooth and kinetically stable boundary conditions at one plasma boundary. For sufficiently small potential to electron temperature ratios, the nonthermal, discontinuous electron distribution resulting at the other plasma boundary is also stable against Landau damped perturbations of the electron distribution.
7. Equations of motion of test particles for solving the spin-dependent Boltzmann–Vlasov equation
Directory of Open Access Journals (Sweden)
Yin Xia
2016-08-01
Full Text Available A consistent derivation of the equations of motion (EOMs of test particles for solving the spin-dependent Boltzmann–Vlasov equation is presented. The resulting EOMs in phase space are similar to the canonical equations in Hamiltonian dynamics, and the EOM of spin is the same as that in the Heisenburg picture of quantum mechanics. Considering further the quantum nature of spin and choosing the direction of total angular momentum in heavy-ion reactions as a reference of measuring nucleon spin, the EOMs of spin-up and spin-down nucleons are given separately. The key elements affecting the spin dynamics in heavy-ion collisions are identified. The resulting EOMs provide a solid foundation for using the test-particle approach in studying spin dynamics in heavy-ion collisions at intermediate energies. Future comparisons of model simulations with experimental data will help to constrain the poorly known in-medium nucleon spin–orbit coupling relevant for understanding properties of rare isotopes and their astrophysical impacts.
8. Specific chemical reactivities of spatially separated 3-aminophenol conformers with cold Ca$^+$ ions
CERN Document Server
Chang, Yuan-Pin; Küpper, Jochen; Rösch, Daniel; Wild, Dieter; Willitsch, Stefan
2013-01-01
Many molecules exhibit multiple rotational isomers (conformers) that interconvert thermally and are difficult to isolate. Consequently, a precise characterization of their role in chemical reactions has proven challenging. We have probed the reactivity of specific conformers using an experimental technique based on their spatial separation in a molecular beam by electrostatic deflection. The separated conformers react with a target of Coulomb-crystallized ions in a trap. In the reaction of Ca$^+$ with 3-aminophenol, we find a twofold larger rate constant for the \\textit{cis}- compared to the \\textit{trans}-conformer (differentiated by the O-H bond orientation). This result is explained by conformer-specific differences in the long-range ion-molecule interaction potentials. Our approach demonstrates the possibility of controlling reactivity through selection of conformational states.
9. Vlasov-type and Liouville-type equations, their microscopic, energetic and hydrodynamical consequences
Science.gov (United States)
Vedenyapin, V. V.; Negmatov, M. A.; Fimin, N. N.
2017-06-01
We give a derivation of the Vlasov-Maxwell and Vlasov-Poisson-Poisson equations from the Lagrangians of classical electrodynamics. The equations of electromagnetic hydrodynamics (EMHD) and electrostatics with gravitation are derived from them by means of a hydrodynamical' substitution. We obtain and compare the Lagrange identities for various types of Vlasov equations and EMHD equations. We discuss the advantages of writing the EMHD equations in Godunov's double divergence form. We analyze stationary solutions of the Vlasov-Poisson-Poisson equation, which give rise to non-linear elliptic equations with various properties and various kinds of behaviour of the trajectories of particles as the mass passes through a critical value. We show that the classical equations can be derived from the Liouville equation by the Hamilton-Jacobi method and give an analogue of this procedure for the Vlasov equation as well as in the non-Hamiltonian case.
10. Trapping scaling for bifurcations in the Vlasov systems.
Science.gov (United States)
Barré, J; Métivier, D; Yamaguchi, Y Y
2016-04-01
We study nonoscillating bifurcations of nonhomogeneous steady states of the Vlasov equation, a situation occurring in galactic models, or for Bernstein-Greene-Kruskal modes in plasma physics. Through an unstable manifold expansion, we show that in one spatial dimension the dynamics is very sensitive to the initial perturbation: the instability may saturate at small amplitude-generalizing the "trapping scaling" of plasma physics-or may grow to produce a large-scale modification of the system. Furthermore, resonances are strongly suppressed, leading to different phenomena with respect to the homogeneous case. These analytical findings are illustrated and extended by direct numerical simulations with a cosine interaction potential.
11. A Vlasov equation with Dirac potential used in fusion plasmas
Energy Technology Data Exchange (ETDEWEB)
Bardos, Claude [Universite Paris-Diderot, Laboratoire J.-L. Lions, BP187, 4 Place Jussieu, 75252 Paris Cedex 05 (France); Nouri, Anne [Laboratoire d' Analyse, Topologie et Probabilites (UMR 6632), Aix-Marseille Universite, 39 Rue Joliot-Curie, 13453 Marseille Cedex 13 (France)
2012-11-15
Well-posedness of the Cauchy problem is analyzed for a singular Vlasov equation governing the evolution of the ionic distribution function of a quasineutral fusion plasma. The Penrose criterium is adapted to the linearized problem around a time and space homogeneous distribution function showing (due to the singularity) more drastic differences between stable and unstable situations. This pathology appears on the full nonlinear problem, well-posed locally in time with analytic initial data, but generally ill-posed in the Hadamard sense. Eventually with a very different class of solutions, mono-kinetic, which constrains the structure of the density distribution, the problem becomes locally in time well-posed.
12. Trapping scaling for bifurcations in the Vlasov systems
Science.gov (United States)
Barré, J.; Métivier, D.; Yamaguchi, Y. Y.
2016-04-01
We study nonoscillating bifurcations of nonhomogeneous steady states of the Vlasov equation, a situation occurring in galactic models, or for Bernstein-Greene-Kruskal modes in plasma physics. Through an unstable manifold expansion, we show that in one spatial dimension the dynamics is very sensitive to the initial perturbation: the instability may saturate at small amplitude—generalizing the "trapping scaling" of plasma physics—or may grow to produce a large-scale modification of the system. Furthermore, resonances are strongly suppressed, leading to different phenomena with respect to the homogeneous case. These analytical findings are illustrated and extended by direct numerical simulations with a cosine interaction potential.
13. Numerical solution to the Vlasov equation: The 2D code
Science.gov (United States)
Fijalkow, Eric
1999-02-01
The present code solves the two-dimensional Vlasov equation for a periodic in space system, in presence of an external magnetic field B O. The self coherent electric field given by Poisson equation is computed by Fast Fourier Transform (FFT). The output of the code consist of a list of diagnostics, such as total mass conservation, total momentum and energies, and of projections of the distribution function in different subspaces as the x- v x space, the x- y space and so on.
14. On the combination of a low energy hydrogen atom beam with a cold multipole ion trap
Energy Technology Data Exchange (ETDEWEB)
Borodi, Gheorghe
2008-12-09
The first part of the activities of this thesis was to develop a sophisticated ion storage apparatus dedicated to study chemical processes with atomic hydrogen. The integration of a differentially pumped radical beam source into an existing temperature variable 22- pole trapping machine has required major modifications. Since astrophysical questions have been in the center of our interest, the introduction first gives a short overview of astrophysics and -chemistry. The basics of ion trapping in temperature variable rf traps is well-documented in the literature; therefore, the description of the basic instrument (Chapter 2) is kept rather short. Much effort has been put into the development of an intense and stable source for hydrogen atoms the kinetic energy of which can be changed. Chapter 3 describes this module in detail with emphasis on the integration of magnetic hexapoles for guiding the atoms and special treatments of the surfaces for reducing H-H recombination. Due to the unique sensitivity of the rf ion trapping technique, this instrument allows one to study a variety of reactions of astrochemical and fundamental interest. The results of this work are summarized in Chapter 4. Reactions of CO{sub 2}{sup +} with hydrogen atoms and molecules have been established as calibration standard for in situ determination of H and H{sub 2} densities over the full temperature range of the apparatus (10 K-300 K). For the first time, reactions of H- and D-atoms with the ionic hydrocarbons CH{sup +}, CH{sub 2}{sup +}, and CH{sub 4}{sup +} have been studied at temperatures of interstellar space. A very interesting, not yet fully understood collision system is the interaction of protonated methane with H. The outlook presents some ideas, how to improve the new instrument and a few reaction systems are mentioned which may be studied next. (orig.)
15. Comparative study between cold plasma and hot plasma with ion beam and loss-cone distribution function by particle aspect approach
Science.gov (United States)
Patel, Soniya; Varma, P.; Tiwari, M. S.
2011-03-01
The electromagnetic ion-cyclotron (EMIC) instabilities with isotropic ion beam and general loss-cone distribution of cold and hot core plasmas are discussed. The growth rate, parallel and perpendicular resonance energies of the electromagnetic ion-cyclotron waves in a low β (ratio of plasma pressure to magnetic pressure), homogeneous plasma have been obtained using the dispersion relation for cold and hot plasmas. The wave is assumed to propagate parallel to the static magnetic field. The whole plasma is considered to consist of resonant and non-resonant particles permeated by isotropic ion beam. It is assumed that resonant particles and ion beam participate in energy exchange with the wave whereas non-resonant particles support the oscillatory motion of the wave. We determined the variation in energies and growth rate in cold and hot plasmas by the energy conservation method with a general loss-cone distribution function. The thermal anisotropy of the core plasma acts as a source of free energy for EMIC wave and enhances the growth rate. It is noted that the EMIC wave emissions occur by extracting energy of perpendicularly heated ions in the presence of up flowing ion beam and steep loss-cone distribution in the anisotropic magnetosphere. The effect of the steep loss-cone distribution is to enhance the growth rate of the EMIC wave. The heating of ions perpendicular and parallel to the magnetic field is discussed along with EMIC wave emission in the auroral acceleration region. The results are interpreted for the space plasma parameters appropriate to the auroral acceleration region of the earth's magnetoplasma.
16. ColDICE: A parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation
Science.gov (United States)
Sousbie, Thierry; Colombi, Stéphane
2016-09-01
Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65-67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a "warm" dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.
17. ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation
CERN Document Server
Sousbie, Thierry
2015-01-01
Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincar\\'e invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density proj...
18. High-resolution spectroscopy of CH2D+ in a cold 22-pole ion trap.
Science.gov (United States)
Gärtner, Sabrina; Krieg, Jürgen; Klemann, André; Asvany, Oskar; Brünken, Sandra; Schlemmer, Stephan
2013-10-03
The method of laser-induced reaction (LIR) is used to obtain high-resolution IR spectra of CH2D(+) in collision with n-H2 at a nominal temperature of 14 K. For this purpose, a home-built optical parametric oscillator (OPO), tunable in the range of 2500-4000 cm(-1), has been coupled to a 22-pole ion trap apparatus. In total, 112 lines of the ν1 and ν4 bands have been recorded. A line list is inferred from a careful analysis of the shape of the LIR signal. Line positions have been determined to an accuracy of 1 × 10(-4) cm(-1), allowing for the prediction of pure rotational transitions with MHz accuracy. In addition, an IR-THz double-resonance LIR depletion technique is applied to H2D(+) to demonstrate the feasibility for pure rotational spectroscopy with LIR.
19. On axisymmetric and stationary solutions of the self-gravitating Vlasov system
Science.gov (United States)
Ames, Ellery; Andréasson, Håkan; Logg, Anders
2016-08-01
Axisymmetric and stationary solutions are constructed to the Einstein-Vlasov and Vlasov-Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein-Vlasov system which contain ergoregions.
20. On Axisymmetric and Stationary Solutions of the Self-Gravitating Vlasov System
CERN Document Server
Ames, Ellery; Logg, Anders
2016-01-01
Axisymmetric and stationary solutions are constructed to the Einstein--Vlasov and Vlasov--Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is fixed at each step. A variety of axisymmetric stationary solutions are exhibited, including solutions with toroidal, disk-like, spindle-like, and composite spatial density configurations, as are solutions with non-vanishing net angular momentum. In the case of toroidal solutions, we show for the first time, solutions of the Einstein--Vlasov system which contain ergoregions.
1. Ion sources with arc-discharge plasma box driven by directly heated LaB(6) electron emitter or cold cathode.
Science.gov (United States)
Ivanov, Alexander A; Davydenko, Vladimir I; Deichuli, Petr P; Shulzhenko, Grigori I; Stupishin, Nikolay V
2008-02-01
In the Budker Institute, Novosibirsk, an ion source with arc-discharge plasma box has been developed in the recent years for application in thermonuclear devices for plasma diagnostics. Several modifications of the ion source were provided with extracted current ranging from 1 to 7 A and pulse duration of up to 4 s. Initially, the arc-discharge plasma box with cold cathode was used, with which pulse duration is limited to 2 s by the cathode overheating and sputtering in local arc spots. Recently, a directly heated LaB(6) electron emitter was employed instead, which has extended lifetime compared to the cold cathode. In the paper, characteristics of the beam produced with both arrangements of the plasma box are presented.
2. A Robust Scheme for Two-Qubit Grover Quantum Search Alogrithm Based on the Motional and Internal States of a Single Cold Trapped Ion
Institute of Scientific and Technical Information of China (English)
秦涛; 高克林
2003-01-01
We propose a scheme to implement a two-qubit Grover quantum search algorithm.The novelty in the proposal is that the motional state is introduced into the computation and the internal state within a single cold trapped ion.The motional and internal states of the ion are manipulated as two qubits by the laser pulses to accomplish an example of a Grover algorithm based on the two qubits.The composite laser pulses that are applied to implement the Grover algorithm have been designed in detail.The issues concerning measurement and decoherence are discussed.
3. Parallelized Vlasov-Fokker-Planck solver for desktop personal computers
Science.gov (United States)
Schönfeldt, Patrik; Brosi, Miriam; Schwarz, Markus; Steinmann, Johannes L.; Müller, Anke-Susanne
2017-03-01
The numerical solution of the Vlasov-Fokker-Planck equation is a well established method to simulate the dynamics, including the self-interaction with its own wake field, of an electron bunch in a storage ring. In this paper we present Inovesa, a modularly extensible program that uses opencl to massively parallelize the computation. It allows a standard desktop PC to work with appropriate accuracy and yield reliable results within minutes. We provide numerical stability-studies over a wide parameter range and compare our numerical findings to known results. Simulation results for the case of coherent synchrotron radiation will be compared to measurements that probe the effects of the microbunching instability occurring in the short bunch operation at ANKA. It will be shown that the impedance model based on the shielding effect of two parallel plates can not only describe the instability threshold, but also the presence of multiple regimes that show differences in the emission of coherent synchrotron radiation.
4. On the contribution of exchange interactions to the Vlasov equation
CERN Document Server
Zamanian, J; Marklund, M
2014-01-01
Exchange effects play an important role in determining the equilibrium properties of dense matter systems, as well as for magnetic phenomena. There exists an extensive literature concerning, e.g., the effects of exchange interactions on the equation of state of dense matter. Here, a generalization of the Vlasov equation to include exchange effects is presented allowing for electromagnetic mean fields, thus incorporating some of the dynamic effects due to the exchange interactions. Treating the exchange term perturbatively, the correction to classical Langmuir waves in plasmas is found, and the results are compared with previous work. It is noted that the relative importance of exchange effects scales similarly with density and temperature as particle dispersive effects, but that the overall magnitude is sensitive to the details of the specific problem. The implications of our results are discussed.
5. PROTON KINETIC EFFECTS IN VLASOV AND SOLAR WIND TURBULENCE
Energy Technology Data Exchange (ETDEWEB)
Servidio, S.; Valentini, F.; Perrone, D.; Veltri, P. [Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza (Italy); Osman, K. T.; Chapman, S. [Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, CV4 7AL (United Kingdom); Califano, F. [Dipartimento di Fisica and CNISM, Università di Pisa, I-56127 Pisa (Italy); Matthaeus, W. H., E-mail: [email protected] [Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, DE 19716 (United States)
2014-02-01
Kinetic plasma processes are investigated in the framework of solar wind turbulence, employing hybrid Vlasov-Maxwell (HVM) simulations. Statistical analysis of spacecraft observation data relates proton temperature anisotropy T /T {sub ∥} and parallel plasma beta β{sub ∥}, where subscripts refer to the ambient magnetic field direction. Here, this relationship is recovered using an ensemble of HVM simulations. By varying plasma parameters, such as plasma beta and fluctuation level, the simulations explore distinct regions of the parameter space given by T /T {sub ∥} and β{sub ∥}, similar to solar wind sub-datasets. Moreover, both simulation and solar wind data suggest that temperature anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. This connection between non-Maxwellian kinetic effects and various types of intermittency may be a key point for understanding the complex nature of plasma turbulence.
6. Proton Kinetic Effects in Vlasov and Solar Wind Turbulence
CERN Document Server
Servidio, S; Valentini, F; Perrone, D; Califano, F; Chapman, S; Matthaeus, W H; Veltri, P
2013-01-01
Kinetic plasma processes have been investigated in the framework of solar wind turbulence, employing Hybrid Vlasov-Maxwell (HVM) simulations. The dependency of proton temperature anisotropy T_{\\perp}/T_{\\parallel} on the parallel plasma beta \\beta_{\\parallel}, commonly observed in spacecraft data, has been recovered using an ensemble of HVM simulations. By varying plasma parameters, such as plasma beta and fluctuation level, the simulations explore distinct regions of the parameter space given by T_{\\perp}/T_{\\parallel} and \\beta_{\\parallel}, similar to solar wind sub-datasets. Moreover, both simulation and solar wind data suggest that temperature anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. This connection between non-Maxwellian kinetic effects and various types of intermittency may be a key point for understanding the complex nature of plasma turbulence.
7. High-order Hamiltonian splitting for Vlasov-Poisson equations
CERN Document Server
Casas, Fernando; Faou, Erwan; Mehrenberger, Michel
2015-01-01
We consider the Vlasov-Poisson equation in a Hamiltonian framework and derive new time splitting methods based on the decomposition of the Hamiltonian functional between the kinetic and electric energy. Assuming smoothness of the solutions, we study the order conditions of such methods. It appears that these conditions are of Runge-Kutta-Nystr{\\"o}m type. In the one dimensional case, the order conditions can be further simplified, and efficient methods of order 6 with a reduced number of stages can be constructed. In the general case, high-order methods can also be constructed using explicit computations of commutators. Numerical results are performed and show the benefit of using high-order splitting schemes in that context. Complete and self-contained proofs of convergence results and rigorous error estimates are also given.
8. Vlasov equation for long-range interactions on a lattice
CERN Document Server
Bachelard, Romain; De Ninno, Giovanni; Ruffo, Stefano; Staniscia, F
2011-01-01
We show that, in the continuum limit, the dynamics of Hamiltonian systems defined on a lattice with long-range couplings is well described by the Vlasov equation. This equation can be linearized around the homogeneous state and a dispersion relation, that depends explicitly on the Fourier modes of the lattice, can be derived. This allows to compute the stability thresholds of the homogeneous state, which turn out to depend on the mode number. When this state is unstable, the growth rates are also function of the mode number. Explicit calculations are performed for the $\\alpha$-HMF model with $0 \\leq \\alpha <1$, for which the zero mean-field mode is always found to dominate the exponential growth. The theoretical predictions are successfully compared with numerical simulations performed on a finite lattice.
9. Vlasov equation for long-range interactions on a lattice.
Science.gov (United States)
Bachelard, R; Dauxois, T; De Ninno, G; Ruffo, S; Staniscia, F
2011-06-01
We show that, in the continuum limit, the dynamics of Hamiltonian systems defined on a lattice with long-range couplings is well described by the Vlasov equation. This equation can be linearized around the homogeneous state, and a dispersion relation, which depends explicitly on the Fourier modes of the lattice, can be derived. This allows one to compute the stability thresholds of the homogeneous state, which turns out to depend on the mode number. When this state is unstable, the growth rates are also functions of the mode number. Explicit calculations are performed for the α-Hamiltonian mean field model with 0≤α<1, for which the mean-field mode is always found to dominate the exponential growth. The theoretical predictions are successfully compared with numerical simulations performed on a finite lattice.
10. Local Existence and Continuation Criterion for Solutions of the Spherically Symmetric Einstein-Vlasov-Maxwell System
CERN Document Server
Noundjeu, P
2003-01-01
Using the iterative Scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation criterion to global in-time solutions.
11. On Invariant Measures for the Vlasov Equation with a Regular Potential
CERN Document Server
Zhidkov, P E
2003-01-01
We consider a Vlasov equation with a smooth bounded potential of interaction between particles in a class of measure-valued solutions and construct a measure which is invariant for this problem in a sense.
12. Finite difference modeling of sinking stage curved beam based on revised Vlasov equations
Institute of Scientific and Technical Information of China (English)
张磊; 朱真才; 沈刚; 曹国华
2015-01-01
For the static analysis of the sinking stage curved beam, a finite difference model was presented based on the proposed revised Vlasov equations. First, revised Vlasov equations for thin-walled curved beams with closed sections were deduced considering the shear strain on the mid-surface of the cross-section. Then, the finite difference formulation of revised Vlasov equations was implemented with the parabolic interpolation based on Taylor series. At last, the finite difference model was built by substituting geometry and boundary conditions of the sinking stage curved beam into the finite difference formulation. The validity of present work is confirmed by the published literature and ANSYS simulation results. It can be concluded that revised Vlasov equations are more accurate than the original one in the analysis of thin-walled beams with closed sections, and that present finite difference model is applicable in the evaluation of the sinking stage curved beam.
13. On Higher-order Corrections to Gyrokinetic Vlasov-Poisson Equations in the Long Wavelength Limit
Energy Technology Data Exchange (ETDEWEB)
W.W. Lee and R.A. Kolesnikov
2009-02-17
In this paper, we present a simple iterative procedure for obtaining the higher order E x B and dE/dt (polarization) drifts associated with the gyrokinetic Vlasov-Poisson equations in the long wavelength limit of k⊥ρi ~ o(ε) and k⊥L ~ o(1), where ρi is the ion gyroradius, L is the scale length of the background inhomogeneity and ε is a smallness parameter. It can be shown that these new higher order k⊥ρi terms, which are also related to the higher order perturbations of the electrostatic potential Φ, should have negligible effects on turbulent and neoclassical transport in tokamaks, regardless of the form of the background distribution and the amplitude of the perturbation. To address further the issue of a non-Maxwellian plasma, higher order finite Larmor radius terms in the gyrokinetic Poisson's equation have been studied and shown to be unimportant as well. On the other hand, the terms of o(k2⊥ρi2) ~ o(ε) and k⊥L ~ o(1) can indeed have impact on microturbulence, especially in the linear stage, such as those arising from the difference between the guiding center and the gyrocenter densities due to the presence of the background gradients. These results will be compared with a recent study questioning the validity of the commonly used gyrokinetic equations for long time simulations.
14. Vlasov Simulation of Electrostatic Solitary Structures in Multi-Component Plasmas
Science.gov (United States)
Umeda, Takayuki; Ashour-Abdalla, Maha; Pickett, Jolene S.; Goldstein, Melvyn L.
2012-01-01
Electrostatic solitary structures have been observed in the Earth's magnetosheath by the Cluster spacecraft. Recent theoretical work has suggested that these solitary structures are modeled by electron acoustic solitary waves existing in a four-component plasma system consisting of core electrons, two counter-streaming electron beams, and one species of background ions. In this paper, the excitation of electron acoustic waves and the formation of solitary structures are studied by means of a one-dimensional electrostatic Vlasov simulation. The present result first shows that either electron acoustic solitary waves with negative potential or electron phase-space holes with positive potential are excited in four-component plasma systems. However, these electrostatic solitary structures have longer duration times and higher wave amplitudes than the solitary structures observed in the magnetosheath. The result indicates that a high-speed and small free energy source may be needed as a fifth component. An additional simulation of a five-component plasma consisting of a stable four-component plasma and a weak electron beam shows the generation of small and fast electron phase-space holes by the bump-on-tail instability. The physical properties of the small and fast electron phase-space holes are very similar to those obtained by the previous theoretical analysis. The amplitude and duration time of solitary structures in the simulation are also in agreement with the Cluster observation.
15. Processing of N2O ice by fast ions: implications on nitrogen chemistry in cold astrophysical environments
Science.gov (United States)
Almeida, G. C.; Pilling, S.; de Barros, A. L. F.; da Costa, C. A. P.; Pereira, R. C.; da Silveira, E. F.
2017-10-01
Nitrous oxide, N2O, is found in the interstellar medium associated with dense molecular clouds and its abundance is explained by active chemistry occurring on N2 rich ice surfaces of dust grains. Such regions are being constantly exposed to ionizing radiation that triggers chemical processes which change molecular abundances with time. Due to its non-zero dipole moment, N2O can be used as an important tracer for the abundance of N2 in such regions as well as for characterization of nitrogen content of ices in outer bodies of Solar system. In this work, we experimentally investigate the resistance of frozen N2O molecules against radiation in attempt to estimate their half-life in astrophysical environments. All the radiolysis products, such as NO2 and NO, were identified by Fourier transform infrared spectroscopy. The infrared absorbance as a function of fluence is modified by ice compaction and by radiolysis, the compaction being dominant at the beginning of the ice processing. The N2O destruction cross-section as well the formation cross-sections of the products NxOy (x = 1-2 and y = 1-5) oxides and ozone (O3) by 1.5 MeV 14N+ ion beam are determined. The characterization of radiation resistance of N2O in cold astrophysical environments is relevant since it yields limits for the nitrogen abundance where the N2O molecule is used to indirectly derive its concentration. The half-life of solid N2O molecules dissociated by medium-mass cosmic rays at Pluto's orbit and at the interstellar medium is estimated.
16. Vlasov-Poisson simulations of electrostatic parametric instability for localized Langmuir wave packets in the solar wind
CERN Document Server
Henri, Pierre; Briand, Carine; Mangeney, André; 10.1029/2009JA014969
2013-01-01
Recent observation of large amplitude Langmuir waveforms during a Type III event in the solar wind have been interpreted as the signature of the electrostatic decay of beam-driven Langmuir waves. This mechanism is thought to be a first step to explain the generation of solar Type III radio emission. The threshold for this parametric instability in typical solar wind condition is investigated here by means of 1D-1V Vlasov-Poisson simulations. We show that the amplitude of the observed Langmuir beat-like waveforms is of the order of the effective threshold computed from the full kinetic simulations. The expected level of associated ion acoustic density fluctuations have also been computed for comparison with observations.
17. The simultaneous determination of active ingredients in cough-cold mixtures by isocratic reversed-phase ion-pair high-performance liquid chromatography.
Science.gov (United States)
Lau, O W; Chan, K; Lau, Y K; Wong, W C
1989-01-01
A simple, rapid and accurate method for the simultaneous determination of active ingredients in cough-cold mixtures using isocratic reversed-phase ion-pair high-performance liquid chromatography has been developed. It involves the use of an octadecylsilane column as the stationary phase with methanol, water, tetrahydrofuran, phosphoric acid mixtures as mobile phase including sodium dioctylsulphosuccinate as the ion-pair agent. The pH of the mobile phase was adjusted to 4.6 by means of phosphoric acid and ammonium hydroxide solutions. The proposed method involves the simple dilution of the samples with the mobile phase and the addition of metoclopramide hydrochloride as the internal standard. The active ingredients under investigation were chlorpheniramine, codeine, diphenhydramine, ephedrine, ethylmorphine, phenylephrine, phenylpropanolamine and pholcodine, which exist as various combinations in cough-cold mixtures. The optimum composition of the mobile phase and the optimum flow rate were determined and are reported. The method was applied to the determination of active ingredients in seven commercially available cough-cold mixtures.
18. Landau damping of Gardner solitons in a dusty bi-ion plasma
Science.gov (United States)
Misra, A. P.; Barman, Arnab
2015-07-01
The effects of linear Landau damping on the nonlinear propagation of dust-acoustic solitary waves (DASWs) are studied in a collisionless unmagnetized dusty plasma with two species of positive ions. The extremely massive, micron-seized, cold, and negatively charged dust particles are described by fluid equations, whereas the two species of positive ions, namely, the cold (heavy) and hot (light) ions are described by the kinetic Vlasov equations. Following Ott and Sudan [Phys. Fluids 12, 2388 (1969)], and by considering lower and higher-order perturbations, the evolution of DASWs with Landau damping is shown to be governed by Korteweg-de Vries (KdV), modified KdV (mKdV), or Gardner (KdV-mKdV)-like equations. The properties of the phase velocity and the Landau damping rate of DASWs are studied for different values of the ratios of the temperatures (σ) and the number densities (μ) of hot and cold ions as well as the cold to hot ion mass ratio m. The distinctive features of the decay rates of the amplitudes of the KdV, mKdV, and Gardner solitons with a small effect of Landau damping are also studied in different parameter regimes. It is found that the Gardner soliton points to lower wave amplitudes than the KdV and mKdV solitons. The results may be useful for understanding the localization of solitary pulses and associated wave damping (collisionless) in laboratory and space plasmas (e.g., the F-ring of Saturn), in which the number density of free electrons is much smaller than that of ions and the heavy, micron seized dust grains are highly charged.
19. A Parallelized Vlasov-Fokker-Planck-Solver for Desktop PCs
CERN Document Server
Schönfeldt,; Brosi,; Miriam,; Schwarz,; Markus,; Steinmann,; L., Johannes; Müller,; Anke-Susanne,
2016-01-01
The numerical solution of the Vlasov-Fokker-Planck equation is a well established method to simulate the dynamics, including the self-interaction with its own wake field, of an electron bunch in a storage ring. In this paper we present Inovesa, a modularly extensible program that uses OpenCL to massively parallelize the computation. It allows a standard desktop PC to work with appropriate accuracy and yield reliable results within minutes. We provide numerical stability-studies over a wide parameter range and compare our numerical findings to known results. Simulation results for the case of coherent synchrotron radiation will be compared to measurements that probe the effects of the micro-bunching instability occurring in the short bunch operation at ANKA. It will be shown that the impedance model based on the shielding effect of two parallel plates can not only describe the instability threshold, but also the presence of multiple regimes that show differences in the emission of coherent synchrotron radiatio...
20. Parallelized Vlasov-Fokker-Planck solver for desktop personal computers
Directory of Open Access Journals (Sweden)
Patrik Schönfeldt
2017-03-01
Full Text Available The numerical solution of the Vlasov-Fokker-Planck equation is a well established method to simulate the dynamics, including the self-interaction with its own wake field, of an electron bunch in a storage ring. In this paper we present Inovesa, a modularly extensible program that uses opencl to massively parallelize the computation. It allows a standard desktop PC to work with appropriate accuracy and yield reliable results within minutes. We provide numerical stability-studies over a wide parameter range and compare our numerical findings to known results. Simulation results for the case of coherent synchrotron radiation will be compared to measurements that probe the effects of the microbunching instability occurring in the short bunch operation at ANKA. It will be shown that the impedance model based on the shielding effect of two parallel plates can not only describe the instability threshold, but also the presence of multiple regimes that show differences in the emission of coherent synchrotron radiation.
1. ADI type preconditioners for the steady state inhomogeneous Vlasov equation
CERN Document Server
Gasteiger, Markus; Ostermann, Alexander; Tskhakaya, David
2016-01-01
The purpose of the current work is to find numerical solutions of the steady state inhomogeneous Vlasov equation. This problem has a wide range of applications in the kinetic simulation of non-thermal plasmas. However, the direct application of either time stepping schemes or iterative methods (such as Krylov based methods like GMRES or relexation schemes) is computationally expensive. In the former case the slowest timescale in the system forces us to perform a long time integration while in the latter case a large number of iterations is required. In this paper we propose a preconditioner based on an ADI type splitting method. This preconditioner is then combined with both GMRES and Richardson iteration. The resulting numerical schemes scale almost ideally (i.e. the computational effort is proportional to the number of grid points). Numerical simulations conducted show that this can result in a speedup of close to two orders of magnitude (even for intermediate grid sizes) with respect to the not preconditio...
2. Vlasov Simulations of Ionospheric Heating Near Upper Hybrid Resonance
Science.gov (United States)
Najmi, A. C.; Eliasson, B. E.; Shao, X.; Milikh, G. M.; Papadopoulos, K.
2014-12-01
It is well-known that high-frequency (HF) heating of the ionosphere can excite field- aligned density striations (FAS) in the ionospheric plasma. Furthermore, in the neighborhood of various resonances, the pump wave can undergo parametric instabilities to produce a variety of electrostatic and electromagnetic waves. We have used a Vlasov simulation with 1-spatial dimension, 2-velocity dimensions, and 2-components of fields, to study the effects of ionospheric heating when the pump frequency is in the vicinity of the upper hybrid resonance, employing parameters currently available at ionospheric heaters such as HAARP. We have found that by seeding theplasma with a FAS of width ~20% of the simulation domain, ~10% depletion, and by applying a spatially uniform HF dipole pump electric field, the pump wave gives rise to a broad spectrum of density fluctuations as well as to upper hybrid and lower hybrid oscillating electric fields. We also observe collisionless bulk-heating of the electrons that varies non-linearly with the amplitude of the pump field.
3. Synergism between rare earth cerium(IV) ion and vanillin on the corrosion of cold rolled steel in 1.0 M HCl solution
Energy Technology Data Exchange (ETDEWEB)
Li Xianghong [Department of Fundamental Courses, Southwest Forestry University, Kunming 650224 (China)], E-mail: [email protected]; Deng Shuduan [Department of Wood Science and Technology, Southwest Forestry University, Kunming 650224 (China); Fu Hui [Department of Fundamental Courses, Southwest Forestry University, Kunming 650224 (China); Mu Guannan [Department of Chemistry, Yunnan University, Kunming 650091 (China)
2008-12-15
The synergism between rare earth cerium(IV) ion and vanillin on the corrosion of cold rolled steel (CRS) in 1.0 M HCl solution was first investigated by weight loss, potentiodynamic polarization, ultraviolet and visible spectrophotometer (UV-vis), X-ray photoelectron spectroscopy (XPS) and atomic force microscope (AFM). The results revealed that vanillin had a moderate inhibitive effect, and the adsorption of vanillin obeyed the Temkin adsorption isotherm. For rare earth Ce{sup 4+}, it had a negligible effect. However, incorporation of Ce{sup 4+} with vanillin significantly improved the inhibition performance, and produced strong synergistic inhibition effect. Depending on the results, the synergism mechanism was proposed.
4. Using the Orbit Tracking Code Z3CYCLONE to Predict the Beam Produced by a Cold Cathode PIG Ion Source for Cyclotrons under DC Extraction
CERN Document Server
Forringer, Edward
2005-01-01
Experimental measurements of the emittance and luminosity of beams produced by a cold-cathode Phillips Ionization Guage (PIG) ion source for cyclotrons under dc extraction are reviewed. (The source being studied is of the same style as ones that will be used in a series of 250 MeV proton cyclotrons being constructed for cancer therapy by ACCEL Inst, Gmbh, of Bergisch Gladbach, Germany.) The concepts of 'plasma boundary' and 'plasma temperature' are presented as a useful set of parameters for describing the initial conditions used in computational orbit tracking. Experimental results for r-pr and z-pz emittance are compared to predictions from the MSU orbit tracking code Z3CYCLONE with results indicating that the code is able to predict the beam produced by these ion sources with adequate accuracy such that construction of actual cyclotrons can proceed with reasonably prudent confidence that the cyclotron will perform as predicted.
5. Transient growth of a Vlasov plasma in a weakly inhomogeneous magnetic field
KAUST Repository
Ratushnaya, Valeria
2016-12-17
We investigate the stability properties of a collisionless Vlasov plasma in a weakly inhomogeneous magnetic field using non-modal stability analysis. This is an important topic in a physics of tokamak plasma rich in various types of instabilities. We consider a thin tokamak plasma in a Maxwellian equilibrium, subjected to a small arbitrary perturbation. Within the framework of kinetic theory, we demonstrate the emergence of short time scale algebraic instabilities evolving in a stable magnetized plasma. We show that the linearized governing operator (Vlasov operator) is non-normal leading to the transient growth of the perturbations on the time scale of several plasma periods that is subsequently followed by Landau damping. We calculate the first-order distribution function and the electric field and study the dependence of the transient growth characteristics on the magnetic field strength and perturbation parameters of the system. We compare our results with uniformly magnetized plasma and field-free Vlasov plasma.
6. Transient growth of a Vlasov plasma in a weakly inhomogeneous magnetic field
Science.gov (United States)
Ratushnaya, Valeria; Samtaney, Ravi
2016-12-01
We investigate the stability properties of a collisionless Vlasov plasma in a weakly inhomogeneous magnetic field using non-modal stability analysis. This is an important topic in a physics of tokamak plasma rich in various types of instabilities. We consider a thin tokamak plasma in a Maxwellian equilibrium, subjected to a small arbitrary perturbation. Within the framework of kinetic theory, we demonstrate the emergence of short time scale algebraic instabilities evolving in a stable magnetized plasma. We show that the linearized governing operator (Vlasov operator) is non-normal leading to the transient growth of the perturbations on the time scale of several plasma periods that is subsequently followed by Landau damping. We calculate the first-order distribution function and the electric field and study the dependence of the transient growth characteristics on the magnetic field strength and perturbation parameters of the system. We compare our results with uniformly magnetized plasma and field-free Vlasov plasma.
7. Relativistic Vlasov-Maxwell modelling using finite volumes and adaptive mesh refinement
CERN Document Server
Wettervik, Benjamin Svedung; Siminos, Evangelos; Fülöp, Tünde
2016-01-01
The dynamics of collisionless plasmas can be modelled by the Vlasov-Maxwell system of equations. An Eulerian approach is needed to accurately describe processes that are governed by high energy tails in the distribution function, but is of limited efficiency for high dimensional problems. The use of an adaptive mesh can reduce the scaling of the computational cost with the dimension of the problem. Here, we present a relativistic Eulerian Vlasov-Maxwell solver with block-structured adaptive mesh refinement in one spatial and one momentum dimension. The discretization of the Vlasov equation is based on a high-order finite volume method. A flux corrected transport algorithm is applied to limit spurious oscillations and ensure the physical character of the distribution function. We demonstrate a speed-up by a factor of five, because of the use of an adaptive mesh, in a typical scenario involving laser-plasma interaction in the self-induced transparency regime.
8. A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation
Energy Technology Data Exchange (ETDEWEB)
Banks, J W; Hittinger, J A
2009-11-24
Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.
9. Cold Stress
Science.gov (United States)
... Publications and Products Programs Contact NIOSH NIOSH COLD STRESS Recommend on Facebook Tweet Share Compartir Workers who ... cold environments may be at risk of cold stress. Extreme cold weather is a dangerous situation that ...
10. On global classical solutions of the three dimensional relativistic Vlasov-Darwin system
Science.gov (United States)
Li, Xiuting; Zhang, Xianwen
2016-08-01
We study the Cauchy problem of the relativistic Vlasov-Darwin system with generalized variables proposed by Sospedra-Alfonso et al. ["Global classical solutions of the relativistic Vlasov-Darwin system with small Cauchy data: the generalized variables approach," Arch. Ration. Mech. Anal. 205, 827-869 (2012)]. We prove global existence of a non-negative classical solution to the Cauchy problem in three space variables under small perturbation of the initial datum, and as a consequence, we obtain that nearly spherically symmetric solutions with required regularity exist globally in time.
11. Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
CERN Document Server
He, Yang; Qin, Hong; Liu, Jian
2016-01-01
In this paper, we develop Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations by applying conforming finite element methods in space and splitting methods in time. For the spatial discretisation, the criteria for choosing finite element spaces are presented such that the semi-discrete system possesses a discrete non-canonical Poisson structure. We apply a Hamiltonian splitting method to the semi-discrete system in time, then the resulting algorithm is Poisson preserving and explicit. The conservative properties of the algorithm guarantee the efficient and accurate numerical simulation of the Vlasov-Maxwell equations over long-time.
12. Hamiltonian reductions of the one-dimensional Vlasov equation using phase-space moments
Science.gov (United States)
Chandre, C.; Perin, M.
2016-03-01
We consider Hamiltonian closures of the Vlasov equation using the phase-space moments of the distribution function. We provide some conditions on the closures imposed by the Jacobi identity. We completely solve some families of examples. As a result, we show that imposing that the resulting reduced system preserves the Hamiltonian character of the parent model shapes its phase space by creating a set of Casimir invariants as a direct consequence of the Jacobi identity. We exhibit three main families of Hamiltonian models with two, three, and four degrees of freedom aiming at modeling the complexity of the bunch of particles in the Vlasov dynamics.
13. Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions
Energy Technology Data Exchange (ETDEWEB)
Batt, J.; Rein, G. (Muenchen Univ. (Germany). Mathematisches Inst.); Morrison, P.J. (Texas Univ., Austin, TX (United States))
1993-03-01
Rigorous results on the stability of stationary solutions of the Vlasov-Poisson system are obtained in both the plasma physics and stellar dynamics contexts. It is proven that stationary solutions in the plasma physics (stellar dynamics) case are linearly stable if they are decreasing (increasing) functions of the local, i.e. particle, energy. The main tool in the analysis is the free energy of the system, a conserved quantity. In addition, an appropriate global existence result is proven for the linearized Vlasov-Poisson system and the existence of stationary solutions that satisfy the above stability condition is established.
14. Wave Propagation in an Ion Beam-Plasma System
DEFF Research Database (Denmark)
Jensen, T. D.; Michelsen, Poul; Juul Rasmussen, Jens
1979-01-01
The spatial evolution of a velocity- or density-modulated ion beam is calculated for stable and unstable ion beam plasma systems, using the linearized Vlasov-Poisson equations. The propagation properties are found to be strongly dependent on the form of modulation. In the case of velocity...
15. Ion Acoustic Waves in the Presence of Langmuir Oscillations
DEFF Research Database (Denmark)
Pécseli, Hans
1976-01-01
The dielectric function for long-wavelength, low-frequency ion acoustic waves in the presence of short-wavelength, high-frequency electron oscillations is presented, where the ions are described by the collision-free Vlasov equation. The effect of the electron oscillations can be appropriately...
16. Photoluminescence of rare earth ions coactivated Ca{sub 9}Y(VO{sub 4}){sub 7} with cold, natural and warm white emission
Energy Technology Data Exchange (ETDEWEB)
Li, Ling, E-mail: [email protected] [Ministry-of-Education Key Laboratory for the Synthesis and Applications of Organic Functional Molecules, Hubei Collaborative Innovation Center for Advanced Organochemical Materials, Hubei University, Wuhan 430062 (China); Department of Physics, Pukyong National University, Busan 608-737 (Korea, Republic of); Liu, Xiaoguang, E-mail: [email protected] [Ministry-of-Education Key Laboratory for the Synthesis and Applications of Organic Functional Molecules, Hubei Collaborative Innovation Center for Advanced Organochemical Materials, Hubei University, Wuhan 430062 (China); Department of Physics, Pukyong National University, Busan 608-737 (Korea, Republic of); Noh, Hyeon Mi, E-mail: [email protected] [Department of Physics, Pukyong National University, Busan 608-737 (Korea, Republic of); Moon, Byung Kee, E-mail: [email protected] [Department of Physics, Pukyong National University, Busan 608-737 (Korea, Republic of); Choi, Byung Chun, E-mail: [email protected] [Department of Physics, Pukyong National University, Busan 608-737 (Korea, Republic of); Jeong, Jung Hyun, E-mail: [email protected] [Department of Physics, Pukyong National University, Busan 608-737 (Korea, Republic of)
2015-05-05
It has been still a challenge to obtain a new single-component white-light phosphor with the vanadates as host lattices and with two types of ions as activators. A systematic Ln{sub 1}{sup 3+}/Ln{sub 2}{sup 3+} (Ln{sub 1}{sup 3+}/Ln{sub 2}{sup 3+} = Dy{sup 3+}/Tm{sup 3+} or Dy{sup 3+}/Sm{sup 3+} or Dy{sup 3+}/Eu{sup 3+} or Tm{sup 3+}/Eu{sup 3+} or Tm{sup 3+}/Sm{sup 3+}) coactivated Ca{sub 9}Y(VO{sub 4}){sub 7} (CYV)samples as well as their singly doped CYV phosphors have been synthesized by the traditional solid state reaction and their photoluminescence properties have been investigated. The photoluminescence properties as a function of the concentration of rare earth ions have been discussed and the tunable luminescent color was found. The warm (CYV: 1%Dy{sup 3+}, 1%Sm{sup 3+}), natural (CYV: 7% Tm{sup 3+},0.5% Eu{sup 3+}; CYV: 1.0% Tm{sup 3+}, 0.5% Sm{sup 3+}), and cold (CYV: 3% Tm{sup 3+},0.5% Eu{sup 3+}; CYV: 0.5% Dy{sup 3+},0.5% Tm{sup 3+}; CYV: 0.5% Dy{sup 3+},0.7% Tm{sup 3+}; CYV: 0.3%Dy{sup 3+}, 0.5% Tm{sup 3+}) white lights can be obtained. Generally, the emission intensity or lifetime of one rare earth ions decreases with increasing of the concentration of another rare earth ions. - Highlights: • Photoluminescence properties of rare earth ions coactivated Ca{sub 9}Y(VO{sub 4}){sub 7} were investigated. • The effects of rare earth ions concentration on photoluminescence have been discussed. • The tunable luminescent color was found. • Cold, natural and warm white emissions were obtained.
17. Magnetic reconnection and kinetic effects in Vlasov turbulence
Science.gov (United States)
Servidio, Sergio
2015-04-01
The process of magnetic reconnection is ubiquitous in nature, being typical of large scale magnetic configurations. Recently [1], reconnection has been observed to emerge locally and intermittently in plasmas, being a crucial element of turbulence itself. Systematic analysis of MHD simulations reveals the presence of a large number of X-type neutral points, where magnetic reconnection occurs. More recently, the same phenomenon has been inspected within plasma models [2]. The link between magnetic reconnection and kinetic effects in the turbulent solar-wind has been investigated by means of multi-dimensional simulations of the hybrid Vlasov-Maxwell (HVM) code [3], using 5D (2D in space and 3D in velocity space) and full 6D simulations of plasma turbulence. Kinetic effects manifest through the deformation of the proton distribution function, with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. Recent analyses [4] of solar-wind data from spacecraft aimed to quantify kinetic effects through the temperature anisotropy T⊥/T|| on the proton velocity distribution function. Values of the anisotropy range broadly, with most values between 10-1 and 101. Moreover, the distribution of temperature anisotropy depends systematically on the ambient proton parallel beta β|| (the ratio of parallel kinetic pressure to magnetic pressure), manifesting a characteristic rhomboidal shape. In order to make contact with solar-wind observations, temperature anisotropy has been evaluated from an ensemble of HVM simulations [5], obtained by varying the global plasma beta and fluctuation level, in such a way to cover distinct regions of the parameter space defined by T⊥/T|| and β||. The HVM simulations presented here demonstrate that, when the distribution function is free to explore the entire velocity subspace, new features appear as complex interactions between the particles and the turbulent background. Comparison of numerical results
18. Landau damping effects on dust-acoustic solitary waves in a dusty negative-ion plasma
Energy Technology Data Exchange (ETDEWEB)
Barman, Arnab; Misra, A. P., E-mail: [email protected], E-mail: [email protected] [Department of Mathematics, Siksha Bhavana, Visva-Bharati University, Santiniketan 731 235, West Bengal (India)
2014-07-15
The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is studied in an unmagnetized dusty negative-ion plasma in the extreme conditions when the free electrons are absent. The cold massive charged dusts are described by fluid equations, whereas the two-species of ions (positive and negative) are described by the kinetic Vlasov equations. A Korteweg-de Vries (KdV) equation with Landau damping, governing the dynamics of weakly nonlinear and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids 12, 2388 (1969)]. It is shown that for some typical laboratory and space plasmas, the Landau damping (and the nonlinear) effects are more pronounced than the finite Debye length (dispersive) effects for which the KdV soliton theory is not applicable to DAWs in dusty pair-ion plasmas. The properties of the linear phase velocity, solitary wave amplitudes (in presence and absence of the Landau damping) as well as the Landau damping rate are studied with the effects of the positive ion to dust density ratio (μ{sub pd}) as well as the ratios of positive to negative ion temperatures (σ) and masses (m)
19. Convergence of the Vlasov-Poisson-Fokker- Planck system to the incompressible Euler equations
Institute of Scientific and Technical Information of China (English)
2006-01-01
We establish the convergence of the Vlasov-Poisson-Fokker-Planck system to the incompressible Euler equations in this paper. The convergence is rigorously proved on the time interval where the smooth solution to the incompressible Euler equations exists. The proof relies on the compactness argument and the so-called relative-entropy method.
20. The Cauchy Problem for the 3-D Vlasov-Poisson System with Point Charges
Science.gov (United States)
Marchioro, Carlo; Miot, Evelyne; Pulvirenti, Mario
2011-07-01
In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov-Poisson system in the presence of point charges with repulsive interaction. The present analysis extends an analogous two-dimensional result (Caprino and Marchioro in Kinet. Relat. Models 3(2):241-254, 2010).
1. The Cauchy problem for the 3-D Vlasov-Poisson system with point charges
CERN Document Server
Marchioro, Carlo; Pulvirenti, Mario
2010-01-01
In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov-Poisson system in presence of point charges in case of repulsive interaction. The present analysis extends an analogeous two-dimensional result by Caprino and Marchioro [On the plasma-charge model, to appear in Kinetic and Related Models (2010)].
2. Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations
Science.gov (United States)
Han-Kwan, Daniel; Nguyen, Toan T.
2016-09-01
In this paper, we develop an abstract framework to establish ill-posedness, in the sense of Hadamard, for some nonlocal PDEs displaying unbounded unstable spectra. We apply this to prove the ill-posedness for the hydrostatic Euler equations as well as for the kinetic incompressible Euler equations and the Vlasov-Dirac-Benney system.
3. On Local Smooth Solutions for the Vlasov Equation with the Potential of Interactions {\\pm} r^{-2}
CERN Document Server
Zhidkov, P E
2003-01-01
For the initial value problem for the Vlasov equation with the potential of interactions {\\pm} r^{-2} we prove the existence and uniqueness of a local solution with values in the Schwartz space S of infinitely differentiable functions rapidly decaying at infinity.
4. On the energy conservation by weak solutions of the relativistic Vlasov-Maxwell system
OpenAIRE
Sospedra-Alfonso, Reinel
2010-01-01
We show that weak solutions of the relativistic Vlasov-Maxwell system preserve the total energy provided that the electromagnetic field is locally of bounded variation and, for any $\\lambda$> 0, the one-particle distribution function has a square integrable $\\lambda$-moment in the momentum variable.
