Search is not available for this dataset
query
stringlengths 1
13.4k
| pos
stringlengths 1
61k
| neg
stringlengths 1
63.9k
| query_lang
stringclasses 147
values | __index_level_0__
int64 0
3.11M
|
|---|---|---|---|---|
What instruments do pilots use to find the runway and fly the correct approach, even if they cannot see the ground? | There are a number of aids available to pilots, though not all airports are equipped with them. A visual approach slope indicator (VASI) helps pilots fly the approach for landing. Some airports are equipped with a VHF omnidirectional range (VOR) to help pilots find the direction to the airport. VORs are often accompanied by a distance measuring equipment (DME) to determine the distance to the VOR. VORs are also located off airports, where they serve to provide airways for aircraft to navigate upon. In poor weather, pilots will use an instrument landing system (ILS) to find the runway and fly the correct approach, even if they cannot see the ground. The number of instrument approaches based on the use of the Global Positioning System (GPS) is rapidly increasing and may eventually be the primary means for instrument landings. | For example, one might refer to the A above middle C as a', A4, or 440 Hz. In standard Western equal temperament, the notion of pitch is insensitive to "spelling": the description "G4 double sharp