5. Cosmology and gravitational waves in the Nordstrom-Vlasov system, a laboratory for Dark Energy
CERN Document Server
Corda, Christian
2013-01-01
We discuss a cosmological solution of the system which was originally introduced by Calogero and is today popularly known as "Nordstrom-Vlasov system". Although the model is un-physical, its cosmological solution results interesting for the same reasons for which the Nordstrom-Vlasov system was originally introduced in the framework of galactic dynamics. In fact, it represents a theoretical laboratory where one can rigorously study some problems, like the importance of the gravitational waves in the dynamics, which at the present time are not well understood within the physical model of the Einstein-Vlasov system. As the cosmology of the Nordstrom-Vlasov system is founded on a scalar field, a better understanding of the system is important also in the framework of the Dark Energy problem. In fact, various attempts to achieve Dark Energy by using scalar fields are present in the literature. In the solution an analytical expression for the time dependence of the cosmological evolution of the Nordstrom's scalar ...
6. Resolution of the Vlasov-Maxwell system by PIC discontinuous Galerkin method on GPU with OpenCL
Directory of Open Access Journals (Sweden)
Crestetto Anaïs
2013-01-01
Full Text Available We present an implementation of a Vlasov-Maxwell solver for multicore processors. The Vlasov equation describes the evolution of charged particles in an electromagnetic field, solution of the Maxwell equations. The Vlasov equation is solved by a Particle-In-Cell method (PIC, while the Maxwell system is computed by a Discontinuous Galerkin method. We use the OpenCL framework, which allows our code to run on multicore processors or recent Graphic Processing Units (GPU. We present several numerical applications to two-dimensional test cases.
7. Cold Urticaria
Science.gov (United States)
Diseases and Conditions Cold urticaria By Mayo Clinic Staff Cold urticaria (ur-tih-KAR-e-uh) is a skin reaction to cold. Skin that has ... in contact with cold develops reddish, itchy welts (hives). The severity of cold urticaria symptoms varies widely. ...
8. Extraction of radioactive positive ions across the surface of superfluid helium : A new method to produce cold radioactive nuclear beams
NARCIS (Netherlands)
Huang, WX; Dendooven, P; Gloos, K; Takahashi, N; Pekola, JP; Aysto, J
2003-01-01
Alpha-decay recoils Rn-219 were stopped in superfluid helium and positive ions were extracted by electric field into the vapour phase. This first quantitative observation of extraction was successfully conducted using highly sensitive radioactivity detection. The efficiency for extraction across the
9. 3D solutions of the Poisson-Vlasov equations for a charged plasma and particle-core model in a line of FODO cells
Science.gov (United States)
Turchetti, G.; Rambaldi, S.; Bazzani, A.; Comunian, M.; Pisent, A.
2003-09-01
We consider a charged plasma of positive ions in a periodic focusing channel of quadrupolar magnets in the presence of RF cavities. The ions are bunched into charged triaxial ellipsoids and their description requires the solution of a fully 3D Poisson-Vlasov equation. We also analyze the trajectories of test particles in the exterior of the ion bunches in order to estimate their diffusion rate. This rate is relevant for a high intensity linac (TRASCO project). A numerical PIC scheme to integrate the Poisson-Vlasov equations in a periodic focusing system in 2 and 3 space dimensions is presented. The scheme consists of a single particle symplectic integrator and a Poisson solver based on FFT plus tri-diagonal matrix inversion. In the 2D version arbitrary boundary conditions can be chosen. Since no analytical self-consistent 3D solution is known, we chose an initial Neuffer-KV distribution in phase space, whose electric field is close to the one generated by a uniformly filled ellipsoid. For a matched (periodic) beam the orbits of test particles moving in the field of an ellipsoidal bunch, whose semi-axis satisfy the envelope equations, is similar to the orbits generated by the self-consistent charge distribition obtained from the PIC simulation, even though it relaxes to a Fermi-Dirac-like distribution. After a transient the RMS radii and emittances have small amplitude oscillations. The PIC simulations for a mismatched (quasiperiodic) beam are no longer comparable with the ellipsoidal bunch model even though the qualitative behavior is the same, namely a stronger diffusion due to the increase of resonances.
10. 3D solutions of the Poisson-Vlasov equations for a charged plasma and particle-core model in a line of FODO cells
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G.; Rambaldi, S.; Bazzani, A. [Dipartimento di Fisica and INFN, Via Irnerio 46, 40126, Bologna (Italy); Comunian, M.; Pisent, A. [INFN Laboratori Nazionali di Legnaro (Italy)
2003-09-01
We consider a charged plasma of positive ions in a periodic focusing channel of quadrupolar magnets in the presence of RF cavities. The ions are bunched into charged triaxial ellipsoids and their description requires the solution of a fully 3D Poisson-Vlasov equation. We also analyze the trajectories of test particles in the exterior of the ion bunches in order to estimate their diffusion rate. This rate is relevant for a high intensity linac (TRASCO project). A numerical PIC scheme to integrate the Poisson-Vlasov equations in a periodic focusing system in 2 and 3 space dimensions is presented. The scheme consists of a single particle symplectic integrator and a Poisson solver based on FFT plus tri-diagonal matrix inversion. In the 2D version arbitrary boundary conditions can be chosen. Since no analytical self-consistent 3D solution is known, we chose an initial Neuffer-KV distribution in phase space, whose electric field is close to the one generated by a uniformly filled ellipsoid. For a matched (periodic) beam the orbits of test particles moving in the field of an ellipsoidal bunch, whose semi-axis satisfy the envelope equations, is similar to the orbits generated by the self-consistent charge distribution obtained from the PIC simulation, even though it relaxes to a Fermi-Dirac-like distribution. After a transient the RMS radii and emittances have small amplitude oscillations. The PIC simulations for a mismatched (quasiperiodic) beam are no longer comparable with the ellipsoidal bunch model even though the qualitative behavior is the same, namely a stronger diffusion due to the increase of resonances. (orig.)
11. Three-dimensional ordering of cold ion beams in a storage ring: A molecular-dynamics simulation study
Energy Technology Data Exchange (ETDEWEB)
Yuri, Yosuke, E-mail: [email protected] [Takasaki Advanced Radiation Research Institute, Japan Atomic Energy Agency, 1233 Watanuki-machi Takasaki, Gunma 370-1292 Japan (Japan)
2015-06-29
Three-dimensional (3D) ordering of a charged-particle beams circulating in a storage ring is systematically studied with a molecular-dynamics simulation code. An ion beam can exhibit a 3D ordered configuration at ultralow temperature as a result of powerful 3D laser cooling. Various unique characteristics of the ordered beams, different from those of crystalline beams, are revealed in detail, such as the single-particle motion in the transverse and longitudinal directions, and the dependence of the tune depression and the Coulomb coupling constant on the operating points.
12. Vlasov simulations of electron hole dynamics in inhomogeneous magnetic field
Science.gov (United States)
Kuzichev, Ilya; Vasko, Ivan; Agapitov, Oleksiy; Mozer, Forrest; Artemyev, Anton
2017-04-01
13. Vlasov fluid stability of a 2-D plasma with a linear magnetic field null
Energy Technology Data Exchange (ETDEWEB)
Kim, J.S.
1984-01-01
Vlasov fluid stability of a 2-dimensional plasma near an O type magnetic null is investigated. Specifically, an elongated Z-pinch is considered, and applied to Field Reversed Configurations at Los Alamos National Laboratory by making a cylindrical approximation of the compact torus. The orbits near an elliptical O type null are found to be very complicated; the orbits are large and some are stochastic. The kinetic corrections to magnetohydrodynamics (MHD) are investigated by evaluating the expectation values of the growth rates of a Vlasov fluid dispersion functional by using set of trial functions based on ideal MHD. The dispersion functional involves fluid parts and orbit dependent parts. The latter involves phase integral of two time correlations. The phase integral is replaced by the time integral both for the regular and for the stochastic orbits. Two trial functions are used; one has a large displacement near the null and the other away from the null.
14. Linear Vlasov solver for microbunching gain estimation with inclusion of CSR, LSC and linac geometric impedances
CERN Document Server
Tsai, Cheng-Ying; Li, Rui; Tennant, Chris
2015-01-01
As is known, microbunching instability (MBI) has been one of the most challenging issues in designs of magnetic chicanes for short-wavelength free-electron lasers or linear colliders, as well as those of transport lines for recirculating or energy recovery linac machines. To more accurately quantify MBI in a single-pass system and for more complete analyses, we further extend and continue to increase the capabilities of our previously developed linear Vlasov solver [1] to incorporate more relevant impedance models into the code, including transient and steady-state free-space and/or shielding coherent synchrotron radiation (CSR) impedances, the longitudinal space charge (LSC) impedances, and the linac geometric impedances with extension of the existing formulation to include beam acceleration [2]. Then, we directly solve the linearized Vlasov equation numerically for microbunching gain amplification factor. In this study we apply this code to a beamline lattice of transport arc [3] following an upstream linac...
15. Non-modal stability analysis and transient growth in a magnetized Vlasov plasma
CERN Document Server
Ratushnaya, Valeria
2014-01-01
Collisionless plasmas, such as those encountered in tokamaks, exhibit a rich variety of instabilities. The physical origin, triggering mechanisms and fundamental understanding of many plasma instabilities, however, are still open problems. We investigate the stability properties of a collisionless Vlasov plasma in a stationary homogeneous magnetic field. We narrow the scope of our investigation to the case of Maxwellian plasma. For the first time using a fully kinetic approach we show the emergence of the local instability, a transient growth, followed by classical Landau damping in a stable magnetized plasma. We show that the linearized Vlasov operator is non-normal leading to the algebraic growth of the perturbations using non-modal stability theory. The typical time scales of the obtained instabilities are of the order of several plasma periods. The first-order distribution function and the corresponding electric field are calculated and the dependence on the magnetic field and perturbation parameters is s...
16. Progress on a Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits
CERN Document Server
Bassi, Gabriele; Warnock, Robert L
2005-01-01
We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates (shielding). The time evolution of the phase space distribution is determined by solving the Vlasov-Maxwell equations in the time domain. This provides lower numerical noise than the macroparticle method, and allows the study of emittance degradation and microbunching in bunch compressors. We calculate the fields excited by the bunch in the lab frame using a formula simpler than that based on retarded potentials.* We have developed an algorithm for solving the Vlasov equation in the beam frame using arc length as the independent variable and our method of local characteristics (discretized Perron-Frobenius operator).We integrate in the interaction picture in the hope that we can adopt a fixed grid. The distribution function will be represented by B-splines, in a scheme preserving positivity and normalization of the distribution. The transformation between l...
17. Vlasov simulations of self generated strong magnetic fields in plasmas and laser-plasma interaction
Directory of Open Access Journals (Sweden)
Inglebert A.
2013-11-01
Full Text Available A new formulation based on Hamiltonian reduction technique using the invariance of generalized canonical momentum is introduced for the study of relativistic Weibel-type instability. An example of application is given for the current filamentation instability resulting from the propagation of two counter-streaming electron beams in the relativistic regime of the instability. This model presents a double advantage. From an analytical point of view, the method is exact and standard fluid dispersion relations for Weibel or filamentation instabilies can be recovered. From a numerical point of view, the method allows a drastic reduction of the computational time. A 1D multi-stream Vlasov-Maxwell code is developed using such dynamical invariants in the perpendicular momentum space. Numerical comparison with a full Vlasov-Maxwell system has also been carried out to show the efficiency of this reduction technique.
18. An asymptotic preserving scheme for the relativistic Vlasov--Maxwell equations in the classical limit
CERN Document Server
Crouseilles, Nicolas; Faou, Erwan
2016-01-01
We consider the relativistic Vlasov--Maxwell (RVM) equations in the limit when the light velocity $c$ goes to infinity. In this regime, the RVM system converges towards the Vlasov--Poisson system and the aim of this paper is to construct asymptotic preserving numerical schemes that are robust with respect to this limit. Our approach relies on a time splitting approach for the RVM system employing an implicit time integrator for Maxwell's equations in order to damp the higher and higher frequencies present in the numerical solution. It turns out that the choice of this implicit method is crucial as even $L$-stable methods can lead to numerical instabilities for large values of $c$. A number of numerical simulations are conducted in order to investigate the performances of our numerical scheme both in the relativistic as well as in the classical limit regime. In addition, we derive the dispersion relation of the Weibel instability for the continuous and the discretized problem.
19. An asymptotic preserving scheme for the relativistic Vlasov-Maxwell equations in the classical limit
Science.gov (United States)
Crouseilles, Nicolas; Einkemmer, Lukas; Faou, Erwan
2016-12-01
We consider the relativistic Vlasov-Maxwell (RVM) equations in the limit when the light velocity c goes to infinity. In this regime, the RVM system converges towards the Vlasov-Poisson system and the aim of this paper is to construct asymptotic preserving numerical schemes that are robust with respect to this limit. Our approach relies on a time splitting approach for the RVM system employing an implicit time integrator for Maxwell's equations in order to damp the higher and higher frequencies present in the numerical solution. A number of numerical simulations are conducted in order to investigate the performances of our numerical scheme both in the relativistic as well as in the classical limit regime. In addition, we derive the dispersion relation of the Weibel instability for the continuous and the discretized problem.
20. Vlasov Fluid stability of a 2-D plasma with a linear magnetic field null
Energy Technology Data Exchange (ETDEWEB)
Kim, J.S.
1984-01-01
Vlasov Fluid stability of a 2-dimensional plasma near an O type magnetic null is investigated. Specifically, an elongated Z-pinch is considered, and applied to Field Reversed Configurations at Los Alamos National Laboratory by making a cylindrical approximation of the compact torus. The orbits near an elliptical O type null are found to be very complicated; the orbits are large and some are stochastic. The kinetic corrections to magnetohydrodynamics (MHD) are investigated by evaluating the expectation values of the growth rates of a Vlasov Fluid dispersion functional by using a set of trial functions based on ideal MHD. The dispersion functional involves fluid parts and orbit dependent parts. The latter involves phase integral of two time correlations. The phase integral is replaced by the time integral both for the regular and for the stochastic orbits. Two trial functions are used; one has a large displacement near the null and the other away from the null.
1. Veiled singularities for the spherically symmetric massless Einstein-Vlasov system
CERN Document Server
Rendall, Alan D
2016-01-01
This paper continues the investigation of the formation of naked singularities in the collapse of collisionless matter initiated in [RV]. There the existence of certain classes of non-smooth solutions of the Einstein-Vlasov system was proved. Those solutions are self-similar and hence not asymptotically flat. To obtain solutions which are more physically relevant it makes sense to attempt to cut off these solutions in a suitable way so as to make them asymptotically flat. This task, which turns out to be technically challenging, will be carried out in this paper. [RV] A. D. Rendall and J. J. L. Vel\\'{a}zquez, A class of dust-like self-similar solutions of the massless Einstein-Vlasov system. Annales Henri Poincare 12, 919-964, (2011).
2. Nonlinear wave evolution in VLASOV plasma: a lie-transform analysis
Energy Technology Data Exchange (ETDEWEB)
Cary, J.R.
1979-08-01
Nonlinear wave evolution in Vlasov plasma is analyzed using the Lie transform, a powerful mathematical tool which is applicable to Hamiltonian systems. The first part of this thesis is an exposition of the Lie transform. Dewar's general Lie transform theory is explained and is used to construct Deprit's Lie transform perturbation technique. The basic theory is illustrated by simple examples.
3. On classical solutions of the relativistic Vlasov-Klein-Gordon system
Directory of Open Access Journals (Sweden)
Michael Kunzinger
2005-01-01
Full Text Available We consider a collisionless ensemble of classical particles coupled with a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that classical solutions are global in time in the one-dimensional case.
4. The Goursat Problem for the Einstein-Vlasov System: (I) The Initial Data Constraints
CERN Document Server
2011-01-01
We show how to assign, on two intersecting null hypersurfaces, initial data for the Einstein-Vlasov system in harmonic coordinates. As all the components of the metric appear in each component of the stress-energy tensor, the hierarchical method of Rendall can not apply strictly speaking. To overcome this difficulty, an additional assumption have been imposed to the metric on the initial hypersurfaces. Consequently, the distribution function is constrained to satisfy some integral equations on the initial hypersurfaces.
5. Variational principles for the guiding-center Vlasov-Maxwell equations
CERN Document Server
Brizard, A J
2016-01-01
The Lagrange, Euler, and Euler-Poincar\\'{e} variational principles for the guiding-center Vlasov-Maxwell equations are presented. Each variational principle presents a different approach to deriving guiding-center polarization and magnetization effects into the guiding-center Maxwell equations. The conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guiding-center stress tensor is now shown to be explicitly symmetric.
6. Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach
Energy Technology Data Exchange (ETDEWEB)
Pham, Huyên, E-mail: [email protected]; Wei, Xiaoli, E-mail: [email protected] [Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris Diderot (France)
2016-12-15
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.
7. One-species Vlasov-Poisson-Landau system for soft potentials in ℝ3
Science.gov (United States)
He, Cong; Lei, Yuanjie
2016-12-01
We consider the global classical solution near a global Maxwellian to the one-species Vlasov-Poisson-Landau system in the whole space Rx 3 . It is shown that our global solvability result is obtained under the weaker smallness condition on the initial perturbation than that of Duan et al., [preprint arXiv:1112.3261 (2011)] and Lei et al., [Kinet. Relat. Models 7(3), 551-590 (2014)].
8. Geometric Integration Of The Vlasov-Maxwell System With A Variational Particle-in-cell Scheme
Energy Technology Data Exchange (ETDEWEB)
J. Squire, H. Qin and W.M. Tang
2012-03-27
A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus [1], the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.
9. Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
Energy Technology Data Exchange (ETDEWEB)
Squire, J.; Tang, W. M. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Qin, H. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)
2012-08-15
A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of discrete exterior calculus [Desbrun et al., e-print arXiv:math/0508341 (2005)], the field solver, interpolation scheme, and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.
10. Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
OpenAIRE
2014-01-01
A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus, the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.
11. Comparison between 1D and 1 1/2D Eulerian Vlasov codes for the numerical simulation of stimulated Raman scattering
Science.gov (United States)
Ghizzo, A.; Bertrand, P.; Lebas, J.; Shoucri, M.; Johnston, T.; Fijalkow, E.; Feix, M. R.
1992-10-01
The present 1 1/2D relativistic Euler-Vlasov code has been used to check the validity of a hydrodynamic description used in a 1D version of the Vlasov code. By these means, detailed numerical results can be compared; good agreement furnishes full support for the 1D electromagnetic Vlasov code, which runs faster than the 1 1/2D code. The results obtained assume a nonrelativistic v(y) velocity.
12. Collisional effects on the numerical recurrence in Vlasov-Poisson simulations
CERN Document Server
Pezzi, Oreste; Valentini, Francesco
2016-01-01
The initial state recurrence in numerical simulations of the Vlasov-Poisson system is a well-known phenomenon. Here we study the effect on recurrence of artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456-1459 (1958)]. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through a Eulerian collisional Vlasov-Poisson code. It is found that, despite being routinely used, an artificial collisionality is not a viable way of preventing recurrence in numerical simulations without compromising the kinetic nature of the solution. Moreover, it is shown how numerical effects associated to the generation of fine velocity scales, can modify the physical features of the system evolution even in nonlinear regime. This mean...
13. Collisional effects on the numerical recurrence in Vlasov-Poisson simulations
Energy Technology Data Exchange (ETDEWEB)
Pezzi, Oreste; Valentini, Francesco [Dipartimento di Fisica and CNISM, Università della Calabria, 87036 Rende (CS) (Italy); Camporeale, Enrico [Center for Mathematics and Computer Science (CWI), 1090 GB Amsterdam (Netherlands)
2016-02-15
The initial state recurrence in numerical simulations of the Vlasov-Poisson system is a well-known phenomenon. Here, we study the effect on recurrence of artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456–1459 (1958)]. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through an Eulerian collisional Vlasov-Poisson code. It is found that, despite being routinely used, an artificial collisionality is not a viable way of preventing recurrence in numerical simulations without compromising the kinetic nature of the solution. Moreover, it is shown how numerical effects associated to the generation of fine velocity scales can modify the physical features of the system evolution even in nonlinear regime. This means that filamentation-like phenomena, usually associated with low amplitude fluctuations contexts, can play a role even in nonlinear regime.
14. Beyond single stream with the Schroedinger method - Closing the Vlasov hierarchy
Energy Technology Data Exchange (ETDEWEB)
Uhlemann, Cora; Kopp, Michael; Haugg, Thomas [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-University, Theresienstr. 37, D-80333 Munich (Germany)
2014-07-01
We investigate large scale structure formation of dark matter in the phase-space description based on the Vlasov equation whose nonlinearity is induced by gravitational interaction according to the Poisson equation. Determining the time-evolution of density and peculiar velocity demands solving the full Vlasov hierarchy for the moments of the phase-space distribution function. In the presence of long-range interaction no consistent truncation of the hierarchy is known apart from the pressureless fluid (dust) model which is incapable of describing virialization due to the occurrence of shell-crossing singularities and the inability to generate higher cumulants like vorticity and velocity dispersion. Our goal is to find a phase-space distribution function that is able to describe regions of multi-streaming and therefore can serve as theoretical N-body double. We use the coarse-grained Wigner probability distribution obtained from a wavefunction fulfilling the Schroedinger equation and show that its evolution equation bears strong resemblance to the Vlasov equation but cures the shell-crossing singularities. This feature was already employed in cosmological simulations of large-scale structure formation by Widrow and Kaiser '93. We are able to show that the coarse-grained Wigner ansatz automatically closes the corresponding hierarchy while incorporating nonzero higher cumulants which are determined self-consistently from density and velocity.
15. Landau damping effects on dust-acoustic solitary waves in a dusty negative-ion plasma
CERN Document Server
Barman, A
2014-01-01
The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is studied in an unmagnetized dusty negative-ion plasma in the extreme conditions when the free electrons are absent. The cold massive charged dusts are described by fluid equations, whereas the two-species of ions (positive and negative) are described by the kinetic Vlasov equations. A Korteweg de-Vries (KdV) equation with Landau damping, governing the dynamics of weakly nonlinear and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids {\\bf 12}, 2388 (1969)]. It is shown that for some typical laboratory and space plasmas, the Landau damping (and the nonlinear) effects are more pronounced than the finite Debye length (dispersive) effects for which the KdV soliton theory is not applicable to DAWs in dusty pair-ion plasmas. The properties of the linear phase velocity, solitary wave amplitudes (in presence and absence of the Landau damping) as well as the Landau damping rate are studied with the effects of the positive io...
16. Cold nuclear fusion
Directory of Open Access Journals (Sweden)
Huang Zhenqiang Huang Yuxiang
2013-10-01
Full Text Available In normal temperature condition, the nuclear force constraint inertial guidance method, realize the combination of deuterium and tritium, helium and lithium... And with a magnetic moment of light nuclei controlled cold nuclear collide fusion, belongs to the nuclear energy research and development in the field of applied technology "cold nuclear collide fusion". According to the similarity of the nuclear force constraint inertial guidance system, the different velocity and energy of the ion beam mixing control, developed ion speed dc transformer, it is cold nuclear fusion collide, issue of motivation and the nuclear power plant start-up fusion and power transfer system of the important equipment, so the merger to apply for a patent
17. Common Cold
Science.gov (United States)
... nose, coughing - everyone knows the symptoms of the common cold. It is probably the most common illness. In the course of a year, people ... avoid colds. There is no cure for the common cold. For relief, try Getting plenty of rest ...
18. A conformational study of protonated noradrenaline by UV-UV and IR dip double resonance laser spectroscopy combined with an electrospray and a cold ion trap method.
Science.gov (United States)
Wako, Hiromichi; Ishiuchi, Shun-Ichi; Kato, Daichi; Féraud, Géraldine; Dedonder-Lardeux, Claude; Jouvet, Christophe; Fujii, Masaaki
2017-05-03
The conformer-selected ultraviolet (UV) and infrared (IR) spectra of protonated noradrenaline were measured using an electrospray/cryogenic ion trap technique combined with photo-dissociation spectroscopy. By comparing the UV photo dissociation (UVPD) spectra with the UV-UV hole burning (HB) spectra, it was found that five conformers coexist under ultra-cold conditions. Based on the spectral features of the IR dip spectra of each conformer, two different conformations on the amine side chain were identified. Three conformers (group I) were assigned to folded and others (group II) to extended structures by comparing the observed IR spectra with the calculated ones. Observation of the significantly less-stable extended conformers strongly suggests that the extended structures are dominant in solution and are detected in the gas phase by kinetic trapping. The conformers in each group are assignable to rotamers of OH orientations in the catechol ring. By comparing the UV-UV HB spectra and the calculated Franck-Condon spectra obtained by harmonic vibrational analysis of the S1 state, with the aid of relative stabilization energies of each conformer in the S0 state, the absolute orientations of catechol OHs of the observed five conformers were successfully determined. It was found that the 0-0 transition of one folded conformer is red-shifted by about 1000 cm(-1) from the others. The significant red-shift was explained by a large contribution of the πσ* state to S1 in the conformer in which an oxygen atom of the meta-OH group is close to the ammonium group.
19. Semiclassical Vlasov and fluid models for an electron gas with spin effects
CERN Document Server
Hurst, Jerome; Manfredi, Giovanni; Hervieux, Paul-Antoine
2014-01-01
We derive a four-component Vlasov equation for a system composed of spin-1/2 fermions (typically electrons). The orbital part of the motion is classical, whereas the spin degrees of freedom are treated in a completely quantum-mechanical way. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. This hydrodynamic model is closed using a maximum entropy principle in the case of three or four constraints on the fluid moments, both for Maxwell-Boltzmann and Fermi-Dirac statistics.
20. Goursat problem for the Yang-Mills-Vlasov system in temporal gauge
Directory of Open Access Journals (Sweden)
Marcel Dossa
2011-12-01
Full Text Available This article studies the characteristic Cauchy problem for the Yang-Mills-Vlasov (YMV system in temporal gauge, where the initial data are specified on two intersecting smooth characteristic hypersurfaces of Minkowski spacetime $(mathbb{R}^{4},eta$. Under a $mathcal{C}^{infty }$ hypothesis on the data, we solve the initial constraint problem and the evolution problem. Local in time existence and uniqueness results are established thanks to a suitable combination of the method of characteristics, Leray's Theory of hyperbolic systems and techniques developed by Choquet-Bruhat for ordinary spatial Cauchy problems related to (YMV systems.
1. Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit
CERN Document Server
Finkelshtein, Dmitri; Kutoviy, Oleksandr; Lytvynov, Eugene
2011-01-01
Let $\\Gamma$ denote the space of all locally finite subsets (configurations) in $\\mathbb R^d$. A stochastic dynamics of binary jumps in continuum is a Markov process on $\\Gamma$ in which pairs of particles simultaneously hop over $\\mathbb R^d$. We discuss a non-equilibrium dynamics of binary jumps. We prove the existence of an evolution of correlation functions on a finite time interval. We also show that a Vlasov-type mesoscopic scaling for such a dynamics leads to a generalized Boltzmann non-linear equation for the particle density.
2. Local null-controllability of the 2-D Vlasov-Navier-Stokes system
OpenAIRE
Moyano, Iván
2016-01-01
We prove a null controllability result for the Vlasov-Navier-Stokes system, which describes the interaction of a large cloud of particles immersed in a fluid. We show that one can modify both the distribution of particles and the velocity field of the fluid from any initial state to the zero steady state, by means of an internal control. Indeed, we can modify the non-linear dynamics of the system in order to absorb the particles and let the fluid at rest. The proof is achieved thanks to the r...
3. Self-similar analysis of Vlasov-Einstein equations in spherical symmetry
Energy Technology Data Exchange (ETDEWEB)
Munier, A.; Burgan, J.R.; Feix, M.; Fijalkow, E.
1980-03-15
The Vlasov-Einstein system of equations is studied from the point of view of group transformations. Continuous groups are shown to generalize the usual infinitesimal treatment of the metric tensor to the case of a distribution function. Reduced equations are obtained, leading to a time-dependent analytical solution, which yields as a limiting case the Schwarzchild metric. The problem of a purely radial motion of null particles is discussed and leads to an expression for the redshift in a nonstatic, inhomogeneous spacetime.
4. Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
Science.gov (United States)
Squire, Jonathan; Qin, Hong; Tang, William
2012-10-01
A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus [1], the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law. This work was supported by USDOE Contract DE-AC02-09CH11466.[4pt] [1] M. Desbrun, A. N. Hirani, M. Leok, and J. E. Marsden, (2005), arXiv:math/0508341
5. Future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a cosmological constant
CERN Document Server
Nungesser, Ernesto
2014-01-01
We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an inductive argument. In a recent research monograph Ringstr\\"{o}m shows future non-linear stability of (not necessarily symmetric) solutions of the Einstein-Vlasov system with a non-linear scalar field if certain local estimates on the geometry and the matter terms are fulfilled. We show that these assumptions are satisfied at late times for the case under consideration here which together with Cauchy stability leads to our main conclusion.
6. Nonlinear wave structures as exact solutions of Vlasov-Maxwell equations.
Science.gov (United States)
Dasgupta, B.; Tsurutani, B. T.; Janaki, M. S.; Sharma, A. S.
2001-12-01
Many recent observations by POLAR and Geotail spacecraft of the low-latitudes magnetopause boundary layer (LLBL) and the polar cap boundary layer (PCBL) have detected nonlinear wave structures [Tsurutani et al, Geophys. Res. Lett., 25, 4117, 1998]. These nonlinear waves have electromagnetic signatures that are identified with Alfven and Whistler modes. Also solitary waves with mono- and bi-polar features were observed. In general such electromagnetic structures are described by the full Vlasov-Maxwell equations for waves propagating at an angle to the ambient magnetic field, but it has been a diffficult task obtaining the solutions because of the inherent nonlinearity. We have obtained an exact nonlinear solution of the full Vlasov-Maxwell equations in the presence of an electromagnetic wave propagating at an arbitrary direction with an ambient magnetic field. This is accomplished by finding the constants of motion of the charged particles in the electromagnetic field of the wave and then constructing a realistic distribution function as a function of these constants of motion. The corresponding trapping conditions for such waves are obtained, yielding the self-consistent description for the particles in the presence of the nonlinear waves. The interpretation of the observed nonlinear structures in terms of these general solutions will be presented.
7. Non-modal stability analysis and transient growth in a magnetized Vlasov plasma
KAUST Repository
Ratushnaya, V.
2014-12-01
Collisionless plasmas, such as those encountered in tokamaks, exhibit a rich variety of instabilities. The physical origin, triggering mechanisms and fundamental understanding of many plasma instabilities, however, are still open problems. We investigate the stability properties of a 3-dimensional collisionless Vlasov plasma in a stationary homogeneous magnetic field. We narrow the scope of our investigation to the case of Maxwellian plasma and examine its evolution with an electrostatic approximation. For the first time using a fully kinetic approach we show the emergence of the local instability, a transient growth, followed by classical Landau damping in a stable magnetized plasma. We show that the linearized Vlasov operator is non-normal leading to the algebraic growth of the perturbations using non-modal stability theory. The typical time scales of the obtained instabilities are of the order of several plasma periods. The first-order distribution function and the corresponding electric field are calculated and the dependence on the magnetic field and perturbation parameters is studied. Our results offer a new scenario of the emergence and development of plasma instabilities on the kinetic scale.
8. Cold Sores
Science.gov (United States)
... Previous Next Related Articles: Canker and Cold Sores Aloe Vera May Help Relieve Mouth Sores Canker Sore or Cold Sore? Mouth Sores: Caused By Student Stress? games Home | InfoBites | Find a Dentist | Your Family's Oral Health | Newsroom | RSS About AGD | Contact AGD | Site Map | ...
9. Asymptotic-preserving Particle-In-Cell methods for the Vlasov-Maxwell system near quasi-neutrality
CERN Document Server
Degond, Pierre; Doyen, David
2015-01-01
In this article, we design Asymptotic-Preserving Particle-In-Cell methods for the Vlasov-Maxwell system in the quasi-neutral limit, this limit being characterized by a Debye length negligible compared to the space scale of the problem. These methods are consistent discretizations of the Vlasov-Maxwell system which, in the quasi-neutral limit, remain stable and are consistent with a quasi-neutral model (in this quasi-neutral model, the electric field is computed by means of a generalized Ohm law). The derivation of Asymptotic-Preserving methods is not straightforward since the quasi-neutral model is a singular limit of the Vlasov-Maxwell model. The key step is a reformulation of the Vlasov-Maxwell system which unifies the two models in a single set of equations with a smooth transition from one to another. As demonstrated in various and demanding numerical simulations, the Asymptotic-Preserving methods are able to treat efficiently both quasi-neutral plasmas and non-neutral plasmas, making them particularly we...
10. Asymptotic-Preserving Particle-In-Cell methods for the Vlasov-Maxwell system in the quasi-neutral limit
Science.gov (United States)
Degond, P.; Deluzet, F.; Doyen, D.
2017-02-01
In this article, we design Asymptotic-Preserving Particle-In-Cell methods for the Vlasov-Maxwell system in the quasi-neutral limit, this limit being characterized by a Debye length negligible compared to the space scale of the problem. These methods are consistent discretizations of the Vlasov-Maxwell system which, in the quasi-neutral limit, remain stable and are consistent with a quasi-neutral model (in this quasi-neutral model, the electric field is computed by means of a generalized Ohm law). The derivation of Asymptotic-Preserving methods is not straightforward since the quasi-neutral model is a singular limit of the Vlasov-Maxwell model. The key step is a reformulation of the Vlasov-Maxwell system which unifies the two models in a single set of equations with a smooth transition from one to another. As demonstrated in various and demanding numerical simulations, the Asymptotic-Preserving methods are able to treat efficiently both quasi-neutral plasmas and non-neutral plasmas, making them particularly well suited for complex problems involving dense plasmas with localized non-neutral regions.
11. On local smooth solutions for the Vlasov equation with the potential of interactions ±r−2
OpenAIRE
Peter Zhidkov
2004-01-01
For the initial value problem for the Vlasov equation with the potential of interactions ±r−2, we prove the existence and uniqueness of a local solution with values in the Schwartz space S of infinitely differentiable functions rapidly decaying at infinity.
12. Gene Expression, Protein Function and Pathways of Arabidopsis thaliana Responding to Silver Nanoparticles in Comparison to Silver Ions, Cold, Salt, Drought, and Heat
Directory of Open Access Journals (Sweden)
Eisa Kohan-Baghkheirati
2015-03-01
Full Text Available Silver nanoparticles (AgNPs have been widely used in industry due to their unique physical and chemical properties. However, AgNPs have caused environmental concerns. To understand the risks of AgNPs, Arabidopsis microarray data for AgNP, Ag+, cold, salt, heat and drought stresses were analyzed. Up- and down-regulated genes of more than two-fold expression change were compared, while the encoded proteins of shared and unique genes between stresses were subjected to differential enrichment analyses. AgNPs affected the fewest genes (575 in the Arabidopsis genome, followed by Ag+ (1010, heat (1374, drought (1435, salt (4133 and cold (6536. More genes were up-regulated than down-regulated in AgNPs and Ag+ (438 and 780, respectively while cold down-regulated the most genes (4022. Responses to AgNPs were more similar to those of Ag+ (464 shared genes, cold (202, and salt (163 than to drought (50 or heat (30; the genes in the first four stresses were enriched with 32 PFAM domains and 44 InterPro protein classes. Moreover, 111 genes were unique in AgNPs and they were enriched in three biological functions: response to fungal infection, anion transport, and cell wall/plasma membrane related. Despite shared similarity to Ag+, cold and salt stresses, AgNPs are a new stressor to Arabidopsis.
13. Existence of Global Weak Solutions to a Hybrid Vlasov-MHD Model for Magnetized Plasmas
CERN Document Server
Cheng, Bin; Tronci, Cesare
2016-01-01
We prove the global-in-time existence of large-data finite-energy weak solutions to an incompressible hybrid Vlasov-magnetohydrodynamic model in three space dimensions. The model couples three essential ingredients of magnetized plasmas: a transport equation for the probability density function, which models energetic rarefied particles of one species; the incompressible Navier--Stokes system for the bulk fluid; and a parabolic evolution equation, involving magnetic diffusivity, for the magnetic field. The physical derivation of our model is given. It is also shown that the weak solution, whose existence is established, has nonincreasing total energy, and that it satisfies a number of physically relevant properties, including conservation of the total momentum, conservation of the total mass, and nonnegativity of the probability density function for the energetic particles. The proof is based on a one-level approximation scheme, which is carefully devised to avoid increase of the total energy for the sequence...
14. Description of the evolution of inhomogeneities on a dark matter halo with the Vlasov equation
Science.gov (United States)
Domínguez-Fernández, Paola; Jiménez-Vázquez, Erik; Alcubierre, Miguel; Montoya, Edison; Núñez, Darío
2017-09-01
We use a direct numerical integration of the Vlasov equation in spherical symmetry with a background gravitational potential to determine the evolution of a collection of particles in different models of a galactic halo in order to test its stability against perturbations. Such collection is assumed to represent a dark matter inhomogeneity which is represented by a distribution function defined in phase-space. Non-trivial stationary states are obtained and determined by the virialization of the system. We describe some features of these stationary states by means of the properties of the final distribution function and final density profile. We compare our results using the different halo models and find that the NFW halo model is the most stable of them, in the sense that an inhomogeneity in this halo model requires a shorter time to virialize.
15. From one-dimensional fields to Vlasov equilibria: Theory and application of Hermite polynomials
CERN Document Server
Allanson, O; Troscheit, S; Wilson, F
2016-01-01
We consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a Vlasov-Maxwell equilibrium for a given macroscopic (fluid) equilibrium. Using Jeans' Theorem, the equilibrium distribution functions are expressed as functions of the constants of motion, in the form of a Maxwellian multiplied by an unknown function of the canonical momenta. In this case it is possible to reduce the inverse problem to inverting Weierstrass transforms, which we achieve by using expansions over Hermite polynomials. A sufficient condition on the pressure tensor is found which guarantees the convergence and the boundedness of the candidate solution, when satisfied. This condition is obtained by elementary means, and it is clear how to put it into practice. We also argue that for a given pressure tensor for which our method applies, there always exists a positive distribution function solution for a sufficiently magnetised plasma. Illustrative examples of th...
16. A Reduction of the Vlasov--Maxwell System Using Phase-Space Blobs
Science.gov (United States)
Shadwick, B. A.; Lee, Frank M.; Faeh, Luke
2011-10-01
We develop a new computational approach to solving the Vlasov-Maxwell equation by representing the distribution function by a supper-position of finite-extent phase- space blobs.'' Each blob evolves as a warm beamletdriven by the collective plasma fields. The underlying approximation treats each blob as a different plasma species and, as such, makes a counting error which we expect to be reflected in the system entropy. This approach results in a non-canonical Hamiltonian model, inheriting various properties of the original system. The primary advance of this technique over traditional Lagrangian particle methods is the near elimination of macro-particle noise.'' Since we are evolving elements of phase-space, the distribution function can be readily reconstructed at any instant. We discuss the performance and convergence of this model using a variety of standard examples. Supported by the U.S. DoE under Contract DE-FG02-08ER55000
17. Vlasov Simulations of Ladder Climbing and Autoresonant Acceleration of Langmuir Waves
Science.gov (United States)
Hara, Kentaro; Barth, Ido; Kaminski, Erez; Dodin, Ilya; Fisch, Nathaniel
2016-10-01
The energy of plasma waves can be moved up and down the spectrum using chirped modulations of plasma parameters, which can be driven by external fields. Depending on the discreteness of the wave spectrum, this phenomenon is called ladder climbing (LC) or autroresonant acceleration (AR) of plasmons, and was first proposed by Barth et al. based on a linear fluid model. Here, we report a demonstration of LC/AR from first principles using fully nonlinear Vlasov simulations of collisionless bounded plasma. We show that, in agreement to the basic theory, plasmons survive substantial transformations of the spectrum and are destroyed only when their wave numbers become large enough to trigger Landau damping. The work was supported by the NNSA SSAA Program through DOE Research Grant No. DE-NA0002948 and the DTRA Grant No. HDTRA1-11-1-0037.
18. A Full Eulerian Vlasov-Maxwell Study of Turbulent Dynamics and Dissipation
Science.gov (United States)
TenBarge, J. M.; Juno, J.; Hakim, A.
2016-12-01
The development of a detailed understanding of turbulence in magnetized plasmas has been a long standing goal of the broader scientific community, both as a fundamental physics process and because of its applicability to a wide variety of phenomena. Turbulence in a magnetized plasma is the primary mechanism responsible for transforming energy at large injection scales into small-scale motions, which are ultimately dissipated as heat in systems such as the solar corona and wind. At large scales, the turbulence is well described by fluid models of the plasma; however, understanding the processes responsible for heating a weakly collisional plasma such as the solar wind requires a kinetic description. We present the first fully kinetic Eulerian Vlasov-Maxwell study of turbulence using the Gkeyll simulation code. We focus on the pristine distribution function dynamics that are possible with the Eulerian approach. We also present the signatures and form of dissipation as diagnosed via field-particle correlation functions.
19. The Hamiltonian structure and Euler-Poincare formulation of the Vlasov-Maxwell and gyrokinetic systems
Energy Technology Data Exchange (ETDEWEB)
Squire, J.; Tang, W. M. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Qin, H. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Chandre, C. [Centre de Physique Theorique, CNRS - Aix-Marseille Universite, Campus de Luminy, Marseille 13009 (France)
2013-02-15
We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in H. Cendra et al., [J. Math. Phys. 39, 3138 (1998)]. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models, and Casimir type stability methods.
20. On the spatially homogeneous and isotropic Einstein-Vlasov-Fokker-Planck system with cosmological scalar field
CERN Document Server
Calogero, Simone
2016-01-01
The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions and prove the existence of both global solutions and solutions that blow-up in finite time depending on the size of certain functions of the initial data. We also derive information on the large-time behavior of global solutions and toward the singularity for solutions which blow-up in fine time. Our results entail the existence of a phase of decelerated expansion followed by a phase of accelerated expansion, in accordance with the physical expectations in cosmology.
1. Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
Science.gov (United States)
He, Yang; Sun, Yajuan; Qin, Hong; Liu, Jian
2016-09-01
In this paper, we study the Vlasov-Maxwell equations based on the Morrison-Marsden-Weinstein bracket. We develop Hamiltonian particle-in-cell methods for this system by employing finite element methods in space and splitting methods in time. In order to derive the semi-discrete system that possesses a discrete non-canonical Poisson structure, we present a criterion for choosing the appropriate finite element spaces. It is confirmed that some conforming elements, e.g., Nédélec's mixed elements, satisfy this requirement. When the Hamiltonian splitting method is used to discretize this semi-discrete system in time, the resulting algorithm is explicit and preserves the discrete Poisson structure. The structure-preserving nature of the algorithm ensures accuracy and fidelity of the numerical simulations over long time.
2. Canonicalizable gyrocenter and structure-preserving geometric algorithms for the Vlasov-Maxwell system
Science.gov (United States)
Qin, Hong
2016-10-01
Littlejohn's introduction of the non-canonical symplectic structure for the gyrocenter dynamics revolutionized plasma kinetic theory. The discovery of the non-canonical symplectic algorithm for gyrocenters initiated the search for symplectic algorithms for the gyrokinetic system. This effort is enforced by the recent discovery of canonical and non-canonical symplectic algorithms for the Vlasov-Maxwell (VM) system. However, symplectic algorithms for the gyrokinetic system remain elusive despite intense effort. In retrospect, the success of the symplectic algorithms for the VM system can be attributed to its global canonicalizability. Darboux's theorem ensures that any symplectic structure is locally canonicalizable, but not necessarily globally. Indeed, Littlejohn's gyrocenter is not globally canonicalizable. In this talk, I will show to construct a different gyrocenter that is globally canonicalizable. It should be a good starting point for developing symplectic algorithms for the gyrokinetic system. Research supported by the U.S. Department of Energy (DE-AC02-09CH11466).
3. On the multistream approach of relativistic Weibel instability. III. Comparison with full-kinetic Vlasov simulations
Energy Technology Data Exchange (ETDEWEB)
Ghizzo, A. [Institut Jean Lamour UMR 7163, Université de Lorraine, BP 239 F-54506 Vandoeuvre les Nancy (France)
2013-08-15
The saturation of the Weibel instability in the relativistic regime is investigated within the Hamiltonian reduction technique based on the multistream approach developed in paper I in the linear case and in paper II for the nonlinear saturation. In this work, the study is compared with results obtained by full kinetic 1D2V Vlasov-Maxwell simulations based on a semi-Lagrangian technique. For a temperature anisotropy, qualitatively different regimes are realized depending on the excitation of the longitudinal (plasma) electric field, in contrast with the existing theories of the Weibel instability based on their purely transverse characters. The emphasis here is on gaining a better understanding of the nonlinear aspects of the Weibel instability. The multistream model offers an alternate way to make calculations or numerical experiments more tractable, when only a few moments of the velocity distribution of the plasma are considered.
4. Vlasov simulations of kinetic Alfvén waves at proton kinetic scales
Energy Technology Data Exchange (ETDEWEB)
Vásconez, C. L. [Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza (Italy); Observatorio Astronómico de Quito, Escuela Politécnica Nacional, Quito (Ecuador); Valentini, F.; Veltri, P. [Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza (Italy); Camporeale, E. [Centrum Wiskunde and Informatica, Amsterdam (Netherlands)
2014-11-15
Kinetic Alfvén waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton gyro radius ρ{sub p} and/or inertial length d{sub p} and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems. In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the kinetic Alfvén waves at proton kinetic scales, in typical conditions of the solar wind environment (proton plasma beta β{sub p} = 1). In particular, linear and nonlinear regimes of propagation of these fluctuations have been investigated in a single-wave situation, focusing on the physical processes of collisionless Landau damping and wave-particle resonant interaction. Interestingly, since for wavelengths close to d{sub p} and β{sub p} ≃ 1 (for which ρ{sub p} ≃ d{sub p}) the kinetic Alfvén waves have small phase speed compared to the proton thermal velocity, wave-particle interaction processes produce significant deformations in the core of the particle velocity distribution, appearing as phase space vortices and resulting in flat-top velocity profiles. Moreover, as the Eulerian hybrid Vlasov-Maxwell algorithm allows for a clean almost noise-free description of the velocity space, three-dimensional plots of the proton velocity distribution help to emphasize how the plasma departs from the Maxwellian configuration of thermodynamic equilibrium due to nonlinear kinetic effects.
5. A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell algorithm
CERN Document Server
Chen, Guangye
2015-01-01
For decades, the Vlasov-Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. Here, we explore a fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space-time-centered, employing particle sub-cycling and orbit-averaging. The algorithm conserves total energy, local charge, canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large time steps and cell sizes, which are determined by accuracy consid...
6. An adaptive, high-order phase-space remapping for the two-dimensional Vlasov-Poisson equations
CERN Document Server
Wang, Bei; Colella, Phil
2012-01-01
The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the distribution function in phase space. To control the numerical error, we introduce an adaptive phase-space remapping which regularizes the particle distribution by periodically reconstructing the distribution function on a hierarchy of phase-space grids with high-order interpolations. The positivity of the distribution function can be preserved by using a local redistribution technique. The method has been successfully applied to a set of classical plasma problems in one dimension. In this paper, we present the algorithm for the two dimensional Vlasov-Poisson equations. An efficient Poisson solver with infinite domain boundary conditions is used. The parallel scalability of the algorithm on massively parallel computers will be discussed.
7. The Einstein-Vlasov system with cosmological constant in a surface-symmetric cosmological model local existence and continuation criteria
CERN Document Server
Tchapnda, S B; Tchapnda, Sophonie Blaise; Noutchegueme, Norbert
2003-01-01
The Einstein-Vlasov system describes a self-gravitating, collisionless gas within the framework of general relativity. We investigate the initial value problem in a cosmological setting with surface symmetry and a non-zero cosmological constant and prove local existence and continuation criteria in both time directions. The continuation criterion says that as long as the maximum velocity remains bounded and the lapse function remains bounded then the solution can be continued. This applies to either time direction.
8. The Vlasov-Navier-Stokes system in a 2D pipe: existence and stability of regular equilibria
OpenAIRE
Glass, Olivier; Han-Kwan, Daniel; Moussa, Ayman
2016-01-01
In this paper, we study the Vlasov-Navier-Stokes system in a 2D pipe with partially absorbing boundary conditions. We show the existence of stationary states for this system near small Poiseuille flows for the fluid phase, for which the kinetic phase is not trivial. We prove the asymptotic stability of these states with respect to appropriately compactly supported perturbations. The analysis relies on geometric control conditions which help to avoid any concentration phenomenon for the kineti...
9. Vlasov equation eigenvalues and eigenvectors for Fourier-Hermite dispersion matrices of order greater than 1,000
Science.gov (United States)
Grant, F. C.
1972-01-01
The connection between the Van Kampen and Landau representations of the Vlasov equations has been extended to Fourier-Hermite expansions containing more than 1000 terms by taking advantage of the properties of tridiagonal matrices. These numerical results are regarded as conclusive indications of the nonuniformly convergent behavior of the approximation curve in the limit of an infinite number of terms and represent an extension of work begun by Grant (1967) and by Grant and Feix (1967).
10. Global existence of solutions to the incompressible Navier-Stokes-Vlasov equations in a time-dependent domain
Science.gov (United States)
Boudin, Laurent; Grandmont, Céline; Moussa, Ayman
2017-02-01
In this article, we prove the existence of global weak solutions for the incompressible Navier-Stokes-Vlasov system in a three-dimensional time-dependent domain with absorption boundary conditions for the kinetic part. This model arises from the study of respiratory aerosol in the human airways. The proof is based on a regularization and approximation strategy designed for our time-dependent framework.
11. Common cold
Science.gov (United States)
... have a low fever or no fever. Young children often run a fever around 100 to 102°F (37.7 to 38.8°C). Depending on which virus caused your cold, you may also have: Cough Decreased appetite Headache Muscle aches Postnasal drip Sore throat
12. Project COLD.
Science.gov (United States)
Kazanjian, Wendy C.
1982-01-01
Describes Project COLD (Climate, Ocean, Land, Discovery) a scientific study of the Polar Regions, a collection of 35 modules used within the framework of existing subjects: oceanography, biology, geology, meterology, geography, social science. Includes a partial list of topics and one activity (geodesic dome) from a module. (Author/SK)
13. A class of dust-like self-similar solutions of the massless Einstein-Vlasov system
CERN Document Server
Rendall, Alan D
2010-01-01
In this paper the existence of a class of self-similar solutions of the Einstein-Vlasov system is proved. The initial data for these solutions are not smooth, with their particle density being supported in a submanifold of codimension one. They can be thought of as intermediate between smooth solutions of the Einstein-Vlasov system and dust. The motivation for studying them is to obtain insights into possible violation of weak cosmic censorship by solutions of the Einstein-Vlasov system. By assuming a suitable form of the unknowns it is shown that the existence question can be reduced to that of the existence of a certain type of solution of a four-dimensional system of ordinary differential equations depending on two parameters. This solution starts at a particular point $P_0$ and converges to a stationary solution $P_1$ as the independent variable tends to infinity. The existence proof is based on a shooting argument and involves relating the dynamics of solutions of the four-dimensional system to that of s...
14. Cold fusion
Energy Technology Data Exchange (ETDEWEB)
Suh, Suk Yong; Sung, Ki Woong; Kang, Joo Sang; Lee, Jong Jik [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1995-02-01
So called cold fusion phenomena are not confirmed yet. Excess heat generation is very delicate one. Neutron generation is most reliable results, however, the records are erratic and the same results could not be repeated. So there is no reason to exclude the malfunction of testing instruments. The same arguments arise in recording {sup 4}He, {sup 3}He, {sup 3}H, which are not rich in quantity basically. An experiment where plenty of {sup 4}He were recorded is attached in appendix. The problem is that we are trying to search cold fusion which is permitted by nature or not. The famous tunneling effect in quantum mechanics will answer it, however, the most fusion rate is known to be negligible. The focus of this project is on the theme that how to increase that negligible fusion rate. 6 figs, 4 tabs, 1512 refs. (Author).
15. Electron/ion whistler instabilities and magnetic noise bursts
Science.gov (United States)
Akimoto, K.; Gary, S. Peter; Omidi, N.
1987-01-01
Two whistler instabilities are investigated by means of the linear Vlasov dispersion equation. They are called the electron/ion parallel and oblique whistler instabilities, and are driven by electron/ion relative drifts along the magnetic field. It is demonstrated that the enhanced fluctuations from these instabilities can explain several properties of magnetic noise bursts in and near the plasma sheet in the presence of ion beams and/or field-aligned currents. At sufficiently high plasma beta, these instabilities may affect the current system in the magnetotail.
16. Investigation of Ion Acoustic Waves in Collisionless Plasmas
DEFF Research Database (Denmark)
Christoffersen, G. B.; Jensen, Vagn Orla; Michelsen, Poul
1974-01-01
The Green's functions for the linearized ion Vlasov equation with a given boundary value are derived. The propagation properties of ion acoustic waves are calculated by performing convolution integrals over the Green's functions. For Te/Ti less than about 3 it is concluded that the collective...... interaction is very weak and that the propagation properties are determined almost completely by freely streaming ions. The wave damping, being due to phase mixing, is determined by the width of the perturbed distribution function rather than by the slope of the undisturbed distribution function at the phase...
17. Vlasov-Fokker-Planck simulations of fast-electron transport with hydrodynamic plasma response
Energy Technology Data Exchange (ETDEWEB)
Kingham, R J; Sherlock, M; Ridgers, C P; Evans, R G, E-mail: [email protected] [Plasma Physics Group, Imperial College London, London SW7 2AZ (United Kingdom)
2010-08-01
We report on kinetic simulations of the transport of laser-produced relativistic electron beams (REB) through solid-density plasma, including the hydrodynamic response of the plasma. We consider REBs with parameters relevant to fast-ignition of compressed inertial confinement fusion capsules. We show that over the 10-20ps timescales required for fast-ignition, thermal pressure (from Ohmic heating) can significantly modify the density which in turn strongly affects the propagation of injected fast-electrons; it allows them to re-collimate into a narrow, intense beam under conditions where they initially undergo beam-hollowing. Similar static-density calculations do not show re-collimation. The re-collimation effect is attributed to PdV cooling in the pressure-induced density-channel, which in turn suppresses defocusing magnetic fields generated by resistivity gradients. These simulations have been carried out using the new 2D-3V Vlasov-Fokker-Planck (VFP) code FIDO running in hybrid mode.
18. A Kinetic Vlasov Model for Plasma Simulation Using Discontinuous Galerkin Method on Many-Core Architectures
Science.gov (United States)
Reddell, Noah
Advances are reported in the three pillars of computational science achieving a new capability for understanding dynamic plasma phenomena outside of local thermodynamic equilibrium. A continuum kinetic model for plasma based on the Vlasov-Maxwell system for multiple particle species is developed. Consideration is added for boundary conditions in a truncated velocity domain and supporting wall interactions. A scheme to scale the velocity domain for multiple particle species with different temperatures and particle mass while sharing one computational mesh is described. A method for assessing the degree to which the kinetic solution differs from a Maxwell-Boltzmann distribution is introduced and tested on a thoroughly studied test case. The discontinuous Galerkin numerical method is extended for efficient solution of hyperbolic conservation laws in five or more particle phase-space dimensions using tensor-product hypercube elements with arbitrary polynomial order. A scheme for velocity moment integration is integrated as required for coupling between the plasma species and electromagnetic waves. A new high performance simulation code WARPM is developed to efficiently implement the model and numerical method on emerging many-core supercomputing architectures. WARPM uses the OpenCL programming model for computational kernels and task parallelism to overlap computation with communication. WARPM single-node performance and parallel scaling efficiency are analyzed with bottlenecks identified guiding future directions for the implementation. The plasma modeling capability is validated against physical problems with analytic solutions and well established benchmark problems.
19. Vlasov simulations of Kinetic Alfv\\'en Waves at proton kinetic scales
CERN Document Server
Vasconez, C L; Camporeale, E; Veltri, P
2014-01-01
Kinetic Alfv\\'en waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton inertial length $d_p$ and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems. In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the kinetic Alfv\\'en waves at proton kinetic scales, in typical conditions of the solar wind environment. In particular, linear and nonlinear regimes of propagation of these fluctuations have been investigated in a single-wave situation, focusing on the physical processes of collisionless Landau damping and wave-particle resonant interaction. Interestingly, since for wavelengths close to $d_p$ and proton plasma beta $\\bet... 20. Comparison of Semi-Lagrangian Algorithms for Solving Vlasov-type Equations Science.gov (United States) Brunner, Stephan 2005-10-01 In view of pursuing CRPP's effort in carrying out gyrokinetic simulations using an Eulerian-type approach [M. Brunetti et. al, Comp. Phys. Comm. 163, 1 (2004)], different alternative algorithms have been considered. The issue is to identify the most appropriate time-stepping scheme, both from a point of view of numerical accuracy and numerical efficiency. Our efforts have concentrated on two semi-Lagrangian approaches: The widely used cubic B-spline interpolation scheme, based on the original work of Cheng and Knorr [C. Z. Cheng and G. Knorr, J. Comp. Phys. 22, 330 (1976)], as well as the Cubic Interpolation Propagation (CIP) scheme, based on cubic Hermite interpolation, which has only more recently been applied for solving Vlasov-type equations [T. Nakamura and T. Yabe, Comp. Phys. Comm. 120, 122 (1999)]. The systematic comparison of these algorithms with respect to their basic spectral (diffusion/dispersion) properties, as well as their ability to avoid the overshoot (Gibbs) problem, is first presented. Results from solving a guiding-center model of the two-dimensional Kelvin-Helmholtz instability are then compared. This test problem enables to address some of the key technical issues also met with the more complex gyrokinetic-type equations. 1. The exact solution of one-dimensional nonrelativistic Vlasov equation: Antitropic electron beams and Landau damping Science.gov (United States) Stepanov, Nikolay S.; Zelekson, Lev A. 2017-03-01 The exact stationary solution of one-dimensional non-relativistic Vlasov equation is obtained in the article. It is shown that in the energy exchange with the self-consistent longitudinal electric field, both wave trapped charged particles and the passing ones take part. It is proved that the trapped electron distribution is fundamentally different from distribution functions described by other authors, which used the Bernstein, Greene, and Kruskal method. So, the correct distribution function is characterized by its sudden change at the equality of wave and electrons' velocity but not on the edges of the potential well. This jump occurs for any arbitrary small value of wave potential. It was also found that the energy density of fast electrons trapped by the wave is less than the energy density of slow trapped electrons. This leads to the fact that the energy of the self-consistent electric field may both increase and decrease due to the nonlinear Landau damping. The conditions under which a similar effect can be observed are defined. Also for the first time, it is shown that the self-generated strong electric field always produces antitropic electron beams. 2. Vlasov-Maxwell, self-consistent electromagnetic wave emission simulations of type III solar radio bursts CERN Document Server Tsiklauri, David 2010-01-01 1.5D Vlasov-Maxwell simulations are employed to model electromagnetic emission generation in a fully self-consistent plasma kinetic model for the first time in the solar physics context. The simulations mimic the plasma emission mechanism and Larmor drift instability in a plasma thread that connects the Sun to Earth with the spatial scales compressed appropriately. The effects of spatial density gradients on the generation of electromagnetic radiation are investigated. It is shown that 1.5D inhomogeneous plasma with a uniform background magnetic field directed transverse to the density gradient is aperiodically unstable to Larmor-drift instability. The latter results in a novel effect of generation of electromagnetic emission at plasma frequency. When density gradient is removed (i.e. when plasma becomes stable to Larmor-drift instability) and a$low$density, super-thermal, hot beam is injected along the domain, in the direction perpendicular to the magnetic field, plasma emission mechanism generates non-esc... 3. Multilevel and Multi-index Monte Carlo methods for the McKean–Vlasov equation KAUST Repository Haji-Ali, Abdul-Lateef 2017-09-12 We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity. This problem is equivalent to estimating the weak solution of the limiting McKean–Vlasov SDE. To that end, our approach uses systems with finite numbers of particles and a time-stepping scheme. In this case, there are two discretization parameters: the number of time steps and the number of particles. Based on these two parameters, we consider different variants of the Monte Carlo and Multilevel Monte Carlo (MLMC) methods and show that, in the best case, the optimal work complexity of MLMC, to estimate the functional in one typical setting with an error tolerance of $$\\\\mathrm {TOL}$$TOL, is when using the partitioning estimator and the Milstein time-stepping scheme. We also consider a method that uses the recent Multi-index Monte Carlo method and show an improved work complexity in the same typical setting of . Our numerical experiments are carried out on the so-called Kuramoto model, a system of coupled oscillators. 4. Identification of low-frequency kinetic wave modes in the Earth's ion foreshock Directory of Open Access Journals (Sweden) X. Blanco-Cano Full Text Available In this work we use ion and magnetic field data from the AMPTE-UKS mission to study the characteristics of low frequency (ωr « Ωp waves observed upstream of the Earth's bow shock. We test the application of various plasma-field correlations and magnetic ratios derived from linear Vlasov theory to identify the modes in this region. We evaluate (for a parameter space consistent with the ion foreshock the Alfvén ratio, the parallel compressibility, the cross-helicity, the noncoplanar ratio, the magnetic compression and the polarization for the two kinetic instabilities that can be generated in the foreshock by the interaction of hot diffuse ions with the solar wind: the left-hand resonant and the right-hand resonant ion beam instabilities. Comparison of these quantities with the observed plasma-field correlations and various magnetic properties of the waves observed during 10 intervals on 30 October 1984, where the waves are associated with diffuse ions, allows us to identify regions with Alfvénic waves and regions where the predominant mode is the right-hand resonant instability. In all the cases the waves are transverse, propagating at angles ≤ 33° and are elliptically polarized. Our results suggest that while the observed Alfvén waves are generated locally by hot diffuse ions, the right-handed waves may result from the superposition of waves generated by two different types of beam distribution (i.e. cold beam and diffuse ions. Even when there was good agreement between the values of observed transport ratios and the values given by the theory, some discrepancies were found. This shows that the observed waves are different from the theoretical modes and that mode identification based only on polarization quantities does not give a complete picture of the waves' characteristics and can lead to mode identification of waves whose polarization may agree with theoretical predictions even when 5. Deterministic methods for the relativistic Vlasov-Maxwell equations and the Van Allen belts dynamics; Methodes deterministes de resolution des equations de Vlasov-Maxwell relativistes en vue du calcul de la dynamique des ceintures de Van Allen Energy Technology Data Exchange (ETDEWEB) Le Bourdiec, S 2007-03-15 Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energetic electrons and the existing electromagnetic waves. This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is chosen in order to obtain the proper velocity resolution. We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv (mono-dimensional for x and three-dimensional for velocity) computations of Weibel and whistler instabilities with one or two electrons species. (author) 6. Cough & Cold Medicine Abuse Science.gov (United States) ... A Week of Healthy Breakfasts Shyness Cough & Cold Medicine Abuse KidsHealth > For Teens > Cough & Cold Medicine Abuse ... DXM Why Do People Use Cough and Cold Medicines to Get High? There's an ingredient in many ... 7. Monte Carlo particle-in-cell methods for the simulation of the Vlasov-Maxwell gyrokinetic equations Science.gov (United States) Bottino, A.; Sonnendrücker, E. 2015-10-01 > The particle-in-cell (PIC) algorithm is the most popular method for the discretisation of the general 6D Vlasov-Maxwell problem and it is widely used also for the simulation of the 5D gyrokinetic equations. The method consists of coupling a particle-based algorithm for the Vlasov equation with a grid-based method for the computation of the self-consistent electromagnetic fields. In this review we derive a Monte Carlo PIC finite-element model starting from a gyrokinetic discrete Lagrangian. The variations of the Lagrangian are used to obtain the time-continuous equations of motion for the particles and the finite-element approximation of the field equations. The Noether theorem for the semi-discretised system implies a certain number of conservation properties for the final set of equations. Moreover, the PIC method can be interpreted as a probabilistic Monte Carlo like method, consisting of calculating integrals of the continuous distribution function using a finite set of discrete markers. The nonlinear interactions along with numerical errors introduce random effects after some time. Therefore, the same tools for error analysis and error reduction used in Monte Carlo numerical methods can be applied to PIC simulations. 8. A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell algorithm Science.gov (United States) Chen, G.; Chacón, L. 2015-12-01 For decades, the Vlasov-Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. Here, we explore a fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space-time-centered, employing particle sub-cycling and orbit-averaging. The algorithm conserves total energy, local charge, canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D-3V. 9. Generation of initial Vlasov distributions for simulation of charged particle beams with high space-charge intensity Energy Technology Data Exchange (ETDEWEB) Lund, S M; Kikuchi, T; Davidson, R C 2007-04-12 Self-consistent Vlasov simulations of beams with high space-charge intensity often require specification of initial phase-space distributions that reflect properties of a beam that is well adapted to the transport channel, both in terms of low-order rms (envelope) properties as well as the higher-order phase-space structure. Here, we first review broad classes of distributions commonly in use as initial Vlasov distributions in simulations of beams with intense space-charge fields including: the Kapchinskij-Vladimirskij (KV) equilibrium, continuous-focusing equilibria with specific detailed examples, and various non-equilibrium distributions, such as the semi-Gaussian distribution and distributions formed from specified functions of linear-field Courant-Snyder invariants. Important practical details necessary to specify these distributions in terms of usual accelerator inputs are presented in a unified format. Building on this presentation, a new class of approximate initial distributions are constructed using transformations that preserve linear-focusing single-particle Courant-Snyder invariants to map initial continuous-focusing equilibrium distributions to a form more appropriate for non-continuous focusing channels. Self-consistent particle-in-cell simulations are employed to show that the approximate initial distributions generated in this manner are better adapted to the focusing channels for beams with high space-charge intensity. This improved capability enables simulation applications that more precisely probe intrinsic stability properties and machine performance. 10. Self-consistent Vlasov-Maxwell description of the longitudinal dynamics of intense charged particle beams Directory of Open Access Journals (Sweden) Ronald C. Davidson 2004-02-01 Full Text Available This paper describes a self-consistent kinetic model for the longitudinal dynamics of a long, coasting beam propagating in straight (linear geometry in the z direction in the smooth-focusing approximation. Starting with the three-dimensional Vlasov-Maxwell equations, and integrating over the phase-space (x_{⊥},p_{⊥} transverse to beam propagation, a closed system of equations is obtained for the nonlinear evolution of the longitudinal distribution function F_{b}(z,p_{z},t and average axial electric field ⟨E_{z}^{s}⟩(z,t. The primary assumptions in the present analysis are that the dependence on axial momentum p_{z} of the distribution function f_{b}(x,p,t is factorable, and that the transverse beam dynamics remains relatively quiescent (absence of transverse instability or beam mismatch. The analysis is carried out correct to order k_{z}^{2}r_{w}^{2} assuming slow axial spatial variations with k_{z}^{2}r_{w}^{2}≪1, where k_{z}∼∂/∂z is the inverse length scale of axial variation in the line density λ_{b}(z,t=∫dp_{z}F_{b}(z,p_{z},t, and r_{w} is the radius of the conducting wall (assumed perfectly conducting. A closed expression for the average longitudinal electric field ⟨E_{z}^{s}⟩(z,t in terms of geometric factors, the line density λ_{b}, and its derivatives ∂λ_{b}/∂z,… is obtained for the class of bell-shaped density profiles n_{b}(r,z,t=(λ_{b}/πr_{b}^{2}f(r/r_{b}, where the shape function f(r/r_{b} has the form specified by f(r/r_{b}=(n+1(1-r^{2}/r_{b}^{2}^{n} for 0≤r 11. Vlasov - Maxwell, Self-consistent Electromagnetic Wave Emission Simulations in the Solar Corona Science.gov (United States) Tsiklauri, David 2010-12-01 1.5D Vlasov - Maxwell simulations are employed to model electromagnetic emission generation in a fully self-consistent plasma kinetic model for the first time in the context of solar physics. The simulations mimic the plasma emission mechanism and Larmor-drift instability in a plasma thread that connects the Sun to Earth with the spatial scales compressed appropriately. The effects of spatial density gradients on the generation of electromagnetic radiation are investigated. It is shown that a 1.5D inhomogeneous plasma with a uniform background magnetic field directed transverse to the density gradient is aperiodically unstable to the Larmor-drift instability. The latter results in a novel effect of generation of electromagnetic emission at plasma frequency. The generated perturbations consist of two parts: i) non-escaping (trapped) Langmuir type oscillations, which are localised in the regions of density inhomogeneity, and are highly filamentary, with the period of appearance of the filaments close to electron plasma frequency in the dense regions; and ii) escaping electromagnetic radiation with phase speeds close to the speed of light. When the density gradient is removed ( i.e. when plasma becomes stable to the Larmor-drift instability) and a low density super-thermal, hot beam is injected along the domain, in the direction perpendicular to the magnetic field, the plasma emission mechanism generates non-escaping Langmuir type oscillations, which in turn generate escaping electromagnetic radiation. It is found that in the spatial location where the beam is injected, standing waves, oscillating at the plasma frequency, are excited. These can be used to interpret the horizontal strips (the narrow-band line emission) observed in some dynamical spectra. Predictions of quasilinear theory are: i) the electron free streaming and ii) the long relaxation time of the beam, in accord with the analytic expressions. These are corroborated via direct, fully-kinetic simulation 12. Cold confusion Energy Technology Data Exchange (ETDEWEB) Chapline, G. 1989-07-01 On March 23 two chemists, Martin Fleischmann and Stanley Pons startled the world with a press conference at the University of Utah where they announced that they had achieved nuclear fusion at room temperatures. As evidence they cited the production of ''excess'' amounts of heat in an electrochemical apparatus and observation of neutron production. While the production of heat in a chemical apparatus is not in itself unusual the observation of neutrons is certainly extraordinary. As it turned out, though, careful measurements of the neutron production in electrochemical apparatus similar to that used by Fleischmann and Pons carried out at dozens of other laboratories has shown that the neutron production fails by many orders of magnitude to support the assertion by Fleischmann and Pons that their discovery represents a new and cheap source of fusion power. In particular, independent measurements of the neutron production rate suggest that the actual rate of fusion energy production probably does not exceed 1 trillionth of a watt. This paper discusses the feasibility that cold fusion is actually being achieved. 7 refs. 13. 3D Maxwell-Vlasov boundary value problem solution in stellarator geometry in ion cyclotron frequency range Energy Technology Data Exchange (ETDEWEB) Vdovin, V.; Watari, T. [National Inst. for Fusion Science, Nagoya (Japan); Fukuyama, A. 1997-12-31 In the work we formulate the basic equations to solve the above ICRF problem in flux coordinates on different equilibria. The kinetic effects like cyclotron and Cherenkov absorptions, along with excitation of kinetic Alfven waves and finite Larmor radius effects are included. The ICRF plasma heating ({omega} {approx} {omega}{sub ci}) methods are prepared for the newly constructed LHD and projected W7-X stellarators or are conducted on operating machines like W7-AS, CHS, etc. For their adequate ICRH modelling and antenna development it is needed to create more complicated in compare with tokamaks ICRF code accounting for non axis symmetrical plasmas in complicated geometry. (author) 14. Cold energy Science.gov (United States) Wallace, John P. 2015-12-01 Deviations in Q for resonant superconducting radio frequency niobium accelerator cavities are generally correlated with resistivity loss mechanisms. Field dependent Qs are not well modeled by these classical loss mechanisms, but rather can represent a form of precision cavity surface thermometry. When the field dependent Q variation shows improvement with increasing B field level the classical treatment of this problem is inadequate. To justify this behavior hydrogen as a ubiquitous impurity in niobium, which creates measurable property changes, even at very low concentrations is typically considered the cause of such anomalous behavior. This maybe the case in some instances, but more importantly any system operating with a highly coherent field with a significant time dependent magnetic component at near 2° K will have the ability to organize the remaining free spins within the London penetration depth to form a coupled energy reservoir in the form of low mass spin waves. The niobium resonant cavities are composed of a single isotope with a large nuclear spin. When the other loss mechanisms are stripped away this may be the gain medium activated by the low level residual magnetic fields. It was found that one resonant cavity heat treatment produced optimum surface properties and then functioned as a MASER extracting energy from the 2° K thermal bath while cooling the cavity walls. The cavity operating in this mode is a simulator of what can take place in the wider but not colder universe using the cosmic microwave background (CMB) as a thermal source. The low mass, long lifetimes, and the scale of the magnetic spin waves on the weakly magnetized interstellar medium allows energy to be stored that is many orders of magnitude colder than the cosmic microwave background. A linear accelerator cavity becomes a tool to explore the properties of the long wave length magnetic spin waves that populate this cold low energy regime. 15. Cold energy Energy Technology Data Exchange (ETDEWEB) Wallace, John P., E-mail: [email protected] [Casting Analysis Corp., PO Box 52, Weyers Cave, VA 24486 (United States) 2015-12-04 Deviations in Q for resonant superconducting radio frequency niobium accelerator cavities are generally correlated with resistivity loss mechanisms. Field dependent Qs are not well modeled by these classical loss mechanisms, but rather can represent a form of precision cavity surface thermometry. When the field dependent Q variation shows improvement with increasing B field level the classical treatment of this problem is inadequate. To justify this behavior hydrogen as a ubiquitous impurity in niobium, which creates measurable property changes, even at very low concentrations is typically considered the cause of such anomalous behavior. This maybe the case in some instances, but more importantly any system operating with a highly coherent field with a significant time dependent magnetic component at near 2° K will have the ability to organize the remaining free spins within the London penetration depth to form a coupled energy reservoir in the form of low mass spin waves. The niobium resonant cavities are composed of a single isotope with a large nuclear spin. When the other loss mechanisms are stripped away this may be the gain medium activated by the low level residual magnetic fields. It was found that one resonant cavity heat treatment produced optimum surface properties and then functioned as a MASER extracting energy from the 2° K thermal bath while cooling the cavity walls. The cavity operating in this mode is a simulator of what can take place in the wider but not colder universe using the cosmic microwave background (CMB) as a thermal source. The low mass, long lifetimes, and the scale of the magnetic spin waves on the weakly magnetized interstellar medium allows energy to be stored that is many orders of magnitude colder than the cosmic microwave background. A linear accelerator cavity becomes a tool to explore the properties of the long wave length magnetic spin waves that populate this cold low energy regime. 16. Kinetic description of electron-proton instability in high-intensity proton linacs and storage rings based on the Vlasov-Maxwell equations Directory of Open Access Journals (Sweden) Ronald C. Davidson 1999-05-01 Full Text Available The present analysis makes use of the Vlasov-Maxwell equations to develop a fully kinetic description of the electrostatic, electron-ion two-stream instability driven by the directed axial motion of a high-intensity ion beam propagating in the z direction with average axial momentum γ_{b}m_{b}β_{b}c through a stationary population of background electrons. The ion beam has characteristic radius r_{b} and is treated as continuous in the z direction, and the applied transverse focusing force on the beam ions is modeled by F_{foc}^{b}=-γ_{b}m_{b}ω_{βb}^{0^{2}}x_{⊥} in the smooth-focusing approximation. Here, ω_{βb}^{0}=const is the effective betatron frequency associated with the applied focusing field, x_{⊥} is the transverse displacement from the beam axis, (γ_{b}-1m_{b}c^{2} is the ion kinetic energy, and V_{b}=β_{b}c is the average axial velocity, where γ_{b}=(1-β_{b}^{2}^{-1/2}. Furthermore, the ion motion in the beam frame is assumed to be nonrelativistic, and the electron motion in the laboratory frame is assumed to be nonrelativistic. The ion charge and number density are denoted by +Z_{b}e and n_{b}, and the electron charge and number density by -e and n_{e}. For Z_{b}n_{b}>n_{e}, the electrons are electrostatically confined in the transverse direction by the space-charge potential φ produced by the excess ion charge. The equilibrium and stability analysis retains the effects of finite radial geometry transverse to the beam propagation direction, including the presence of a perfectly conducting cylindrical wall located at radius r=r_{w}. In addition, the analysis assumes perturbations with long axial wavelength, k_{z}^{2}r_{b}^{2}≪1, and sufficiently high frequency that |ω/k_{z}|≫v_{Tez} and |ω/k_{z}-V_{b}|≫v_{Tbz}, where v_{Tez} and v_{Tbz} are the characteristic axial thermal speeds of the background electrons and beam ions. In this regime, Landau damping (in axial velocity space v_{z} by resonant ions and 17. Multirate Particle-in-Cell Time Integration Techniques of Vlasov-Maxwell Equations for Collisionless Kinetic Plasma Simulations Energy Technology Data Exchange (ETDEWEB) Chen, Guangye [Los Alamos National Laboratory; Chacon, Luis [Los Alamos National Laboratory; Knoll, Dana Alan [Los Alamos National Laboratory; Barnes, Daniel C [Coronado Consulting 2015-07-31 A multi-rate PIC formulation was developed that employs large timesteps for slow field evolution, and small (adaptive) timesteps for particle orbit integrations. Implementation is based on a JFNK solver with nonlinear elimination and moment preconditioning. The approach is free of numerical instabilities (ωpeΔt >>1, and Δx >> λD), and requires many fewer dofs (vs. explicit PIC) for comparable accuracy in challenging problems. Significant gains (vs. conventional explicit PIC) may be possible for large scale simulations. The paper is organized as follows: Vlasov-Maxwell Particle-in-cell (PIC) methods for plasmas; Explicit, semi-implicit, and implicit time integrations; Implicit PIC formulation (Jacobian-Free Newton-Krylov (JFNK) with nonlinear elimination allows different treatments of disparate scales, discrete conservation properties (energy, charge, canonical momentum, etc.)); Some numerical examples; and Summary. 18. Hamiltonian fluid closures of the Vlasov-Amp{\\e}re equations: from water-bags to N moment models CERN Document Server Perin, M; Morrison, P J; Tassi, E 2015-01-01 Moment closures of the Vlasov-Amp{\\e}re system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two and three water-bags are treated and their Hamiltonian structures are provided. In each case, we give the associated fluid closures and we discuss their Casimir invariants. We show how the method can be extended to an arbitrary number of fields, i.e., an arbitrary number of water-bags and associated moments. The thermodynamic interpretation of the resulting models is discussed. Finally, a general procedure to derive Hamiltonian N-field fluid models is proposed. 19. Proof of the cosmic no-hair conjecture in the T^3-Gowdy symmetric Einstein-Vlasov setting CERN Document Server Andréasson, Håkan 2013-01-01 The currently preferred models of the universe undergo accelerated expansion induced by dark energy. One model for dark energy is a positive cosmological constant. It is consequently of interest to study Einstein's equations with a positive cosmological constant coupled to matter satisfying the ordinary energy conditions; the dominant energy condition etc. Due to the difficulty of analysing the behaviour of solutions to Einstein's equations in general, it is common to either study situations with symmetry, or to prove stability results. In the present paper, we do both. In fact, we analyse, in detail, the future asymptotic behaviour of T^3-Gowdy symmetric solutions to the Einstein-Vlasov equations with a positive cosmological constant. In particular, we prove the cosmic no-hair conjecture in this setting. However, we also prove that the solutions are future stable (in the class of all solutions). Some of the results hold in a more general setting. In fact, we obtain conclusions concerning the causal structure... 20. Vlasov modelling of laser-driven collisionless shock acceleration of protons Energy Technology Data Exchange (ETDEWEB) Svedung Wettervik, B.; DuBois, T. C.; Fülöp, T. [Department of Applied Physics, Chalmers University of Technology, Gothenburg (Sweden) 2016-05-15 Ion acceleration due to the interaction between a short high-intensity laser pulse and a moderately overdense plasma target is studied using Eulerian Vlasov–Maxwell simulations. The effects of variations in the plasma density profile and laser pulse parameters are investigated, and the interplay of collisionless shock and target normal sheath acceleration is analyzed. It is shown that the use of a layered-target with a combination of light and heavy ions, on the front and rear side, respectively, yields a strong quasi-static sheath-field on the rear side of the heavy-ion part of the target. This sheath-field increases the energy of the shock-accelerated ions while preserving their mono-energeticity. 1. Cold stress alters transcription in meiotic anthers of cold tolerant chickpea (Cicer arietinum L.). Science.gov (United States) Sharma, Kamal Dev; Nayyar, Harsh 2014-10-11 Cold stress at reproductive phase in susceptible chickpea (Cicer arietinum L.) leads to pollen sterility induced flower abortion. The tolerant genotypes, on the other hand, produce viable pollen and set seed under cold stress. Genomic information on pollen development in cold-tolerant chickpea under cold stress is currently unavailable. DDRT-PCR analysis was carried out to identify anther genes involved in cold tolerance in chickpea genotype ICC16349 (cold-tolerant). A total of 9205 EST bands were analyzed. Cold stress altered expression of 127 ESTs (90 up-regulated, 37 down-regulated) in anthers, more than two third (92) of which were novel with unknown protein identity and function. Remaining about one third (35) belonged to several functional categories such as pollen development, signal transduction, ion transport, transcription, carbohydrate metabolism, translation, energy and cell division. The categories with more number of transcripts were carbohydrate/triacylglycerol metabolism, signal transduction, pollen development and transport. All but two transcripts in these categories were up-regulated under cold stress. To identify time of regulation after stress and organ specificity, expression levels of 25 differentially regulated transcripts were also studied in anthers at six time points and in four organs (anthers, gynoecium, leaves and roots) at four time points. Limited number of genes were involved in regulating cold tolerance in chickpea anthers. Moreover, the cold tolerance was manifested by up-regulation of majority of the differentially expressed transcripts. The anthers appeared to employ dual cold tolerance mechanism based on their protection from cold by enhancing triacylglycerol and carbohydrate metabolism; and maintenance of normal pollen development by regulating pollen development genes. Functional characterization of about two third of the novel genes is needed to have precise understanding of the cold tolerance mechanisms in chickpea anthers. 2. Long Life Cold Cathodes for Hall effect Thrusters Project Data.gov (United States) National Aeronautics and Space Administration — An electron source incorporating long life, high current density cold cathodes inside a microchannel plate for use with ion thrusters is proposed. Cathode lifetime... 3. Cold Stress and the Cold Pressor Test Science.gov (United States) Silverthorn, Dee U.; Michael, Joel 2013-01-01 Temperature and other environmental stressors are known to affect blood pressure and heart rate. In this activity, students perform the cold pressor test, demonstrating increased blood pressure during a 1- to 2-min immersion of one hand in ice water. The cold pressor test is used clinically to evaluate autonomic and left ventricular function. This… 4. Fluid nonlinear frequency shift of nonlinear ion acoustic waves in multi-ion species plasmas in small wave number region CERN Document Server Feng, Q S; Wang, Q; Zheng, C Y; Liu, Z J; Cao, L H; He, X T 2016-01-01 The properties of the nonlinear frequency shift (NFS) especially the fluid NFS from the harmonic generation of the ion-acoustic wave (IAW) in multi-ion species plasmas have been researched by Vlasov simulation. The pictures of the nonlinear frequency shift from harmonic generation and particles trapping are shown to explain the mechanism of NFS qualitatively. The theoretical model of the fluid NFS from harmonic generation in multi-ion species plasmas is given and the results of Vlasov simulation are consistent to the theoretical result of multi-ion species plasmas. When the wave number$k\\lambda_{De}$is small, such as$k\\lambda_{De}=0.1$, the fluid NFS dominates in the total NFS and will reach as large as nearly$15\\%$when the wave amplitude$|e\\phi/T_e|\\sim0.1$, which indicates that in the condition of small$k\\lambda_{De}$, the fluid NFS dominates in the saturation of stimulated Brillouin scattering especially when the nonlinear IAW amplitude is large. 5. Cold and Cough Medicines Science.gov (United States) ... What can you do for your cold or cough symptoms? Besides drinking lots of fluids and getting ... medicines. There are lots of different cold and cough medicines, and they do different things. Nasal decongestants - ... 6. Cold-induced metabolism NARCIS (Netherlands) van Marken Lichtenbelt, W.D.; Daanen, A.M. 2003-01-01 Cold-induced metabolism. van Marken Lichtenbelt WD, Daanen HA. Department of Human Biology, Maastricht University, Maastricht, The Netherlands. PURPOSE OF REVIEW: Cold response can be insulative (drop in peripheral temperature) or metabolic (increase in energy expenditure). Nonshivering thermogenesi 7. Cold nuclear fusion National Research Council Canada - National Science Library Huang Zhenqiang Huang Yuxiang 2013-01-01 ...... And with a magnetic moment of light nuclei controlled cold nuclear collide fusion, belongs to the nuclear energy research and development in the field of applied technology "cold nuclear collide fusion... 8. Magnetoacoustic heating by ion Landau damping Science.gov (United States) Turner, L. 1980-01-01 The Vlasov-fluid model of Freidberg (1972) is used to study the resonance heating of a sharp-boundary screw pinch. The analysis provides the first treatment of the magnetoacoustic heating of a cylindrical plasma by means of ion Landau damping, which was identified as a viable dissipative mechanism for the conversion of magnetoacoustic wave energy into ion thermal energy. In addition, local and global energy conservation are considered, and formulae and numerical results for the thermal energy doubling time and the associated induced rf electric fields are presented. It is shown that collisionless absorption can provide a heating mechanism when an equilibrium plasma column is pumped by oscillations of the confining magnetic field at a frequency near the oblique magnetoacoustic frequency. 9. Thermalization and isotropization in heavy-ion collisions Indian Academy of Sciences (India) Michael Strickland 2015-05-01 Our current understanding of the processes driving the thermalization and isotropization of the quark gluon plasma (QGP) created in ultrarelativistic heavy-ion collisions (URHICs) is reviewed. Initially, the phenomenological evidence in favour of the creation of a thermal but momentum–space anisotropic QGP in URHICs is discussed. Further, the degree of isotropization using viscous (dissipative) hydrodynamics, weak-coupling approaches to QGP dynamics, and strong-coupling approaches to QGP dynamics are discussed. Finally, recent progress in the area of real-time non-Abelian gauge field simulations and non-Abelian Boltzmann–Vlasov-based hard-loop simulations are reported. 10. Absolute and Convective Ion Beam Instability Studied through Green's Function DEFF Research Database (Denmark) Jensen, Vagn Orla; Michelsen, Poul; Hsuan, H. C. S. 1974-01-01 A Vlasov plasma with a double‐humped, unstable ion velocity distribution function is considered. A δ function in space is assumed as the initial perturbation and the plasma response to this perturbation is calculated, i.e., the Green's function for the problem is found. The response can be divide...... into two parts: a self‐similar, damped part of the form t−1h(x/t), and an unstable, exponentially growing part. The conditions for absolute and convective growth of the latter are discussed.... 11. Estimation of cold plasma outflow during geomagnetic storms CERN Document Server Haaland, S; André, M; Maes, L; Baddeley, L; Barakat, A; Chappell, R; Eccles, V; Johnsen, C; Lybekk, B; Li, K; Pedersen, A; Schunk, R; Welling, D 2016-01-01 Low-energy ions of ionospheric origin constitute a significant contributor to the magnetospheric plasma population. Measuring cold ions is difficult though. Observations have to be done at sufficiently high altitudes and typically in regions of space where spacecraft attain a positive charge due to solar illumination. Cold ions are therefore shielded from the satellite particle detectors. Furthermore, spacecraft can only cover key regions of ion outflow during segments of their orbit, so additional complications arise if continuous longtime observations, such as during a geomagnetic storm, are needed. In this paper we suggest a new approach, based on a combination of synoptic observations and a novel technique to estimate the flux and total outflow during the various phases of geomagnetic storms. Our results indicate large variations in both outflow rates and transport throughout the storm. Prior to the storm main phase, outflow rates are moderate, and the cold ions are mainly emanating from moderately sized ... 12. The Einstein-Vlasov system in spherical symmetry: reduction of the equations of motion and classification of single-shell static solutions, in the limit of massless particles CERN Document Server Gundlach, Carsten 2016-01-01 We express the Einstein-Vlasov system in spherical symmetry in terms of a dimensionless momentum variable$z$(radial over angular momentum). This regularises the limit of massless particles, and in that limit allows us to obtain a reduced system in independent variables$(t,r,z)$only. Similarly, in this limit the Vlasov density function$f$for static solutions depends on a single variable$Q$(energy over angular momentum). This reduction allows us to show that any given static metric which has vanishing Ricci scalar, is vacuum at the centre and for$r>3M$and obeys certain energy conditions uniquely determines a consistent$f=\\bar k(Q)$(in closed form). Vice versa, any$\\bar k(Q)$within a certain class uniquely determines a static metric (as the solution of a system of two first-order quasilinear ODEs). Hence the space of static spherically symmetric solutions of Einstein-Vlasov is locally a space of functions of one variable. For a simple 2-parameter family of functions$\\bar k(Q)$, we construct the co... 13. Interferometry with Strontium Ions Science.gov (United States) Jackson, Jarom; Lambert, Enoch; Otterstrom, Nils; Jones, Tyler; Durfee, Dallin 2014-05-01 We describe progress on a cold ion matter-wave interferometer. Cold Strontium atoms are extracted from an LVIS. The atoms will be photo-ionized with a two-photon transition to an auto-ionizing state in the continuum. The ions will be split and recombined using stimulated Raman transitions from a pair of diode lasers injection locked to two beams from a master laser which have been shifted up and down by half the hyperfine splitting. We are developing laser instrumentation for this project including a method to prevent mode-hopping by analyzing laser frequency noise, and an inexpensive, robust wavelength meter. Supported by NSF Award No. 1205736. 14. Heavy ion storage rings Energy Technology Data Exchange (ETDEWEB) Schuch, R. 1987-01-01 A brief overview of synchrotron storage rings for heavy ions, which are presently under construction in different accelerator laboratories is given. Ions ranging from protons up to uranium ions at MeV/nucleon energies will be injected into these rings using multiturn injection from the accelerators available or being built in these laboratories. After injection, it is planned to cool the phase space distribution of the ions by merging them with cold electron beams or laser beams, or by using stochastic cooling. Some atomic physics experiments planned for these rings are presented. 15. Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems CERN Document Server Xiao, Jianyuan; Liu, Jian; He, Yang; Zhang, Ruili; Sun, Yajuan 2015-01-01 Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithm conserves a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially-discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a splitting method discovered by He et al., which produces five exactly-soluable sub-systems, and high-order structure- preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom ... 16. Vlasov simulations of electron heating by Langmuir turbulence near the critical altitude in the radiation-modified ionosphere Science.gov (United States) Wang, J. G.; Newman, D. L.; Goldman, M. V. 1997-12-01 One-dimensional Vlasov equations are solved numerically for conditions appropriate to the ionospheric F-region during the initial stages of HF-radiation modification experiments at two altitudes: one at the critical altitude, the other approximately 1.5 km lower. Numerical simulations of wave growth and saturation with self-consistent evolution of particle distributions are run past the point at which a statistically steady state is reached. At the critical altitude the wave turbulence is dominated by coherent collapsing wave packets or cavitons' and at the lower altitude by a combination of coherent (strong) and incoherent (weak) turbulence. Our results are consistent with the predictions of Hanssen et al. [Journal of Geophysical Research, 97, 12,073 (1992)]. Semi-open boundary conditions, in which a small fraction of the hot electrons generated by interactions with the strong localized caviton fields are replaced by electrons from the cool background distribution, are employed to model a heated region of finite length that is large compared to the simulation domain. The resultant steady-state electron distributions are characterized by power-law tails of hot electrons superposed on an approximately Maxwellian bulk distribution. The Langmuir-wave dissipation spectra are found to be in good agreement with predictions based on linear Landau damping on the nonthermal electron tails. 17. Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems Energy Technology Data Exchange (ETDEWEB) Xiao, Jianyuan [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Qin, Hong [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA; Liu, Jian [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; He, Yang [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Zhang, Ruili [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Sun, Yajuan [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, China 2015-11-01 Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint arXiv: 1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave. (C) 2015 AIP Publishing LLC. 18. Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems Energy Technology Data Exchange (ETDEWEB) Xiao, Jianyuan; Liu, Jian; He, Yang; Zhang, Ruili [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026 (China); Qin, Hong, E-mail: [email protected] [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Sun, Yajuan [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190 (China) 2015-11-15 Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave. 19. Langmuir wave filamentation in the kinetic regime. I. Filamentation instability of Bernstein-Greene-Kruskal modes in multidimensional Vlasov simulations Science.gov (United States) Silantyev, Denis A.; Lushnikov, Pavel M.; Rose, Harvey A. 2017-04-01 A nonlinear Langmuir wave in the kinetic regime k λ D ≳ 0.2 may have a filamentation instability, where k is the wavenumber and λD is the Debye length. The nonlinear stage of that instability develops into the filamentation of Langmuir waves which in turn leads to the saturation of the stimulated Raman scattering in laser-plasma interaction experiments. Here, we study the linear stage of the filamentation instability of the particular family (H. A. Rose and D. A. Russell, Phys. Plasmas 8, 4784 (2001)) of Bernstein-Greene-Kruskal (BGK) modes (I. B. Bernstein et al., Phys. Rev. 108, 546 (1957)) that is a bifurcation of the linear Langmuir wave. Performing direct 2 + 2D Vlasov-Poisson simulations of collisionless plasma, we find the growth rates of oblique modes of the electric field as a function of BGK's amplitude, wavenumber, and the angle of the oblique mode's wavevector relative to the BGK's wavevector. Simulation results are compared to theoretical predictions. 20. AP-Cloud: Adaptive Particle-in-Cloud method for optimal solutions to Vlasov-Poisson equation Science.gov (United States) Wang, Xingyu; Samulyak, Roman; Jiao, Xiangmin; Yu, Kwangmin 2016-07-01 We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov-Poisson equation. Unlike the traditional particle-in-cell (PIC) method, which is commonly used for solving this problem, the AP-Cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non-uniform. Unlike other adaptive techniques for PIC, our method balances the errors in PDE discretization and Monte Carlo integration, and discretizes the differential operators using a generalized finite difference (GFD) method based on a weighted least square formulation. As a result, AP-Cloud is independent of the geometric shapes of computational domains and is free of artificial parameters. Efficient and robust implementation is achieved through an octree data structure with 2:1 balance. We analyze the accuracy and convergence order of AP-Cloud theoretically, and verify the method using an electrostatic problem of a particle beam with halo. Simulation results show that the AP-Cloud method is substantially more accurate and faster than the traditional PIC, and it is free of artificial forces that are typical for some adaptive PIC techniques. 1. Global well-posedness and large time behavior of classical solutions to the Vlasov-Fokker-Planck and magnetohydrodynamics equations Science.gov (United States) Jiang, Peng 2017-02-01 We are concerned with the global well-posedness of the fluid-particle system which describes the evolutions of disperse two-phase flows. The system consists of the Vlasov-Fokker-Planck equation for the dispersed phase (particles) coupled to the compressible magnetohydrodynamics equations modelling a dense phase (fluid) through the friction forcing. Global well-posedness of the Cauchy problem is established in perturbation framework, and rates of convergence of solutions toward equilibrium, which are algebraic in the whole space and exponential on torus, are also obtained under some additional conditions on initial data. The existence of global solution and decay rate of the solution are proved based on the classical energy estimates and Fourier multiplier technique, which are considerably complicated and some new ideas and techniques are thus required. Moreover, it is shown that neither shock waves nor vacuum and concentration in the solution are developed in a finite time although there is a complex interaction between particle and fluid. 2. Kinetic Simulations - Oshun (Vlasov-Fokker-Planck) and PIC (Osiris) - Physics and Open Source Software In The UCLA PICKSE Initiative Science.gov (United States) Tableman, Adam; Tzoufras, Michail; Fonseca, Ricardo; Mori, W. B. 2016-10-01 We present physics results and general updates for two plasma kinetic simulation codes developed under the UCLA PICKSE initiative. We also discuss the issues around making these codes open source such that they can be used (and contributed too) by a large audience. The first code discussed is Oshun - a Vlasov-Fokker-Planck (VFP) code. Recent simulations with the VFP code OSHUN will be presented for all of the aforementioned problems. The algorithmic improvements that have facilitated these studies will be also be discussed. The second code discussed is the PIC code Osiris. Osiris is a widely respected code used in hundreds of papers. Osiris was first developed for laser-plasma interactions but has grown into a robust framework covering most areas of plasma research. One defining feature of Osiris is that it is highly optimized for a variety of hardware configurations and scales linearly over 1 million + CPU nodes. We will discuss the recently released version 4.0 written in modern, fully-object oriented FORTRAN. Funding provided by Grants NSF ACI 1339893 and DOE DE NA 0001833. 3. AN ASYMPTOTIC PRESERVING SCHEME FOR THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM IN THE HIGH FIELD REGIME Institute of Scientific and Technical Information of China (English) Shi Jin; Li Wang 2011-01-01 The Vlasov-Poisson-Fokker-Planck system under the high field scaling describes the Brownian motion of a large system of particles in a surrounding bath where both collision and field effects (electrical or gravitational) are dominant. Numerically solving this system becomes challenging due to the stiff collision term and stiff nonlinear transport term with respect to the high field.We present a class of Asymptotic-Preserving scheme which is efficient in the high field regime,namely,large time steps and coarse meshes can be used,yet the high field limit is still captured.The idea is to combine the two stiff terms and treat them implicitly.Thanks to the linearity of the collision term,using the discretization described in [Jin S,Yan B.J.Comp.Phys.,2011,230:6420-6437]we only need to invert a symmetric matrix.This method can be easily extended to higher dimensions.The method is shown to be positive,stable,mass and asymptotic preserving.Numerical experiments validate its efficiency in both kinetic and high field regimes including mixing regimes. 4. Kinetic study of ion acoustic twisted waves with kappa distributed electrons Science.gov (United States) Arshad, Kashif; Aman-ur-Rehman, Mahmood, Shahzad 2016-05-01 The kinetic theory of Landau damping of ion acoustic twisted modes is developed in the presence of orbital angular momentum of the helical (twisted) electric field in plasmas with kappa distributed electrons and Maxwellian ions. The perturbed distribution function and helical electric field are considered to be decomposed by Laguerre-Gaussian mode function defined in cylindrical geometry. The Vlasov-Poisson equation is obtained and solved analytically to obtain the weak damping rates of the ion acoustic twisted waves in a non-thermal plasma. The strong damping effects of ion acoustic twisted waves at low values of temperature ratio of electrons and ions are also obtained by using exact numerical method and illustrated graphically, where the weak damping wave theory fails to explain the phenomenon properly. The obtained results of Landau damping rates of the twisted ion acoustic wave are discussed at different values of azimuthal wave number and non-thermal parameter kappa for electrons. 5. Atomic absorption spectroscopy in ion channel screening. Science.gov (United States) Stankovich, Larisa; Wicks, David; Despotovski, Sasko; Liang, Dong 2004-10-01 This article examines the utility of atomic absorption spectroscopy, in conjunction with cold flux assays, to ion channel screening. The multiplicity of ion channels that can be interrogated using cold flux assays and atomic absorption spectroscopy is summarized. The importance of atomic absorption spectroscopy as a screening tool is further elaborated upon by providing examples of the relevance of ion channels to various physiological processes and targeted diseases. 6. Nonlinear Evolution of the Ion-Ion Beam Instability DEFF Research Database (Denmark) Pécseli, Hans; Trulsen, J. 1982-01-01 The criterion for the existence of vortexlike ion phase-space configurations, as obtained by a standard pseudopotential method, is found to coincide with the criterion for the linear instability for two (cold) counterstreaming ion beams. A nonlinear equation is derived, which demonstrates... 7. Cold suppresses agonist-induced activation of TRPV1. Science.gov (United States) Chung, M-K; Wang, S 2011-09-01 Cold therapy is frequently used to reduce pain and edema following acute injury or surgery such as tooth extraction. However, the neurobiological mechanisms of cold therapy are not completely understood. Transient receptor potential vanilloid 1 (TRPV1) is a capsaicin- and heat-gated nociceptive ion channel implicated in thermosensation and pathological pain under conditions of inflammation or injury. Although capsaicin-induced nociception, neuropeptide release, and ionic currents are suppressed by cold, it is not known if cold suppresses agonist-induced activation of recombinant TRPV1. We demonstrate that cold strongly suppressed the activation of recombinant TRPV1 by multiple agonists and capsaicin-evoked currents in trigeminal ganglia neurons under normal and phosphorylated conditions. Cold-induced suppression was partially impaired in a TRPV1 mutant that lacked heat-mediated activation and potentiation. These results suggest that cold-induced suppression of TRPV1 may share a common molecular basis with heat-induced potentiation, and that allosteric inhibition may contribute, in part, to the cold-induced suppression. We also show that combination of cold and a specific antagonist of TRPV1 can produce an additive suppression. Our results provide a mechanistic basis for cold therapy and may enhance anti-nociceptive approaches that target TRPV1 for managing pain under inflammation and tissue injury, including that from tooth extraction. 8. Cooling of ions and antiprotons with magnetized electrons CERN Document Server Mollers, B; Walter, M; Zwicknagel, G; Carli, Christian; Nersisyan, H 2004-01-01 Electron cooling is a well-established method to improve the phase space quality of ion beams in storage rings. More recently antiprotons have been cooled in traps, first by electrons and then by positrons in order to produce antihydrogen atoms as simplest form of antimatter for CPT-tests. During these cooling processes the light particles are guided by strong external magnetic fields which imposes a challenge to the theoretical description. Within the binary collision model we treat the Coulomb interaction as second-order perturbation to the helix motion of the light particles and also by numerical simulations. In the complementary dielectric theory we calculate the polarization of the light particles by solving the nonlinear Vlasov-Poisson equation as well as linear response. It turns out that the linearization becomes dubious at low ion velocities. In the presence of a strong magnetic field the numerically expensive solution of the Vlasov-Poisson equation is the method of choice, alternatively one may empl... 9. Normal modes of confined cold ionic systems Energy Technology Data Exchange (ETDEWEB) Schiffer, J.P.; Dubin, D.H. [Univ. of California, San Diego, CA (United States) 1995-08-01 The normal modes of a cloud of confined ions forming a strongly-correlated plasma were investigated. The results of molecular-dynamics simulations were compared to predictions of a cold fluid mode. Mode frequencies are observed to shift slightly compared to the cold fluid predictions, and the modes are also observed to damp in time. Simulations also reveal a set of torsional oscillations which have no counterpart in cold fluid theory. The frequency shift, damping, and torsional effects are compared to a model that treats trapped plasmas as a visco-elastic spheroid. It may be possible to measure high-frequency bulk and shear moduli of a strongly-correlated plasma from mode excitation experiments on trapped non-neutral plasmas. An example of the results of the calculation is presented. 10. COLD-WORKED HARDWARE Directory of Open Access Journals (Sweden) N. M. Strizhak 2007-01-01 Full Text Available The different types of cold-worked accessory are examined in the article. The necessity of development of such type of accessory in the Republic of Belarus due to requirements of market is shown. High emphasis is placed on the methods of increase of plasticity of cold-worked accessory from usual mill of RUP and CIS countries. 11. Cold Sores (HSV-1) Science.gov (United States) ... A Week of Healthy Breakfasts Shyness Cold Sores (HSV-1) KidsHealth > For Teens > Cold Sores (HSV-1) A A A What's in this article? ... or around a person's lips, are caused by herpes simplex virus-1 (HSV-1) . But they don't ... 12. Working in the Cold Centers for Disease Control (CDC) Podcasts 2016-02-08 During the winter, many workers are outdoors, working in cold, wet, icy, or snowy conditions. Learn how to identify symptoms that tell you there may be a problem and protect yourself from cold stress. Created: 2/8/2016 by National Institute for Occupational Safety and Health (NIOSH). Date Released: 2/8/2016. 13. Cold fusion research Energy Technology Data Exchange (ETDEWEB) None 1989-11-01 I am pleased to forward to you the Final Report of the Cold Fusion Panel. This report reviews the current status of cold fusion and includes major chapters on Calorimetry and Excess Heat, Fusion Products and Materials Characterization. In addition, the report makes a number of conclusions and recommendations, as requested by the Secretary of Energy. 14. Cold-Weather Sports Science.gov (United States) ... Surgery? A Week of Healthy Breakfasts Shyness Cold-Weather Sports KidsHealth > For Teens > Cold-Weather Sports A A A What's in this article? ... Equipment Ahh, winter! Shorter days. Frigid temperatures. Foul weather. What better time to be outdoors? Winter sports ... 15. Coping with Colds Science.gov (United States) ... have heard that chicken soup can cure a cold. There's no real proof of this, but sick people have been swearing by it for more than 800 years. When Should I Go to the Doctor? Teens who catch colds usually don't get very sick or need ... 16. How Cold is Cold Dark Matter? CERN Document Server Armendariz-Picon, Cristian 2013-01-01 If cold dark matter consists of particles, these must be non-interacting and non-relativistic by definition. In most cold dark matter models, however, dark matter particles inherit a non-vanishing velocity dispersion from interactions in the early universe, a velocity that redshifts with cosmic expansion but certainly remains non-zero. In this article, we place model-independent constraints on the dark matter temperature to mass ratio, whose square root determines the dark matter velocity dispersion. We only assume that dark matter particles decoupled kinetically while non-relativistic, when galactic scales had not entered the horizon yet, and that their momentum distribution has been Maxwellian since that time. Under these assumptions, using cosmic microwave background and matter power spectrum observations, we place upper limits on the temperature to mass ratio of cold dark matter. The latter imply that its velocity dispersion extrapolated to the present has to be smaller than 56 m/s. Cold dark matter has t... 17. New Insight into Short-Wavelength Solar Wind Fluctuations from Vlasov Theory Science.gov (United States) Sahraoui, Fouad; Belmont, G.; Goldstein, M. L. 2012-01-01 The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations gave evidence of the dominance of kinetic Alfven waves (KAWs) at sub-ion scales with omega omega (sub ci)) is more relevant. Here, we study key properties of the short-wavelength plasma modes under limited, but realistic, SW conditions, Typically Beta(sub i) approx. > Beta (sub e) 1 and for high oblique angles of propagation 80 deg 1 to frequencies either larger or smaller than omega (sub ci), depending on the anisotropy kappa (parallel )/ kappa(perpendicular). This extension into small scales is more readily called whistler (omega > omega (sub ci)) or KAW (omega < omega (sub ci)) although the mode is essentially the same. This contrasts with the well-accepted idea that the whistler branch always develops as a continuation at high frequencies of the fast magnetosonic mode. We show, furthermore, that the whistler branch is more damped than the KAW one, which makes the latter the more relevant candidate to carry the energy cascade down to electron scales. We discuss how these new findings may facilitate resolution of the controversy concerning the nature of the small-scale turbulence, and we discuss the implications for present and future spacecraft wave measurements in the SW. 18. New Insight into Short-wavelength Solar Wind Fluctuations from Vlasov Theory Science.gov (United States) Sahraoui, F.; Belmont, G.; Goldstein, M. L. 2012-04-01 The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations gave evidence of the dominance of kinetic Alfvén waves (KAWs) at sub-ion scales with ω ωci) is more relevant. Here, we study key properties of the short-wavelength plasma modes under limited, but realistic, SW conditions, typically β i >~ β e ~ 1 and for high oblique angles of propagation 80° ~ 1 to frequencies either larger or smaller than ωci, depending on the anisotropy k par/k . This extension into small scales is more readily called whistler (ω > ωci) or KAW (ω < ωci), although the mode is essentially the same. This contrasts with the well-accepted idea that the whistler branch always develops as a continuation at high frequencies of the fast magnetosonic mode. We show, furthermore, that the whistler branch is more damped than the KAW one, which makes the latter the more relevant candidate to carry the energy cascade down to electron scales. We discuss how these new findings may facilitate resolution of the controversy concerning the nature of the small-scale turbulence, and we discuss the implications for present and future spacecraft wave measurements in the SW. 19. New insight into short wavelength solar wind fluctuations from Vlasov theory CERN Document Server Sahraoui, Fouad; Goldstein, Melvyn 2011-01-01 The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays. Although recent observations gave evidence of the dominance of Kinetic Alfv\\'en Waves (KAW) at sub-ion scales with$\\omega\\omega_{ci}$) is more relevant. Here, we propose to study key properties of the short wavelength plasma modes under realistic SW conditions, typically$\\beta_i\\gtrsim \\beta_e\\sim 1$and for high oblique angles of propagation$80^\\circ\\leq \\Theta_{\\bf kB}\\omega_{ci}$) or a KAW mode (with$\\omega<\\omega_{ci}$) depending on the anisotropy$k_\\parallel/ k_\\perp. This contrasts with the well-accepted idea that the whistler branch develops as a continuation at high frequencies of the fast magnetosonic mode. We show, furthermore, that the whistler branch is more damped than the KAW one, which makes the latter a more relevant candidate to carry the energy cascade down to electron scales. We discuss how these new findings may facilitate resolution of the controversy co... 20. Ion–Cyclotron Resonance Frequency Interval Dependence on the O VI Ion Number Density in the North Polar Coronal Hole 1.5–3 Region Indian Academy of Sciences (India) Özgür Gültekin; Emine Rızaoǧlu; K. Gediz Akdeniz 2013-12-01 The frequency intervals in which O VI ions get in resonance with ion–cyclotron waves are calculated using the kinetic model, for the latest six values found in literature on O VI ion number densities in the 1.5–3 region of the NPCH. It is found that the common resonance interval is 1.5 kHz to 3 kHz. The -variations of wave numbers necessary for the above calculations are evaluated numerically, solving the cubic dispersion relation with the dielectric response derived from the quasi-linear Vlasov equation for the left-circularly polarized ion-cyclotron waves. 1. Einstein-Vlasov system in spherical symmetry: Reduction of the equations of motion and classification of single-shell static solutions in the limit of massless particles Science.gov (United States) Gundlach, Carsten 2016-12-01 We express the Einstein-Vlasov system in spherical symmetry in terms of a dimensionless momentum variable z (radial over angular momentum). This regularizes the limit of massless particles, and in that limit allows us to obtain a reduced system in independent variables (t ,r ,z ) only. Similarly, in this limit the Vlasov density function f for static solutions depends on a single variable Q (energy over angular momentum). This reduction allows us to show that any given static metric that has vanishing Ricci scalar, is vacuum at the center and for r >3 M and obeys certain energy conditions uniquely determines a consistent f =k ¯(Q ) (in closed form). Vice versa, any k ¯(Q ) within a certain class uniquely determines a static metric (as the solution of a system of two first-order quasilinear ordinary differential equations). Hence the space of static spherically symmetric solutions of the Einstein-Vlasov system is locally a space of functions of one variable. For a simple two-parameter family of functions k ¯(Q ), we construct the corresponding static spherically symmetric solutions, finding that their compactness is in the interval 0.7 ≲maxr(2 M /r )≤8 /9 . This class of static solutions includes one that agrees with the approximately universal type-I critical solution recently found by Akbarian and Choptuik (AC) in numerical time evolutions. We speculate on what singles it out as the critical solution found by fine-tuning generic data to the collapse threshold, given that AC also found that all static solutions are one-parameter unstable and sit on the threshold of collapse. 2. Flows of non-smooth vector fields and degenerate elliptic equations with applications to the Vlasov-Poisson and semigeostrophic systems CERN Document Server Colombo, Maria 2017-01-01 The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows. 3. Uniformly accurate Particle-in-Cell method for the long time solution of the two-dimensional Vlasov-Poisson equation with uniform strong magnetic field Science.gov (United States) Crouseilles, Nicolas; Lemou, Mohammed; Méhats, Florian; Zhao, Xiaofei 2017-10-01 In this work, we focus on the numerical resolution of the four dimensional phase space Vlasov-Poisson system subject to a uniform strong external magnetic field. To do so, we consider a Particle-in-Cell based method, for which the characteristics are reformulated by means of the two-scale formalism, which is well-adapted to handle highly-oscillatory equations. Then, a numerical scheme is derived for the two-scale equations. The so-obtained scheme enjoys a uniform accuracy property, meaning that its accuracy does not depend on the small parameter. Several numerical results illustrate the capabilities of the method. 4. Ion-atom hybrid systems CERN Document Server Willitsch, Stefan 2014-01-01 The study of interactions between simultaneously trapped cold ions and atoms has emerged as a new research direction in recent years. The development of ion-atom hybrid experiments has paved the way for investigating elastic, inelastic and reactive collisions between these species at very low temperatures, for exploring new cooling mechanisms of ions by atoms and for implementing new hybrid quantum systems. The present lecture reviews experimental methods, recent results and upcoming developments in this emerging field. 5. Cold Suppresses Agonist-induced Activation of TRPV1 OpenAIRE 2011-01-01 Cold therapy is frequently used to reduce pain and edema following acute injury or surgery such as tooth extraction. However, the neurobiological mechanisms of cold therapy are not completely understood. Transient receptor potential vanilloid 1 (TRPV1) is a capsaicin- and heat-gated nociceptive ion channel implicated in thermosensation and pathological pain under conditions of inflammation or injury. Although capsaicin-induced nociception, neuropeptide release, and ionic currents are suppress... 6. Cold Vacuum Drying Facility Data.gov (United States) Federal Laboratory Consortium — Located near the K-Basins (see K-Basins link) in Hanford's 100 Area is a facility called the Cold Vacuum Drying Facility (CVDF).Between 2000 and 2004, workers at the... 7. Cold-induced metabolism NARCIS (Netherlands) Lichtenbelt, W. van Marken; Daanen, H.A.M. 2003-01-01 Purpose of review Cold response can be insulative (drop in peripheral temperature) or metabolic (increase in energy expenditure). Nonshivering thermogenesis by sympathetic, norepinephrine-induced mitochondrial heat production in brown adipose tissue is a well known component of this metabolic 8. The cold reading technique. Science.gov (United States) Dutton, D L 1988-04-15 For many people, belief in the paranormal derives from personal experience of face-to-face interviews with astrologers, palm readers, aura and Tarot readers, and spirit mediums. These encounters typically involve cold reading, a process in which a reader makes calculated guesses about a client's background and problems and, depending on the reaction, elaborates a reading which seems to the client so uniquely appropriate that it carries with it the illusion of having been produced by paranormal means. The cold reading process is shown to depend initially on the Barnum effect, the tendency for people to embrace generalized personality descriptions as idiosyncratically their own. Psychological research into the Barnum effect is critically reviewed, and uses of the effect by a professional magician are described. This is followed by detailed analysis of the cold reading performances of a spirit medium. Future research should investigate the degree to which cold readers may have convinced themselves that they actually possess psychic or paranormal abilities. 9. A Cold Alarm Institute of Scientific and Technical Information of China (English) 2010-01-01 Since the end of 2009, north China has been repeatedly struck by arctic-like blasts of cold weather. As temperatures have plummeted to historic lows, they have inflicted considerable suffering as well. 10. A Cold Alarm Institute of Scientific and Technical Information of China (English) ZHOU JIANXIONG 2010-01-01 @@ Since the end of 2009, north China has been repeatedly struck by arctic-like blasts of cold weather. As temperatures have plummeted to historic lows, they have inflicted considerable suffering as well. 11. Hemolymph metabolites and osmolality are tightly linked to cold tolerance of Drosophila species DEFF Research Database (Denmark) Olsson, Trine; MacMillan, Heath A.; Nyberg, Nils 2016-01-01 Drosophila, like most insects, are susceptible to low temperatures, and will succumb to temperatures above the freezing point of their hemolymph. For these insects, cold exposure causes a loss of extracellular ion and water homeostasis, leading to chill injury and eventually death. Chill...... that the larger contribution of classical cryoprotectants in chill-tolerant Drosophila plays a non-colligative role for cold tolerance that contributes to osmotic and ion homeostasis during cold exposure and, in addition, we discuss how these comparative differences may represent an evolutionary pathway toward...... more extreme cold tolerance of insects.... 12. QCD Factorization Approach to Cold Nuclear Matter Effects Science.gov (United States) Qiu, Jianwe 2016-09-01 Cold nuclear matter effects exist in all high energy collisions involving identified nucleus (or nuclei). They have been manifested in very significant ways in e-A and p-A, as well as A-A collisions, where the cold nuclear effect is a part of the initial condition which plays a critical role in determining the outcome of heavy ion collisions. In this talk, I will discuss if it is possible to consistently calculate or extract the cold nuclear effect, the advantage and limitation of QCD factorization approach, and the predictive power or the testability of the QCD calculations. 13. KCNQ channels in nociceptive cold-sensing trigeminal ganglion neurons as therapeutic targets for treating orofacial cold hyperalgesia. Science.gov (United States) Abd-Elsayed, Alaa A; Ikeda, Ryo; Jia, Zhanfeng; Ling, Jennifer; Zuo, Xiaozhuo; Li, Min; Gu, Jianguo G 2015-07-31 Hyperexcitability of nociceptive afferent fibers is an underlying mechanism of neuropathic pain and ion channels involved in neuronal excitability are potentially therapeutic targets. KCNQ channels, a subfamily of voltage-gated K(+) channels mediating M-currents, play a key role in neuronal excitability. It is unknown whether KCNQ channels are involved in the excitability of nociceptive cold-sensing trigeminal afferent fibers and if so, whether they are therapeutic targets for orofacial cold hyperalgesia, an intractable trigeminal neuropathic pain. Patch-clamp recording technique was used to study M-currents and neuronal excitability of cold-sensing trigeminal ganglion neurons. Orofacial operant behavioral assessment was performed in animals with trigeminal neuropathic pain induced by oxaliplatin or by infraorbital nerve chronic constrictive injury. We showed that KCNQ channels were expressed on and mediated M-currents in rat nociceptive cold-sensing trigeminal ganglion (TG) neurons. The channels were involved in setting both resting membrane potentials and rheobase for firing action potentials in these cold-sensing TG neurons. Inhibition of KCNQ channels by linopirdine significantly decreased resting membrane potentials and the rheobase of these TG neurons. Linopirdine directly induced orofacial cold hyperalgesia when the KCNQ inhibitor was subcutaneously injected into rat orofacial regions. On the other hand, retigabine, a KCNQ channel potentiator, suppressed the excitability of nociceptive cold-sensing TG neurons. We further determined whether KCNQ channel could be a therapeutic target for orofacial cold hyperalgesia. Orofacial cold hyperalgesia was induced in rats either by the administration of oxaliplatin or by infraorbital nerve chronic constrictive injury. Using the orofacial operant test, we showed that retigabine dose-dependently alleviated orofacial cold hyperalgesia in both animal models. Taken together, these findings indicate that KCNQ channel plays a 14. Electron-ion collisional effect on Weibel instability in a Kappa distributed unmagnetized plasma Energy Technology Data Exchange (ETDEWEB) Kumar Kuri, Deep, E-mail: [email protected]; Das, Nilakshi, E-mail: [email protected] [Department of Physics, Tezpur University, Tezpur, Assam 784 028 (India) 2014-04-15 Weibel instability has been investigated in the presence of electron-ion collisions by using standard Vlasov-Maxwell equations. The presence of suprathermal electrons has been included here by using Kappa distribution for the particles. The growth rate γ of Weibel instability has been calculated for different values of spectral index κ, collision frequency ν{sub ei}, and temperature anisotropy parameter β. A comparative study between plasma obeying Kappa distribution and that obeying Maxwellian distribution shows that the growth of instability is higher for the Maxwellian particles. However, in the presence of collisions, the suprathermal particles result in lower damping of Weibel mode. 15. Effects of Magnetic Shear on Ion-Cyclotron Modes. Science.gov (United States) Ganguli, Gurudas Effects of Magnetic Shear on electrostatic Ion -Bernstein Modes (IBM) are examined. Shear affects the mode structure in 3 principal ways: (i) Local effect, (ii) Global effect and (iii) Orbital effect. The role of shear at the above three levels is investigated for IBM in general and in the context of parametric instability of two Ion-Bernstein modes by a magnetosonic wave in a multispecies plasma in particular. An improved marginal stability criterion is presented at Local and Global levels and the region where the Orbital effects are influential is defined and discussed. An electron drift relative to the ions is introduced parallel to the external magnetic field giving rise to Current Driven Ion Cyclotron Instability (CDICI). An improved theory of CDICI in a sheared magnetic field is given. For temperature ratios (tau) = T(,i)/T(,e) > .25, the imaginary part of the local dispersion relation, (as a function of k(,(PARLL)) (('x)), the local parallel wavevector), can be approximated by a parabola, while for weaker (tau) it can be approximated by a pair of straight lines; in each case a second order differential equation is solved for complex roots, (omega). Growth rates ((gamma)/(OMEGA)), are plotted against the square of the normalized pependicular wavevector ((TURN)b) for various values of shear, temperature ratios and electron drift strengths. The main effect of shear is to localize this instability in x-space around some x(,0) such that k(,(PARLL))('0) = ('s)k(,y)x(,0), (('s) being inverse shear length), corresponds to the ((gamma)/(OMEGA))(,max) in the absence of shear. Shear also reduces the growth rate in general: however, ((gamma)/(OMEGA)) for the b values away from the value corresponding to the maximum growth rate are affected more than those which are closer, thereby making the instability more coherent in b. Operator methods employing the Vlasov operator to obtain orbits and velocities in external magnetic fields are studied. Particle orbits and 16. Ionic mechanisms of spinal neuronal cold hypersensitivity in ciguatera. Science.gov (United States) Patel, Ryan; Brice, Nicola L; Lewis, Richard J; Dickenson, Anthony H 2015-12-01 Cold hypersensitivity is evident in a range of neuropathies and can evoke sensations of paradoxical burning cold pain. Ciguatoxin poisoning is known to induce a pain syndrome caused by consumption of contaminated tropical fish that can persist for months and include pruritus and cold allodynia; at present no suitable treatment is available. This study examined, for the first time, the neural substrates and molecular components of Pacific ciguatoxin-2-induced cold hypersensitivity. Electrophysiological recordings of dorsal horn lamina V/VI wide dynamic range neurones were made in non-sentient rats. Subcutaneous injection of 10 nm ciguatoxin-2 into the receptive field increased neuronal responses to innocuous and noxious cooling. In addition, neuronal responses to low-threshold but not noxious punctate mechanical stimuli were also elevated. The resultant cold hypersensitivity was not reversed by 6-({2-[2-fluoro-6-(trifluoromethyl)phenoxy]-2-methylpropyl}carbamoyl)pyridine-3-carboxylic acid, an antagonist of transient receptor potential melastatin 8 (TRPM8). Both mechanical and cold hypersensitivity were completely prevented by co-injection with the Nav 1.8 antagonist A803467, whereas the transient receptor potential ankyrin 1 (TRPA1) antagonist A967079 only prevented hypersensitivity to innocuous cooling and partially prevented hypersensitivity to noxious cooling. In naive rats, neither innocuous nor noxious cold-evoked neuronal responses were inhibited by antagonists of Nav 1.8, TRPA1 or TRPM8 alone. Ciguatoxins may confer cold sensitivity to a subpopulation of cold-insensitive Nav 1.8/TRPA1-positive primary afferents, which could underlie the cold allodynia reported in ciguatera. These data expand the understanding of central spinal cold sensitivity under normal conditions and the role of these ion channels in this translational rat model of ciguatoxin-induced hypersensitivity. 17. Cold asymmetrical fermion superfluids Energy Technology Data Exchange (ETDEWEB) Caldas, Heron 2003-12-19 The recent experimental advances in cold atomic traps have induced a great amount of interest in fields from condensed matter to particle physics, including approaches and prospects from the theoretical point of view. In this work we investigate the general properties and the ground state of an asymmetrical dilute gas of cold fermionic atoms, formed by two particle species having different densities. We have show in a recent paper, that a mixed phase composed of normal and superfluid components is the energetically favored ground state of such a cold fermionic system. Here we extend the analysis and verify that in fact, the mixed phase is the preferred ground state of an asymmetrical superfluid in various situations. We predict that the mixed phase can serve as a way of detecting superfluidity and estimating the magnitude of the gap parameter in asymmetrical fermionic systems. 18. Cold regions isotope applications Energy Technology Data Exchange (ETDEWEB) Perrigo, L.D.; Divine, T.E. 1976-04-01 Pacific Northwest Laboratories (PNL) started the Cold Regions Isotope Applications Program in FY-1975 to identify special conditions in the Arctic and similar geographic areas (Cold Regions) where radioisotope power, heater, or sterilization systems would be desirable and economically viable. Significant progress was made in the first year of this program and all objectives for this initial 12-month period were achieved. The major conclusions and recommendations resulting for this effort are described below. The areas of interest covered include: radiosterilization of sewage; heating of septic tanks; and radioisotope thermoelectric generators as power sources for meteorological instruments and navigational aids. (TFD) 19. Ion Behavior and Gas Mixing in electron cyclotron resonance plasmas as sources of highly charged ions (concept OpenAIRE Melin, G.; Drentje, A. G.; Girard, A; Hitz, D. 1999-01-01 Abstract: An ECR ion source is basically an ECR heated plasma confinement machine, with hot electrons and cold ions. The main parameters of the ion population have been analyzed, including temperature, losses, and confinement time. The "gas mixing" effect has been studied in this context. An expression is derived for determining the ion temperature from the values of all extracted ion currents. One aim is to study the ion temperature behavior in argon plasmas without and with mixing different... 20. How cold is it? TRPM8 and TRPA1 in the molecular logic of cold sensation Directory of Open Access Journals (Sweden) McKemy David D 2005-04-01 Full Text Available Abstract Recognition of temperature is a critical element of sensory perception and allows us to evaluate both our external and internal environments. In vertebrates, the somatosensory system can discriminate discrete changes in ambient temperature, which activate nerve endings of primary afferent fibers. These thermosensitive nerves can be further segregated into those that detect either innocuous or noxious (painful temperatures; the latter neurons being nociceptors. We now know that thermosensitive afferents express ion channels of the transient receptor potential (TRP family that respond at distinct temperature thresholds, thus establishing the molecular basis for thermosensation. Much is known of those channels mediating the perception of noxious heat; however, those proposed to be involved in cool to noxious cold sensation, TRPM8 and TRPA1, have only recently been described. The former channel is a receptor for menthol, and links the sensations provided by this and other cooling compounds to temperature perception. While TRPM8 almost certainly performs a critical role in cold signaling, its part in nociception is still at issue. The latter channel, TRPA1, is activated by the pungent ingredients in mustard and cinnamon, but has also been postulated to mediate our perception of noxious cold temperatures. However, a number of conflicting reports have suggested that the role of this channel in cold sensation needs to be confirmed. Thus, the molecular logic for the perception of cold-evoked pain remains enigmatic. This review is intended to summarize our current understanding of these cold thermoreceptors, as well as address the current controversy regarding TRPA1 and cold signaling. 1. How cold is it? TRPM8 and TRPA1 in the molecular logic of cold sensation. Science.gov (United States) McKemy, David D 2005-04-22 Recognition of temperature is a critical element of sensory perception and allows us to evaluate both our external and internal environments. In vertebrates, the somatosensory system can discriminate discrete changes in ambient temperature, which activate nerve endings of primary afferent fibers. These thermosensitive nerves can be further segregated into those that detect either innocuous or noxious (painful) temperatures; the latter neurons being nociceptors. We now know that thermosensitive afferents express ion channels of the transient receptor potential (TRP) family that respond at distinct temperature thresholds, thus establishing the molecular basis for thermosensation. Much is known of those channels mediating the perception of noxious heat; however, those proposed to be involved in cool to noxious cold sensation, TRPM8 and TRPA1, have only recently been described. The former channel is a receptor for menthol, and links the sensations provided by this and other cooling compounds to temperature perception. While TRPM8 almost certainly performs a critical role in cold signaling, its part in nociception is still at issue. The latter channel, TRPA1, is activated by the pungent ingredients in mustard and cinnamon, but has also been postulated to mediate our perception of noxious cold temperatures. However, a number of conflicting reports have suggested that the role of this channel in cold sensation needs to be confirmed. Thus, the molecular logic for the perception of cold-evoked pain remains enigmatic. This review is intended to summarize our current understanding of these cold thermoreceptors, as well as address the current controversy regarding TRPA1 and cold signaling. 2. Commemoration of a cold war DEFF Research Database (Denmark) Farbøl, Rosanna 2015-01-01 This article brings together the fields of Cold War studies and memory studies. In Denmark, a remarkable institutionalisation of Cold War memory has taken place in the midst of a heated ideological battle over the past and whether to remember the Cold War as a ‘war’. Using Danish Cold War museums...... and heritage sites as case studies, this article sheds new light on the politics of history involved in Cold War commemoration. It suggests that the Cold War is commemorated as a war, yet this war memory is of a particular kind: it is a war memory without victims.... 3. Detection of cold pain, cold allodynia and cold hyperalgesia in freely behaving rats Directory of Open Access Journals (Sweden) Woolf Clifford J 2005-12-01 Full Text Available Abstract Background Pain is elicited by cold, and a major feature of many neuropathic pain states is that normally innocuous cool stimuli begin to produce pain (cold allodynia. To expand our understanding of cold induced pain states we have studied cold pain behaviors over a range of temperatures in several animal models of chronic pain. Results We demonstrate that a Peltier-cooled cold plate with ± 1°C sensitivity enables quantitative measurement of a detection withdrawal response to cold stimuli in unrestrained rats. In naïve rats the threshold for eliciting cold pain behavior is 5°C. The withdrawal threshold for cold allodynia is 15°C in both the spared nerve injury and spinal nerve ligation models of neuropathic pain. Cold hyperalgesia is present in the spared nerve injury model animals, manifesting as a reduced latency of withdrawal response threshold at temperatures that elicit cold pain in naïve rats. We also show that following the peripheral inflammation produced by intraplantar injection of complete Freund's adjuvant, a hypersensitivity to cold occurs. Conclusion The peltier-cooled provides an effective means of assaying cold sensitivity in unrestrained rats. Behavioral testing of cold allodynia, hyperalgesia and pain will greatly facilitate the study of the neurobiological mechanisms involved in cold/cool sensations and enable measurement of the efficacy of pharmacological treatments to reduce these symptoms. 4. Stabilit\\'e orbitale pour le syst\\eme de Vlasov-Poisson gravitationnel, d'apr\\es Lemou-M\\'ehats-Rapha\\"el, Guo, Lin, Rein et al. [Orbital stability for the gravitational Vlasov-Poisson system, after Lemou-M\\'ehats-Rapha\\"el, Guo, Lin, Rein et al. CERN Document Server Mouhot, Clément 2012-01-01 This paper reviews the recent mathematical progresses made on the study of the orbital stability properties for the gravitational Vlasov-Poisson system. We present in details the paper of Lemou, M\\'ehats and Rapha\\"el (Inventiones 2011) and we review also the previous works by Dolbeault, Guo, Hadzic, Lin, Rein, S\\'anchez, Soler, Wan, Wolansky. We also include a discussion of the history of this topic and the pioneering works by physicists like Antonov, Lynden-Bell and Aly. This is the text of a Bourbaki seminar given in november 2011 (in french). 5. Cold spray nozzle design Science.gov (United States) Haynes, Jeffrey D.; Sanders, Stuart A. 2009-06-09 A nozzle for use in a cold spray technique is described. The nozzle has a passageway for spraying a powder material, the passageway having a converging section and a diverging section, and at least the diverging section being formed from polybenzimidazole. In one embodiment of the nozzle, the converging section is also formed from polybenzimidazole. 6. Finger cold induced vasodilation NARCIS (Netherlands) Daanen, H.A.M. 2007-01-01 There are indications that subjects with a reduced finger CIVD response are more prone to get local cold injuries, but more epidemiological research is needed to establish a firm relationship. Although it was observed that an early CIVD onset was associated with initially superior manual performance 7. Teaching "In Cold Blood." Science.gov (United States) Berbrich, Joan D. 1967-01-01 The Truman Capote nonfiction novel, "In Cold Blood," which reflects for adolescents the immediacy of the real world, illuminates (1) social issues--capital punishment, environmental influence, and the gap between the "haves" and "have-nots," (2) moral issues--the complexity of man's nature, the responsibility of one… 8. Cold Weather Pet Safety Science.gov (United States) ... they can be knocked over, potentially starting a fire. Check your furnace before the cold weather sets in to make ... avoided because of the risk of burns or fire. Heated pet mats should also be used ... to burrow, get them back inside quickly because they are showing signs of ... 9. Cold-induced metabolism NARCIS (Netherlands) Lichtenbelt, W. van Marken; Daanen, H.A.M. 2003-01-01 Purpose of review Cold response can be insulative (drop in peripheral temperature) or metabolic (increase in energy expenditure). Nonshivering thermogenesis by sympathetic, norepinephrine-induced mitochondrial heat production in brown adipose tissue is a well known component of this metabolic respon 10. Chilling Out With Colds Science.gov (United States) ... some feel-better tips if you get a cold: Bring on the heat. Hot drinks soothe coughs and sore throats while also clearing mucus. So eat (or drink) your chicken soup! Get steamed up. A steamy shower helps stuffy or irritated noses. Or run a ... 11. Out in the cold. Science.gov (United States) Bates, Jane 2016-05-04 Every now and then, you say something to a patient and wonder whether you should have kept quiet. On this occasion, a female patient and I were indulging in a moment of shared empathy over an annoying symptom we both experience - permanently cold feet. 12. Cold War Propaganda. Science.gov (United States) Bennett, Paul W. 1988-01-01 Briefly discusses the development of Cold War propaganda in the United States, Canada, and the USSR after 1947. Presents two movie reviews and a Canadian magazine advertisement of the period which illustrate the harshness of propaganda used by both sides in the immediate postwar years. (GEA) 13. Recent Cold War Studies Science.gov (United States) Pineo, Ronn 2003-01-01 Cold War historiography has undergone major changes since the 1991 collapse of the Soviet Union. For two years (1992-1993) the principal Soviet archives fell open to scholars, and although some of the richest holdings are now once again closed, new information continues to find its way out. Moreover, critical documentary information has become… 14. A fast and efficient determination of amines and preservatives in cough and cold liquid and suspension formulations using a single isocratic ion-pairing high performance [correction of power] liquid chromatography method. Science.gov (United States) Paciolla, M D; Jansen, S A; Martellucci, S A; Osei, A A 2001-08-01 A single, highly selective ion-pairing reverse phase-high power liquid chromatography (RP-HPLC) method has been developed for the determination of amines and preservatives in a wide range of Tylenol((R)) liquid and suspension liquid products. As with many OTC products, the challenge is to quantitatively extract the analytes from difficult matrices and specifically analyze them in the presence of various excipients and flavors. Historically, separate analytical methods were used for each class of analytes (acids, bases and neutral compounds). In this method a mobile phase consisting of a buffered ion-pairing agent with acetonitrile, methanol and tetrahydrofuran was used to separate the charged amines from neutral and acidic compounds on a Phenomenex LUNA C8(2) 75 x 4.6 mm i.d. analytical column with a 3-microm particle size. The analytes include acids (benzoic acid), bases (pseudoephedrine, chlorpheniramine, dextromethorphan, doxylamine and diphenhydramine) and a neutral compound (butylparaben). The effects of pH, the chain length of the ion-pairing reagent, ionic strength and organic modifiers on the separation are discussed. The method is linear from 15 to 150% of the target amounts. The optimized method proves to be specific, robust and accurate for the analysis of the compounds. 15. Herpes Simplex Virus (Cold Sores) Science.gov (United States) ... Print Share Cold Sores in Children: About the Herpes Simplex Virus Page Content A child's toddler and ... Cold sores (also called fever blisters or oral herpes) start as small blisters that form around the ... 16. The dynamics of electron and ion holes in a collisionless plasma Directory of Open Access Journals (Sweden) B. Eliasson 2005-01-01 Full Text Available We present a review of recent analytical and numerical studies of the dynamics of electron and ion holes in a collisionless plasma. The new results are based on the class of analytic solutions which were found by Schamel more than three decades ago, and which here work as initial conditions to numerical simulations of the dynamics of ion and electron holes and their interaction with radiation and the background plasma. Our analytic and numerical studies reveal that ion holes in an electron-ion plasma can trap Langmuir waves, due the local electron density depletion associated with the negative ion hole potential. Since the scale-length of the ion holes are on a relatively small Debye scale, the trapped Langmuir waves are Landau damped. We also find that colliding ion holes accelerate electron streams by the negative ion hole potentials, and that these streams of electrons excite Langmuir waves due to a streaming instability. In our Vlasov simulation of two colliding ion holes, the holes survive the collision and after the collision, the electron distribution becomes flat-topped between the two ion holes due to the ion hole potentials which work as potential barriers for low-energy electrons. Our study of the dynamics between electron holes and the ion background reveals that standing electron holes can be accelerated by the self-created ion cavity owing to the positive electron hole potential. Vlasov simulations show that electron holes are repelled by ion density minima and attracted by ion density maxima. We also present an extension of Schamel's theory to relativistically hot plasmas, where the relativistic mass increase of the accelerated electrons have a dramatic effect on the electron hole, with an increase in the electron hole potential and in the width of the electron hole. A study of the interaction between electromagnetic waves with relativistic electron holes shows that electromagnetic waves can be both linearly and nonlinearly 17. Trainability of cold induced vasodilation NARCIS (Netherlands) Daanen, H.A.M.; Raymann, R.J.E.M.; Stoop, M. 2007-01-01 Peripheral cold injuries are often reported in mountaineers. Not only low ambient temperatures, but also the hypobaric circumstances are known to be major environmental risk factors. When the fingers are exposed to extreme cold for several minutes, cold induced vasodilation (CIVD) occurs, that is 18. Trainability of cold induced vasodilation NARCIS (Netherlands) Daanen, H.A.M.; Raymann, R.J.E.M.; Stoop, M. 2007-01-01 Peripheral cold injuries are often reported in mountaineers. Not only low ambient temperatures, but also the hypobaric circumstances are known to be major environmental risk factors. When the fingers are exposed to extreme cold for several minutes, cold induced vasodilation (CIVD) occurs, that is re 19. Differential kinetic dynamics and heating of ions in the turbulent solar wind CERN Document Server Valentini, F; Stabile, S; Pezzi, O; Servidio, S; De Marco, R; Marcucci, F; Bruno, R; Lavraud, B; De Keyser, J; Consolini, G; Brienza, D; Sorriso-Valvo, L; Retinò, A; Vaivads, A; Salatti, M; Veltri, P 2016-01-01 The solar wind plasma is a fully ionized and turbulent gas ejected by the outer layers of the solar corona at very high speed, mainly composed by protons and electrons, with a small percentage of helium nuclei and a significantly lower abundance of heavier ions. Since particle collisions are practically negligible, the solar wind is typically not in a state of thermodynamic equilibrium. Such a complex system must be described through self-consistent and fully nonlinear models, taking into account its multi-species composition and turbulence. We use a kinetic hybrid Vlasov-Maxwell numerical code to reproduce the turbulent energy cascade down to ion kinetic scales, in typical conditions of the uncontaminated solar wind plasma, with the aim of exploring the differential kinetic dynamics of the dominant ion species, namely protons and alpha particles. We show that the response of different species to the fluctuating electromagnetic fields is different. In particular, a significant differential heating of alphas w... 20. Kinetically modified parametric instabilities of circularly-polarized Alfven waves: Ion kinetic effects CERN Document Server Nariyuki, Y; Nariyuki, Yasuhiro; Hada, Tohru 2006-01-01 Parametric instabilities of parallel propagating,circularly polarized Alfv\\'en waves in a uniform background plasma is studied, within a framework of one-dimensional Vlasov equation for ions and massless electron fluid, so that kinetic perturbations in the longitudinal direction (ion Landau damping) are included. The present formulation also includes the Hall effect. The obtained results agree well with relevant analysis in the past, suggesting that kinetic effects in the longitudinal direction play essential roles in the parametric instabilities of Alfven waves when the kinetic effects react "passively". Furthermore, existence of the kinetic parametric instabilities is confirmed for the regime with small wave number daughter waves. Growth rates of these instabilities are sensitive to ion temperature. 1. WISPy cold dark matter Energy Technology Data Exchange (ETDEWEB) Arias, Paola [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Pontificia Univ. Catolica de Chile, Santiago (Chile). Facultad de Fisica; Cadamuro, Davide; Redondo, Javier [Max-Planck-Institut fuer Physik, Muenchen (Germany); Goodsell, Mark [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); European Organization for Nuclear Research (CERN), Geneva (Switzerland); Jaeckel, Joerg [Durham Univ. (United Kingdom). Inst. for Particle Physics Phenomenology; Ringwald, Andreas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany) 2012-01-15 Very weakly interacting slim particles (WISPs), such as axion-like particles (ALPs) or hidden photons (HPs), may be non-thermally produced via the misalignment mechanism in the early universe and survive as a cold dark matter population until today. We find that, both for ALPs and HPs whose dominant interactions with the standard model arise from couplings to photons, a huge region in the parameter spaces spanned by photon coupling and ALP or HP mass can give rise to the observed cold dark matter. Remarkably, a large region of this parameter space coincides with that predicted in well motivated models of fundamental physics. A wide range of experimental searches - exploiting haloscopes (direct dark matter searches exploiting microwave cavities), helioscopes (searches for solar ALPs or HPs), or light-shining-through-a-wall techniques - can probe large parts of this parameter space in the foreseeable future. (orig.) 2. "Miniature Cold War?" Institute of Scientific and Technical Information of China (English) 2004-01-01 @@ Fu: Relations between America and Russia are one of the most important bilateral ties that could affect the trend of world situation.What's the matter with U. S. -Russia ties? What's wrong with their bilateral relations? People tend to ask these days. Some observers on both sides suggest that post 9/11 honeymoon has turned sour when joint effort against challenges from nontraditional security issues failed to remove original bilateral contradictions over traditional security concerns.Japanese Jiji News Agency saw "a miniature Cold War" evolving and the British Guardian even bluntly pronounced "a new Cold War" on January 3, asserting that disintegration of the former Soviet Union did not terminate bilateral contention, which has only been performed on an international stage more complicated than ever before, with covert scheming against each other replacing overt, direct confrontation. How about starting our discussion with those comments? 3. Engine Cold Start Science.gov (United States) 2015-09-01 14. ABSTRACT These fuels were used for testing a GEP 6.5L turbocharged V-8 diesel engine operation in a cold box. This engine architecture is... engines . The U.S. military currently uses petroleum-based jet fuels in diesel engine -powered ground vehicles and is studying the use of alternative jet...to identify a window, or range, of cetane number which would be acceptable to ensure the reliable operation of diesel engine -powered military ground 4. Electronic Equipment Cold Plates Science.gov (United States) 1976-04-01 equations for such a flow regiae. For laainar flow and Moderate teaperature differwwe« between the well «nd coolant, a aodifled Sieder -Tate...con- figuration. The heat-transfer coefficients, therefore, were determined by using both the Sieder -Tate and McAdams equations and the coaputed...values used In the analytical predictions. As with th* previous cold Plates, the Sieder -Tate equation gave too low of values for the heat- transfer 5. The CMS COLD BOX CERN Multimedia Brice, Maximilien 2015-01-01 The CMS detector is built around a large solenoid magnet. This takes the form of a cylindrical coil of superconducting cable that generates a field of 3.8 Tesla: about 100,000 times the magnetic field of the Earth. To run, this superconducting magnet needs to be cooled down to very low temperature with liquid helium. Providing this is the job of a compressor station and the so-called “cold box”. 6. 稀土离子和香兰素在H2SO4溶液中对冷轧钢的缓蚀协同效应%Synergistic Inhibition Effect of Rare Earth Ions and Vanillin on Corrosion of Cold Rolled Steel in H2SO4 Solution Institute of Scientific and Technical Information of China (English) 李向红; 邓书端; 付惠; 木冠南 2009-01-01 用失重法研究了四种稀土离子(La3+,Ce3+,Ce4+,Nd3+)和香兰素(4-羟基-3-甲氧基-苯甲醛)在1.0 mol/LH2SO4介质中对冷轧钢的缓蚀协同效应.结果表明,香兰素对冷轧钢有中等程度的缓蚀作用,缓蚀率随其浓度的增加而增大;四种稀土离子对冷轧钢的缓蚀作用均较差,最大缓蚀率仅为20%左右.香兰素和稀土Ce4+复配后对冷轧钢产生了明显的缓蚀协同效应,最大缓蚀率可达95%左右;而与La3+,Ce3+和Nd3+复配后均无缓蚀协同效应.%The synergistic inhibition effect of four rare earth ions (La3+, Ce3+, Ce4+, Nd3+) and vanillin (4-hydroxy-3-methoxy-benzaldehyde) on the corrosion of cold rolled steel (CRS) in 1.0 mol/L H2SO4 solution was studied by weight loss method. The present study revealed that vanillin had a moderate inhibitive effect on the corrosion of CRS in 1.0 mol/L H2SO4 solution, and the inhibition efficiency increased with the concentration. The rare earth ions of La3+,Ce3+,Ce4+ and Nd3+ had a negligible effect in 1.0 mol/L H2SO4, and the maximum inhibition efficiency was not more than 20%. The experiments of incorporation of rare earth ions and vanillin, indicated that Ce4+ and vanillin produced strong synergistic effect on corrosion inhibition for CRS, and the maximum inhibition efficiency was about 95%. However, there was no synergistic inhibition effect between other rare earth ions (La3+, Ce3+ and Nd3+) and vanillin. 7. Cold Atmosphere Plasma in Cancer Therapy Science.gov (United States) Keidar, Michael 2012-10-01 Plasma is an ionized gas that is typically generated in high-temperature laboratory conditions. Recent progress in atmospheric plasmas led to the creation of cold plasmas with ion temperature close to room temperature. Areas of potential application of cold atmospheric plasmas (CAP) include dentistry, drug delivery, dermatology, cosmetics, wound healing, cellular modifications, and cancer treatment. Various diagnostic tools have been developed for characterization of CAP including intensified charge-coupled device cameras, optical emission spectroscopy and electrical measurements of the discharge propertied. Recently a new method for temporally resolved measurements of absolute values of plasma density in the plasma column of small-size atmospheric plasma jet utilizing Rayleigh microwave scattering was proposed [1,2]. In this talk we overview state of the art of CAP diagnostics and understanding of the mechanism of plasma action of biological objects. The efficacy of cold plasma in a pre-clinical model of various cancer types (long, bladder, and skin) was recently demonstrated [3]. Both in-vitro and in-vivo studies revealed that cold plasmas selectively kill cancer cells. We showed that: (a) cold plasma application selectively eradicates cancer cells in vitro without damaging normal cells. For instance a strong selective effect was observed; the resulting 60--70% of lung cancer cells were detached from the plate in the zone treated with plasma, whereas no detachment was observed in the treated zone for the normal lung cells under the same treatment conditions. (b) Significantly reduced tumor size in vivo. Cold plasma treatment led to tumor ablation with neighbouring tumors unaffected. These experiments were performed on more than 10 mice with the same outcome. We found that tumors of about 5mm in diameter were ablated after 2 min of single time plasma treatment. The two best known cold plasma effects, plasma-induced apoptosis and the decrease of cell migration 8. Ionization of Sodium Cluster by Heavy Ion Impact Institute of Scientific and Technical Information of China (English) 2001-01-01 Energetic ions have recently been used as an efficient means to produce highly charged cold clusters~[1]. There are two ways to obtain highly-charged clusters: low-fluence nano-second lasers irradiation and energetic highly charged ions impact. Compared to the low-density laser, heavy ions, e.g. delivered by ECR sources, have the 9. Paroxysmal cold hemoglobinuria. Science.gov (United States) Shanbhag, Satish; Spivak, Jerry 2015-06-01 Paroxysmal cold hemoglobinuria is a rare cause of autoimmune hemolytic anemia predominantly seen as an acute form in young children after viral illnesses and in a chronic form in some hematological malignancies and tertiary syphilis. It is a complement mediated intravascular hemolytic anemia associated with a biphasic antibody against the P antigen on red cells. The antibody attaches to red cells at colder temperatures and causes red cell lysis when blood recirculates to warmer parts of the body. Treatment is mainly supportive and with red cell transfusion, but immunosuppressive therapy may be effective in severe cases. 10. Exception in Cold War Institute of Scientific and Technical Information of China (English) 2004-01-01 @@ In the Cold War, India mainly focused its Southeast Asia Strategy on preserving the regional peace and stability, fearing that changes in Southeast Asia would impact India. Generally speaking, India would like to see a relatively strong, stable and independent Southeast Asia, which would guarantee the stability of its east wing. However, fettered by its limited power, its non-alignment policy and its special relation with Soviet Union, India's policy toward Southeast Asia remained relatively passive and its relation with Southeast Asia was, to some extent, trapped in a historical "intermission." 11. Ion Behavior and Gas Mixing in electron cyclotron resonance plasmas as sources of highly charged ions (concept NARCIS (Netherlands) Melin, G.; Drentje, A. G.; Girard, A.; Hitz, D. 1999-01-01 Abstract: An ECR ion source is basically an ECR heated plasma confinement machine, with hot electrons and cold ions. The main parameters of the ion population have been analyzed, including temperature, losses, and confinement time. The "gas mixing" effect has been studied in this context. An express 12. Chill-tolerant Gryllus crickets maintain ion balance at low temperatures. Science.gov (United States) Coello Alvarado, Litza E; MacMillan, Heath A; Sinclair, Brent J 2015-06-01 Insect cold tolerance is both phenotypically-plastic and evolutionarily labile, but the mechanisms underlying this variation are uncertain. Chill-susceptible insects lose ion and water homeostasis in the cold, which contributes to the development of injuries and eventually death. We thus hypothesized that more cold-tolerant insects will better maintain ion and water balance at low temperatures. We used rapid cold-hardening (RCH) and cold acclimation to improve cold tolerance of male Gryllus pennsylvanicus, and also compared this species to its cold-tolerant relative (Gryllus veletis). Cold acclimation and RCH decreased the critical thermal minimum (CTmin) and chill coma recovery time (CCR) in G. pennsylvanicus, but while cold acclimation improved survival of 0 °C, RCH did not; G. veletis was consistently more cold-tolerant (and had lower CCR and CTmin) than G. pennsylvanicus. During cold exposure, hemolymph water and Na(+) migrated to the gut of warm-acclimated G. pennsylvanicus, which increased hemolymph [K(+)] and decreased muscle K(+) equilibrium potentials. By contrast, cold-acclimated G. pennsylvanicus suffered a smaller loss of ion and water homeostasis during cold exposure, and this redistribution did not occur at all in cold-exposed G. veletis. The loss of ion and water balance was similar between RCH and warm-acclimated G. pennsylvanicus, suggesting that different mechanisms underlie decreased CCR and CTmin compared to increased survival at 0 °C. We conclude that increased tolerance of chilling is associated with improved maintenance of ion and water homeostasis in the cold, and that this is consistent for both phenotypic plasticity and evolved cold tolerance. Copyright © 2015 Elsevier Ltd. All rights reserved. 13. Ion-Ion Neutralization. Science.gov (United States) 1980-12-31 plasma were identified using a downstream quadrupole mass spectrometer. In these experimento it is a simple matter to establish H+(H 2 0):f as the...pressure as predicted by the Thomson t2rnary mechanism whicK hzr been suownr to be valid experimentally at hiTh rrsurs (,han and Peron, 1:EI4 hereafter t...of NO , NO2 ions in various gases and the ternary recombination coefficients of these ions in the higher pres:;ure ( Thomson ) re"ie. Equation (5) cr>n 14. Effect of a short weak prepulse on laser-triggered front-surface heavy-ion acceleration Energy Technology Data Exchange (ETDEWEB) Bochkarev, S. G.; Bychenkov, V. Yu. [P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow (Russian Federation); Golovin, G. V.; Uryupina, D. S.; Shulyapov, S. A.; Savel' ev, A. B. [M. V. Lomonosov Moscow State University, International Laser Centre and Faculty of Physics, Moscow (Russian Federation); Andriyash, A. V. [The All-Russia Research Institute of Automatics, Moscow (Russian Federation) 2012-10-15 A suppression of light-ion acceleration (from surface water contaminants) was observed when a moderate-intensity subpicosecond laser pulse was focused on a thick metal target. Simultaneously, an effective generation of high-energy multicharge ions of the target material (Fe) was experimentally observed. A numerical simulation based on the Boltzmann-Vlasov-Poisson model revealed that this is due to the very specific regime of cleaning contaminants from the target surface by the short weak prepulse preceding the main pulse by more than 10 ns and having an intensity below the surface breakdown threshold. Because this prepulse causes the contaminant layer to boil explosively, a low-density gap forms above the target surface. These conditions are consequently favorable for boosting the energy of heavy ions. 15. Cold nuclear matter CERN Document Server Dorso, C O; Nichols, J I; López, J A 2012-01-01 We study the behavior of cold nuclear matter near saturation density (\\rho 0) and very low temperature using classical molecular dynamics. We used three different (classical) nuclear interaction models that yield medium' or stiff' compressibilities. For high densities and for every model the ground state is a classical crystalline solid, but each one with a different structure. At subsaturation densities, we found that for every model the transition from uniform (crystal) to non-uniform matter occurs at \\rho ~ 0.12 fm^(-3) = 0.75 \\rho 0. Surprisingly, at the non-uniform phase, the three models produce pasta-like' structures as those allegedly present in neutron star matter but without the long-range Coulomb interaction and with different length scales. 16. Cold dark matter resuscitated? CERN Document Server White, M; Silk, J; Davis, M; White, Martin; Scott, Douglas; Silk, Joe; Davis, Marc 1995-01-01 The Cold Dark Matter (CDM) model has an elegant simplicitly which makes it very predictive, but when its parameters are fixed at their canonical' values its predictions are in conflict with observational data. There is, however, much leeway in the initial conditions within the CDM framework. We advocate a re-examination of the CDM model, taking into account modest variation of parameters from their canonical values. We find that CDM models with n=0.8--0.9 and h=0.45--0.50 can fit the available data. Our best fit'' CDM model has n=0.9, h=0.45 and C_2^{T}/C_2^{S}=0.7. We discuss the current state of observations which could definitely rule out this model. 17. Cold gelation of globular proteins NARCIS (Netherlands) Alting, A.C. 2003-01-01 Keywords : globular proteins, whey protein, ovalbumin, cold gelation, disulfide bonds, texture, gel hardnessProtein gelation in food products is important to obtain desirable sensory and textural properties. Cold gelation is a novel method to produce protein-based gels. It is a two step process in w 18. Cold gelation of globular proteins NARCIS (Netherlands) Alting, A.C. 2003-01-01 Keywords : globular proteins, whey protein, ovalbumin, cold gelation, disulfide bonds, texture, gel hardnessProtein gelation in food products is important to obtain desirable sensory and textural properties. Cold gelation is a novel method to produce protein-based gels. It is a two step process in w 19. The status of cold fusion Science.gov (United States) Storms, E. This report attempts to update the status of the phenomenon of cold fusion. The new field is continuing to grow as a variety of nuclear reactions are discovered to occur in a variety of chemical environments at modest temperatures. However, it must be cautioned that most scientists consider cold fusion as something akin to UFO's, ESP, and numerology. 20. Cold Crystal Reflector Filter Concept CERN Document Server Muhrer, G 2014-01-01 In this paper the theoretical concept of a cold crystal reflector filter will be presented. The aim of this concept is to balance the shortcoming of the traditional cold polycrystalline reflector filter, which lies in the significant reduction of the neutron flux right above (in energy space) or right below (wavelength space) the first Bragg edge. 1. The Vlasov formalism for extended relativistic mean field models: the crust-core transition and the stellar matter equation of state CERN Document Server Pais, Helena 2016-01-01 The Vlasov formalism is extended to relativistic mean-field hadron models with non-linear terms up to fourth order and applied to the calculation of the crust-core transition density. The effect of the nonlinear\\omega\\rho$and$\\sigma\\rho$coupling terms on the crust-core transition density and pressure, and on the macroscopic properties of some families of hadronic stars is investigated. For that purpose, six families of relativistic mean field models are considered. Within each family, the members differ in the symmetry energy behavior. For all the models, the dynamical spinodals are calculated, and the crust-core transition density and pressure, and the neutron star mass-radius relations are obtained. The effect on the star radius of the inclusion of a pasta calculation in the inner crust is discussed. The set of six models that best satisfy terrestrial and observational constraints predicts a radius of 13.6$\\pm$0.3 km and a crust thickness of$1.36\\pm 0.06$km for a 1.4$M_\\odot$star. 2. High Order Vlasov Solvers for the Simulation of KEEN Wavea Including the L-B and F-P Collision Models Science.gov (United States) Sonnendrucker, Eric; Crouseilles, Nicolas; Afeyan, Bedros 2012-10-01 Since the discovery of KEEN waves in 2002, it has been an open question whether the detailed phase space structures found in those well resolved simulations of Afeyan et al., would survive (essentially) intact, if instead of cubic splines, higher order interpolation schemes were used, up to spectral accuracy. In this work, the Vlasov-Poisson system is solved using Fourier-Fourier descriptions in phase space, and Fourier spline. The splines can be any order approaching spectral accuracy quickly. These simulations show what the role of numerical dissipation is for the stable simulation of driven KEEN waves, how delicate structures found in low order simulations survive and persist even when the microscope with which they are being scrutinized is much more powerful. The Fourier capability also allows truncated descriptions for the theoretical advancement of reduced models of fully formed KEEN waves, as described previously by Afeyan et al. The partitioned phase space structures they found is further tested by the use of a Lenard-Bernstein collision model on the way to including the full Fokker Planck collision operator in cylindrical (in velocity space) geometry, advanced by Greengard et al. 3. Accuracy analysis of a 2D Poisson-Vlasov PIC solver and estimates of the collisional effects in space charge dynamics CERN Document Server Bazzani, A; Franchi, A; Rambaldi, S; Turchetti, G 2005-01-01 We analyze the accuracy of a 2D Poisson-Vlasov PIC integrator, taking the KV as a reference solution for a FODO cell. The particle evolution is symplectic and the Poisson solver is based on FFT. The numerical error, evaluated by comparing the moments of the distribution and the electric field with the exact solution, shows a linear growth. This effect can be modeled by a white noise in the envelope equations for the KV beam. In order to investigate the collisional effects we have integrated the Hamilton's equations for N charged macro-particles with a hard-core r/sub H/ reducing the computational complexity to N/sup 3/2/. In the constant focusing case we observed that a KV beam, matched or mismatched relaxes to the Maxwell-Boltzmann self consistent distribution on a time interval, which depends on r/sub H/ and has a finite limit, for r/sub H/ to 0. A fully 3D PIC code for short bunches was developed for the ADS linac design at LNL (Italy). A 3D particle-core model, based on Langevin's equations with the drift... 4. A high-resolution global Vlasov simulation of a small dielectric body with a weak intrinsic magnetic field on the K computer Science.gov (United States) Umeda, Takayuki; Fukazawa, Keiichiro 2015-04-01 The interaction between the solar wind and solar system bodies, such as planets, satellites, and asteroids, is one of the fundamental global-scale phenomena in space plasma physics. In the present study, the electromagnetic environment around a small dielectric body with a weak intrinsic magnetic field is studied by means of a first-principle kinetic plasma simulation, which is a challenging task in space plasma physics as well as high-performance computing. Due to several computational limitations, five-dimensional full electromagnetic Vlasov simulations with two configuration space and three velocity space coordinates are performed with two different spatial resolutions. The Debye-scale charge separation is not solved correctly in the simulation run with a low spatial resolution, while all the physical processes in collisionless plasma are included in the simulation run with a high spatial resolution. The direction comparison of electromagnetic fields between the two runs shows that there is small difference in the structure of magnetic field lines. On the other hand, small-scale fine structures of electrostatic fields are enhanced by the electric charge separation and the charge accumulation on the surface of the body in the high-resolution run, while these structures are absent in the low-resolution runs. These results are consistent with the conventional understanding of plasma physics that the structure and dynamics of global magnetic fields, which are generally described by the magneto-hydro-dynamics (MHD) equations, are not affected by electron-scale microphysics. 5. A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov-Poisson Equation CERN Document Server Myers, Andrew; Van Straalen, Brian 2016-01-01 Numerical solutions to the Vlasov-Poisson system of equations have important applications to both plasma physics and cosmology. In this paper, we present a new Particle-in-Cell (PIC) method for solving this system that is 4th-order accurate in both space and time. Our method is a high-order extension of one presented previously [B. Wang, G. Miller, and P. Colella, SIAM J. Sci. Comput., 33 (2011), pp. 3509--3537]. It treats all of the stages of the standard PIC update - charge deposition, force interpolation, the field solve, and the particle push - with 4th-order accuracy, and includes a 6th-order accurate phase-space remapping step for controlling particle noise. We demonstrate the convergence of our method on a series of one- and two- dimensional electrostatic plasma test problems, comparing its accuracy to that of a 2nd-order method. As expected, the 4th-order method can achieve comparable accuracy to the 2nd-order method with many fewer resolution elements. 6. Complex Korteweg-de Vries equation and Nonlinear dust-acoustic waves in a magnetoplasma with a pair of trapped ions CERN Document Server Misra, A P 2015-01-01 The nonlinear propagation of dust-acoustic (DA) waves in a magnetized dusty plasma with a pair of trapped ions is investigated. Starting from a set of hydrodynamic equations for massive dust fluids as well as kinetic Vlasov equations for ions, and applying the reductive perturbation technique, a Korteweg-de Vries (KdV)-like equation with a complex coefficient of nonlinearity is derived, which governs the evolution of small-amplitude DA waves in plasmas. The complex coefficient arises due to vortex-like distributions of both positive and negative ions. An analytical as well as numerical solution of the KdV equation are obtained and analyzed with the effects of external magnetic field, the dust pressure as well as different mass and temperatures of positive and negative ions. 7. Cough and Cold Medicine Abuse (For Parents) Science.gov (United States) ... Old Feeding Your 1- to 2-Year-Old Cough and Cold Medicine Abuse KidsHealth > For Parents > Cough ... cough and cold medicine. Why Do Kids Abuse Cough and Cold Remedies? Before the U.S. Food and ... 8. Cold-Weather Sports and Your Family Science.gov (United States) ... Feeding Your 1- to 2-Year-Old Cold-Weather Sports and Your Family KidsHealth > For Parents > Cold- ... once the weather turns frosty. Beating the Cold-Weather Blahs Once a chill is in the air, ... 9. Understanding Colds: Anatomy of the Nose Science.gov (United States) ... at least one-half of colds. (5) Cold viruses can only multiply when they are inside of living cells. When on an environmental surface, cold viruses cannot multiply. However, they are still infectious if ... 10. Cold plasma decontamination of foods. Science.gov (United States) Niemira, Brendan A 2012-01-01 Cold plasma is a novel nonthermal food processing technology that uses energetic, reactive gases to inactivate contaminating microbes on meats, poultry, fruits, and vegetables. This flexible sanitizing method uses electricity and a carrier gas, such as air, oxygen, nitrogen, or helium; antimicrobial chemical agents are not required. The primary modes of action are due to UV light and reactive chemical products of the cold plasma ionization process. A wide array of cold plasma systems that operate at atmospheric pressures or in low pressure treatment chambers are under development. Reductions of greater than 5 logs can be obtained for pathogens such as Salmonella, Escherichia coli O157:H7, Listeria monocytogenes, and Staphylococcus aureus. Effective treatment times can range from 120 s to as little as 3 s, depending on the food treated and the processing conditions. Key limitations for cold plasma are the relatively early state of technology development, the variety and complexity of the necessary equipment, and the largely unexplored impacts of cold plasma treatment on the sensory and nutritional qualities of treated foods. Also, the antimicrobial modes of action for various cold plasma systems vary depending on the type of cold plasma generated. Optimization and scale up to commercial treatment levels require a more complete understanding of these chemical processes. Nevertheless, this area of technology shows promise and is the subject of active research to enhance efficacy. 11. Cold nuclear fusion reactor and nuclear fusion rocket Directory of Open Access Journals (Sweden) Huang Zhenqiang 2013-10-01 Full Text Available "Nuclear restraint inertial guidance directly hit the cold nuclear fusion reactor and ion speed dc transformer" [1], referred to as "cold fusion reactor" invention patents, Chinese Patent Application No. CN: 200910129632.7 [2]. The invention is characterized in that: at room temperature under vacuum conditions, specific combinations of the installation space of the electromagnetic field, based on light nuclei intrinsic magnetic moment and the electric field, the first two strings of the nuclei to be bound fusion on the same line (track of. Re-use nuclear spin angular momentum vector inherent nearly the speed of light to form a super strong spin rotation gyro inertial guidance features, to overcome the Coulomb repulsion strong bias barrier to achieve fusion directly hit. Similar constraints apply nuclear inertial guidance mode for different speeds and energy ion beam mixing speed, the design of ion speed dc transformer is cold fusion reactors, nuclear fusion engines and such nuclear power plants and power delivery systems start important supporting equipment, so apply for a patent merger 12. Laser ablation production of Ba, Ca, Dy, Er, La, Lu, and Yb ions CERN Document Server Olmschenk, S 2016-01-01 We use a pulsed nitrogen laser to produce atomic ions by laser ablation, measuring the relative ion yield for several elements, including some that have only recently been proposed for use in cold trapped ion experiments. For barium, we monitor the ion yield as a function of the number of applied ablation pulses for different substrates. We also investigate the ion production as a function of the pulse energy, and the efficiency of loading an ion trap as a function of radiofrequency voltage. 13. Friendly units for coldness CERN Document Server Fraundorf, P 2006-01-01 Measures of temperature that center around human experience get lots of use. Of course thermal physics insights of the last century have shown that reciprocal temperature (1/kT) has applications that temperature addresses less well. In addition to taking on negative absolute values under population inversion (e.g. of magnetic spins), bits and bytes turn 1/kT into an informatic measure of the thermal ambient for developing correlations within any complex system. We show here that, in the human-friendly units of bytes and food Calories, water freezes when 1/kT ~200 ZB/Cal or kT ~5 Cal/YB. Casting familiar benchmarks into these terms shows that habitable human space requires coldness values (part of the time, at least) between 0 and 40 ZB/Cal with respect body temperature ~100 degrees F, a range in kT of ~1 Cal/YB. Insight into these physical quantities underlying thermal equilibration may prove useful for budding scientists, as well as the general public, in years ahead. 14. Zitterbewegung in Cold Atoms Science.gov (United States) Penteado, Poliana; Egues, J. Carlos 2013-03-01 In condensed matter systems, the coupling between spatial and spin degrees of freedom through the spin-orbit (SO) interaction offers the possibility of manipulating the electron spin via its orbital motion. The proposal by Datta and Das of a `spin transistor' for example, highlights the use of the SO interaction to control the electron spin via electrical means. Recently, arrangements of crossed lasers and magnetic fields have been used to trap and cool atoms in optical lattices and also to create light-induced gauge potentials, which mimic the SO interactions in real solids. In this work, we investigate the Zitterbewegung in cold atoms by starting from the effective SO Hamiltonian derived in Ref.. Cross-dressed atoms as effective spins can provide a proper setting in which to observe this effect, as the relevant parameter range of SO strengths may be more easily attainable in this context. We find a variety of peculiar Zitterbewegung orbits in real and pseudo-spin spaces, e.g., cycloids and ellipses - all of which obtained with realistic parameters. This work is supported by FAPESP, CAPES and CNPq. 15. Understanding the conductivity in ion propulsion devices Energy Technology Data Exchange (ETDEWEB) Garrigues, L.; Boeuf, J.P.; Pitchford, L.C. [Univ. Paul Sabatier, Toulouse (France) 1996-12-31 A SPT (stationary plasma thruster) is a type of ion source developed primarily in Russian over the past 30 years and used as an electromagnetic propulsion device in applications requiring a low to moderate thrust with a high efficiency (satellite station keeping, for example). Although SPTs have been used in space, the principles of operation are far from clear. One of the outstanding issues is the identification of the mechanisms leading to the observed high conductivity in these devices. The neutral density is low and the plasma at the cathode end is fully ionized. Electron-neutral and electron-ion collisions are insufficient to account for the observed conductivity across the magnetic field lines. Bohm diffusion resulting from turbulence is a possible explanation for the observed high conductivity but other effects such as electron-wall interaction seem to play a very important role, due to the particular structure of this device where magnetic field lines are directed toward the walls. Electron collisions with the dielectric walls can enhance the conductivity in SPTs. Because the B field is perpendicular to the walls, the electron current is forced to the walls and secondary electron emission can occur for electron energies greater than about 30 eV on these surfaces. The authors have performed Monte Carlo calculations to study the effect of reflection and secondary emission on the calculated conductivity. Results from the Monte Carlo simulation are used to estimate the electron conductivity and energy loss in the device. These data are used as input in a self-consistent quasi-neutral hybrid model of the discharge where ions are described by a Vlasov equation, and the electric field distribution is deduced from the electron momentum equation, assuming quasi-neutrality. 16. Cold-formed steel design CERN Document Server Yu, Wei-Wen 2010-01-01 The definitive text in the field, thoroughly updated and expanded Hailed by professionals around the world as the definitive text on the subject, Cold-Formed Steel Design is an indispensable resource for all who design for and work with cold-formed steel. No other book provides such exhaustive coverage of both the theory and practice of cold-formed steel construction. Updated and expanded to reflect all the important developments that have occurred in the field over the past decade, this Fourth Edition of the classic text provides you with more of the detailed, up-to-the-minute techni 17. Quantum logic with molecular ions CERN Document Server Wolf, Fabian; Heip, Jan C; Gebert, Florian; Shi, Chunyan; Schmidt, Piet O 2015-01-01 Laser spectroscopy of cold and trapped molecular ions is a powerful tool for fundamental physics, including the determination of fundamental constants, the laboratory test for their possible variation, and the search for a possible electric dipole moment of the electron. Optical clocks based on molecular ions sensitive to some of these effects are expected to achieve uncertainties approaching the$10^{-18}$level. While the complexity of molecular structure facilitates these applications, the absence of cycling transitions poses a challenge for direct laser cooling, quantum state control, and detection. Previously employed state detection techniques based on photo-dissociation or chemical reactions are destructive and therefore inefficient. Here we experimentally demonstrate non-destructive state detection of a single trapped molecular ion through its strong Coulomb coupling to a well-controlled co-trapped atomic ion. An algorithm based on a state-dependent optical dipole force(ODF) changes the internal state... 18. Tunneling process in heavy-ion fusion and fission Energy Technology Data Exchange (ETDEWEB) Iwamoto, Akira [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Kondratyev, V.; Bonasera, A. 1998-10-01 We present a model towards the many-body description of sub-barrier fusion and spontaneous fission based on the semiclassical Vlasov equation and the Feynman path integral method. We define suitable collective variables from the Vlasov solution and use the imaginary time technique for the dynamics below the Coulomb barrier. (author) 19. Operant behavioral responses to orofacial cold stimuli in rats with chronic constrictive trigeminal nerve injury: effects of menthol and capsazepine Science.gov (United States) 2013-01-01 Both spinal and trigeminal somatosensory systems use the TRPM8 channel as a principal transducer for detecting cold stimuli. It is currently unclear whether this cold transducer may play a role in trigeminal neuropathic pain manifesting cold allodynia and hyperalgesia. In the present study, trigeminal neuropathy was induced by chronic constrictive nerve injury of the infraorbital nerve (ION-CCI). Behavioral responses to cold stimuli in orofacial regions were assessed by the newly developed orofacial operant test in the ION-CCI rats. We tested menthol and capsazepine, two compounds that can activate and inhibit TRPM8 respectively, on orofacial operant responses to cold stimuli in ION-CCI rats. Testing animals performed operant tasks by voluntarily contacting their orofacial regions to a cold stimulation module in order to access sweetened milk as a reward, and contact time and number of the operant behaviors were automatically recorded. Total contact time was significantly reduced at the cooling temperatures of 17°C and 12°C in ION-CCI group in comparison with sham group, indicating the presence of cold allodynia and hyperalgesia in ION-CCI rats. When menthol was administered to ION-CCI rats, total contact time was further reduced and total contact number increased at the cooling temperatures. In contrast, after administration of capsazepine to ION-CCI rats, total contact time was significantly increased at the cooling temperatures. The behavioral outcomes support the idea that TRPM8 plays a role in cold allodynia and hyperalgesia following chronic trigeminal nerve injury. PMID:23767981 20. PANDA: Cold three axes spectrometer Directory of Open Access Journals (Sweden) Astrid Schneidewind 2015-08-01 Full Text Available The cold three axes spectrometer PANDA, operated by JCNS, Forschungszentrum Jülich, offers high neutron flux over a large dynamic range keeping the instrumental background comparably low. 1. Flu and Colds: In Depth Science.gov (United States) ... studies have evaluated the use of American ginseng (Panax quinquefolius) to prevent colds. A 2011 evaluation of ... E561. Seida JK, Durec T, Kuhle S. North American (Panax quinquefolius) and Asian ginseng (Panax ginseng) preparations for ... 2. Cold nuclear fusion Energy Technology Data Exchange (ETDEWEB) Tsyganov, E.N., E-mail: [email protected] [Cold Fusion Power, International (United States); Bavizhev, M.D. [LLC “Radium”, Moscow (Russian Federation); Buryakov, M.G. [Joint Institute for Nuclear Research (JINR), Dubna (Russian Federation); Dabagov, S.B. [RAS P.N. Lebedev Physical Institute, Leninsky pr. 53, 119991 Moscow (Russian Federation); National Research Nuclear University MEPhI, Kashirskoe shosse 31, 115409 Moscow (Russian Federation); Golovatyuk, V.M.; Lobastov, S.P. [Joint Institute for Nuclear Research (JINR), Dubna (Russian Federation) 2015-07-15 If target deuterium atoms were implanted in a metal crystal in accelerator experiments, a sharp increase in the probability of DD-fusion reaction was clearly observed when compared with the reaction’s theoretical value. The electronic screening potential, which for a collision of free deuterium atoms is about 27 eV, reached 300–700 eV in the case of the DD-fusion in metallic crystals. These data leads to the conclusion that a ban must exist for deuterium atoms to be in the ground state 1s in a niche filled with free conduction electrons. At the same time, the state 2p whose energy level is only 10 eV above that of state 1s is allowed in these conditions. With anisotropy of 2p, 3p or above orbitals, their spatial positions are strictly determined in the lattice coordinate system. When filling out the same potential niches with two deuterium atoms in the states 2p, 3p or higher, the nuclei of these atoms can be permanently positioned without creating much Coulomb repulsion at a very short distance from each other. In this case, the transparency of the potential barrier increases dramatically compared to the ground state 1s for these atoms. The probability of the deuterium nuclei penetrating the Coulomb barrier by zero quantum vibration of the DD-system also increases dramatically. The so-called cold nuclear DD-fusion for a number of years was registered in many experiments, however, was still rejected by mainstream science for allegedly having no consistent scientific explanation. Finally, it received the validation. Below, we outline the concept of this explanation and give the necessary calculations. This paper also considers the further destiny of the formed intermediate state of {sup 4}He{sup ∗}. 3. Garlic for the common cold. Science.gov (United States) Lissiman, Elizabeth; Bhasale, Alice L; Cohen, Marc 2014-11-11 Background Garlic is alleged to have antimicrobial and antiviral properties that relieve the common cold, among other beneficial effects. There is widespread usage of garlic supplements. The common cold is associated with significant morbidity and economic consequences. On average, children have six to eight colds per year and adults have two to four.Objectives To determine whether garlic (Allium sativum) is effective for the prevention or treatment of the common cold, when compared to placebo, no treatment or other treatments.Search methods We searched CENTRAL (2014, Issue 7),OLDMEDLINE (1950 to 1965),MEDLINE (January 1966 to July week 5, 2014), EMBASE(1974 to August 2014) and AMED (1985 to August 2014).Selection criteria Randomised controlled trials of common cold prevention and treatment comparing garlic with placebo, no treatment or standard treatment.Data collection and analysis Two review authors independently reviewed and selected trials from searches, assessed and rated study quality and extracted relevant data.Main results In this updated review, we identified eight trials as potentially relevant from our searches. Again, only one trial met the inclusion criteria.This trial randomly assigned 146 participants to either a garlic supplement (with 180 mg of allicin content) or a placebo (once daily)for 12 weeks. The trial reported 24 occurrences of the common cold in the garlic intervention group compared with 65 in the placebo group (P value garlic group compared with the placebo group (111 versus 366). The number of days to recovery from an occurrence of the common cold was similar in both groups (4.63 versus 5.63). Only one trial met the inclusion criteria, therefore limited conclusions can be drawn. The trial relied on self reported episodes of the common cold but was of reasonable quality in terms of randomisation and allocation concealment. Adverse effects included rash and odour. Authors' conclusions There is insufficient clinical trial evidence 4. Proton and heavy ion acceleration by stochastic fluctuations in the Earth's magnetotail Energy Technology Data Exchange (ETDEWEB) Catapano, Filomena; Zimbardo, Gaetano; Perri, Silvia; Greco, Antonella [Calabria Univ., Rende (Italy). Dept. of Physics; Artemyev, Anton V. [Russian Academy of Science, Moscow (Russian Federation). Space Research Inst.; California Univ., Los Angeles, CA (United States). Dept. of Earth, Planetary, and Space Science and Inst. of Geophysics and Planetary Physics 2016-07-01 Spacecraft observations show that energetic ions are found in the Earth's magnetotail, with energies ranging from tens of keV to a few hundreds of keV. In this paper we carry out test particle simulations in which protons and other ion species are injected in the Vlasov magnetic field configurations obtained by Catapano et al. (2015). These configurations represent solutions of a generalized Harris model, which well describes the observed profiles in the magnetotail. In addition, three-dimensional time-dependent stochastic electromagnetic perturbations are included in the simulation box, so that the ion acceleration process is studied while varying the equilibrium magnetic field profile and the ion species. We find that proton energies of the order of 100 keV are reached with simulation parameters typical of the Earth's magnetotail. By changing the ion mass and charge, we can study the acceleration of heavy ions such as He{sup ++} and O{sup +}, and it is found that energies of the order of 100-200 keV are reached in a few seconds for He{sup ++}, and about 100 keV for O{sup +}. 5. Ion acoustic solitons/double layers in two-ion plasma revisited Energy Technology Data Exchange (ETDEWEB) Lakhina, G. S., E-mail: [email protected]; Singh, S. V., E-mail: [email protected]; Kakad, A. P., E-mail: [email protected] [Indian Institute of Geomagnetism, New Panvel (W), Navi Mumbai 410218 (India) 2014-06-15 Ion acoustic solitons and double layers are studied in a collisionless plasma consisting of cold heavier ion species, a warm lighter ion species, and hot electrons having Boltzmann distributions by Sagdeev pseudo-potential technique. In contrast to the previous results, no double layers and super-solitons are found when both the heavy and lighter ion species are treated as cold. Only the positive potential solitons are found in this case. When the thermal effects of the lighter ion species are included, in addition to the usual ion-acoustic solitons occurring at M > 1 (where the Mach number, M, is defined as the ratio of the speed of the solitary wave and the ion-acoustic speed considering temperature of hot electrons and mass of the heavier ion species), slow ion-acoustic solitons/double layers are found to occur at low Mach number (M < 1). The slow ion-acoustic mode is actually a new ion-ion hybrid acoustic mode which disappears when the normalized number density of lighter ion species tends to 1 (i.e., no heavier species). An interesting property of the new slow ion-acoustic mode is that at low number density of the lighter ion species, only negative potential solitons/double layers are found whereas for increasing densities there is a transition first to positive solitons/double layers, and then only positive solitons. The model can be easily applicable to the dusty plasmas having positively charged dust grains by replacing the heavier ion species by the dust mass and doing a simple normalization to take account of the dust charge. 6. Finger and toe temperature response to cold water and cold air exposure NARCIS (Netherlands) Struijs, N.R. van der; Es, E.M. van; Raymann, R.J.E.M.; Daanen, H.A.M. 2008-01-01 Introduction: Subjects with a weak cold-induced vasodilatation response (CIVD) to experimental cold-water immersion of the fingers in a laboratory setting have been shown to have a higher risk for local cold injuries when exposed to cold in real life. Most of the cold injuries in real life, however, 7. 2D fluid simulations of interchange turbulence with ion dynamics DEFF Research Database (Denmark) Nielsen, Anders Henry; Madsen, Jens; Xu, G. S. 2013-01-01 In this paper we present a first principle global two-dimensional fluid model. The HESEL (Hot Edge SOL Electrostatic) model is a 2D numerical fluid code, based on interchange dynamics and includes besides electron also the ion pressure dynamic. In the limit of cold ions the model almost reduces... 8. Feedback cooling of a single trapped ion CERN Document Server Bushev, P; Wilson, A; Dubin, F; Becher, C; Eschner, J; Blatt, R; Steixner, V; Rabl, P; Zoller, P; Bushev, Pavel; Rotter, Daniel; Wilson, Alex; Dubin, Francois; Becher, Christoph; Eschner, Juergen; Blatt, Rainer; Steixner, Viktor; Rabl, Peter; Peter Zoller 2005-01-01 Based on a real-time measurement of the motion of a single ion in a Paul trap, we demonstrate its electro-mechanical cooling below the Doppler limit by homodyne feedback control (cold damping). The feedback cooling results are well described by a model based on a quantum mechanical Master Equation. 9. Ion Colliders CERN Document Server Fischer, W 2014-01-01 High-energy ion colliders are large research tools in nuclear physics to study the Quark-Gluon-Plasma (QGP). The range of collision energy and high luminosity are important design and operational considerations. The experiments also expect flexibility with frequent changes in the collision energy, detector fields, and ion species. Ion species range from protons, including polarized protons in RHIC, to heavy nuclei like gold, lead and uranium. Asymmetric collision combinations (e.g. protons against heavy ions) are also essential. For the creation, acceleration, and storage of bright intense ion beams, limits are set by space charge, charge change, and intrabeam scattering effects, as well as beam losses due to a variety of other phenomena. Currently, there are two operating ion colliders, the Relativistic Heavy Ion Collider (RHIC) at BNL, and the Large Hadron Collider (LHC) at CERN. 10. Laser spectroscopy of cold molecules CERN Document Server Borri, Simone 2016-01-01 This paper reviews the recent results in high-resolution spectroscopy on cold molecules. Laser spectroscopy of cold molecules addresses issues of symmetry violation, like in the search for the electric dipole moment of the electron and the studies on energy differences in enantiomers of chiral species; tries to improve the precision to which fundamental physical constants are known and tests for their possible variation in time and space; tests quantum electrodynamics, and searches for a fifth force. Further, we briefly review the recent technological progresses in the fields of cold molecules and mid-infrared lasers, which are the tools that mainly set the limits for the resolution that is currently attainable in the measurements. 11. COLD-SAT dynamic model Science.gov (United States) Adams, Neil S.; Bollenbacher, Gary 1992-01-01 This report discusses the development and underlying mathematics of a rigid-body computer model of a proposed cryogenic on-orbit liquid depot storage, acquisition, and transfer spacecraft (COLD-SAT). This model, referred to in this report as the COLD-SAT dynamic model, consists of both a trajectory model and an attitudinal model. All disturbance forces and torques expected to be significant for the actual COLD-SAT spacecraft are modeled to the required degree of accuracy. Control and experimental thrusters are modeled, as well as fluid slosh. The model also computes microgravity disturbance accelerations at any specified point in the spacecraft. The model was developed by using the Boeing EASY5 dynamic analysis package and will run on Apollo, Cray, and other computing platforms. 12. A linear dispersion relation for the hybrid kinetic-ion/fluid-electron model of plasma physics CERN Document Server Told, Daniel; Astfalk, Patrick; Jenko, Frank 2016-01-01 A dispersion relation for a commonly used hybrid model of plasma physics is developed, which combines fully kinetic ions and a massless-electron fluid description. Although this model and variations of it have been used to describe plasma phenomena for about 40 years, to date there exists no general dispersion relation to describe the linear wave physics contained in the model. Previous efforts along these lines are extended here to retain arbitrary wave propagation angles, temperature anisotropy effects, as well as additional terms in the generalized Ohm's law which determines the electric field. A numerical solver for the dispersion relation is developed, and linear wave physics is benchmarked against solutions of a full Vlasov-Maxwell dispersion relation solver. This work opens the door to a more accurate interpretation of existing and future wave and turbulence simulations using this type of hybrid model. 13. Insect capa neuropeptides impact desiccation and cold tolerance. Science.gov (United States) Terhzaz, Selim; Teets, Nicholas M; Cabrero, Pablo; Henderson, Louise; Ritchie, Michael G; Nachman, Ronald J; Dow, Julian A T; Denlinger, David L; Davies, Shireen-A 2015-03-03 The success of insects is linked to their impressive tolerance to environmental stress, but little is known about how such responses are mediated by the neuroendocrine system. Here we show that the capability (capa) neuropeptide gene is a desiccation- and cold stress-responsive gene in diverse dipteran species. Using targeted in vivo gene silencing, physiological manipulations, stress-tolerance assays, and rationally designed neuropeptide analogs, we demonstrate that the Drosophila melanogaster capa neuropeptide gene and its encoded peptides alter desiccation and cold tolerance. Knockdown of the capa gene increases desiccation tolerance but lengthens chill coma recovery time, and injection of capa peptide analogs can reverse both phenotypes. Immunohistochemical staining suggests that capa accumulates in the capa-expressing Va neurons during desiccation and nonlethal cold stress but is not released until recovery from each stress. Our results also suggest that regulation of cellular ion and water homeostasis mediated by capa peptide signaling in the insect Malpighian (renal) tubules is a key physiological mechanism during recovery from desiccation and cold stress. This work augments our understanding of how stress tolerance is mediated by neuroendocrine signaling and illustrates the use of rationally designed peptide analogs as agents for disrupting protective stress tolerance. 14. Development of cold neutron depth profiling system at HANARO Energy Technology Data Exchange (ETDEWEB) Park, B.G. [Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of); Korea Atomic Energy Research Institute, 989-111 Daedeok-daero, Yuseong-gu, Daejeon 305-355 (Korea, Republic of); Sun, G.M., E-mail: [email protected] [Korea Atomic Energy Research Institute, 989-111 Daedeok-daero, Yuseong-gu, Daejeon 305-355 (Korea, Republic of); Choi, H.D. [Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of) 2014-07-01 A neutron depth profiling (NDP) system has been designed and developed at HANARO, a 30 MW research reactor at the Korea Atomic Energy Research Institute (KAERI). The KAERI-NDP system utilizes cold neutrons that are transported along the CG1 neutron guide from the cold neutron source and it consists of a neutron beam collimator, a target chamber, a beam stopper, and charged particle detectors along with NIM-standard modules for charged particle pulse-height analysis. A 60 cm in diameter stainless steel target chamber was designed to control the positions of the sample and detector. The energy distribution of the cold neutron beam at the end of the neutron guide was calculated by using the Monte Carlo simulation code McStas, and a neutron flux of 1.8×10{sup 8} n/cm{sup 2} s was determined by using the gold foil activation method at the sample position. The performance of the charged particle detection of the KAERI-NDP system was tested by using Standard Reference Materials. The energy loss spectra of alpha particles and Li ions emitted from {sup 10}B, which was irradiated by cold neutrons, were measured. The measured peak concentration and the areal density of {sup 10}B in the Standard Reference Material are consistent with the reference values within 1% and 3.4%, respectively. 15. Development of cold neutron depth profiling system at HANARO Science.gov (United States) Park, B. G.; Sun, G. M.; Choi, H. D. 2014-07-01 A neutron depth profiling (NDP) system has been designed and developed at HANARO, a 30 MW research reactor at the Korea Atomic Energy Research Institute (KAERI). The KAERI-NDP system utilizes cold neutrons that are transported along the CG1 neutron guide from the cold neutron source and it consists of a neutron beam collimator, a target chamber, a beam stopper, and charged particle detectors along with NIM-standard modules for charged particle pulse-height analysis. A 60 cm in diameter stainless steel target chamber was designed to control the positions of the sample and detector. The energy distribution of the cold neutron beam at the end of the neutron guide was calculated by using the Monte Carlo simulation code McStas, and a neutron flux of 1.8×108 n/cm2 s was determined by using the gold foil activation method at the sample position. The performance of the charged particle detection of the KAERI-NDP system was tested by using Standard Reference Materials. The energy loss spectra of alpha particles and Li ions emitted from 10B, which was irradiated by cold neutrons, were measured. The measured peak concentration and the areal density of 10B in the Standard Reference Material are consistent with the reference values within 1% and 3.4%, respectively. 16. Insect capa neuropeptides impact desiccation and cold tolerance Science.gov (United States) Terhzaz, Selim; Teets, Nicholas M.; Cabrero, Pablo; Henderson, Louise; Ritchie, Michael G.; Nachman, Ronald J.; Dow, Julian A. T.; Denlinger, David L.; Davies, Shireen-A. 2015-01-01 The success of insects is linked to their impressive tolerance to environmental stress, but little is known about how such responses are mediated by the neuroendocrine system. Here we show that the capability (capa) neuropeptide gene is a desiccation- and cold stress-responsive gene in diverse dipteran species. Using targeted in vivo gene silencing, physiological manipulations, stress-tolerance assays, and rationally designed neuropeptide analogs, we demonstrate that the Drosophila melanogaster capa neuropeptide gene and its encoded peptides alter desiccation and cold tolerance. Knockdown of the capa gene increases desiccation tolerance but lengthens chill coma recovery time, and injection of capa peptide analogs can reverse both phenotypes. Immunohistochemical staining suggests that capa accumulates in the capa-expressing Va neurons during desiccation and nonlethal cold stress but is not released until recovery from each stress. Our results also suggest that regulation of cellular ion and water homeostasis mediated by capa peptide signaling in the insect Malpighian (renal) tubules is a key physiological mechanism during recovery from desiccation and cold stress. This work augments our understanding of how stress tolerance is mediated by neuroendocrine signaling and illustrates the use of rationally designed peptide analogs as agents for disrupting protective stress tolerance. PMID:25730885 17. Sampling of ions at atmospheric pressure: ion transmission and ion energy studied by simulation and experiment Science.gov (United States) Große-Kreul, Simon; Hübner, Simon; Benedikt, Jan; von Keudell, Achim 2016-04-01 Mass spectrometry of ions from atmospheric pressure plasmas is a challenging diagnostic method that has been applied to a large variety of cold plasma sources in the past. However, absolute densities can usually not be obtained, moreover, the process of sampling of ions and neutrals from such a plasma inherently influences the measured composition. These issues are studied in this contribution by a combination of experimental and numerical methods. Different numerical domains are sequentially coupled to calculate the ion transmission from the source to the mass analyzer. It is found that the energy of the sampled ions created by a radio-frequency microplasma operated in a He-N2 mixture at atmospheric pressure is of the order of 0.1 eV and that it depends linearly on the ion mass in good agreement with the expectation for seeded particles accelerated in a supersonic expansion. Moreover, the measured ion energy distribution from an afterglow of an atmospheric pressure plasma can be reproduced on basis of the particle trajectories in the sampling system. Eventually, an estimation of the absolute flux of ions to the detector is deduced. 18. Cold Tolerance of Plants Used for Cold-Regions Revegetation Science.gov (United States) 1990-10-01 from tempted to transfer the rye cold-tolerance genome to increased concentrations of solutes in cells and extra- wheat in hybrids. While the gene...Journal, 76: 516-517. Tryon, E.H. and R.P. True (1952) Blister shake of Yelenosky, G. (1988) Capacity of citrus flowers to yellow poplar. Bulletin of the 19. Adiabatic Cooling for Rovibrational Spectroscopy of Molecular Ions DEFF Research Database (Denmark) Fisher, Karin 2017-01-01 The field of cold molecular ions is a fast growing one, with applications in high resolution spectroscopy and metrology, the search for time variations of fundamental constants, cold chemistry and collisions, and quantum information processing, to name a few. The study of single molecular ions...... is attractive as it enables one to push the limits of spectroscopic accuracy. Non-destructive spectroscopic detection of molecular ions can be achieved by co-trapping with an easier to detect atomic ion. The ion chain has coupled motion, and transitions which change both the internal and motional states...... to the measured heating rates, almost perfectly fitting existing heating rate theory. Further, the same model successfully predicted the heating rates of the in-phase mode of a two-ion crystal, indicating that we can use it to predict the heating rates in experiments on molecule-atom chains. Adiabatic cooling... 20. Avionics Box Cold Plate Damage Prevention Science.gov (United States) Stambolian, Damon B.; Larchar, Steven W.; Henderson, Gena; Tran, Donald; Barth, Tim 2012-01-01 Problem Introduction: 1. Prevent Cold Plate Damage in Space Shuttle. 1a. The number of cold plate problems had increased from an average of 16.5 per/year between 1990 through 2000, to an average of 39.6 per year between 2001through 2005. 1b. Each complete set of 80 cold plates cost approximately$29 million, an average of $362,500 per cold plate. 1c It takes four months to produce a single cold plate. 2. Prevent Cold Plate Damage in Future Space Vehicles. 1. Excitation of nonlinear ion acoustic waves in CH plasmas CERN Document Server Feng, Q S; Liu, Z J; Xiao, C Z; Wang, Q; He, X T 2016-01-01 Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number$ k\\lambda_{De} $increases, the linear Landau damping of the fast mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of$ T_i/T_e < 0.2 $in which the fast mode is weakly damped mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with$k\\lambda_{De}$increasing. When$k\\lambda_{De}$is not large, such as$k\\lambda_{De}=0.1, 0.3, 0.5$, the nonlinear IAW can be excited by the driver with the linear frequency of the modes. However, when$k\\lambda_{De}$is large, such as$k\\lambda_{De}=0.7, the linear ... 2. Phonon forces and cold denaturatio DEFF Research Database (Denmark) Bohr, Jakob 2003-01-01 the molecule Is a continuum. The frequencies of the vibrational modes depend on the molecular dimensionality; hence, the zero-point energies for the folded and the denatured protein are estimated to differ by several electron volts. For a biomolecule such an energy is significant and may contribute to cold... 3. Images of the Cold War. Science.gov (United States) Chomsky, Noam 1989-01-01 The conventional U.S. picture traces the Cold War to Soviet violation of wartime agreements, while the U.S.S.R. defends its actions as responses to American violations and foreign adventurism. An understanding of how ideology is shaped by national self-interest will help students see beyond propaganda and myth in interpreting past and current… 4. Encyclopedia of the Cold War NARCIS (Netherlands) van Dijk, R. 2008-01-01 Between 1945 and 1991, tension between the USA, its allies, and a group of nations led by the USSR, dominated world politics. This period was called the Cold War - a conflict that stopped short to a full-blown war. Benefiting from the recent research of newly open archives, the Encyclopedia of the C 5. Encyclopedia of the Cold War NARCIS (Netherlands) van Dijk, R. 2008-01-01 Between 1945 and 1991, tension between the USA, its allies, and a group of nations led by the USSR, dominated world politics. This period was called the Cold War - a conflict that stopped short to a full-blown war. Benefiting from the recent research of newly open archives, the Encyclopedia of the 6. Vaccines for the common cold. Science.gov (United States) Simancas-Racines, Daniel; Franco, Juan Va; Guerra, Claudia V; Felix, Maria L; Hidalgo, Ricardo; Martinez-Zapata, Maria José 2017-05-18 The common cold is a spontaneously remitting infection of the upper respiratory tract, characterised by a runny nose, nasal congestion, sneezing, cough, malaise, sore throat, and fever (usually Register of Controlled Trials (CENTRAL) (September 2016), MEDLINE (1948 to September 2016), Embase (1974 to September 2016), CINAHL (1981 to September 2016), and LILACS (1982 to September 2016). We also searched three trials registers for ongoing studies and four websites for additional trials (February 2017). We included no language or date restrictions. Randomised controlled trials (RCTs) of any virus vaccines compared with placebo to prevent the common cold in healthy people. Two review authors independently evaluated methodological quality and extracted trial data. We resolved disagreements by discussion or by consulting a third review author. We found no additional RCTs for inclusion in this update. This review includes one RCT dating from the 1960s with an overall high risk of bias. The RCT included 2307 healthy participants, all of whom were included in analyses. This trial compared the effect of an adenovirus vaccine against placebo. No statistically significant difference in common cold incidence was found: there were 13 (1.14%) events in 1139 participants in the vaccines group and 14 (1.19%) events in 1168 participants in the placebo group (risk ratio 0.95, 95% confidence interval 0.45 to 2.02; P = 0.90). No adverse events related to the live vaccine were reported. The quality of the evidence was low due to limitations in methodological quality and a wide 95% confidence interval. This Cochrane Review was based on one study with low-quality evidence. We found no conclusive results to support the use of vaccines for preventing the common cold in healthy people compared with placebo. We identified a need for well-designed, adequately powered RCTs to investigate vaccines for the common cold in healthy people. Any future trials on medical treatments for preventing the 7. Common cold - how to treat at home Science.gov (United States) ... this page: //medlineplus.gov/ency/patientinstructions/000466.htm Common cold - how to treat at home To use ... this page, please enable JavaScript. Colds are very common. A visit to your health care provider's office ... 8. The cold equation of state of tantalum Energy Technology Data Exchange (ETDEWEB) Greeff, Carl W [Los Alamos National Laboratory; Rudin, Sven P [Los Alamos National Laboratory; Corckett, Scott D [Los Alamos National Laboratory; Wills, John M [Los Alamos National Laboratory 2009-01-01 In high-pressure isentropic compression experiments (ICE), the pressure is dominated by the cold curve. In order to obtain an accurate semi-empirical cold curve for Ta, we calculate the thermal pressure from ab initio phonon and electronic excitation spectra. The cold curve is then inferred from ultrasonic and shock data. Our empirical cold pressure is compared to density functional calculations and found to be closer to GGA results at low pressure and to approach LDA at high pressure. 9. SCIENCES IN COLD AND ARID REGIONS Institute of Scientific and Technical Information of China (English) 2008-01-01 Aims and Scope Sciences in Cold and Arid Regions, an international Engiish-language journal, is devoted to publishing the latest research achievements on the process and the pattern of Earth surface system in cold and arid regions. Researches in cold regions 1) emphasize particularly on the cold-region-characterized physical, chemical and biological processes and their interactions, and on the response of Cryosphere to Global change and Human activities as well as its effect to environment and the acclimatizable 10. Ion Chromatography. Science.gov (United States) Mulik, James D.; Sawicki, Eugene 1979-01-01 Accurate for the analysis of ions in solution, this form of analysis enables the analyst to directly assay many compounds that previously were difficult or impossible to analyze. The method is a combination of the methodologies of ion exchange, liquid chromatography, and conductimetric determination with eluant suppression. (Author/RE) 11. Common Cold in Babies: Symptoms and Causes Science.gov (United States) Common cold in babies Symptoms and causes By Mayo Clinic Staff The first indication of the common cold in a baby is often: A congested ... or green Other signs and symptoms of a common cold in a baby may include: Fever Sneezing ... 12. 1. contribution of the dynamics on the reactions mechanisms in the heavy ions collisions at the intermediary energies (20-100 MeV/A) for the light systems. 2. management of radioactive wastes by new options: nuclear data measurement programme between 20 and 150 MeV; 1. role de la dynamique sur les mecanismes de reactions dans les collisions d'ions lourds aux energies intermediaires (20-100 MeV/A) pour des systemes legers. 2. gestion des dechets radioactifs par des options nouvelles: programme de mesures de donnees nucleaires entre 20 et 150 MeV Energy Technology Data Exchange (ETDEWEB) Eudes, Ph 2000-09-22 The first part concerns the features of emitted charged particles in heavy ions reactions that have been studied in the framework of the semi classical Landau-Vlasov approach for the light system Ar + Al at 65 MeV/nucleon incident energy. The second part is devoted to the radioactive waste management (transmutation), but it was necessary to increase the data banks evaluated in neutrons up to 150-200 MeV and to create a data bank in protons. In the European framework it was decide to focus on three representative elements: lead (spallation target), iron (structure material) and uranium (actinide). (N.C.) 13. 77 FR 43117 - Meeting of the Cold War Advisory Committee for the Cold War Theme Study Science.gov (United States) 2012-07-23 ... National Park Service Meeting of the Cold War Advisory Committee for the Cold War Theme Study AGENCY... with the Federal Advisory Committee Act, 5 U.S.C. Appendix, that the Cold War Advisory Committee for the Cold War Theme Study will conduct a teleconference meeting on August 3, 2012. Members of the... 14. Observation of a power-law energy distribution in atom-ion hybrid system Science.gov (United States) Meir, Ziv; Akerman, Nitzan; Sikorsky, Tomas; Ben-Shlomi, Ruti; Dallal, Yehonatan; Ozeri, Roee 2016-05-01 Understanding atom-ion collision dynamics is at the heart of the growing field of ultra-cold atom-ion physics. The naive picture of a hot ion sympathetically-cooled by a cold atomic bath doesn't hold due to the time dependent potentials generated by the ion Paul trap. The energy scale of the atom-ion system is determined by a combination of the atomic bath temperature, the ion's excess micromotion (EMM) and the back action of the atom-ion attraction on the ion's position in the trap. However, it is the position dependent ion's inherent micromotion which acts as an amplifier for the ion's energy during random consecutive collisions. Due to this reason, the ion's energy distribution deviates from Maxwell-Boltzmann (MB) characterized by an exponential tail to one with power-law tail described by Tsallis q-exponential function. Here we report on the observation of a strong deviation from MB to Tsallis energy distribution of a trapped ion. In our experiment, a ground-state cooled 88 Sr+ ion is immersed in an ultra-cold cloud of 87 Rb atoms. The energy scale is determined by either EMM or solely due to the back action on the ion position during a collision with an atom in the trap. Energy distributions are obtained using narrow optical clock spectroscopy. 15. Cold Stress at High Altitudes Directory of Open Access Journals (Sweden) N. C. Majumdar 1983-04-01 Full Text Available The problem of cold at high altitudes has been analysed from a purely physical standpoint. It has been shown that Siple's Wind-Chill Index is not reliable because (i it does not make use of the well established principles governing the physical processes of heat transfer by convection and radiation, and (ii it assumes that the mean radiant temperature of the surroundings is the same as the ambient dry bulb temperature. A Cold Stress Index has been proposed which is likely to be a more reliable guide for assessing the climatic hazards of high altitude environments. The Index can be quickly estimated with the help of two nomograms devised for the purpose. 16. Ultra-cold molecule production. Energy Technology Data Exchange (ETDEWEB) Ramirez-Serrano, Jamie; Chandler, David W.; Strecker, Kevin; Rahn, Larry A. 2005-12-01 The production of Ultra-cold molecules is a goal of many laboratories through out the world. Here we are pursuing a unique technique that utilizes the kinematics of atomic and molecular collisions to achieve the goal of producing substantial numbers of sub Kelvin molecules confined in a trap. Here a trap is defined as an apparatus that spatially localizes, in a known location in the laboratory, a sample of molecules whose temperature is below one degree absolute Kelvin. Further, the storage time for the molecules must be sufficient to measure and possibly further cool the molecules. We utilize a technique unique to Sandia to form cold molecules from near mass degenerate collisions between atoms and molecules. This report describes the progress we have made using this novel technique and the further progress towards trapping molecules we have cooled. 17. Pseudoneutropenia from cold agglutinin leucoagglutination Directory of Open Access Journals (Sweden) Momin M 2015-01-01 Full Text Available Pseudoneutropenia or low leucocyte count secondary to leucoagglutination is caused by ethylene diamine tetra acetic acid (EDTA or cold agglutinins and is seen in benign and malignant disorders. We report a 34-year-old lady who was admitted with fever, vomiting, respiratory distress and productive cough. Complete blood count (CBC at initial presentation revealed low haemoglobin (11.6 g/dL, total leucocyte count (TLC (5900/mm3 with 50% polymorphs. Peripheral blood smear showed leucocytes in clusters. Another sample was asked for in citrate anticoagulant which showed a TLC of 5900/mm3 with 50% polymorphs and evidence of auto agglutination. Another collected in a prewarmed ethylene diamine tetra acetic acid (EDTA tube, CBC showed a TLC of 9800/mm3 with 39% neutrophils suggestive of pseudoneutropenia due to cold agglutinins. 18. Cold dark matter heats up. Science.gov (United States) Pontzen, Andrew; Governato, Fabio 2014-02-13 A principal discovery in modern cosmology is that standard model particles comprise only 5 per cent of the mass-energy budget of the Universe. In the ΛCDM paradigm, the remaining 95 per cent consists of dark energy (Λ) and cold dark matter. ΛCDM is being challenged by its apparent inability to explain the low-density 'cores' of dark matter measured at the centre of galaxies, where centrally concentrated high-density 'cusps' were predicted. But before drawing conclusions, it is necessary to include the effect of gas and stars, historically seen as passive components of galaxies. We now understand that these can inject heat energy into the cold dark matter through a coupling based on rapid gravitational potential fluctuations, explaining the observed low central densities. 19. THOR Cold Solar Wind (CSW) instrument Science.gov (United States) Lavraud, Benoit 2017-04-01 Turbulence Heating ObserveR (THOR) is the first mission concept dedicated to the study of plasma turbulence. We present the Cold Solar Wind (CSW) instrument that is being designed for THOR. CSW will measure the full three dimensional distribution function of solar wind protons and alphas with unprecedented accuracies. It will measure solar wind proton distributions down to at least 50 ms with energy resolution of 7% and angular resolution of 1.5°. CSW is based on a top-hat electrostatic analyzer (with very large geometric factor) design with deflectors at the entrance. The particle detection system uses Channel Electron Multipliers (CEM) associated with an analog front end Application-Specific Integrated Circuit (ASIC). CSW electronics comprises a fast sweeping high voltage board, as well as an FPGA and low voltage power supply boards to perform its operations. CSW is designed to address many of the key science objectives of THOR, in particular regarding ion-scale kinetic aspects of solar wind turbulence. 20. Symmetry energy in cold dense matter Energy Technology Data Exchange (ETDEWEB) Jeong, Kie Sang, E-mail: [email protected]; Lee, Su Houng, E-mail: [email protected] 2016-01-15 We calculate the symmetry energy in cold dense matter both in the normal quark phase and in the 2-color superconductor (2SC) phase. For the normal phase, the thermodynamic potential is calculated by using hard dense loop (HDL) resummation to leading order, where the dominant contribution comes from the longitudinal gluon rest mass. The effect of gluonic interaction on the symmetry energy, obtained from the thermodynamic potential, was found to be small. In the 2SC phase, the non-perturbative BCS paring gives enhanced symmetry energy as the gapped states are forced to be in the common Fermi sea reducing the number of available quarks that can contribute to the asymmetry. We used high density effective field theory to estimate the contribution of gluon interaction to the symmetry energy. Among the gluon rest masses in 2SC phase, only the Meissner mass has iso-spin dependence although the magnitude is much smaller than the Debye mass. As the iso-spin dependence of gluon rest masses is even smaller than the case in the normal phase, we expect that the contribution of gluonic interaction to the symmetry energy in the 2SC phase will be minimal. The different value of symmetry energy in each phase will lead to different prediction for the particle yields in heavy ion collision experiment. 1. Superheavy nuclei – cold synthesis and structure Indian Academy of Sciences (India) Raj K Gupta 2001-08-01 The quantum mechanical fragmentation theory (QMFT), given for the cold synthesis of new and superheavy elements, is reviewed and the use of radioactive nuclear beams (RNB) and targets (RNT) is discussed. The QMFT is a complete theory of cold nuclear phenomena, namely, the cold fission, cold fusion and cluster radioactivity. Also, the structure calculations based on the axially deformed relativistic mean field (DRMF) approach are presented which predict new regions of spherical magicity, namely = 120 and = 172 or 184, for superheavy nuclei. This result is discussed in the light of recent experiments reporting the cold synthesis of = 118 element. 2. Acclimatization to cold in humans Science.gov (United States) Kaciuba-Uscilko, Hanna; Greenleaf, John E. 1989-01-01 This review focuses on the responses and mechanisms of both natural and artificial acclimatization to a cold environment in mammals, with specific reference to human beings. The purpose is to provide basic information for designers of thermal protection systems for astronauts during intra- and extravehicular activities. Hibernation, heat production, heat loss, vascular responses, body insulation, shivering thermogenesis, water immersion, exercise responses, and clinical symptoms and hypothermia in the elderly are discussed. 3. Superheated rubber for cold storage Energy Technology Data Exchange (ETDEWEB) Katzenberg, Frank; Heuwers, Benjamin; Tiller, Joerg Christian [Biomaterials and Polymer Science, Department of Biochemical and Chemical Engineering, TU Dortmund, D-44221 Dortmund (Germany) 2011-04-26 Highly stretched rubber cools down upon relaxation. A natural rubber material that stores high elongations up to 1000% strain upon strain-induced crystallization at room temperature is reported. The strain recovered and, with this, the stored ''cold'' is released only by a thermal or athermal trigger. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) 4. Micro-Kelvin cold molecules. Energy Technology Data Exchange (ETDEWEB) Strecker, Kevin E.; Chandler, David W. 2009-10-01 We have developed a novel experimental technique for direct production of cold molecules using a combination of techniques from atomic optical and molecular physics and physical chemistry. The ability to produce samples of cold molecules has application in a broad spectrum of technical fields high-resolution spectroscopy, remote sensing, quantum computing, materials simulation, and understanding fundamental chemical dynamics. Researchers around the world are currently exploring many techniques for producing samples of cold molecules, but to-date these attempts have offered only limited success achieving milli-Kelvin temperatures with low densities. This Laboratory Directed Research and Development project is to develops a new experimental technique for producing micro-Kelvin temperature molecules via collisions with laser cooled samples of trapped atoms. The technique relies on near mass degenerate collisions between the molecule of interest and a laser cooled (micro-Kelvin) atom. A subset of collisions will transfer all (nearly all) of the kinetic energy from the 'hot' molecule, cooling the molecule at the expense of heating the atom. Further collisions with the remaining laser cooled atoms will thermally equilibrate the molecules to the micro-Kelvin temperature of the laser-cooled atoms. 5. Quantum-State-Resolved Ion-Molecule Chemistry Science.gov (United States) Chen, Gary; Yang, Tiangang; Campbell, Wesley; Hudson, Eric 2016-05-01 We propose a method to achieve quantum-state-resolved ion-molecule chemistry by utilizing cryogenic buffer gas cooling techniques and a combination of ion imaging and mass spectrometry of targets in an RF Paul trap. Cold molecular species produced by a cryogenic buffer gas beam (CBGB) are introduced to target ion species in an linear quadrupole trap (LQT) where ion imaging techniques and time of flight mass spectrometry (ToF) are then used to observe the target ions and the charged reaction products [1,2]. By taking advantage of the large ion-neutral interaction cross sections and characteristically long ion trap lifetimes, we can utilize the precision control over quantum states allowed by an ion trap to resolve state-to-state quantum chemical reactions without high-density molecular sample production, well within proposed capabilities. The combination of these two very general cold species production techniques allows for production and observation of a broad range of ion-neutral reactions. We initially plan to study chemical reactions between sympathetically cooled carbon ions (via laser cooled beryllium ions) with buffer gas cooled water. This work is supported by the US Air Force Office of Scientific Research. 6. Charge transfer in the cold Yb^+$+ Rb collisions CERN Document Server Sayfutyarova, Elvira R; Yakovleva, Svetlana A; Belyaev, Andrey K 2013-01-01 Charge-transfer cold Yb$^+$+ Rb collision dynamics is investigated theoretically using high-level {\\it ab initio} potential energy curves, dipole moment functions and nonadiabatic coupling matrix elements. Within the scalar-relativistic approximation, the radiative transitions from the entrance$A^1\\Sigma^+$to the ground$X^1\\Sigma^+$state are found to be the only efficient charge-transfer pathway. The spin-orbit coupling does not open other efficient pathways, but alters the potential energy curves and the transition dipole moment for the$A-X$pair of states. The radiative, as well as the nonradiative, charge-transfer cross sections calculated within the$10^{-3}-10$cm$^{-1}$collision energy range exhibit all features of the Langevin ion-atom collision regime, including a rich structure associated with centrifugal barrier tunneling (orbiting) resonances. Theoretical rate coefficients for two Yb isotopes agree well with those measured by immersing Yb$^+$ion in an ultracold Rb ensemble in a hybrid trap.... 7. Atomic physics experiments with cooled stored ions Science.gov (United States) Schuch, Reinhold 2004-10-01 This presentation contains examples of recent atomic physics experiments with stored and cooled ion beams from the CRYRING facility in Stockholm. One of these experiments uses the high luminosity of a cooled MeV proton beam in a He COLTRIMS apparatus (COLd supersonic He gas-jet Target for Recoil Ion Momentum Spectroscopy) for measuring correlation effects in transfer ionization. Another class of experiments exploits the cold electron beam available in the CRYRING electron cooler and cooled heavy-ion beams for recombination experiments. A section concerns the still rather open question of the puzzling recombination enhancement over the radiative recombination theory. Dielectronic resonances at meV-eV energy are measured with a resolution in the order of 10-3-10-2 eV with highly charged ions stored at several hundreds of MeV kinetic energy in the ring. These resonances provide a serious challenge to theories for describing correlation, relativistic, QED effects, and isotope shifts in highly ionized ions. Applications of recombination rates with complex highly charged ions for fusion and astrophysical plasmas are shown. 8. Atomic physics experiments with cooled stored ions Energy Technology Data Exchange (ETDEWEB) Schuch, Reinhold E-mail: [email protected] 2004-10-11 This presentation contains examples of recent atomic physics experiments with stored and cooled ion beams from the CRYRING facility in Stockholm. One of these experiments uses the high luminosity of a cooled MeV proton beam in a He COLTRIMS apparatus (COLd supersonic He gas-jet Target for Recoil Ion Momentum Spectroscopy) for measuring correlation effects in transfer ionization. Another class of experiments exploits the cold electron beam available in the CRYRING electron cooler and cooled heavy-ion beams for recombination experiments. A section concerns the still rather open question of the puzzling recombination enhancement over the radiative recombination theory. Dielectronic resonances at meV-eV energy are measured with a resolution in the order of 10{sup -3}-10{sup -2} eV with highly charged ions stored at several hundreds of MeV kinetic energy in the ring. These resonances provide a serious challenge to theories for describing correlation, relativistic, QED effects, and isotope shifts in highly ionized ions. Applications of recombination rates with complex highly charged ions for fusion and astrophysical plasmas are shown. 9. Ion focusing Energy Technology Data Exchange (ETDEWEB) Cooks, Robert Graham; Baird, Zane; Peng, Wen-Ping 2017-01-17 The invention generally relates to apparatuses for focusing ions at or above ambient pressure and methods of use thereof. In certain embodiments, the invention provides an apparatus for focusing ions that includes an electrode having a cavity, at least one inlet within the electrode configured to operatively couple with an ionization source, such that discharge generated by the ionization source is injected into the cavity of the electrode, and an outlet. The cavity in the electrode is shaped such that upon application of voltage to the electrode, ions within the cavity are focused and directed to the outlet, which is positioned such that a proximal end of the outlet receives the focused ions and a distal end of the outlet is open to ambient pressure. 10. Interaction of cosmic rays with cold clouds in galactic haloes Science.gov (United States) Wiener, Joshua; Oh, S. Peng; Zweibel, Ellen G. 2017-05-01 We investigate the effects of cosmic ray (CR) dynamics on cold, dense clouds embedded in a hot, tenuous galactic halo. If the magnetic field does not increase too much inside the cloud, the local reduction in Alfvén speed imposes a bottleneck on CRs streaming out from the star-forming galactic disc. The bottleneck flattens the upstream CR gradient in the hot gas, implying that multiphase structure could have global effects on CR-driven winds. A large CR pressure gradient can also develop on the outward-facing edge of the cloud. This pressure gradient has two independent effects. The CRs push the cloud upwards, imparting it with momentum. On smaller scales, the CRs pressurize cold gas in the fronts, reducing its density, consistent with the low densities of cold gas inferred in recent Cosmic Origins Spectrograph (COS) observations of local L* galaxies. They also heat the material at the cloud edge, broadening the cloud-halo interface and causing an observable change in interface ionic abundances. Due to the much weaker temperature dependence of CR heating relative to thermal-conductive heating, CR mediated fronts have a higher ratio of low-to-high ions compared to conduction fronts, in better agreement with observations. We investigate these effects separately using 1D simulations and analytic techniques. 11. Interaction of Cosmic Rays with Cold Clouds in Galactic Halos Science.gov (United States) Wiener, Joshua; Peng Oh, S.; Zweibel, Ellen G. 2017-01-01 We investigate the effects of cosmic ray (CR) dynamics on cold, dense clouds embedded in a hot, tenuous galactic halo. If the magnetic field does not increase too much inside the cloud, the local reduction in Alfvén speed imposes a bottleneck on CRs streaming out from the star-forming galactic disk. The bottleneck flattens the upstream CR gradient in the hot gas, implying that multi-phase structure could have global effects on CR driven winds. A large CR pressure gradient can also develop on the outward-facing edge of the cloud. This pressure gradient has two independent effects. The CRs push the cloud upward, imparting it with momentum. On smaller scales, the CRs pressurize cold gas in the fronts, reducing its density, consistent with the low densities of cold gas inferred in recent COS observations of local L★ galaxies. They also heat the material at the cloud edge, broadening the cloud-halo interface and causing an observable change in interface ionic abundances. Due to the much weaker temperature dependence of cosmic ray heating relative to thermal conductive heating, CR mediated fronts have a higher ratio of low to high ions compared to conduction fronts, in better agreement with observations. We investigate these effects separately using 1D simulations and analytic techniques. 12. Cold inactivation and dissociation into dimers of Escherichia coli tryptophanase and its W330F mutant form. Science.gov (United States) Erez, T; Gdalevsky GYa; Torchinsky, Y M; Phillips, R S; Parola, A H 1998-05-19 The kinetics and mechanism of reversible cold inactivation of the tetrameric enzyme tryptophanase have been studied. Cold inactivation is shown to occur slowly in the presence of K+ ions and much faster in their absence. The W330F mutant tryptophanase undergoes rapid cold inactivation even in the presence of K+ ions. In all cases the inactivation is accompanied by a decrease of the coenzyme 420-nm CD and absorption peaks and a shift of the latter peak to shorter wavelengths. The spectral changes and the NaBH4 test indicate that cooling of tryptophanase leads to breaking of the internal aldimine bond and release of the coenzyme. HPLC analysis showed that the ensuing apoenzyme dissociates into dimers. The dissociation depends on the nature and concentration of anions in the buffer solution. It readily occurs at low protein concentrations in the presence of salting-in anions Cl-, NO3- and I-, whereas salting-out anions, especially HPO4(2-), hinder the dissociation. K+ ions do not influence the dissociation of the apoenzyme, but partially protect holotryptophanase from cold inactivation. Thus, the two processes, cold inactivation of tryptophanase and dissociation of its apoform into dimers exhibit different dependencies on K+ ions and anions. 13. EDITORIAL: Focus on Cold and Ultracold Molecules FOCUS ON COLD AND ULTRACOLD MOLECULES Science.gov (United States) Carr, Lincoln D.; Ye, Jun 2009-05-01 öhlich, A Griesmaier, T Pfau, H Saito, Y Kawaguchi and M Ueda High-energy-resolution molecular beams for cold collision studies L P Parazzoli, N Fitch, D S Lobser and H J Lewandowski Collisional effects in the formation of cold guided beams of polar molecules M Motsch, C Sommer, M Zeppenfeld, L D van Buuren, P W H Pinkse and G Rempe Towards sympathetic cooling of large molecules: cold collisions between benzene and rare gas atoms P Barletta, J Tennyson and P F Barker Efficient formation of ground-state ultracold molecules via STIRAP from the continuum at a Feshbach resonance Elena Kuznetsova, Marko Gacesa, Philippe Pellegrini, Susanne F Yelin and Robin Côté Emergent timescales in entangled quantum dynamics of ultracold molecules in optical lattices M L Wall and L D Carr Rotational state resolved photodissociation spectroscopy of translationally and vibrationally cold MgH+ ions: toward rotational cooling of molecular ions K Højbjerre, A K Hansen, P S Skyt, P F Staanum and M Drewsen Collective transverse cavity cooling of a dense molecular beam Thomas Salzburger and Helmut Ritsch A Stark decelerator on a chip Samuel A Meek, Horst Conrad and Gerard Meijer Deceleration of molecules by dipole force potential: a numerical simulation Susumu Kuma and Takamasa Momose Ultracold molecules: vehicles to scalable quantum information processing Kathy-Anne Brickman Soderberg, Nathan Gemelke and Cheng Chin Magnetic field modification of ultracold molecule-molecule collisions T V Tscherbul, Yu V Suleimanov, V Aquilanti and R V Krems Spectroscopy of 39K85Rb triplet excited states using ultracold a 3Σ+ state molecules formed by photoassociation J T Kim, D Wang, E E Eyler, P L Gould and W C Stwalley Pumping vortex into a Bose-Einstein condensate of heteronuclear molecules Z F Xu, R Q Wang and L You Intense atomic and molecular beams via neon buffer-gas cooling David Patterson, Julia Rasmussen and John M Doyle Dynamical properties of dipolar Fermi gases T Sogo, L He, T Miyakawa, S Yi, H Lu 14. Cold dark matter by heavy double charged leptons? CERN Document Server Fargion, D; Stephan, C A 2005-01-01 A new candidate of cold dark matter arises by a novel elementary particle model that is adding two heavy leptons, each one sharing a double opposite electric charge and an own lepton flavor number: the almost-commutative (AC)-geometrical framework. In this scenario two new heavy ($ m_L \\geq 100 GeV$), oppositely double charged leptons (E,P), (E with charge -2 and P with charge +2 and opposite Z-charge), are born with no twin quark companions. Their final cosmic relics are bounded into "neutral" stable atoms (EP) forming the mysterious cold dark matter, in the spirit of the Glashow's Sinister model. An (EP) state is reached in the early Universe along a tail of a few secondary frozen exotic components. They should be now here somehow hidden in the surrounding matter. The two main secondary manifest relics are P (mostly hidden in a neutral (e e P) "anomalous helium" atom, at a 10^{-8} ratio) and a corresponding "ion" E bounded with an ordinary helium ion which preserves the leptons to later recombine with neutr... 15. Biodiversity and cold adaptive mechanisms of psychrophiles Directory of Open Access Journals (Sweden) Yuhua Xin 2013-07-01 Full Text Available Cold-adapted bacteria and archaea are widely distributed in cold environments on Earth, such as permafrost, cold soils and deserts, glaciers, lakes, sea ice in the Arctic, Antarctic and high mountains, as well as the deep sea, ice caves and the atmospheric stratosphere etc. Cold-adapted organisms inhabiting these environments exhibit rich diversity. Studies on the biogeography of psychrophiles will enable us to understand their biodiversity, distribution and origins. Due to long-term living in cold regions, cold-adapted bacteria and archeae have developed specific physiological mechanisms of adaptation to cold environments. These mechanisms include: regulating the fluidity of the cytoplasmic membrane through adjusting the composition of membrane lipids; achieving low-temperature protection through compatibility solute, antifreeze proteins, ice-binding proteins, ice-nucleation proteins and anti-nucleating proteins; production of heat-shock and coldshock proteins, cold acclimation protein and DEAD-box RNA helicase at low temperatures; production of cold-active enzymes; increasing energy generation and conservation. With the rapid development of sequencing technology, various omics-based approaches have been used to reveal cold-adaptive mechanisms of psychrophiles at the genomic level. 16. Cooling of highly charged ions in a Penning trap Energy Technology Data Exchange (ETDEWEB) Gruber, L 2000-03-31 Highly charged ions are extracted from an electron beam ion trap and guided to Retrap, a cryogenic Penning trap, where they are merged with laser cooled Be{sup +} ions. The Be{sup +} ions act as a coolant for the hot highly charged ions and their temperature is dropped by about 8 orders of magnitude in a few seconds. Such cold highly charged ions form a strongly coupled nonneutral plasma exhibiting, under such conditions, the aggregation of clusters and crystals. Given the right mixture, these plasmas can be studied as analogues of high density plasmas like white dwarf interiors, and potentially can lead to the development of cold highly charged ion beams for applications in nanotechnology. Due to the virtually non existent Doppler broadening, spectroscopy on highly charged ions can be performed to an unprecedented precision. The density and the temperature of the Be{sup +} plasma were measured and highly charged ions were sympathetically cooled to similar temperatures. Molecular dynamics simulations confirmed the shape, temperature and density of the highly charged ions. Ordered structures were observed in the simulations. 17. Probing Cold Dense Nuclear Matter Energy Technology Data Exchange (ETDEWEB) Subedi, Ramesh; Shneor, R.; Monaghan, Peter; Anderson, Bryon; Aniol, Konrad; Annand, John; Arrington, John; Benaoum, Hachemi; Benmokhtar, Fatiha; Bertozzi, William; Boeglin, Werner; Chen, Jian-Ping; Choi, Seonho; Cisbani, Evaristo; Craver, Brandon; Frullani, Salvatore; Garibaldi, Franco; Gilad, Shalev; Gilman, Ronald; Glamazdin, Oleksandr; Hansen, Jens-Ole; Higinbotham, Douglas; Holmstrom, Timothy; Ibrahim, Hassan; Igarashi, Ryuichi; De Jager, Cornelis; Jans, Eddy; Jiang, Xiaodong; Kaufman, Lisa; Kelleher, Aidan; Kolarkar, Ameya; Kumbartzki, Gerfried; LeRose, John; Lindgren, Richard; Liyanage, Nilanga; Margaziotis, Demetrius; Markowitz, Pete; Marrone, Stefano; Mazouz, Malek; Meekins, David; Michaels, Robert; Moffit, Bryan; Perdrisat, Charles; Piasetzky, Eliazer; Potokar, Milan; Punjabi, Vina; Qiang, Yi; Reinhold, Joerg; Ron, Guy; Rosner, Guenther; Saha, Arunava; Sawatzky, Bradley; Shahinyan, Albert; Sirca, Simon; Slifer, Karl; Solvignon, Patricia; Sulkosky, Vince; Sulkosky, Vincent; Sulkosky, Vince; Sulkosky, Vincent; Urciuoli, Guido; Voutier, Eric; Watson, John; Weinstein, Lawrence; Wojtsekhowski, Bogdan; Wood, Stephen; Zheng, Xiaochao; Zhu, Lingyan 2008-06-01 The protons and neutrons in a nucleus can form strongly correlated nucleon pairs. Scattering experiments, in which a proton is knocked out of the nucleus with high-momentum transfer and high missing momentum, show that in carbon-12 the neutron-proton pairs are nearly 20 times as prevalent as proton-proton pairs and, by inference, neutron-neutron pairs. This difference between the types of pairs is due to the nature of the strong force and has implications for understanding cold dense nuclear systems such as neutron stars. 18. Probing Cold Dense Nuclear Matter CERN Document Server Subedi, R; Monaghan, P; Anderson, B D; Aniol, K; Annand, J; Arrington, J; Benaoum, H; Benmokhtar, F; Bertozzi, W; Boeglin, W; Chen, J -P; Choi, Seonho; Cisbani, E; Craver, B; Frullani, S; Garibaldi, F; Gilad, S; Gilman, R; Glamazdin, O; Hansen, J -O; Higinbotham, D W; Holmstrom, T; Ibrahim, H; Igarashi, R; De Jager, C W; Jans, E; Jiang, X; Kaufman, L; Kelleher, A; Kolarkar, A; Kumbartzki, G; LeRose, J J; Lindgren, R; Liyanage, N; Margaziotis, D J; Markowitz, P; Marrone, S; Mazouz, M; Meekins, D; Michaels, R; Moffit, B; Perdrisat, C F; Piasetzky, E; Potokar, M; Punjabi, V; Qiang, Y; Reinhold, J; Ron, G; Rosner, G; Saha, A; Sawatzky, B; Shahinyan, A; Širca, S; Slifer, K; Solvignon, P; Sulkosky, V; Urciuoli, G; Voutier, E; Watson, J W; Weinstein, L B; Wojtsekhowski, B; Wood, S; Zheng, X -C; Zhu, L; 10.1126/science.1156675 2009-01-01 The protons and neutrons in a nucleus can form strongly correlated nucleon pairs. Scattering experiments, where a proton is knocked-out of the nucleus with high momentum transfer and high missing momentum, show that in 12C the neutron-proton pairs are nearly twenty times as prevalent as proton-proton pairs and, by inference, neutron-neutron pairs. This difference between the types of pairs is due to the nature of the strong force and has implications for understanding cold dense nuclear systems such as neutron stars. 19. The Herschel Cold Debris Disks CERN Document Server Gaspar, Andras 2013-01-01 The Herschel "DUst around NEarby Stars (DUNES)" survey has found a number of debris disk candidates that are apparently very cold, with temperatures near 22K. It has proven difficult to fit their spectral energy distributions with conventional models for debris disks. Given this issue we carefully examine the alternative explanation, that the detections arise from confusion with IR cirrus and/or background galaxies that are not physically associated with the foreground star. We find that such an explanation is consistent with all of these detections. 20. Cold atoms close to surfaces DEFF Research Database (Denmark) Krüger, Peter; Wildermuth, Stephan; Hofferberth, Sebastian 2005-01-01 Microscopic atom optical devices integrated on atom chips allow to precisely control and manipulate ultra-cold (T atoms and Bose-Einstein condensates (BECs) close to surfaces. The relevant energy scale of a BEC is extremely small (down to ... be utilized as a sensor for variations of the potential energy of the atoms close to the surface. Here we describe how to use trapped atoms as a measurement device and analyze the performance and flexibility of the field sensor. We demonstrate microscopic magnetic imaging with simultaneous high spatial... 1. Harmonics Effect on Ion-Bulk Waves in CH Plasmas CERN Document Server Feng, Q S; Liu, Z J; Cao, L H; Xiao, C Z; Wang, Q; He, X T 2016-01-01 The harmonics effect on ion-bulk (IBk) waves has been researched by Vlasov simulation. The condition of excitation of a large-amplitude IBk waves is given to explain the phenomenon of strong short-wavelength electrostatic activity in solar wind. When$k$is much lower than$k_{lor}/2$($k_{lor}$is the wave number at loss-of-resonance point), the IBk waves will not be excited to a large amplitude, because a large part of energy will be spread to harmonics. The nature of nonlinear IBk waves in the condition of$k
2. Cold hardiness increases with age in juvenile Rhododendron populations
Directory of Open Access Journals (Sweden)
Rajeev eArora
2014-10-01
Full Text Available Winter survival in woody plants is controlled by environmental and genetic factors that affect the plant's ability to cold acclimate. Because woody perennials are long-lived and often have a prolonged juvenile (pre-flowering phase, it is conceivable that both chronological and physiological age factors influence adaptive traits such as stress tolerance. This study investigated annual cold hardiness (CH changes in several hybrid Rhododendron populations based on Tmax, an estimate of the maximum rate of freezing injury (ion leakage in cold-acclimated leaves from juvenile progeny. Data from F2 and backcross populations derived from R. catawbiense and R. fortunei parents indicated significant annual increases in Tmax ranging from 3.7 to to 6.4 C as the seedlings aged from 3 to 5 years old. A similar yearly increase (6.7° C was observed in comparisons of 1- and 2-year-old F1 progenies from a R. catawbiense x R. dichroanthum cross. In contrast, CH of the mature parent plants (> 10 years old did not change significantly over the same evaluation period. In leaf samples from a natural population of R. maximum, CH evaluations over two years resulted in an average Tmax value for juvenile 2- to 3- year- old plants that was 9.2 C lower than the average for mature (~30 years old plants. . A reduction in CH was also observed in three hybrid rhododendron cultivars clonally propagated by rooted cuttings (ramets - Tmax of 4-year-old ramets was significantly lower than the Tmax estimates for the 30- to 40-year-old source plants (ortets. In both the wild R. maximum population and the hybrid cultivar group, higher accumulation of a cold-acclimation responsive 25kDa leaf dehydrin was associated with older plants and higher CH. The feasibility of identifying hardy phenotypes at juvenile period and research implications of age-dependent changes in CH are discussed.
3. Synthesis of the heaviest nuclei in cold fusion reactions
Science.gov (United States)
Münzenberg, G.; Morita, K.
2015-12-01
Cold fusion of heavy ions paved the way to superheavy elements. It was proposed by Yu.Ts. Oganessian more than forty years ago in 1974 [1,2]. First experiments were carried out at JINR Dubna, starting with the reaction 40Ar + 208Pb → 248Fm* where several hundreds to thousand atoms were produced on one day. The large production rate indicating an enhancement of the fusion cross section, especially for the evaporation of two or three neutrons, proved the concept of cold-fusion with the use of the doubly magic nucleus 208Pb as a target. The Dubna experiments were extended to the transactinide region beyond rutherfordium. The breakthrough came with the separation in-flight. Two different approaches were used: kinematic separation with the velocity filter SHIP [3] at GSI Darmstadt, and with the gasfilled separator GARIS [4,5] at RIKEN. With SHIP the concept of cold fusion of massive nuclear systems was convincingly confirmed by the observation of the one-neutron evaporation channel in the production of 247Rf in an irradiation of 208Pb with 50Ti [6] in 1981 which opened the way to the transactinide region. At SHIP the elements bohrium (107) to copernicium (112) were discovered [7]. A new closed shell region around hassium was found. The RIKEN experiments started in 2002. They confirmed the GSI results and in addition improved the data on structure and production of elements hassium to copernicium significantly. The heaviest element ever created in a cold fusion reaction, Z = 113, was observed at GARIS [8,9].
4. 2D fluid simulations of interchange turbulence with ion dynamics
DEFF Research Database (Denmark)
Nielsen, Anders Henry; Madsen, Jens; Xu, G. S.
2013-01-01
In this paper we present a first principle global two-dimensional fluid model. The HESEL (Hot Edge SOL Electrostatic) model is a 2D numerical fluid code, based on interchange dynamics and includes besides electron also the ion pressure dynamic. In the limit of cold ions the model almost reduces......B vorticity as well as the ion diamagnetic vorticity. The 2D domain includes both open and closed field lines and is located on the out-board midplane of a tokamak. On open field field lines the parallel dynamics are parametrized as sink terms depending on the dynamic quantities; density, electron and ion...
5. International workshop on cold neutron sources
Energy Technology Data Exchange (ETDEWEB)
Russell, G.J.; West, C.D. (comps.) (Los Alamos National Lab., NM (United States))
1991-08-01
The first meeting devoted to cold neutron sources was held at the Los Alamos National Laboratory on March 5--8, 1990. Cosponsored by Los Alamos and Oak Ridge National Laboratories, the meeting was organized as an International Workshop on Cold Neutron Sources and brought together experts in the field of cold-neutron-source design for reactors and spallation sources. Eighty-four people from seven countries attended. Because the meeting was the first of its kind in over forty years, much time was spent acquainting participants with past and planned activities at reactor and spallation facilities worldwide. As a result, the meeting had more of a conference flavor than one of a workshop. The general topics covered at the workshop included: Criteria for cold source design; neutronic predictions and performance; energy deposition and removal; engineering design, fabrication, and operation; material properties; radiation damage; instrumentation; safety; existing cold sources; and future cold sources.
6. Diagnosis and management of cold urticaria.
Science.gov (United States)
Singleton, Reid; Halverstam, Caroline P
2016-01-01
Cold urticaria is a physical urticaria characterized by a localized or systemic eruption of papules upon exposure of the skin to cold air, liquids, and/or objects. In some cases, angioedema and anaphylaxis also may occur. The symptoms of cold urticaria can have a negative impact on patients' quality of life. Second-generation H1 antihistamines are the first line of treatment in cold urticaria; however, patients who are unresponsive to initial treatment with H1 antihistamines may require further management options. Avoidance of cold exposure is the most effective prophylactic measure. In mild to moderate cases, the primary goal of therapy is to improve the patient's quality of life. In more severe cases, treatment measures to protect the patient's airway, breathing, and circulation may be necessary. We report the case of a 23-year-old man with cold urticaria who was refractory to initial therapy with H1 antihistamines. A review of the literature also is provided.
7. Cognitive Egocentrism Differentiates Warm and Cold People
OpenAIRE
Ryan L. Boyd; Bresin, Konrad; Ode, Scott; Robinson, Michael D.
2013-01-01
Warmth-coldness is a fundamental dimension of social behavior. Cold individuals are egocentric in their social relations, whereas warm individuals are not. Previous theorizing suggests that cognitive egocentrism underlies social egocentrism. It was hypothesized that higher levels of interpersonal coldness would predict greater cognitive egocentrism. Cognitive egocentrism was assessed in basic terms through tasks wherein priming a lateralized self-state biased subsequent visual perceptions in ...
8. Electrical shielding box measurement of the negative hydrogen beam from Penning ion gauge ion source.
Science.gov (United States)
Wang, T; Yang, Z; Dong, P; long, J D; He, X Z; Wang, X; Zhang, K Z; Zhang, L W
2012-06-01
The cold-cathode Penning ion gauge (PIG) type ion source has been used for generation of negative hydrogen (H(-)) ions as the internal ion source of a compact cyclotron. A novel method called electrical shielding box dc beam measurement is described in this paper, and the beam intensity was measured under dc extraction inside an electrical shielding box. The results of the trajectory simulation and dc H(-) beam extraction measurement were presented. The effect of gas flow rate, magnetic field strength, arc current, and extraction voltage were also discussed. In conclusion, the dc H(-) beam current of about 4 mA from the PIG ion source with the puller voltage of 40 kV and arc current of 1.31 A was extrapolated from the measurement at low extraction dc voltages.
9. On the Stability of Pick-up Ion Ring Distributions in the Outer Heliosheath
Science.gov (United States)
Summerlin, Errol J.; Viñas, Adolfo F.; Moore, Thomas E.; Christian, Eric R.; Cooper, John F.
2014-10-01
The "secondary energetic neutral atom (ENA)" hypothesis for the ribbon feature observed by the Interstellar Boundary Explorer (IBEX) posits that the neutral component of the solar wind continues beyond the heliopause and charge exchanges with interstellar ions in the Outer Heliosheath (OHS). This creates pick-up ions that gyrate about the draped interstellar magnetic field (ISMF) lines at pitch angles near 90° on the locus where the ISMF lies tangential to the heliopause and perpendicular to the heliocentric radial direction. This location closely coincides with the location of the ribbon feature according to the prevailing inferences of the ISMF orientation and draping. The locally gyrating ions undergo additional charge exchange and escape as free-flying neutral atoms, many of which travel back toward the inner solar system and are imaged by IBEX as a ribbon tracing out the locus described above. For this mechanism to succeed, the pick-up ions must diffuse in pitch angle slowly enough to permit secondary charge exchange before their pitch angle distribution substantially broadens away from 90°. Previous work using linear Vlasov dispersion analysis of parallel propagating waves has suggested that the ring distribution in the OHS is highly unstable, which, if true, would make the secondary ENA hypothesis incapable of rendering the observed ribbon. In this paper, we extend this earlier work to more realistic ring distribution functions. We find that, at the low densities necessary to produce the observed IBEX ribbon via the secondary ENA hypothesis, growth rates are highly sensitive to the temperature of the beam and that even very modest temperatures of the ring beam corresponding to beam widths of <1° are sufficient to damp the self-generated waves associated with the ring beam. Thus, at least from the perspective of linear Vlasov dispersion analysis of parallel propagating waves, there is no reason to expect that the ring distributions necessary to produce the
10. On the stability of pick-up ion ring distributions in the outer heliosheath
Energy Technology Data Exchange (ETDEWEB)
Summerlin, Errol J.; Viñas, Adolfo F.; Moore, Thomas E.; Christian, Eric R.; Cooper, John F., E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [Heliophysics Science Division, NASAs Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD (United States)
2014-10-01
The 'secondary energetic neutral atom (ENA)' hypothesis for the ribbon feature observed by the Interstellar Boundary Explorer (IBEX) posits that the neutral component of the solar wind continues beyond the heliopause and charge exchanges with interstellar ions in the Outer Heliosheath (OHS). This creates pick-up ions that gyrate about the draped interstellar magnetic field (ISMF) lines at pitch angles near 90° on the locus where the ISMF lies tangential to the heliopause and perpendicular to the heliocentric radial direction. This location closely coincides with the location of the ribbon feature according to the prevailing inferences of the ISMF orientation and draping. The locally gyrating ions undergo additional charge exchange and escape as free-flying neutral atoms, many of which travel back toward the inner solar system and are imaged by IBEX as a ribbon tracing out the locus described above. For this mechanism to succeed, the pick-up ions must diffuse in pitch angle slowly enough to permit secondary charge exchange before their pitch angle distribution substantially broadens away from 90°. Previous work using linear Vlasov dispersion analysis of parallel propagating waves has suggested that the ring distribution in the OHS is highly unstable, which, if true, would make the secondary ENA hypothesis incapable of rendering the observed ribbon. In this paper, we extend this earlier work to more realistic ring distribution functions. We find that, at the low densities necessary to produce the observed IBEX ribbon via the secondary ENA hypothesis, growth rates are highly sensitive to the temperature of the beam and that even very modest temperatures of the ring beam corresponding to beam widths of <1° are sufficient to damp the self-generated waves associated with the ring beam. Thus, at least from the perspective of linear Vlasov dispersion analysis of parallel propagating waves, there is no reason to expect that the ring distributions necessary to
11. The North Atlantic Cold Bias
Science.gov (United States)
Greatbatch, Richard; Drews, Annika; Ding, Hui; Latif, Mojib; Park, Wonsun
2016-04-01
The North Atlantic cold bias, associated with a too zonal path of the North Atlantic Current and a missing "northwest corner", is a common problem in coupled climate and forecast models. The bias affects the North Atlantic and European climate mean state, variability and predictability. We investigate the use of a flow field correction to adjust the path of the North Atlantic Current as well as additional corrections to the surface heat and freshwater fluxes. Results using the Kiel Climate Model show that the flow field correction allows a northward flow into the northwest corner, largely eliminating the bias below the surface layer. A surface cold bias remains but can be eliminated by additionally correcting the surface freshwater flux, without adjusting the surface heat flux seen by the ocean model. A model version in which only the surface fluxes of heat and freshwater are corrected continues to exhibit the incorrect path of the North Atlantic Current and a strong subsurface bias. Removing the bias impacts the multi-decadal time scale variability in the model and leads to a better representation of the SST pattern associated with the Atlantic Multidecadal Variability than the uncorrected model.
12. Ion accelerator system mounting design and operating characteristics for a 5 kW 30-cm xenon ion engine
Science.gov (United States)
Aston, Graeme; Brophy, John R.
1987-01-01
Results from a series of experiments to determine the effect of accelerator grid mount geometry on the performance of the J-series ion optics assembly are described. Three mounting schemes, two flexible and one rigid, are compared for their relative ion extraction capability over a range of total accelerating voltages. The largest ion beam current, for the maximum total voltage investigated, is shown to occur using one of the flexible grid mounting geometries. However, at lower total voltages and reduced engine input power levels, the original rigid J-series ion optics accelerator grid mounts result in marginally better grid system performance at the same cold interelectrode gap.
13. Prediction of cold flow properties of Biodiesel
Directory of Open Access Journals (Sweden)
Parag Saxena
2016-08-01
Full Text Available Biodiesel being environmentally friendly is fast gaining acceptance in the market as an alternate diesel fuel. But compared to petroleum diesel it has certain limitations and thus it requires further development on economic viability and improvement in its properties to use it as a commercial fuel. The cold flow properties play a major role in the usage of biodiesel commercially as it freezes at cold climatic conditions. In the present study, cold flow properties of various types of biodiesel were estimated by using correlations available in literature. The correlations were evaluated based on the deviation between the predicted value and experimental values of cold flow properties.
14. Review on Cold-Formed Steel Connections
Science.gov (United States)
Tan, Cher Siang; Mohammad, Shahrin; Md Tahir, Mahmood; Shek, Poi Ngian
2014-01-01
The concept of cold-formed light steel framing construction has been widespread after understanding its structural characteristics with massive research works over the years. Connection serves as one of the important elements for light steel framing in order to achieve its structural stability. Compared to hot-rolled steel sections, cold-formed steel connections perform dissimilarity due to the thin-walled behaviour. This paper aims to review current researches on cold-formed steel connections, particularly for screw connections, storage rack connections, welded connections, and bolted connections. The performance of these connections in the design of cold-formed steel structures is discussed. PMID:24688448
15. Cold vacuum drying facility design requirements
Energy Technology Data Exchange (ETDEWEB)
IRWIN, J.J.
1999-07-01
This document provides the detailed design requirements for the Spent Nuclear Fuel Project Cold Vacuum Drying Facility. Process, safety, and quality assurance requirements and interfaces are specified.
16. Cold panniculitis: delayed onset in an adult.
Science.gov (United States)
Lipke, Michelle M; Cutlan, Jonathan E; Smith, Ann C
2015-01-01
The panniculitides are a complex dermatologic entity for both dermatologists and dermatopathologists. Panniculitis is an inflammation of the subcutaneous adipose tissue and can be associated with systemic diseases. We present a case of cold panniculitis, a form of traumatic panniculitis, in a 37-year-old woman that was caused by a cold therapy unit. Our patient did not develop lesions until 10 days following initiation of therapy, which is a unique presentation of cold panniculitis, as lesions usually develop 1 to 3 days after cold exposure.
17. Collisional Cooling of Light Ions by Cotrapped Heavy Atoms.
Science.gov (United States)
Dutta, Sourav; Sawant, Rahul; Rangwala, S A
2017-03-17
We experimentally demonstrate cooling of trapped ions by collisions with cotrapped, higher-mass neutral atoms. It is shown that the lighter ^{39}K^{+} ions, created by ionizing ^{39}K atoms in a magneto-optical trap (MOT), when trapped in an ion trap and subsequently allowed to cool by collisions with ultracold, heavier ^{85}Rb atoms in a MOT, exhibit a longer trap lifetime than without the localized ^{85}Rb MOT atoms. A similar cooling of trapped ^{85}Rb^{+} ions by ultracold ^{133}Cs atoms in a MOT is also demonstrated in a different experimental configuration to validate this mechanism of ion cooling by localized and centered ultracold neutral atoms. Our results suggest that the cooling of ions by localized cold atoms holds for any mass ratio, thereby enabling studies on a wider class of atom-ion systems irrespective of their masses.
18. IMPROVED, FAVORABLE FOR ENVIRONMENT POLYURETHANE COLD-BOX-PROCESS (COLD BOX «HUTTENES-ALBERTUS» .
Directory of Open Access Journals (Sweden)
A. Sergini
2005-01-01
Full Text Available The results of the laboratory and industrial investigations, the purpose of which is improvement of the classical Cold-box-process, i.e. the process of the slugs hardening in cold boxes, are presented.
19. Cold neutral atoms via charge exchange from excited state positronium: a proposal
CERN Document Server
Bertsche, W A; Eriksson, S
2016-01-01
We present a method for generating cold neutral atoms via charge exchange reactions between trapped ions and Rydberg positronium. The high charge exchange reaction cross section leads to efficient neutralisation of the ions and since the positronium-ion mass ratio is small, the neutrals do not gain appreciable kinetic energy in the process. When the original ions are cold the reaction produces neutrals that can be trapped or further manipulated with electromagnetic fields. Because a wide range of species can be targeted we envisage that our scheme may enable experiments at low temperature that have been hitherto intractable due to a lack of cooling methods. We present an estimate for achievable temperatures, neutral number and density in an experiment where the neutrals are formed at a milli-Kelvin temperature from either directly or sympathetically cooled ions confined on an ion chip. The neutrals may then be confined by their magnetic moment in a co-located magnetic minimum well also formed on the chip. We ...
20. Polarized ion source operation at IUCF
Energy Technology Data Exchange (ETDEWEB)
Derenchuk, V. [Indiana University Cyclotron Facility, Bloomington, Indiana 47408 (United States); Belov, A. [Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, 117312, Russian Federation (Russian Federation); Brown, R.; Collins, J.; Sowinski, J.; Stephenson, E.; Wedekind, M. [Indiana University Cyclotron Facility, Bloomington, Indiana 47408 (United States)
1995-07-15
The IUCF high intensity polarized ion source (HIPIOS), based on the source in operation at TUNL (1) and employing cold ({similar_to}30 K) atomic beam technology with an electron cyclotron resonance ionizer, has recently delivered beam to the first users. The results of the development work required to make the source operate reliably, with reasonable beam parameters are described. Methods used to measure the polarization and possible sources of unpolarized background are also discussed.
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https://www.physicsforums.com/threads/simplify-the-follwoing-equation.508163/
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# Simplify the follwoing Equation
1. Jun 19, 2011
### andrey21
Sounds waves in a pipe of varying cross-section are described by the equation
V2 d/dx (1/A dAu/dx) = d2u/dt2
Where A = 0.2+0.3x
So first I substituted A into the equation:
V2 d/dx (1/(0.2+0.3x) d(0.2+0.3x)u/dx) = d2u/dt2
V2 d/dx (0.3u/(0.2+0.3x) du/dx) = d2u/dt2
This is as far as I can get, any help would be fantastic.
2. Jun 19, 2011
### grey_earl
I suppose this is V² d/dx (1/A d(Au)/dx) = d²u/dt², true? Then expand first before substituting, which gives
d²u/dx² + d(ln A)/dx du/dx + d²(ln A)/dx² u = 1/V² d²u/dt².
Now substitute to get
d²u/dx² + 1/(x + 2/3) du/dx - 1/(x + 2/3)² u = 1/V² d²u/dt², which I think is about as simple as it gets.
(PS: This has a solution u(x,t) = [ C1 x² (1 + x)/(2 + 3 x) + C2 (1 + (2 + 3 x)²)/(2 + 3 x) + C3 (
(1 - (2 + 3 x)²))/(2 + 3 t) ] [ 1/2 C1 t² V² + C4 + t C5 ], where C1 to C5 are arbitrary constants. But that may not be the solution you are looking for.)
Last edited: Jun 19, 2011
3. Jun 19, 2011
### hunt_mat
So the equation you have is:
$$v^{2}\frac{\partial}{\partial x}\frac{1}{A(x)}\frac{\partial}{\partial x}(A(x)u)=\frac{\partial^{2}u}{\partial t^{2}}$$
Use:
$$\frac{\partial}{\partial x}(Au)=A\frac{\partial u}{\partial x}+0.3u$$
Likewise for the 1/A term too.
4. Jun 19, 2011
### andrey21
Thank you for the replies, hunt_mat could u please explain your post a little more please im confused
5. Jun 19, 2011
### hunt_mat
I will explain the second point:
$$\frac{\partial}{\partial x}(A(x)u)=A\frac{\partial u}{\partial x}+u\frac{\partial A}{\partial x}=A\frac{\partial u}{\partial x}+0.3u$$
6. Jun 19, 2011
### andrey21
Ok using what you have said I have obtained:
V2 d/dx (0.3u/0.2+0.3x + du/dx)
V2 d/dx (0.15u+ u/x + du/dx)
Is this correct??
7. Jun 19, 2011
### hunt_mat
You have to use the quotient rule which is:
$$\frac{d}{dx}\left(\frac{X}{A}\right) =\frac{A\frac{dX}{dx}-X\frac{dA}{dx}}{A^{2}}$$
Where:
$$X=\frac{\partial }{\partial x}(A(x)u))$$
8. Jun 19, 2011
### andrey21
Ok so I should use the quotient rule on:
0.3u/0.2+0.3x
(0.2+0.3x) (0.3) - 0.3u (0.3) / (0.2+0.3x)2
0.6 +0.9x -0.9u / (0.2+0.3x)2
am I on the right track??
9. Jun 19, 2011
### hunt_mat
Not quite, you should have:
(0.3du/dx-(0.3)^2u)/(0.2+0.3x)2
10. Jun 19, 2011
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https://stats.libretexts.org/Courses/Lake_Tahoe_Community_College/LTCC%3A_MATH_201_-_Elements_of_Statistics_and_Probability/Text/12%3A_Linear_Regression_and_Correlation/12.03%3A_Scatter_Plots/Scatter_Plots_(Exercises)
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# Scatter Plots (Exercises)
Exercise $$\PageIndex{1}$$
Does the scatter plot appear linear? Strong or weak? Positive or negative?
The data appear to be linear with a strong, positive correlation.
Exercise 12.3.3
Does the scatter plot appear linear? Strong or weak? Positive or negative?
Exercise 12.3.4
Does the scatter plot appear linear? Strong or weak? Positive or negative?
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https://en.wikibooks.org/wiki/User:Daviddaved/On_inhomogeneous_string_of_Krein
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# User:Daviddaved/On inhomogeneous string of Krein
The following physical model of a vibrating inhomogeneous string (or string w/with beads) by Krein provides mechanical interpretation for the study of Stieltjes continued fractions. The model is one-dimensional, but it arises as a restriction of n-dimensional inverse problems with rotational symmetry.
The string is represented by a non-decreasing positive mass function m(x) on a possibly infinite interval [0, l]. The right end of the string is fixed. The ratio of the forced oscillation to an applied periodic force @ the left end of the string is the function of frequency, called coefficient of dynamic compliance of the string.
The small vertical vibration of the string is described by the following differential equation:
${\displaystyle {\frac {1}{\rho (x)}}{\frac {\partial ^{2}f(x,\lambda )}{\partial x^{2}}}=\lambda f(x,\lambda ),}$
where
${\displaystyle \rho (x)={\frac {dm}{dx}}}$
is the density of the string, possibly including atomic masses. One can express the coefficient in terms of the fundamental solution of the ODE:
${\displaystyle H(\lambda )={\frac {f'(0,\lambda )}{f(0,\lambda )}},}$
where, ${\displaystyle f(l,\lambda )=0.}$
A fundamental theorem of Krein and Kac, see [10], & also [19] essentially states that an analytic function ${\displaystyle H(\lambda )}$ is the coefficient of dynamic compliance of a string if and only if the function
${\displaystyle \beta (\lambda )=\lambda H(-\lambda ^{2})}$
is an analytic automorphism of the right half-plane C+, that is real on the real line.
Exercise(**). Use the theorem above, Fourier transform and a change of variables to characterize the set of Dirichlet-to-Neumann maps for a unit disc with conductivity depending only on radius.
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http://poesophicalbits.blogspot.com/2013/03/three-paths-to-becoming-mathematical.html
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## Sunday, March 3, 2013
### Three paths to becoming a mathematical anti-platonist
It may be the case that "no good arguments exist either for or against mathematical platonism" (Platonism and Anti-Platonism in Mathematics by Mark Balaguer). Mathematical anti-platonists may come from a certain naturalistic belief that there's nothing outside nature, so if it's the case that there are no infinities in nature, how can one believe in platonist mathematical objects like infinite sets and the real number continuum?
The three paths below are not arguments against mathematical platonism. They are just ways mathematical anti-platonists can travel. (The first path is complete in the sense that it actually gets to a goal of a truly non-platonistic alternative to interpreting standard mathematics. The other two are incomplete in the sense that they result either with a somewhat restrictive or a non-standard mathematics.)
1. Finite mathematics (of indefinitely large size sets)*
In Understanding the Infinite, Shaughan Lavine describes the mathematics of Jan Mycielski ("The meaning of pure mathematics", "Locally finite theories"). In this approach, the quantifiers (∀, ∃) within the sentences of standard mathematics are replaced with indexed quantifiers (∀i, ∃j), and the interpretation of these quantifiers is that the variables they govern range over finite sets (Ωi, Ωj) with the same index. The key to this approach is that the finite sets can be of different sizes (unlike in the standard interpretation where the variables range over the same set). This indexing of quantifiers in sentences of a standard-mathematical theory T is done by process called relativization, and the result of applying this process to a sentence φ of standard mathematics is called a regular relativization φ' of φ. Beginning with a standard theory T, the result is the corresponding finitary theory Fin(T). The key theorem of this approach is:
"If φ is a sentence in the language of T and φ' is a regular relativization of φ, then φ is a theorem of T if and only if φ' is a theorem of Fin(T)."
Thus every theorem of T (interpreted with possibly infinite sets) has a corresponding theorem of Fin(T) (interpreted with only finite sets).
Note: Mycielski calls this interpretation intentionalism (which is different from intuitionism), in contrast with formalism and platonism. For some examples, see:
Mathematica materialis, or How not to be lured into Plato's cave
Persons without infinities
Plato's cave is closed
Transfinity
* or MIFS: Mathematics of Indefinitely-large Finite Sets
The other two paths I mention briefly.
2. Computable analysis
Can computable numbers be used instead of the reals?
Computable analysis
Constructive mathematics
E.g., only consider numbers and methods of analysis that can be represented by computer programs. It would interesting to link path 2 to path 1.
3. Paraconsistent mathematics (with finite models)
Inconsistent mathematics
Paraconsistent Logic
"One interesting implication of the existence of inconsistent models of arithmetic is that some of them are finite (unlike the classical non-standard models)."
Inconsistent models of arithmetic:
Part I: Finite models, Part II: The general case
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https://gitter.im/SmingHub/Sming?at=62953146c9382316a62e895b
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## Where communities thrive
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##### Activity
• Aug 08 09:27
slaff closed #2540
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Mike
@mikee47
That particular library doesn't require patches at its current version. I've just updated it to latest and it's missing Adafruit_I2CDevice so would require some work to get it there. I guess the question ATM is whether the later versions have bugfixes or features you require?
Vity
@Vity01
I just need it to make (their) examples compilable
Vity
@Vity01
there might be a side effect for other Adafruit libs in Sming
Vity
@Vity01
I found another issue with the flashing on Windows make flash
...
ESPTOOL2 out/Esp8266/debug/firmware/rom0.bin
SSL support disabled
make[1]: Nothing to be done for application'.
Killing Terminal to free COM5
make: [kill_term] Error 127 (ignored)
WriteFlash 0x00000=out/Esp8266/debug/firmware/rboot.bin 0x000fa000=out/Esp8266/debug/firmware/partitions.bin 0x00002000=out/Esp8266/debug/firmware/rom0.bin 0x000fc000=/C/tools/Sming/Sming/Arch/Esp8266/Components/esp8266/ESP8266_NONOS_SDK/bin/esp_init_data_default.bin
Traceback (most recent call last):
File "c:\tools\Sming\Sming\Components\Storage\Tools\hwconfig\hwconfig.py", line 114, in <module>
main()
File "c:\tools\Sming\Sming\Components\Storage\Tools\hwconfig\hwconfig.py", line 106, in main
output = globals()['handle_' + args.command](args, config, part)
File "c:\tools\Sming\Sming\Components\Storage\Tools\hwconfig\hwconfig.py", line 52, in handle_flashcheck
filesize = os.path.getsize(filename)
File "c:\Python310\lib\genericpath.py", line 50, in getsize
return os.stat(filename).st_size
FileNotFoundError: [WinError 3] The system cannot find the path specified: '/C/tools/Sming/Sming/Arch/Esp8266/Components/esp8266/ESP8266_NONOS_SDK/bin/esp_init_data_default.bin'
make: *** [flash] Error 1
The file c:\tools\Sming\Sming\Arch\Esp8266\Components\esp8266\ESP8266_NONOS_SDK\bin\esp_init_data_default.bin is there, but it looks like it's used somewhere where the path is not inflated into Windows path
Mike
@mikee47
I've started a PR #2407 which updates the library. Also, only requires #include <Adafruit_BME280_Library>. Perhaps you could test it?
Re. problem with flashing, the 'file not found' relates to '/C/tools/...' but previous info. indicates path should be '/c/tools/...'. Windows doesn't care but Make does. I suspect this is related to #2000. Try a make config-clean clean components-clean then rebuild.
Mike
@mikee47
Ignore that last comment. The problem is in Components/Storage/Tools/hwconfig/hwconfig.py line 52, requires filesize = os.path.getsize(fixpath(filename)). NB. I develop on Windows but haven't encountered this problem - I switched to WSL2 as it's considerably faster. I'll get a fix submitted shortly once I've checked it.
Vity
@Vity01
@mikee47 thanks for the PR, I will try it , it looks like I am not unable to build up I2C and I hope the newer library contains some fix
Yeah, meanwhile I disabled the filesize safety check - it will work for you in WSL2 because /c/ path works there
Mike
@mikee47
@Vity01 I've identified the likely problem with the new BME280 library, changes pushed to update/adafruit-bme280 branch. You'll need a git pull. Also updated adafruit libraries so will requiremake submodules-clean before building.
vesley
@vesley
Hello @slaff, FileStream worked, but I have two problems with the file upload.
1. When I initialize the FileStream in the fileUploadMapper, I don't have the file name. I put a static name for testing, but I want to store the file with the name provided by the multipart/form-data request.
2. Before persisting the file I want to check if there is enough storage space on the SPIFFS file system and if the file name is not bigger than 32 characters (as SPIFFS doesn't allow filenames with more than 32 characters). If this conditions are not met I want not to store the file.
Is there a way to achieve what I want with Sming?
16 replies
Vity
@Vity01
hurray 97% for v4.5.0 :-)
slaff
@slaff
gpio: gpio_set_level(215): GPIO output gpio_num error
Should be fixed in the latest develop
slaff
@slaff
@/all We are planning a new release for 25th of December. Please test the code in the latest develop branch and let us know if you have noticed some issues.
vesley
@vesley
Hello @mikee47 & @slaff, is it possible to add a new method signature for HttpResourceTree::setDefault, which allows to register a default path and a plugin or a list of plugins? I want to secure all registered paths with basic authentication. Currently there is no way to secure the default path.
vesley
@vesley
Hello @mikee47 & @slaff, is it possible to add a new method signature for HttpResourceTree::setDefault, which allows to register a default path and a plugin or a list of plugins? I want to secure all registered paths with basic authentication. Currently there is no way to secure the default path.
I found out that I can use
server.path.set("*", handler, plugin)
to set a handler for the default path with a plugin.
slaff
@slaff
@/all Merry Christmas everyone - we have a present for you: https://github.com/SmingHub/Sming/releases/tag/4.5.0
Mike
@mikee47
@slaff Awesome teamwork and Merry Christmas to all !
kmihaylov
@kmihaylov
Hello. I'm trying to use multiple SPI buses (one for SD card and another one for some ICs). The global SPI object works fine (I setup it on SpiBus::HSPI). But I struggle to set secondary SPI object utilizing VSPI. I declare it with SpiClass spi2 and later try to spi2.setup(SpiBus::SPI3, SDpins);.
The application builds fine, but on startup I get 392117 [SPI] Bus #3 already assigned
These are the exact init lines for SPI:
SPI.setup(SpiBus::HSPI, spispi);
SPI.begin();
spi2.setup(SpiBus::SPI3, SDpins);
spi2.begin();
Mike
@mikee47
I've just tested this and no issue. Can you post the complete code please? Open an issue if necessary.
kmihaylov
@kmihaylov
Thank you @mikee47 Let me check precisely and I'll post my results.
kmihaylov
@kmihaylov
@mikee47 , you're correct, as usual. I'm using the SDCard library. I did spi2.begin() before runTest(); that triggers SDCard_begin(PIN_CARD_SS, SPI_FREQ_LIMIT). This was the reason for the 'already assigned' bus.
It is possible that SDCard_begin() somehow overwrites stuff for the global SPI object? I'm loosing communication with the ICs on SPI's bus after runTest();.
I write the app with both SPI and spi2 buses and the first time after flashing both the SD card (on spi2) and the ICs on SPI's bus work OK. On the second restart of the board, however, the devices on the SPI bus do not work. I tried also flashinit and it still has this strange behavior.
kmihaylov
@kmihaylov
@mikee47 Well, my board is running now. I don't know how the above mentioned issue actually happens. What I found is that SPI and GPIO pins configuration might be tricky. Namely, if I set some GPIO pins (input/output) after SPI.setup(), then SPI might brake. I changed the order of some GPIO initialization functions and now the board is alive. I might have missed something and later I may try to reproduce this. Also I prepared pretty basic code to test (with MISO<->MOSI pins shorted) 2 SPI instances. https://pastebin.com/3w43sgPT (till 07.03.2023)
Anyway, thank you @mikee47 for your work on Sming and for your time providing support! Also thank you @slaff for managing and supporting the project!
slaff
@slaff
@/all we will release at the end of the month Sming v4.6. Help us find bugs by testing the latest develop version on your devices and report any issues. You can read more about the new features from here: #2509
vesley
@vesley
Hello @slaff, hello @mikee47, I'm playing with the Basic_Ota sample. I can successfully flash rom0 and rom1. But the spiff partition is only flashed when rom0 is written. When rom1 is written, then I see following message in the console:
Updating...
52062981 Partition 'spiffs1' not found
As there is only one spiffs partition, it is always 'spiffs0'. There is no 'spiffs1'. How can I determine the spiffs partition when rom1 is written?
The spiff partition is determined in the example with following lines:
auto spiffsPart = findSpiffsPartition(part);
if(spiffsPart) {
// use user supplied values (defaults for 4mb flash in hardware config)
}
When part=rom1 then no spiff partition is found and therefore the update is skipped.
13 replies
Mateusz Zakarczemny
@Matzz
Hi guys,
I'm trying to write simple program which will write something to file and then read from it. My attempt compiles but I see unexpected (empty file output). Could I kindly as for some guide?
Storage::Partition dataPart;
String name = F("spiffs0");
dataPart = Storage::findPartition(name);
if(!dataPart) {
}
spiffs_mount(dataPart);
uint64_t time = RTC.getRtcNanoseconds();
String startString = "=== Start time: ";
startString.concat(time);
startString.concat("\n");
data.write(startString);
data.flush();
Serial.println("Current data:");
String c = data.getContent();
Serial.println(c);
Serial.println("==== Data end");
The output is:
60056 mount() returned 0 (Success)
60673 File system initialised
Current data:
==== Data end
Why I cannot see what I wrote to this file?
Mike
@mikee47
Try adding data.seek(0, SeekOrigin::Start) before the call to getContent..
Mike
@mikee47
Issue is because of global File object, which takes a reference to the global filesystem pointer in its constructor. However, this hasn't yet been created. I've created a PR to fix this...
I hadn't considered using long-term file handles. If you're only accessing the file once every 5 seconds I would recommend using a temporary File object instead.
Mateusz Zakarczemny
@Matzz
@mikee47 Fixed, now it works fine. Thanks!
BTW is that normal that I cannot use
System.deepSleep when nework is disabled DISABLE_NETWORK := 0?
/opt/esp-quick-toolchain/xtensa-lx106-elf/bin/../lib/gcc/xtensa-lx106-elf/10.2.0/../../../../xtensa-lx106-elf/bin/ld: /opt/sming/Sming/out/Esp8266/debug/lib/clib-Sming-f4fec80f9836e7cd9a2801547ac6ca01.a(System.o): in function _ZN11SystemClass10initializeEv':
/opt/sming/Sming/Platform/System.cpp:69: undefined reference to system_deep_sleep_set_option'
/opt/esp-quick-toolchain/xtensa-lx106-elf/bin/../lib/gcc/xtensa-lx106-elf/10.2.0/../../../../xtensa-lx106-elf/bin/ld: /opt/sming/Sming/Platform/System.cpp:75: undefined reference to system_deep_sleep'
/opt/esp-quick-toolchain/xtensa-lx106-elf/bin/../lib/gcc/xtensa-lx106-elf/10.2.0/../../../../xtensa-lx106-elf/bin/ld: /opt/sming/Sming/out/Esp8266/debug/lib/clib-Sming-f4fec80f9836e7cd9a2801547ac6ca01.a(System.o): in function _ZN11SystemClass9deepSleepEj16DeepSleepOptions':
/opt/sming/Sming/Platform/System.cpp:134: undefined reference to system_deep_sleep_set_option'
/opt/esp-quick-toolchain/xtensa-lx106-elf/bin/../lib/gcc/xtensa-lx106-elf/10.2.0/../../../../xtensa-lx106-elf/bin/ld: /opt/sming/Sming/Platform/System.cpp:138: undefined reference to system_deep_sleep'
collect2: error: ld returned 1 exit status
Mike
@mikee47
Sleep hasn't been implemented with No-WiFi. See SmingHub/Sming#2004 for some background.
(It would be a lot easier if Espressif released the SDK source code!)
Mateusz Zakarczemny
@Matzz
@mikee47 Thanks for update. I tried to implement that with wifi enabled but also failed.
When I use System.deepSleep(1*1000); in init method I get:
r123568 mount() returned 0 (Success)
123938 File system initialised
124004 spif5fs mounted
Current data:
=== Start time: 180289815482625
==== Data end
Startup end,
mode : null
enter deep sleep��sll��|�d�|�d�
c|����s�cd�b��oo�log���
cx��drlrl�{��o�c�gcp�
On console and program hangs.
If I try to use deepSleep in timer method the result is quite similar
==== Data end
Printing sensors data end.
enter deep sleep��
and nothing later.
I didn't found any examples for using that method with Sming. Maybe I need to preconfigure something?
slaff
@slaff
@mikee47 I hope your solar installation is going forward. Do you think you will have time to share also your faster button library? See SmingHub/Sming#2250
Mike
@mikee47
@Matzz In SDK description for system_deep_sleep says "Hardware has to support deep-sleep wake up (XPD_DCDC connects to
EXT_RSTB with a 0-Ωresistor)". Connecting a jumper between RST and GPIO 16 has the desired effect. Probably also worth adding a pinMode(16, WAKEUP_PULLUP); in init().
Mike
@mikee47
@Matzz Latest develop has a fix so that global/static File objects work as expected.
Simon Brazell
@SimonBrazell
Hello, I'm attempting to build an ultrasonic tank level sensor using the JSN-SR04T and an ESP8266, I decided to use Sming as it had all the networking features I desired (Wifi, MQTT) but I'm unable to get even the most basic example of distance measurements working as it should. All measurements the device takes are consistently low (about 20cm lower than they should be). This same or similar code works on an Arduino build perfectly. Any ideas what the issue could be? Here is the latest iteration of my code using the included Ultrasonic package:
#include <SmingCore.h>
#include <Libraries/Ultrasonic/Ultrasonic.h>
#define TRIG_PIN 2
#define ECHO_PIN 5
#define SAMPLES 10
Timer procTimer;
Ultrasonic ultrasonic = Ultrasonic();
void measure()
{
uint32_t distance = 0;
for (int i = 0; i < SAMPLES; i++)
{
uint32_t dist = ultrasonic.rangeCM();
Serial.print(dist);
Serial.println(" cm");
distance += dist;
delayMilliseconds(60);
}
distance /= SAMPLES;
Serial.print("Average: ");
Serial.print(distance);
Serial.println(" cm");
}
void init()
{
Serial.begin(SERIAL_BAUD_RATE);
ultrasonic.begin(TRIG_PIN, ECHO_PIN);
delayMilliseconds(60);
measure();
procTimer.initializeMs(10000, measure).start();
}
Or rather they seem to be around 30% lower than they should be.
Same problem occurs if I build and upload the Ultrasonic_HCSR04 example from the provided samples.
Mike
@mikee47
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|
http://science.sciencemag.org/content/114/2951/78.2
|
Book Reviews
# Biometric Analysis: An Introduction. Alan E. Treloar. Minneapolis: Burgess Pub., 1951. 251 pp. \$4.50
+ See all authors and affiliations
Science 20 Jul 1951:
Vol. 114, Issue 2951, pp. 78-79
DOI: 10.1126/science.114.2951.78-a
This is a PDF-only article. The first page of the PDF of this article appears below.
|
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http://www.guitaretab.com/t/three-days-grace/196764.html
|
Song name
# A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
# Three Days Grace - Time Of Dying drum
```C=Crash
Sp=Splash
R=Ride
H=Hi-hats
S=Snare
FT=Floor tom/Low tom
B=Bass
x=closed hi-hat
X=normal strike/open hi-hat
o=normal hit
f=flam
g=ghost note
d=double hit
h=double ghost
r=roll
Intro 0:03
S |rd--o------o--o-| |o--o-dooo-oo----|
B |o--oo---o-------| |o---o---o-------|
C |X---X---X---X---| |X---X-------X---|
Sp |----------------| |--------X-------|
S |----o-------o---| |----o-------o---|
B |o-------o-------| |o-------o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---X---X---X---|
FT |--------------o-|
S |----o-------ooo-|
B |o-------o-------|
|1e+a2e+a3e+a4e+a|
S |----o---g---o---| |----o---g---o---|
B |o-o---o--o—-go--| |o-o--o---o--go--|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
Verse 0:13
S |----o---g---o---| |----f-------f---|
B |o-o--o--o--o-o--| |o--o----o--o----|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---------------| |----------------|
H |--x-x-x-x-x-X---| |x-x-x-x-x-x-X---|
S |----o-------o---| |----o-------o---|
B |o-o---oo-o-----o| |o-o---oo-o-----o|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |x-x-x-x-x-x-X---| |x-x-x-x-x-x-X---|
S |----o-------o---| |----o-------o---|
B |o-o---oo-o-----o| |o-o---o-o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
PreChorus 0:33
R |g---g---g---g-gg| |g---g---gg--gg--|
B |----------------| |o---------------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
R |g---g---g---gh--| |g---------------|
FT |----------------| |-------------f--|
B |o---------------| |o---------------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
Chorus 0:43
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-----|
ST |----------------| |------------d---|
MT |----------------| |-------------d--|
FT |----------------| |--------------o-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o--f|
B |o---o-ooo—--o-oo| |o---o-ooo---o---|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
Post-Chorus 1:02
S |-------------f--|
B |-------------ooo|
|1e+a2e+a3e+a4e+a|
Verse 1:05
C |X---------------| |----------------|
H |--x-x-x-x-x-X---| |x-x-x-x-x-x-X---|
S |----o-------o---| |----o-------o---|
B |o-o---oo-o-----o| |o-o---oo-o-----o|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |x-x-x-x-x-x-X---| |x-x-x-x-x-x-X---|
S |----o-------o---| |----o-------o---|
B |o-o---oo-o-----o| |o-o---o-o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---------------| |----------------|
H |--x-x-x-x-x-X---| |x-x-x-x-x-x-X---|
S |----o-------o---| |----o-------o---|
B |o-o---oo-o-----o| |o-o---oo-o-----o|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |x-x-x-x-x-x-X---| |x-x-x-x-x-x-X---|
S |----o-------o---| |----o-------o---|
B |o-o---oo-o-----o| |o-o---o-o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
PreChorus 1:23
R |g---g---g---g-gg| |g---g---gg--gg--|
FT |------------o---| |o-----------o---|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
[ Tab from: http://www.guitaretab.com/t/three-days-grace/196764.html ]
R |g---g---g---gh--| |X---------------|
S |----------------| |-------------f--|
FT |o-----------o---| |----------------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
Chorus 1:34
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o---|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
Bridge 1:53 (I couldn’t get the timing perfect but it locks in with the riff)
R |x--xx-x--xxxxx--| |x---x---xxx-xx--|
S |o---------------| |----------------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
S |o---o-o----o----| |o--o-dooo-oo----|
B |o--oo---o-------| |o---o---o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---X---X---X---| |X---X-------X---|
Sp |----------------| |--------X-------|
S |----o-------o---| |----o-------o---|
B |o-------o-------| |o-------o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---X---X---X---|
S |----o-------o-f-|
B |o-------o-------|
|1e+a2e+a3e+a4e+a|
Chorus 2:08
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o--d|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-X-X-|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o-oo|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
H |X-X-X-X-X-X-X-X-| |X-X-X-X-X-X-----|
S |----o--g----o---| |----o--g----o---|
B |o---o-ooo—--o-oo| |o---o-ooo---o---|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
Outro 2:46
C |X---X---X---X---| |X---X-------X---|
Sp |----------------| |--------X-------|
S |----o-------o---| |----o-------o---|
B |o-------o-------| |o-------o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---X---X---X---| |----X---X---X---|
Sp |----------------| |X---------------|
S |----o-------o---| |----o-------o---|
B |o-------o-------| |o-------o-------|
|1e+a2e+a3e+a4e+a| |1e+a2e+a3e+a4e+a|
C |X---X---X---X---| |----------------|
Sp |----------------| |----------------|
S |o---o-do----o---| |o--o-dooo-oo----|
B |o-------o-------| |o-------o-------|
```
Related for Time Of Dying drum
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Best way to learn
"Time Of Dying"
|
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|
https://www.gradesaver.com/textbooks/math/statistics-probability/elementary-statistics-12th-edition/chapter-1-introduction-to-statistics-review-cumulative-review-exercises-page-38/3
|
## Elementary Statistics (12th Edition)
$\frac{247-176}{6}=\frac{71}{6}=11.833333$. This is large compared to 3.
|
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https://thecentercolumn.com/2018/04/09/approximating-tripod-stiffness-vs-height/
|
Approximating Tripod Stiffness vs Height
In a previous series of posts, I have laid out the models used for fitting stiffness vs height data, tested the Manfrotto MT055 tripods, tested a bunch of tripods, and compared the stiffness vs height for some very similar Really Right Stuff tripods. In these posts we learned that we could not fit the stiffness vs height data well with a simple power law, but had to throw in another constant that varied significantly between different models. This extinguished the dream of being able to accurately approximate the stiffness of a tripod over its entire range simply by measuring the stiffness at a single height. Yet, that is exactly what I aim to do here in this post. If we cannot get a perfectly accurate approximation, perhaps we can find one that is good enough.
I simply do not have the time to measure the stiffness vs height for each tripod I test. As we have seen in this series though, tripods perform much better at shorter heights. For two tripods that are otherwise identical in construction except for height, the taller one will perform worse simply because it is easier to bend a long beam (tripod leg) than a shorter one. To construct the tripod rankings score, I thus want a simple metric that rewards taller tripods versus shorter ones. The taller tripod could of course be used at a shorter height, with a corresponding gain in stiffness, and we don’t want to unduly penalize it just for being tall. In fact, you may want to reward it for its increased versatility, but I don’t want to assign any value judgments. I just want to level the playing field in the most numerically backed way possible.
In the previous posts, I fit the stiffness vs height data to some simple functions that best approximated the height over the tested range. I am going to simplify things further. I am going to force my fit to go through the data point corresponding to the tallest height, and then fit the powerlaw function:
$\kappa = \kappa_0 h^p$
Now though, $\kappa_0$ is not a free parameter, but fixed the above constraint such that:
$\kappa_0 = \frac{Stiffness_{hmax}}{hmax^p}$
So we now have one fewer degree of freedom. The resulting fit looks like:
I have added to the graph five curves corresponding to what the fit would look like for a variety of other possible exponents. All of the curves pass through the point corresponding to the maximum height, as they are constrained to do. The exponent that creates the best fit to the data, according to a least squares optimization, is -1.29. However, we can easily see that for the upper ranges of the tripod height, the exponent of -1.50 provides a much closer fit to the data. This is important because this is the range in which we are more interested in normalizing the data. We would never care about comparing this tripod to one that is less than 0.75m in height, where the -1.50 line diverges from the data. However, in a ranking that involves tripods of wildly differing heights, an exponent of -1.50 may be too generous to tall tripods.
Below is a list of the exponent fitted in the same manner as above, for all of the tripods I have data for stiffness vs height. I also added the exponent for the fit that I felt best approximated the behavior around the maximum height, but diverged for lower heights.
Tripod Fitted Exponent Eyeballed Exponent Sirui T2205X -1.11 -1.5 Oben CT2491 -1.35 -1.5 Gitzo GT2542 -1.18 -1.5 MT055XPRO3 -1.35 -1.5 MT055CXPRO3 -1.25 -1.5 MT055CXPRO4 -1.36 -1.5 RRS TFC14 -1.29 -1.5 RRS TVC23 -1.13 -1.13 RRS TVC24L -1.30 -1.5 RRS TVC33 -1.13 -1.25 RRS TVC34L -1.15 -1.25 Average -1.24 -1.42
The behavior of these tripods is pretty similar to one another. The plot generated for each tripod can be found at the bottom of the post. These averages present lower and upper bounds for what the exponent used in normalization should be, and fortunately, it is a pretty narrow range. We aren’t going to see massive swings in the rankings based on what exponent is chosen. If you have thoughts on where in this range the normalization exponent should be chosen, please say so in the comments. I will be mulling this over before choosing a value to reconstruct the rankings page.
Appendix: Data to make your own judgement
6 thoughts on “Approximating Tripod Stiffness vs Height”
1. Dave says:
Nice showing from the Manfrotto, in particular the 055 carbon fiber 3 leg version. RRS appears disappointing
here for the cost.
1. David Berryrieser says:
The MT055CXPRO3 is a great value. The Really Right Stuff tripods still top the charts in performance in their classes. Whether that performance is worth the cost is up to you.
2. Dave says:
Dave, What are your thoughts on the RRS damping? The TVC-33 does not appear to have test data that
supports buying a near \$1,000 tripod. The Gitzo 4 series test results are awesome.
1. David Berryrieser says:
The damping on the RRS TVC-33 is poor and yes, thus far the Gitzo systematic tripods do perform better. I have a Gitzo Series 3 in the mail, which should provide a more fair comparison. The TVC-33 I tested is on the old side, and the newer RRS models seem to perform better in terms of damping. Stiffness is king though for most applications, and the TVC-33 results are strong.
3. Dave says:
Dave, Again thank you for the great site. One suggestion to standardize measurements while not causing you
too much time to take the measurements is to measure at maximum height and then a “standard” height that
most all tripods would be able to reach like say 1.0 or 1.2m.
Some tripods like the TVC-24L and TVC-34L that are very tall suffer in the rankings due to the added height and
make direct comparison difficult.
Thoughts?
1. David Berryrieser says:
That is a pretty reasonable approach, and I have considered it. It wouldn’t be that much additional work. The primary problem is that tripods have somewhat different behavior as a function of height. Thus, using a measurement of the stiffness at some standard height does not accurately reflect the stiffness of the tripod that most people will use it at, which is the maximum height. The current approach does seem to overly penalize tall tripods, but not by much. For example, if we take a look at the TVC 34L and compute the score using the stiffness at the same height as the TVC-33, we find that the score should be 11% lower than the TVC-33 as it isn’t as stiff at the same height, and it weighs more. The score I report using the height^1.25 correction factor is 13% lower. So yes, there is a small penalty, but it is small enough to not matter much. The rankings are simply a guide, not some definitive metric. But the rankings are correctly saying in this case that you should only buy the taller version of the tripod if you need the extra height.
|
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|
http://planetmath.org/antiharmonicnumber
|
# antiharmonic number
## Primary tabs
Major Section:
Reference
Type of Math Object:
Definition
Groups audience:
## Mathematics Subject Classification
### a new article invisible
Hi admins! My new article ”antiharmonic number” turned invisible. When I deleted it, my score increased(!) 100 points. Then I wrote the article anew, the score increased again 100 points and the article is again invisible. There must be some system bug. Jussi
### make test entry and delete
You earn 200 points!
### gratis PM author points
Hi admins, making a new entry gives 100 points, deleting it also gives 100 points!! I have lately deleted one of my entries (getting 100 p) and made two test entries and deleted them (thus getting 400 p).
Please correct this system bug and subtract 500 points from me!
Jussi
### re: gratis PM author points - oops
I’ll look into that shortly, thanks for the alert!
Joe
### re: gratis PM author points - fixed
Jussi: it was the old classic, ”missing a minus sign”. Fixed now!
Thanks kindly!
Joe
### re: re: gratis PM author points -- fixed
Thanks Joe, it’s very good! I also have tested it. But please subtract the 500 gratis points of me!
Best wishes, Jussi
### Re: a new article invisible
I don’t know about the deletion, but I can say why it is invisible. At the end of the second paragraph, the equation starts with a double dollar sign but ends with a single dollar sign. This is the TeX bug which is causing it not to render. Unfortuinately, as it stands now, when it runs across such a bug and cannot render the article, LaTeXML simply produces no output whatsoever rather than producing an error message which could help the user fix the problem or at least be made aware of what happened.
### Thank you very much, rspuzio!
Thank you very much, rspuzio! You were right; I did’nt see the lacking dollar sign since I have only a 14”-monitor =o(
Regards, Jussi
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http://math.stackexchange.com/questions/3976/on-the-binary-decimal-expansion-of-the-reciprocal-primes
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# On the binary decimal expansion of the reciprocal prime's
I have been thinking a little bit about the binary decimal expansion of reciprocal prime numbers; and I have a few questions.
I found this neat table which lists the binary expansion of many fractions, and I was trying to find some patterns.
Here are my questions, for brevity I say a natural number has a period N if the binary decimal expansion of it's reciprocal has period N: (for example, 1/7 = .001001... has period 3)
1. Given an arbitrary natural number N, does there exist a prime number of minimum period N?
(By minimum period I mean to exclude the case that one prime has a period which is a multiple of the period of another prime. For example, 1/3 = .0101... has period 2, and 1/5 = .00110011... has period 4; so while 1/3 has period 4, what I call it's "minimum period" is 2)
2. Can two prime numbers have the same minimum period?
A useful result which I believe is well known, is that a natural number has a period N if and only if it is a factor of 2N - 1.
Does anyone know of a good reference that describes some theory behind the relationship between the period of the reciprocal of a natural number, and the prime factorization of that number?
-
I recommend changing the phrase "inverse prime numbers" to "reciprocals of prime numbers". The latter has a clear meaning, the former does not. – Arturo Magidin Sep 3 '10 at 19:41
I edited the OP, thanks for the suggestion. – Matt Calhoun Sep 3 '10 at 19:46
If you look at my answer together with mau's answer on this question, adjusting the base form 10 to 2, that gives you the criteria you're looking for or at least a start on it. – Isaac Sep 3 '10 at 19:51
For the second question: both 1/41 & 1/271 have period 5; 1/7 & 1/13 have period 6; 1/73 & 1/137 have period 8, ... Relevant Mathematica code: Sort[{Length[Nest[First, RealDigits[1/#], 2]], #} & /@ Prime[Range[500]]] – J. M. Sep 3 '10 at 20:04
From the table I linked: 1/7 = .001 (repeating); 1/13 = .000100111011 (repeating); so although it's true that 7 and 13 have the same period (12), they do not have the same minimum period, so this is not what I am looking for, sorry for the confusing way I stated the question, I am happy to make any edits which are suggested for clarity. Actually I noticed most primes p have a repeating sequence which is p-1 digits long (such as 13, but not 7)... – Matt Calhoun Sep 3 '10 at 22:47
(In the below post there are several links with the apostrophes omitted; fill them in if the links don't work.)
The phenomenon you are studying is a phenomenon in modular arithmetic. If a prime $p$ has period $n$, this means that there is some numerator $N$ such that $\frac{N}{2^n - 1} = \frac{1}{p}$. This is equivalent to $Np = 10^n - 1$, or $p | 2^n - 1$, or $2^n \equiv 1 \bmod p$. The smallest $n$ for which this is true is called the order of $2 \bmod p$, sometimes denoted $\text{ord}_p(2)$ (although this is confusingly also used to denote the greatest power of $p$ which divides $2$...).
Fermat's little theorem guarantees that $\text{ord}_p(2)$ always divides $p-1$; you have already observed this yourself. However, predicting the exact order is very difficult to do in general. For example, knowing that the order is actually equal to $p-1$ is equivalent to knowing that $2$ is a primitive root, and it is not currently even known whether this is true infinitely often. In any case, you should be able to find basic information about order in any good textbook on elementary number theory.
With that background out of the way...
The answer to question 1 is no. The only exception is $n = 6$ by Zsigmondy's theorem.
The answer to question 2 is yes. If $p$ and $n$ are relatively prime, then $p$ has period $n$ if and only if $p$ divides $\Phi_n(2)$, where $\Phi_n(x)$ is the $n^{th}$ cyclotomic polynomial. (This is more or less a restatement of the condition that $p | 2^n - 1$ but $p$ doesn't divide $2^k - 1$ for $k < n$.) So it suffices to show that some number of this form has more than one prime factor relatively prime to $n$. There are two cases here which are particularly classical:
• $n$ is a prime $q$. In this case $\Phi_q(2) = 2^q - 1$ is a Mersenne number, and $2^{11} - 1 = 23 \cdot 89$ is the smallest composite Mersenne number, hence $23$ and $89$ both have period $11$.
• $n = 2^k$ for some $k$. In this case $\Phi_{2^k}(2) = 2^{2^{k-1}} + 1$ is a Fermat number, and $\Phi_{64}(2) = 2^{32} + 1 = 641 \cdot 6700417$ is the smallest composite Fermat number, hence $641$ and $6700417$ both have period $64$.
The answer to question 3 is the following.
Lemma: If $n, m$ are relatively prime odd numbers, then $\text{ord}_{mn}(2) = \text{lcm}(\text{ord}_n(2), \text{ord}_m(2))$.
Proof. $\text{ord}_{mn}(2)$ is the order of the element $2$ in the multiplicative group of $\mathbb{Z}/mn\mathbb{Z}$, which we will denote $U(mn)$. By the Chinese remainder theorem, $U(mn)$ is isomorphic to the direct product $U(m) \times U(n)$, so the order of $2$ in $U(mn)$ must be the $\text{lcm}$ of the orders of $2$ in $U(m)$ and $U(n)$.
It follows that to compute $\text{ord}_m(2)$ for arbitrary $m$ it suffices to compute it for the odd prime power factors of $m$ and then to take the $\text{lcm}$ of the resulting numbers. (Note that if $m$ is divisible by a power of $2$ this only contributes a leading string of zeroes to the binary expansion of $\frac{1}{m}$ and hence does not affect the computation of the period.) Again, you can find a discussion of the Chinese remainder theorem in any good textbook on elementary number theory. (I am particularly bad at recommending textbooks on elementary number theory because I learned mine through a summer program, not a textbook...)
-
@Matt: as a general rule, you should wait maybe a day or so to accept answers. That makes it easier for other answers to accrue which might offer additional insights (as well as specific references, which I haven't provided), and it also allows the relevant answers to receive more votes. (Finally, it allows people to correct anything wrong I might've said :P) – Qiaochu Yuan Sep 4 '10 at 1:16
|
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|
https://alihosseiny.com/statistical-field-theory/
|
An introduction to the quantum field theory and its application in statistical physics.
Topics are as follows:
• A review on the critical phenomena
• Landau Ginsburg theory
• Perturbation and Feynman diagrams
• Renormalization
Textbooks:
Quantum and Statistical Field Theory, M. Le Bellac
Statistical theory of fields, M. Kardar
|
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|
http://www.fregu856.com/post/19apr/
|
# Getting started with PyTorch: 1 - Linear regression
All code found in this blog post is also available on Google Colab where it can be executed directly in the browser.
When I first got interested in deep learning a couple of years ago, I started out using TensorFlow. In early 2018 I then decided to switch to PyTorch, a decision that I’ve been very happy with ever since. Today, the difference between the two frameworks is probably quite small in practice (and both are extensively used by researchers in the field), but I personally still find PyTorch more convenient to use.
In a short series of blog posts I thus intend to try and help anyone interested in the field to get started with PyTorch and deep learning, by providing (hopefully) clearly written code examples.
In this first post, we’ll start with perhaps the most simple example problem there is and try to fit a straight line to some noisy data points. We will however do so using mini-batch Stochastic Gradient Descent (SGD) and use the same basic code structure that can be used also for significantly more interesting problems, such as street-scene semantic segmentation or automotive 3D object detection.
Essentially, we need to specify just three things: a dataset class, a model class and a training loop.
### Dataset
For our dataset class, we need to specify a constructor and two member functions.
In the constructor __init__, we create a synthetic dataset $D = \{(x_1, y_1), \dots, (x_N, y_N)\}$ by drawing $x_i$ uniformly from an interval and adding Gaussian noise to a given straight line: $x_i \sim U[-3, 3], \quad i = 1, \dots, N,$ $y_i = \bar{k}x_i + \bar{m} + \epsilon_i, \quad \epsilon_i \sim \mathcal{N}(0, 0.5), \quad i = 1, \dots, N.$
We also assign the number of examples, $N$, to a member variable so that it can be returned by __len__.
Finally, in __getitem__ we return the corresponding example $(x_i, y_i)$ given an index $i \in \{1, \dots, N\}$.
import torch
import torch.utils.data
import numpy as np
import matplotlib.pyplot as plt
class LinearRegressionDataset(torch.utils.data.Dataset):
def __init__(self, k, m, N):
self.X = np.random.uniform(low=-3.0, high=3.0, size=(N, )) # (shape: (N, ))
epsilon = np.random.normal(loc=0.0, scale=0.5, size=(N, )) # (shape: (N, ))
self.Y = k*self.X + m + epsilon # (shape: (N, ))
plt.figure(figsize=(8, 6))
plt.plot(self.X, self.Y, "^k", label="Training data examples")
plt.plot([-3, 3], [k*(-3)+m, k*3+m], "r", label="True straight line")
plt.legend()
plt.ylabel("y")
plt.xlabel("x")
plt.show()
self.num_examples = N
self.X = self.X.astype(np.float32)
self.Y = self.Y.astype(np.float32)
def __getitem__(self, index):
x = self.X[index]
y = self.Y[index]
return (x, y)
def __len__(self):
return self.num_examples
In __init__, we also plot our created dataset $D = \{(x_1, y_1), \dots, (x_N, y_N)\}$ together with the true straight line $y = \bar{k}x + \bar{m}$. For $\bar{k} = 3$, $\bar{m}= 5$, $N= 50$, we get the following plot:
### Model
For our model class, we need to specify a constructor and one member function.
In the constructor __init__, we create our two model parameters $k, m$ and assign them to member variables. These are then used in forward to output a prediction $\hat{y} = kx + m$ for a given input $x$.
import torch.nn as nn
class LinearRegressionModel(nn.Module):
def __init__(self):
super(LinearRegressionModel, self).__init__()
self.k = nn.Parameter(torch.zeros(1)) # (shape: (1))
self.m = nn.Parameter(torch.zeros(1)) # (shape: (1))
def forward(self, x):
# (x has shape: (batch_size))
y_hat = self.k*x + self.m # (shape: (batch_size))
return y_hat
### Training loop
To train our model on the dataset using SGD, we create instances of LinearRegressionDataset and LinearRegressionModel, we create the data loader train_loader (which will repeatedly call LinearRegressionDataset.__getitem__ to create mini-batches), and create the SGD optimizer object optimizer.
We then iterate through the entire dataset with mini-batches of size batch_size, and for each mini-batch we compute the L2 loss $L(k, m) = \frac{1}{N} \sum_{i=1}^{N} (y_i - \hat{y}_i)^2,$ we compute the gradients of this mini-batch loss with respect to our model parameters, and finally use these gradients in the SGD step to update the parameters.
One such iteration through the dataset is called an epoch, and we repeat this process num_epochs times.
num_epochs = 25
learning_rate = 0.01
batch_size = 8
k = 3
m = 5
N = 50
train_dataset = LinearRegressionDataset(k=k, m=m, N=N)
num_train_batches = int(len(train_dataset)/batch_size)
print ("num train batches per epoch: %d" % num_train_batches)
batch_size=batch_size, shuffle=True,
num_workers=1)
model = LinearRegressionModel()
model = model.cuda()
model.train() # (set in training mode, this affects BatchNorm and dropout)
optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)
epoch_losses_train = []
for epoch in range(num_epochs):
print ("###########################")
print ("epoch: %d/%d" % (epoch+1, num_epochs))
batch_losses = []
for step, (x, y) in enumerate(train_loader):
x = Variable(x).cuda() # (shape: (batch_size))
y = Variable(y).cuda() # (shape: (batch_size))
y_hat = model(x) # (shape: (batch_size))
loss = torch.mean(torch.pow(y - y_hat, 2))
# optimization step:
optimizer.step() # (perform the SGD update of the model parameters)
# store the loss value:
loss_value = loss.data.cpu().numpy()
batch_losses.append(loss_value)
epoch_loss = np.mean(batch_losses)
epoch_losses_train.append(epoch_loss)
print ("train loss: %g" % epoch_loss)
plt.figure(figsize=(8, 6))
plt.plot(epoch_losses_train, "^k")
plt.plot(epoch_losses_train, "k")
plt.ylabel("Loss")
plt.xlabel("Epoch")
plt.title("Loss per epoch")
plt.show()
print ("k, true value: %g, estimated value: %g" % (k, model.k))
print ("m, true value: %g, estimated value: %g" % (m, model.m))
plt.figure(figsize=(8, 6))
plt.plot(train_dataset.X, train_dataset.Y, "^k", label="Training data examples")
plt.plot([-3, 3], [k*(-3)+m, k*3+m], "r", label="True straight line")
plt.plot([-3, 3], [model.k*(-3)+model.m, model.k*3+model.m], "b",
label="Estimated straight line")
plt.legend()
plt.ylabel("y")
plt.xlabel("x")
plt.show()
In each epoch, we also store all mini-batch losses and then average them to get a loss value for the entire dataset. Once training is completed, we plot these epoch losses:
As we can see, the loss quickly decreases in the beginning and then starts to level out as our model parameters $k, m$ get close to the true values $\bar{k} = 3$, $\bar{m}= 5$. We also plot our estimated straight line $\hat{y} = kx + m$ and compare it to the true one:
Since we in this simple example problem have just two model parameters, we can gain additional insight by computing our loss function $L(k, m) = \frac{1}{N} \sum_{i=1}^{N} (y_i - \hat{y}_i)^2$ (over the entire dataset) for different values of $k, m$ and plot the loss surface:
num_values=100
k_plot_values = np.linspace(start=(k-7.0), stop=(k+7.0), num=num_values)
m_plot_values = np.linspace(start=(m-7.0), stop=(m+7.0), num=num_values)
# (k_plot_values and m_plot_values both have shape: (num_values, ))
loss_values = np.zeros((num_values, num_values))
for k_i in range(num_values):
for m_i in range(num_values):
Y_hat = k_plot_values[k_i]*train_dataset.X + m_plot_values[m_i]
# (Y_hat has shape: (N, ))
loss = np.mean((train_dataset.Y - Y_hat)**2)
loss_values[m_i, k_i] = loss
plt.figure(figsize=(8, 6))
K, M = np.meshgrid(k_plot_values, m_plot_values)
plt.contour(K, M, loss_values, levels=20)
plt.plot(k, m, "r*", label="True parameters")
plt.legend()
plt.ylabel("m")
plt.xlabel("k")
plt.title("Loss surface")
plt.show()
Finally, we can also store the current values of $k, m$ at different points during training and plot the parameter trajectory, starting at the initial point $(k_0 = 0, m_0 = 0)$ and ending at our final estimate $(k = 3.03, m = 4.86)$:
model = LinearRegressionModel()
model = model.cuda()
model.train() # (set in training mode, this affects BatchNorm and dropout)
optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)
epoch_losses_train = []
k_values = []
m_values = []
k_values.append(model.k.data.cpu().numpy())
m_values.append(model.m.data.cpu().numpy())
for epoch in range(num_epochs):
print ("###########################")
print ("epoch: %d/%d" % (epoch+1, num_epochs))
batch_losses = []
for step, (x, y) in enumerate(train_loader):
x = Variable(x).cuda() # (shape: (batch_size))
y = Variable(y).cuda() # (shape: (batch_size))
y_hat = model(x) # (shape: (batch_size))
loss = torch.mean(torch.pow(y - y_hat, 2))
# optimization step:
optimizer.step() # (perform the SGD update of the model parameters)
# store the loss value:
loss_value = loss.data.cpu().numpy()
batch_losses.append(loss_value)
epoch_loss = np.mean(batch_losses)
epoch_losses_train.append(epoch_loss)
print ("train loss: %g" % epoch_loss)
k_values.append(model.k.data.cpu().numpy())
m_values.append(model.m.data.cpu().numpy())
plt.figure(figsize=(8, 6))
plt.plot(epoch_losses_train, "^k")
plt.plot(epoch_losses_train, "k")
plt.ylabel("Loss")
plt.xlabel("Epoch")
plt.title("Loss per epoch")
plt.show()
print ("k, true value: %g, estimated value: %g" % (k, model.k))
print ("m, true value: %g, estimated value: %g" % (m, model.m))
plt.figure(figsize=(8, 6))
plt.plot(train_dataset.X, train_dataset.Y, "^k", label="Training data examples")
plt.plot([-3, 3], [k*(-3)+m, k*3+m], "r", label="True straight line")
plt.plot([-3, 3], [model.k*(-3)+model.m, model.k*3+model.m], "b",
label="Estimated straight line")
plt.legend()
plt.ylabel("y")
plt.xlabel("x")
plt.show()
num_values=100
k_plot_values = np.linspace(start=(k-7.0), stop=(k+7.0), num=num_values)
m_plot_values = np.linspace(start=(m-7.0), stop=(m+7.0), num=num_values)
# (k_plot_values and m_plot_values both have shape: (num_values, ))
loss_values = np.zeros((num_values, num_values))
for k_i in range(num_values):
for m_i in range(num_values):
Y_hat = k_plot_values[k_i]*train_dataset.X + m_plot_values[m_i]
# (Y_hat has shape: (N, ))
loss = np.mean((train_dataset.Y - Y_hat)**2)
loss_values[m_i, k_i] = loss
plt.figure(figsize=(8, 6))
K, M = np.meshgrid(k_plot_values, m_plot_values)
plt.contour(K, M, loss_values, levels=20)
plt.plot(k, m, "r*", label="True parameters")
plt.plot(k_values, m_values, "xb", label="Estimated parameters")
plt.plot(k_values, m_values, "b")
plt.legend()
plt.ylabel("m")
plt.xlabel("k")
plt.title("Parameter trajectory")
plt.show()
plt.figure(figsize=(8, 6))
K, M = np.meshgrid(k_plot_values, m_plot_values)
plt.contour(K, M, loss_values, levels=20)
plt.plot(k, m, "r*", label="True parameters")
plt.plot(k_values, m_values, "xb", label="Estimated parameters")
plt.plot(k_values, m_values, "b")
plt.legend()
plt.ylabel("m")
plt.xlabel("k")
plt.xlim([k-3.0, k+3.0])
plt.ylim([m-3.0, m+3.0])
plt.title("Parameter trajectory - Zoomed")
plt.show()
Feel free to contact me or post a comment below if you have any questions or comments. In the next blog post, we’ll do nonlinear curve-fitting using feed-forward neural networks.
|
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|
http://mathhelpforum.com/algebra/31864-factoring-again.html
|
# Math Help - Factoring again
1. ## Factoring again
Factor:
$27x^2+64$
I am completely lost...
2. $
27x^2+64
$
this is a binomial expression- an expression with two terms, the variable, x is only present in the first term and thus you cannot factor it. We are only left with the constants 27 and 64. These numbers do not have a common favtor hence we cannot factor again. Thus the expression canot be factored
3. Originally Posted by mt_lapin
Factor:
$27x^2+64$
I am completely lost...
I'll assume you're required to factorise over the complex number field. Otherwise, as has been previously correctly noted, it can't be done and the question is pointless.
Recall: $A^2 + B^2 = (A + iB)(A - iB)$.
In your case, $A = \sqrt{27} \, x = 3 \sqrt{3} \, x$ and B = 8 ....
4. Oh dear. I meant $27^3+64$. Does that make it solvable now? Really sorry :/
5. Originally Posted by mt_lapin
Oh dear. I meant $27^3+64$. Does that make it solvable now? Really sorry :/
$= (27)^3 + (4)^3$.
Factorise using the sum of two cubes formula.
6. I keep missing things. It's supposed to be $27x^3+64$
I promise this is correct.
7. Would I then need $(3x)^3+4^3$ and to factorise using the sum of two cubes formula?
8. The answer would be: $(3x+4)(9x^2-12x+16)$
Is this correct?
9. Originally Posted by mt_lapin
The answer would be: $(3x+4)(9x^2-12x+16)$
Is this correct?
Yes.
|
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http://math.stackexchange.com/users/1752/olumide?tab=activity
|
Olumide
Reputation
479
Top tag
Next privilege 500 Rep.
Access review queues
Sep 10 asked Coordinates of an n-sphere May 12 awarded Favorite Question Apr 12 awarded Popular Question Jan 20 awarded Good Question Dec 20 awarded Caucus Nov 13 awarded Popular Question Sep 24 awarded Autobiographer Jul 13 awarded Notable Question Jul 2 awarded Curious Feb 2 comment Polynomial Simplification Where do those differentials come from? And is there a way to get maxima to take these steps by itself? Feb 2 comment I'm a teenager hoping to become a mathematician, but math isn't my forte. Is it possible? Ditto @Thomas. I too was terribe at maths in secondary school but in 2 short years, at my mother's insistence that I take additional mathematics classes, maths went from my worst to my best subject. The only one I scored the hightest possible grade in. I now have a PhD in computer science and I still love mathematics and frankly regret that I studied engineering and not maths for my BSc. Feb 2 comment Polynomial Simplification I can see several $w_1w_2$ terms that can be factored out in the inner expression. Feb 2 comment Polynomial Simplification Here you go pastebin.com/bsizpcR3 Feb 2 revised Polynomial Simplification added 42 characters in body Feb 2 asked Polynomial Simplification Jan 30 revised Gradient of a rational Bezier curve edited body Jan 30 revised Gradient of a rational Bezier curve added 35 characters in body Jan 30 revised Gradient of a rational Bezier curve added 380 characters in body Jan 30 revised Gradient of a rational Bezier curve added 93 characters in body Jan 30 asked Gradient of a rational Bezier curve
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https://la.mathworks.com/help/ident/ref/iddata.greyest.html;jsessionid=c10fa192f5c1577a5fd1d40a007d
|
# greyest
Linear grey-box model estimation
## Syntax
```sys = greyest(data,init_sys) sys = greyest(data,init_sys,opt) [sys,x0] = greyest(___) ```
## Description
`sys = greyest(data,init_sys)` estimates a linear grey-box model, `sys`, using time or frequency domain data, `data`. The dimensions of the inputs and outputs of `data` and `init_sys`, an `idgrey` model, must match. `sys` is an identified `idgrey` model that has the same structure as `init_sys`.
`sys = greyest(data,init_sys,opt)` estimates a linear grey-box model using the option set, `opt`, to configure the estimation options.
`[sys,x0] = greyest(___)` returns the value of the initial states computed during estimation. You can use this syntax with any of the previous input-argument combinations.
## Input Arguments
`data` Estimation data. The dimensions of the inputs and outputs of `data` and `init_sys` must match. For time-domain estimation, `data` is an `iddata` object containing the input and output signal values. For frequency domain estimation, `data` can be one of the following: Recorded frequency response data (`frd` (Control System Toolbox) or `idfrd`)`iddata` object with its `Domain` property set to `'Frequency'` `init_sys` Identified linear grey-box model that configures the initial parameterization of `sys`. `init_sys`, an `idgrey` model, must have the same input and output dimensions as `data`. `opt` Estimation options. `opt` is an option set, created using `greyestOptions`, which specifies options including: Estimation objectiveInitialization choiceDisturbance model handlingNumerical search method to be used in estimation
## Output Arguments
`sys`
Estimated grey-box model, returned as an `idgrey` model. This model is created using the specified initial system, and estimation options.
Information about the estimation results and options used is stored in the `Report` property of the model. ``` Report``` has the following fields:
Report FieldDescription
`Status`
Summary of the model status, which indicates whether the model was created by construction or obtained by estimation.
`Method`
Estimation command used.
`InitialState`
Handling of initial states during estimation, returned as one of the following:
• `'model'` — The initial state is parameterized by the ODE file used by the `idgrey` model.
• `'zero'` — The initial state is set to zero.
• `'estimate'` — The initial state is treated as an independent estimation parameter.
• `'backcast'` — The initial state is estimated using the best least squares fit.
• Vector of doubles of length Nx, where Nx is the number of states. For multiexperiment data, a matrix with Ne columns, where Ne is the number of experiments.
This field is especially useful to view how the initial states were handled when the `InitialState` option in the estimation option set is `'auto'`.
`DisturbanceModel`
Handling of the disturbance component (K) during estimation, returned as one of the following values:
• `'model'`K values are parameterized by the ODE file used by the `idgrey` model.
• `'fixed'` — The value of the `K` property of the `idgrey` model is fixed to its original value.
• `'none'`K is fixed to zero.
• `'estimate'`K is treated as an independent estimation parameter.
This field is especially useful to view the how the disturbance component was handled when the `DisturbanceModel` option in the estimation option set is `'auto'`.
`Fit`
Quantitative assessment of the estimation, returned as a structure. See Loss Function and Model Quality Metrics for more information on these quality metrics. The structure has the following fields:
FieldDescription
`FitPercent`
Normalized root mean squared error (NRMSE) measure of how well the response of the model fits the estimation data, expressed as the percentage `fit` = 100(1-NRMSE).
`LossFcn`
Value of the loss function when the estimation completes.
`MSE`
Mean squared error (MSE) measure of how well the response of the model fits the estimation data.
`FPE`
Final prediction error for the model.
`AIC`
Raw Akaike Information Criteria (AIC) measure of model quality.
`AICc`
Small sample-size corrected AIC.
`nAIC`
Normalized AIC.
`BIC`
Bayesian Information Criteria (BIC).
`Parameters`
Estimated values of model parameters.
`OptionsUsed`
Option set used for estimation. If no custom options were configured, this is a set of default options. See `greyestOptions` for more information.
`RandState`
State of the random number stream at the start of estimation. Empty, `[]`, if randomization was not used during estimation. For more information, see `rng`.
`DataUsed`
Attributes of the data used for estimation, returned as a structure with the following fields:
FieldDescription
`Name`
Name of the data set.
`Type`
Data type.
`Length`
Number of data samples.
`Ts`
Sample time.
`InterSample`
Input intersample behavior, returned as one of the following values:
• `'zoh'` — Zero-order hold maintains a piecewise-constant input signal between samples.
• `'foh'` — First-order hold maintains a piecewise-linear input signal between samples.
• `'bl'` — Band-limited behavior specifies that the continuous-time input signal has zero power above the Nyquist frequency.
`InputOffset`
Offset removed from time-domain input data during estimation. For nonlinear models, it is `[]`.
`OutputOffset`
Offset removed from time-domain output data during estimation. For nonlinear models, it is `[]`.
`Termination`
Termination conditions for the iterative search used for prediction error minimization, returned as a structure with the following fields:
FieldDescription
`WhyStop`
Reason for terminating the numerical search.
`Iterations`
Number of search iterations performed by the estimation algorithm.
`FirstOrderOptimality`
$\infty$-norm of the gradient search vector when the search algorithm terminates.
`FcnCount`
Number of times the objective function was called.
`UpdateNorm`
Norm of the gradient search vector in the last iteration. Omitted when the search method is `'lsqnonlin'` or `'fmincon'`.
`LastImprovement`
Criterion improvement in the last iteration, expressed as a percentage. Omitted when the search method is `'lsqnonlin'` or `'fmincon'`.
`Algorithm`
Algorithm used by `'lsqnonlin'` or `'fmincon'` search method. Omitted when other search methods are used.
For estimation methods that do not require numerical search optimization, the `Termination` field is omitted.
For more information on using `Report`, see Estimation Report.
`x0`
Initial states computed during the estimation, returned as a matrix containing a column vector corresponding to each experiment.
This array is also stored in the `Parameters` field of the model `Report` property.
## Examples
collapse all
Estimate the parameters of a DC motor using the linear grey-box framework.
Load the measured data.
```load(fullfile(matlabroot, 'toolbox', 'ident', 'iddemos', 'data', 'dcmotordata')); data = iddata(y, u, 0.1, 'Name', 'DC-motor'); data.InputName = 'Voltage'; data.InputUnit = 'V'; data.OutputName = {'Angular position', 'Angular velocity'}; data.OutputUnit = {'rad', 'rad/s'}; data.Tstart = 0; data.TimeUnit = 's';```
`data` is an `iddata` object containing the measured data for the outputs, the angular position, the angular velocity. It also contains the input, the driving voltage.
Create a grey-box model representing the system dynamics.
For the DC motor, choose the angular position (rad) and the angular velocity (rad/s) as the outputs and the driving voltage (V) as the input. Set up a linear state-space structure of the following form:
`$\underset{}{\overset{˙}{x}}\left(t\right)=\left[\begin{array}{cc}0& 1\\ 0& -\frac{1}{\tau }\end{array}\right]x\left(t\right)+\left[\begin{array}{c}0\\ \frac{G}{\tau }\end{array}\right]u\left(t\right)$`
`$y\left(t\right)=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]x\left(t\right).$`
$\tau$ is the time constant of the motor in seconds, and $G$ is the static gain from the input to the angular velocity in rad/(V*s) .
```G = 0.25; tau = 1; init_sys = idgrey('motorDynamics',tau,'cd',G,0);```
The governing equations in state-space form are represented in the MATLAB® file `motorDynamics.m`. To view the contents of this file, enter `edit motorDynamics.m` at the MATLAB command prompt.
$G$ is a known quantity that is provided to `motorDynamics.m` as an optional argument.
$\tau$ is a free estimation parameter.
`init_sys` is an `idgrey` model associated with `motor.m`.
Estimate $\tau$.
`sys = greyest(data,init_sys);`
`sys` is an `idgrey` model containing the estimated value of $\tau$.
To obtain the estimated parameter values associated with `sys`, use `getpvec(sys)`.
Analyze the result.
```opt = compareOptions('InitialCondition','zero'); compare(data,sys,Inf,opt)```
`sys` provides a 98.35% fit for the angular position and an 84.42% fit for the angular velocity.
Estimate the parameters of a DC motor by incorporating prior information about the parameters when using regularization constants.
The model is parameterized by static gain `G` and time constant $\tau$. From prior knowledge, it is known that `G` is about 4 and $\tau$ is about 1. Also, you have more confidence in the value of $\tau$ than `G` and would like to guide the estimation to remain close to the initial guess.
`load regularizationExampleData.mat motorData`
The data contains measurements of motor's angular position and velocity at given input voltages.
Create an `idgrey` model for DC motor dynamics. Use the function `DCMotorODE` that represents the structure of the grey-box model.
```mi = idgrey(@DCMotorODE,{'G', 4; 'Tau', 1},'cd',{}, 0); mi = setpar(mi, 'label', 'default');```
If you want to view the `DCMotorODE` function, type:
`type DCMotorODE.m`
```function [A,B,C,D] = DCMotorODE(G,Tau,Ts) %DCMOTORODE ODE file representing the dynamics of a DC motor parameterized %by gain G and time constant Tau. % % [A,B,C,D,K,X0] = DCMOTORODE(G,Tau,Ts) returns the state space matrices % of the DC-motor with time-constant Tau and static gain G. The sample % time is Ts. % % This file returns continuous-time representation if input argument Ts % is zero. If Ts>0, a discrete-time representation is returned. % % See also IDGREY, GREYEST. % Copyright 2013 The MathWorks, Inc. A = [0 1;0 -1/Tau]; B = [0; G/Tau]; C = eye(2); D = [0;0]; if Ts>0 % Sample the model with sample time Ts s = expm([[A B]*Ts; zeros(1,3)]); A = s(1:2,1:2); B = s(1:2,3); end ```
Specify regularization options Lambda.
```opt = greyestOptions; opt.Regularization.Lambda = 100;```
Specify regularization options R.
`opt.Regularization.R = [1, 1000];`
You specify more weighting on the second parameter because you have more confidence in the value of $\tau$ than `G`.
Specify the initial values of the parameters as regularization option $\theta$*.
`opt.Regularization.Nominal = 'model';`
Estimate the regularized grey-box model.
`sys = greyest(motorData, mi, opt);`
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https://homework.cpm.org/category/CCI_CT/textbook/int3/chapter/11/lesson/11.2.2/problem/11-68
|
### Home > INT3 > Chapter 11 > Lesson 11.2.2 > Problem11-68
11-68.
For each of the following equations, list every point where its three-dimensional graph intersects one of the coordinate axes. That is, what are the $x$, $y$, and $z$‑intercepts? Express your answers in $\left(x, y, z\right)$ form.
1. $6y+15z=60$
To find the intercept of a given axis, set all other variables to zero.
For example, the $y$-intercept will be $\left(0, ?, 0\right)$.
To find the $y$-intercept, let $x = 0$ and $z = 0$
Repeat the process to find the $z$-intercept. $\left(0, 0, ?\right)$.
$\left(0, 10, 0\right)$ and $\left(0, 0, 4\right)$
1. $3x+4y+2z=24$
See part (a):
1. $(x+3)^2+z^2=25$
See part (a).
Note: You will have two $x$-intercepts and two $z$-intercepts. Why?
1. $z=6$
See part (a):
Use the eTool below to test your solutions to parts (a), (b) and (c) above.
Click on the link at right for the full eTool version: INT3 11-68 HW eTool
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http://www.theincredibletruths.com/2018/08/duality-of-light.html
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# DUAL-NATURE OF LIGHT
From the very beginning we know that light is a wave. A wave travels through a medium. But it was found that light can travel even through vacuum or empty space. Before Einstein, scientists thought that “ether” is a thing which is present everywhere in this universe, even in the empty space or vacuum. That’s why light can travel through vacuum. But Einstein said that the whole concept about ether is meaningless. Rather he proposed that light has a dual-nature.
More specifically we can say that light behaves in two different ways depending upon situations. Like in medium light behaves like wave and in vacuum light behaves like particle. This is called the dual nature of light.
## WAVE NATURE
The wave nature of light says how light can bent. In 17th century, Isaac Newton believed light is composed of a stream of corpuscles. Then a Dutch physicist and astronomer Christiaan Huygens thought that light is a wave vibrating in some sort of ether.
Some experiments like diffraction, interference, refraction etc. proves that light has a wave property.
Wavelength is the parameter which can differentiate between waves. In case of refraction we can differentiate mediums by their refractive Indexes. The Refractive Index of every medium is different. It is defined as
n = c/v
Where, n= Refractive index of the medium
c= speed of light in vacuum
v= speed of the light in the medium
List of Refractive Index of some mediums –
MEDIUM n Vacuum 1 Air 1.00029 Water 1.33 Diamond 2.417 Amber 1.55 Ice 1.31 glass 1.52 Human lens 1.386-1.406 Germanium 4.05-4.01
## PARTICLE NATURE
The fundamental particle of light is photon. We can define light as a packet of photons. Photon is a mass less particle but it has energy. It was first found by Albert Einstein in his Photoelectric effect experiment. In this experiment a high energy photon strikes a metal surface and an electron is ejected from the metal and the photon disappears. When the frequency of the light increases, the speed of the electron being ejected, increases. This experiment shows the particle nature of light.
The energy (E) of photon is defined as –
E = hf
Where, h = Plank’s constant
f = frequency of the light
Quantum Theory: In Quantum theory light is taken as a particle. It means we study the particle nature of light in quantum physics. Light is an energy packet or packet of photon. Particle nature of light explains how light travels in straight lines or reflects.
ETHER : http://www.theincredibletruths.com/search/label/ether
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https://eleanorrigby-movie.com/how-create-pdf-in-php-explain-with-example/
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# How create PDF in PHP explain with example?
## How create PDF in PHP explain with example?
php require(‘./fpdf. php’); $pdf=new FPDF();$pdf->AddPage(); $pdf->SetFont(‘Arial’,’B’,16);$pdf->Cell(40,10,’Hello World! ‘); \$pdf->Output();?> Upon execution, the PHP script will generate a PDF file in your browser.
How do I create a PDF from a web application?
To convert a webpage to PDF, do the following:
1. Go to the web page. For Windows, use Internet Explorer, Firefox, or Chrome. For Mac, use Firefox.
2. Using the Convert menu on the Adobe PDF toolbar, do one of the following: To create a PDF from the currently open web page, choose Convert Web Page To PDF.
How do I create an HTML page from a PDF?
The steps are:
1. Include the jsPDF CDN in the tag in HTML document. The CDN is given below, search ‘JsPDF CDN’ at google for the latest version.
2. Generate a pdf from the HTML div using ‘fromHTML’ method.
3. Save the file using the save() method in javascript.
### How do I save a PHP file as a PDF?
PHP to PDF
2. There go to File -> Print or just press. Ctrl. + P.
3. Choose “Microsoft XPS Document Writer” as your printer.
4. Click on “OK” or “Print”.
5. Select a destination for your XPS file and click on “Save”.
How do I create a PDF code?
Let’s get started with these steps.
1. Step 1: Installation.
2. Step 2: Set up your project.
3. Step 3: Create a new PDF document.
4. Step 4: Add titles for the PDF document.
5. Step 5: Add a paragraph.
6. Step 6: Add widow and orphan control.
7. Step 7: Render the text and images.
8. Step 8: Save to PDF.
What is PHP programming language PDF?
The PHP Hypertext Preprocessor (PHP) is a programming language that allows web developers to create dynamic content that interacts with databases. PHP is basically used for developing web-based software applications.
## How do I open PHP files in PDF?
Can I convert a PHP file?
You can’t convert PHP files to non-text-based formats like MP4 or JPG. If you have a file with the . PHP file extension that you know should have been downloaded in a format like one of those, just rename it from . PHP to .
What is a PDF API?
PDF Generator API allows you easily generate PDF documents from pre-defined PDF templates with JSON data. Enable your users to create PDFs and manage their document templates using a browser-based drag-and-drop PDF editor to reduce development and support costs.
### What is a PDF generator?
PDF Generator API enables you to create personalized PDFs from the software you’re already using. You can create a range of templates, which can automatically merge with data from your software, using an API to create unique PDF documents instantly.
What is the web PDF?
webPDF is a server-side, Java-based software solution that converts the most extensive range of documents to PDF, enables the editing of scanned and faxed documents, lets you affix signatures and time stamps to PDF files, and supports compliant long-term email archiving.
How do I save a long web page as a PDF?
The simplest of those methods is to press the Print Screen key (or Alt+Print Screen) in Windows, or either Command+Shift+3 or Command+Shift+4 on a Mac. Another is to use the Chrome browser’s Print > PDF > Save as PDF option.
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http://mathhelpforum.com/calculus/24296-integral-trig.html
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1. ## integral (trig)
Find the integral of:
csc(x) * dx
2. csc(x) = cos(x) / (cos(x)^2)
u = sin(x)
du = cos(x)dx
now using the trigonometric identity sin^2(x) + cos^2(x) = 1
we arrive at the following equivalent integral
du/(1-u^2)
which can be written as:
0.5*[1/(1-u) + 1/(1+u)]du
integrating we get:
0.5*[ln(1+u) - ln(1-u)] = 0.5*ln[(1+u)/(1-u)]
3. Originally Posted by Peritus
csc(x) = cos(x) / (cos(x)^2)
I'd re-think that.
--
About the integral, multiply it by $\csc x-\cot x.$
4. Originally Posted by DINOCALC09
Find the integral of:
csc(x) * dx
My first method is a bit long, but I propose double substitution of:
$u=sin(x)$, so $csc(x) = \frac{1}{u}$
You will then have $du=cos(x)dx$
To solve for cosine in terms of u, use the sine, cosine relationship:
$cos^2(x)+sin^2(x)=1$
$cos^2(x)=1-u^2$
$cos(x)=\sqrt{1-u^2}$
You will then have an integrand of $\frac{1}{u\sqrt{1-u^2}}$
To simplify that, you need to make the substitution: $v=1-u^2$
$dv=-2udu$
$u=\sqrt{v-1}$
The resulting integrand becomes:
$\frac{-2}{\sqrt{v}} = -2v^{-1/2}$
Integrating that, you get: $-4v^{1/2}$
Substitution of $v=1-u^2$ leads to...
$-4{(1-u^2)}^{1/2}$
Substitution of $u=sin(x)$ leads to...
$-4{(1-sin^2(x))}^{1/2} = -4\sqrt{cos(x)}$
Hmmm, doesn't look like the answer I should get?
5. sorry my mistake, but the solution changes only slightly
csc(x) = sin(x) / (sin(x)^2)
u = cos(x)
du = -sin(x)dx
now using the trigonometric identity sin^2(x) + cos^2(x) = 1
we arrive at the following equivalent integral
-du/(1-u^2)
which can be written as:
-0.5*[1/(1-u) + 1/(1+u)]du
integrating we get:
-0.5*[ln(1+u) - ln(1-u)] = 0.5*ln[(1-u)/(1+u)] + const =
0.5*ln[(1-cos(x))/(1+cos(x))] + const
6. The book has the answer as:
-ln|csc(x)+cot(x)| + c
The only problem is that it doesn't show me how to get there.
7. -ln[csc(x)+cot(x)]=-ln[(1/sin(x) + cos(x)/sin(x)] = ln[sin(x)/(1+cos(x))]
<=> 0.5*ln[sin^2(x) / ((1+cos(x))^2)] =
= 0.5*ln[(1-cos^2(x)) / ((1+cos(x))^2)] =
= 0.5*ln{[(1-cos(x))*(1+cos(x))] / ((1+cos(x))^2)} = 0.5*ln[(1-cos(x))/(1+cos(x))]
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http://www.ck12.org/statistics/Theoretical-and-Experimental-Spinners/lecture/Theoretical-and-Experimental-Spinners-Examples/r1/
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<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Theoretical and Experimental Spinners
## Using APPS on the TI 84 calculator for spinner simulations
%
Progress
Progress
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Theoretical and Experimental Spinners Examples
This video shows how to work step-by-step through one or more of the examples in Theoretical and Experimental Spinners.
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http://math.stackexchange.com/questions/153302/summation-of-frac12-frac34-frac78-frac1516-cdots
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# Summation of $\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + \cdots$ till $n$ terms
What is the pattern in the following?
• Sum to $n$ terms of the series: $$\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + \cdots$$
-
Hint: The $k$th term is $1-\frac1{2^k}$. – Did Jun 3 '12 at 15:39
## 2 Answers
Hint:
Write it as $(1-{1\over2})+(1-{1\over4})+(1-{1\over 8})+\cdots+(1-{1\over 2^n}).$
-
Here is the pattern:
\begin{align*} \frac{1}{2} + \frac{3}{4} + \cdots &= \biggl(1-\frac{1}{2}\biggr) + \biggl(1-\frac{1}{2^2}\biggr) + \cdots \\\ &= (1+1+\cdots + 1) - \biggl(\frac{1}{2}+\frac{1}{2^2} + \cdots +\frac{1}{2^n}\biggr) \end{align*}
-
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https://brilliant.org/problems/polynomial-nt/
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# Polynomial NT
Compute the degree of the least common multiple of the polynomials $$x-1,x^2-1, x^3-1, ..., x^{10}-1.$$ This is not original.
×
Problem Loading...
Note Loading...
Set Loading...
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https://mathematica.stackexchange.com/questions/86058/mathematica-vs-python-how-does-mathematica-compare-to-pythons-scientific-com
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# Mathematica vs. Python - how does Mathematica compare to Python's scientific computing suite?
Python's family of packages for scientific computing has matured rapidly. I can pretty much replicate all of Mathematica's functionalities, but with production level and open-source code using the following:
• Numpy, Scipy, Sklearn for math and algorithmics
• matplotlib for graphics
• ipython notebooks for notebooks and cells
• SWIG or Cython for c-speed enchancements
• PYPY and many other project to cover other functionalities
Mathematica does still have a few advantages though:
• Everything is nicely integrated and documented in one place
• Dynamic's and Manipulates are fun!
• Mathematica's functional language is neat and allows rapid prototyping
However,
• It takes little effort to download and integrate any needed python package
• Notebooks and their contents are not truly deployable (even pdf printing doesn't work)
• Python already has much of the same functional constructs
• Most Mathematica functions (especially anything with graphics, graphs, or images) are not compilable, but about everything in Python is!
As a developer I'd like to ask if there any other significant advantages to Mathematica - are there any areas where Mathematica is still vastly superior to the Python stack other than in computer algebra?
Are there any insightful Mathematica vs Python performance benchmark studies like this one for Mathematica vs. Maple?
• I would hardly call that Maple comparison "insightful"!!! See (60124) – dr.blochwave Jun 16 '15 at 15:21
• @N.J.Evans In my opinion printing pdfs usually always mangles the graphics. – M.R. Jun 16 '15 at 15:50
• @N.J.Evans Mathematica could be so awesome if Wolfram offered more export flexibility. My "exporting wishlist": fully textured 3d graphics, (multi)Markdown!, latex (right now mostly broken for complex Box constructs), Dynamics to html5 widgets (wolfram cloud does not truly support Dynamic[] as everything is computed server-side causing horrible lag). – M.R. Jun 16 '15 at 17:29
• For the record, I do not agree that the question was too broad. "Are there any areas where Mathematica is still vastly superior to the Python stack other than in computer algebra?" seems like quite a narrow question to me, actually. Perhaps it was the title that caused people to vote this way. If anyone else casts a reopen vote, I will add mine. – Oleksandr R. Jun 16 '15 at 23:35
• Maybe this is a stupid question and until now, I had very little contact with python but which package of python lets you do analytical stuff like Integrate[Sqrt[x + Sqrt[x]], x]? – halirutan Jun 17 '15 at 12:25
You're asking for the biggest distinguishing feature of Mathematica - other than computer algebra. To give a really general answer, I would list as my number one choice the availability of curated knowledge, including free-form input. Other languages also have some limited ability to do this, but I think Mathematica has a head start and is moreover benefiting from simultaneous ongoing developments in Wolfram Alpha.
Given the nature of the question, I think it's pointless to start listing all the incarnation of curated knowledge. But as examples, version 10 offers things like DNA sequences, the current position of satellites, financial data with an elaborate array of visualization functions (often more polished than the "hard science" counterparts), "social" network data, etc. Being able to connect all this with the more traditional strengths of Mathematica, which clearly are in computer algebra, is in itself a strength. Of course, this also includes the availability of more traditional data from many fields of mathematics.
So to conclude, Mathematica seems to be ahead in the field of computable data.
## General remarks
Before giving several (biased) answers to the question
As a developer I'd like to ask if there any other significant advantages to Mathematica - are there any areas where Mathematica is still vastly superior to the Python stack other than in computer algebra?
I would like to mention my Python background.
• 17 years ago I programmed in Python a little, now I do not. But many of the people I work with do. I often support them with analysis, interfaces, and algorithms written in R and Mathematica.
• I am fairly biased toward Mathematica. In principle, I like Python for its language design consistency, but I would rather program in R (which has all the characteristics of a design by a committee) than in Python.
## Functional programming (Mathematica is better)
From what I have read about Functional Programming (FP) in Python the OP statement
Python already has much of the same functional constructs
should be interpreted as "Python provides functional programming lite support."
### What Python's author is saying
In this post, “The fate of reduce() in Python 3000” Guido van Rossum discusses his difficulties understanding code that has reduce (Fold) and how he generally finds functional programming redundant within Python.
This, I would say, means that if you decide to use functional programming in Python you are not going to be supported by the language design much. (And probably you are going against Python's design fundamentals.)
### What others are saying
Here is a very relevant quote from a recent interview with Larry Wall (the creator of Perl):
Some Pythonistas claim that Python is a good functional programming language, mostly on the strength of list comprehensions, but in my estimation Python has only half-hearted FP support; it really doesn't provide the benefits of lexical scoping, closures, laziness, or higher-order programming that I'd expect in a strong FP contender, nor does it encourage you to think that way.
And a more general programming statement from the same interview:
If Python's object model matches how you want to do things, it's fine for that. If it's not, Python doesn't really provide a coherent meta-object model underneath, just a lot of hooks, which might or might not give you the flexibility you need.
Here is a somewhat old (2009) discussion on Stack Overflow: "Why isn't Python very good for functional programming?"; but also see this newer (2012) presentation "Functional Programming with Python".
### Pattern matching
From what I read Python does not have pattern matching of function signatures as Mathematica does. Of course Python has method / signature overloading capabilities, but that is not as powerful.
## Numerical computations (Mathematica is better)
### Sparse arrays
Python's scipy has support of sparse matrices, but not higher dimension sparse arrays. (Probably not very important numerics-wise, but really usefull sometimes in programming.)
### Numerical integration
I consider Mathematica's NIntegrate to be much better than the integration algorithms in scipy. The algorithms in scipy do not have proper multi-dimensional integration rules and strategies.
See this related discussion: "Numerical integration — Mathematica vs Python (w/ Scipy) performance".
### Numerical solutions of ODEs and PDEs
From what I see in scipy page ODEs and PDEs solving in Mathematica is much more sophisticated. NDSolve is more powerful, and provides a plug-in framework. The ODE algorithms in scipy seem to be based on old ODE software designs. For example, the methodology of feedback control theory applications to ODEs is a fundamental part of NDSolve's OOP design.
### Special functions
Mathematica has extensive coverage of special functions. I really doubt that Python has such an extensive coverage too. Again, I have only looked at scipy. (An impressive list, by the way.)
## Numerics with little symbolics
Often enough some algorithms are really hard without symbolics, and the symbolical part of these algorithms is really small. How easy it is with Python to program
• "I would rather program in R (which has all the characteristics of a design by a committee) than in Python." - ouch. :D – J. M. will be back soon Jul 19 '16 at 16:06
• @J.M. :) I think, this is mostly saying things about me, than Python. After I read the linked interview with Larry Wall, I start to think that I do not like to program in Python for the same reasons I like its design -- Python is too monocultural. – Anton Antonov Jul 19 '16 at 16:10
• @Jens, yes, which is why I think the Mathieu example is prolly more demonstrative. Not knowing how exactly is Mathematica evaluating those functions certainly does not help in working around those weaknesses. – J. M. will be back soon Jul 19 '16 at 16:57
• @AntonAntonov Fair point, but the functions we're discussing are very important examples! Anyway, this is probably not the right place to vent such grievances. Although - where is the right place, I wonder. – Jens Jul 19 '16 at 17:04
• Anton, @Jens' point, if I read him correctly, was that the "large coverage" is certainly a symbolic boon, but it is admittedly a bit spotty in the numerics front. Arbitrary precision sometimes helps, but not always. – J. M. will be back soon Jul 19 '16 at 17:05
Do not underestimate Mathematica's notebook. The fact that your code looks like math (you can make it be in fractions with the exponents up, etc.) can make it much easier to work with. This, and the fact that its FullSimplify and GroebnerBasis algorithms tend to perform pretty well for being such a generic package, make it still a staple in symbolic computing.
• True (+1) but OP wants computer algebra to be excluded from the comparison... – Anton Antonov Dec 1 '16 at 22:59
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https://iris.unibs.it/handle/11379/567206
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The production of J/psi is measured at midrapidity (vertical bar y vertical bar < 0.9) in proton-proton collisions at root s = 5.02 and 13 TeV, through the dielectron decay channel, using the ALICE detector at the Large Hadron Collider. The data sets used for the analyses correspond to integrated luminosities of L-int = 19.4 +/- 0.4 nb(-1 )and L-int = 32.2 +/- 0.5 nb(-1) at root s = 5.02 and 13 TeV, respectively. The fraction of non-prompt J/psi mesons, i.e. those originating from the decay of beauty hadrons, is measured down to a transverse momentum p(T) = 2 GeV/c (1GeV/c) at root s = 5.02 TeV (13 TeV). The p(T) and rapidity (y) differential cross sections, as well as the corresponding values integrated over p(T) and y, are carried out separately for prompt and non-prompt J/psi mesons. The results are compared with measurements from other experiments and theoretical calculations based on quantum chromodynamics (QCD). The shapes of the p(T) and y distributions of beauty quarks predicted by state-of-the-art perturbative QCD models are used to extrapolate an estimate of the b (b) over bar pair cross section at midrapidity and in the total phase space. The total b (b) over bar cross sections are found to be sigma(b (b) over bar) = 541 +/- 45 (stat.) +/- 69 (syst.)(-12)(+10) (extr.) mu b and sigma(b (b) over bar) = 218 +/- 37 (stat.)+/- 31 (syst.)(-9.1)(+8.2) (extr.) mu b at root s = 13 and 5.02 TeV, respectively. The value obtained from the combination of ALICE and LHCb measurements in pp collisions at root s = 13 TeV is also provided.
### Prompt and non-prompt J/?? production cross sections at midrapidity in proton-proton collisions at $$\sqrt{\mathrm{s}}$$ = 5.02 and 13 TeV
#### Abstract
The production of J/psi is measured at midrapidity (vertical bar y vertical bar < 0.9) in proton-proton collisions at root s = 5.02 and 13 TeV, through the dielectron decay channel, using the ALICE detector at the Large Hadron Collider. The data sets used for the analyses correspond to integrated luminosities of L-int = 19.4 +/- 0.4 nb(-1 )and L-int = 32.2 +/- 0.5 nb(-1) at root s = 5.02 and 13 TeV, respectively. The fraction of non-prompt J/psi mesons, i.e. those originating from the decay of beauty hadrons, is measured down to a transverse momentum p(T) = 2 GeV/c (1GeV/c) at root s = 5.02 TeV (13 TeV). The p(T) and rapidity (y) differential cross sections, as well as the corresponding values integrated over p(T) and y, are carried out separately for prompt and non-prompt J/psi mesons. The results are compared with measurements from other experiments and theoretical calculations based on quantum chromodynamics (QCD). The shapes of the p(T) and y distributions of beauty quarks predicted by state-of-the-art perturbative QCD models are used to extrapolate an estimate of the b (b) over bar pair cross section at midrapidity and in the total phase space. The total b (b) over bar cross sections are found to be sigma(b (b) over bar) = 541 +/- 45 (stat.) +/- 69 (syst.)(-12)(+10) (extr.) mu b and sigma(b (b) over bar) = 218 +/- 37 (stat.)+/- 31 (syst.)(-9.1)(+8.2) (extr.) mu b at root s = 13 and 5.02 TeV, respectively. The value obtained from the combination of ALICE and LHCb measurements in pp collisions at root s = 13 TeV is also provided.
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2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/567206
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https://www.physicsforums.com/threads/evaluation-of-a-parabolic-line-integral-with-respect-to-arc-length.298756/
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# Homework Help: Evaluation of a (parabolic) line integral with respect to arc length
1. Mar 10, 2009
### GelatinousFur
1. The problem statement, all variables and given/known data
Evaluate the line integral $$$\int_c yz\,ds.$$$
where C is a parabola with z=y^2 , x=1 for 0<=y<=2
2. Relevant equations
A hint was given by the teacher to substitute p=t^2 , dp=(2t)dt and use integration by parts.
I also know from other line integrals with respect to arc length that:
ds=sqrt((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2)
3. The attempt at a solution
I think that from the information given, the beginning and end points are (1,0,0) to (1,2,4).
My first guess is:
x(t) = t
y(t) = 2t
z(t) = t^2
This will be when t goes from 0 to 2.
So after I have parameterized the curve, I would substitute the functions of t back into the integral to get:
int((2t)^3*sqrt(1^2+2^2+(2t)^2),t,0,2)
=8*int(t^3*sqrt(4t^2+5),t,0,2)
=12032/3
This doesn't look right to me though. Any help would be appreciated!
Last edited: Mar 10, 2009
2. Mar 11, 2009
### tiny-tim
Welcome to PF!
Hi GelatinousFur! Welcome to PF!
No, x is constant
x(t) = 1
(and your y and z don't fit each other)
3. Mar 11, 2009
### GelatinousFur
Re: Welcome to PF!
Ah, I see. Thanks for the help (and the welcome)!
So then...
X(t) is constant, so x(t)=1
y(t) =t
z(t) = t^2
when t goes from 0 to 2.
The line integral would then become:
int(y^3,s) over the curve C, because z=y^2.
=int(t^3*sqrt(0^2+1^2+(2t)^2),t,0,2)
=int(t^3*2t,t,0,2)
=2*int(t^4,t,0,2)
=64/5
This answer feels a bit more correct but I still cannot see why the teacher gave us the hint to use integration by parts, as I didn't have to when I just performed that integral.
4. Mar 11, 2009
### lanedance
Re: Welcome to PF!
Hi
in you integrand you have
$$t^3\sqrt{1+4t^2}$$
I think you simplified away the one from the squareroot
5. Mar 11, 2009
### GelatinousFur
Re: Welcome to PF!
Thanks, you are correct.
The correct integral is:
int(t^3*sqrt(1+4*t^2),t,0,2)
So here's where I use integration by parts, but when I integrate sqrt(1+4*t^2) I have to go to an integral table.
I punched int(t^3*sqrt(1+4*t^2),t,0,2) into MATLAB and it spits this answer out:
-1/64/pi^(1/2)*(-3128/15*pi^(1/2)*17^(1/2)-8/15*pi^(1/2))
Is this the wrong answer? Looks a bit weird to me.
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http://www.nag.com/numeric/MB/manual64_24_1/html/G01/g01gbf.html
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Integer type: int32 int64 nag_int show int32 show int32 show int64 show int64 show nag_int show nag_int
Chapter Contents
Chapter Introduction
NAG Toolbox
# NAG Toolbox: nag_stat_prob_students_t_noncentral (g01gb)
## Purpose
nag_stat_prob_students_t_noncentral (g01gb) returns the lower tail probability for the noncentral Student's t$t$-distribution.
## Syntax
[result, ifail] = g01gb(t, df, delta, 'tol', tol, 'maxit', maxit)
[result, ifail] = nag_stat_prob_students_t_noncentral(t, df, delta, 'tol', tol, 'maxit', maxit)
Note: the interface to this routine has changed since earlier releases of the toolbox:
Mark 23: tol now optional (default 0)
.
## Description
The lower tail probability of the noncentral Student's t$t$-distribution with ν$\nu$ degrees of freedom and noncentrality parameter δ$\delta$, P(Tt : ν;δ)$P\left(T\le t:\nu \text{;}\delta \right)$, is defined by
P(Tt : ν;δ) = Cν
( αu − δ ) 1/(sqrt(2π)) ∫ e − x2 / 2dx − ∞
uν1eu2 / 2du, ν > 0.0
0
$P(T≤t:ν;δ)=Cν∫0∞ (12π∫-∞ αu-δe-x2/2dx) uν-1e-u2/2du, ν>0.0$
with
Cν = 1/(Γ ((1/2)ν)2(ν − 2) / 2), α = t/(sqrt(ν)). $Cν=1Γ (12ν )2(ν- 2)/2 , α=tν.$
The probability is computed in one of two ways.
(i) When t = 0.0$t=0.0$, the relationship to the normal is used:
∞ P(T ≤ t : ν;δ) = 1/(sqrt(2π)) ∫ e − u2 / 2du. δ
$P(T≤t:ν;δ)=12π∫δ∞e-u2/2du.$
(ii) Otherwise the series expansion described in Equation 9 of Amos (1964) is used. This involves the sums of confluent hypergeometric functions, the terms of which are computed using recurrence relationships.
## References
Amos D E (1964) Representations of the central and non-central t$t$-distributions Biometrika 51 451–458
## Parameters
### Compulsory Input Parameters
1: t – double scalar
t$t$, the deviate from the Student's t$t$-distribution with ν$\nu$ degrees of freedom.
2: df – double scalar
ν$\nu$, the degrees of freedom of the Student's t$t$-distribution.
Constraint: df1.0${\mathbf{df}}\ge 1.0$.
3: delta – double scalar
δ$\delta$, the noncentrality parameter of the Students t$t$-distribution.
### Optional Input Parameters
1: tol – double scalar
The absolute accuracy required by you in the results. If nag_stat_prob_students_t_noncentral (g01gb) is entered with tol greater than or equal to 1.0$1.0$ or less than 10 × machine precision (see nag_machine_precision (x02aj)), then the value of 10 × machine precision is used instead.
Default: 0.0$0.0$
2: maxit – int64int32nag_int scalar
The maximum number of terms that are used in each of the summations.
Default: 100$100$. See Section [Further Comments] for further comments.
Constraint: maxit1${\mathbf{maxit}}\ge 1$.
None.
### Output Parameters
1: result – double scalar
The result of the function.
2: ifail – int64int32nag_int scalar
${\mathrm{ifail}}={\mathbf{0}}$ unless the function detects an error (see [Error Indicators and Warnings]).
## Error Indicators and Warnings
Errors or warnings detected by the function:
If on exit ${\mathbf{ifail}}\ne {\mathbf{0}}$, then nag_stat_prob_students_t_noncentral (g01gb) returns 0.0$0.0$.
ifail = 1${\mathbf{ifail}}=1$
On entry, df < 1.0${\mathbf{df}}<1.0$.
ifail = 2${\mathbf{ifail}}=2$
On entry, maxit < 1${\mathbf{maxit}}<1$.
ifail = 3${\mathbf{ifail}}=3$
One of the series has failed to converge. Reconsider the requested tolerance and/or maximum number of iterations.
ifail = 4${\mathbf{ifail}}=4$
The probability is too small to calculate accurately.
## Accuracy
The series described in Amos (1964) are summed until an estimated upper bound on the contribution of future terms to the probability is less than tol. There may also be some loss of accuracy due to calculation of gamma functions.
The rate of convergence of the series depends, in part, on the quantity t2 / (t2 + ν)${t}^{2}/\left({t}^{2}+\nu \right)$. The smaller this quantity the faster the convergence. Thus for large t$t$ and small ν$\nu$ the convergence may be slow. If ν$\nu$ is an integer then one of the series to be summed is of finite length.
If two tail probabilities are required then the relationship of the t$t$-distribution to the F$F$-distribution can be used:
F = T2,λ = δ2,ν1 = 1 and ν2 = ν, $F=T2,λ=δ2,ν1=1 and ν2=ν,$
and a call made to nag_stat_prob_f_noncentral (g01gd).
Note that nag_stat_prob_students_t_noncentral (g01gb) only allows degrees of freedom greater than or equal to 1$1$ although values between 0$0$ and 1$1$ are theoretically possible.
## Example
```function nag_stat_prob_students_t_noncentral_example
t = -1.528;
df = 20;
delta = 2;
[result, ifail] = nag_stat_prob_students_t_noncentral(t, df, delta)
```
```
result =
3.1800e-04
ifail =
0
```
```function g01gb_example
t = -1.528;
df = 20;
delta = 2;
[result, ifail] = g01gb(t, df, delta)
```
```
result =
3.1800e-04
ifail =
0
```
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http://www.fields.utoronto.ca/programs/scientific/07-08/liegroups/abstracts.html
|
# SCIENTIFIC PROGRAMS AND ACTIVITIES
September 2, 2014
## CRM-Fields-MITACS Workshop on Lie Groups, Group Transforms and Image Processing
### Abstracts
Jirí Hrivnák, University of Montreal
(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
We consider recently introduced symmetric or antisymmetric exponential and trigonometric functions. These are defined as determinants or antideterminants of matrices whose elements are corresponding functions of one variable. To each of these multivariate functions correspond expansion into Fourier series, integral Fourier transform and finite Fourier transform. We give explicit formulas of these functions, expansions and Fourier transforms in dimension two. We also present some examples and discuss possible applications of these functions and transforms.
Frederic Lesage, École Polytechnique de Montréal
Compressed sensing in photo-acoustic tomography, a potential application for Lie Algebra bases.
Recent work in photo-acoustic tomography indicates that this modality might bring high resolution imaging at low cost. The technique however is hampered by long acquisition times. In this work we describe new image acquisition techniques based on the theory of compressed sensing are able to partly solve this problem. Here the choice of basis is crucial in having the compressed sensing work properly and Lie Algebra bases could provide an avenue to extend to new applications.
Maryna Nesterenko, Université de Montréal
Computing with almost periodic functions
Computational Fourier analysis of functions defined on quasicrystals is developed. A key point is to build the analysis around the emergent
theory of quasicrystals and diffraction based on local hulls and dynamical systems. Numerically computed approximations arising in this way are built out of the precise Fourier module of the quasicrystal in question, and approximate their target functions uniformly on the entire infinite space. This is in striking contrast with numerical approximations based on periodization of some finite part of the crystal. The methods are practical and computable. Examples of functions based on the standard Fibonacci quasicrystal serve to illustrate the method.
Jiri Petera, University of Montreal
Morning short course
Discrete and continuous multidimensional transforms based on $C$-, $S$-, and $E$-functions of a compact semisinple Lie group
References:
J. Patera, {\it Compact simple Lie groups and theirs $C$-, $S$-, and
$E$-transforms,\/} SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) {\bf 1} (2005) 025, 6 pages, math-ph/0512029.
R.V. Moody, J.~Patera, {\it Orthogonality within the families of \ $C$-,
$S$-, and $E$-functions of any compact semisimple Lie group,\/} SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) {\bf 2} (2006) 076, 14 pages, math-ph/0611020.
A. Klimyk, J. Patera, {\it Orbit functions,\/} SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) {\bf 2} (2006), 006, 60 pages, math-ph/0601037
A. Klimyk, J. Patera, {\it Antisymmetric orbit functions,\/} SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) {\bf 3} (2007), paper 023, 83 pages; math-ph/0702040v1
A. Klimyk, J. Patera, {\it $E$-orbit functions,\/} SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) {\bf 4} (2008), 002, 57 pages; arXiv:0801.0822
Matthieu Voorons, Université de Montréal
Interpolation based on Lie group theory and comparison with standard techniques
New interpolation algorithms, based on the Lie group theory, were recently developed by Mr Patera and his team. The Continuous Extension of the Discrete Orbit Function Transform (CEDOFT) based on the C-functions of the Lie groups leading to square lattices were considered as interpolators. More precisely, Lie groups SU(2)xSU(2) and O(5) were used to interpolate 2-dimensional data, and the cubic lattice SU(2)xSU(2)xSU(2) for 3-dimensional data. All algorithms presented for 2 and 3-dimensional data have the advantage to give the exact value of the original data at the points of the grid lattice, and interpolate well the data values between the grid points. The quality and speed of the interpolation are comparable with the most efficient classical interpolation techniques. Interpolation results for many application are presented, from simple zooming and filtering of still images to video interpolation and refinement of volume estimation in medical imagery.
Yusong Yan and Hongmei Zhu, York University
Integer Lie group transforms
The C- or S-functions derived from the Lie Group C2 form an orthogonal basis in its corresponding fundamental region F. Discretizing such a basis results in a class of discrete orthogonal transforms. Using the lifting schemes, we develop the integer-to-integer transforms associated to these discrete orthogonal transforms on a discrete grid FM of F of density defined by a positive integer M. Since these integer transforms are invertible, it has potential applications such as lossless image compression and encryption.
Hongmei Zhu, York University
Interpolation using the discrete group transforms
Interpolation methods are often used in many applications for image generation and processing, such as image resampling and zooming.
Here, we introduce a new family of interpolation algorithms based on a compact semisimple Lie groups of rank n, although here we explore mainly the cases n = 2. The performance of the algorithms is compared with the other commonly used interpolation methods.
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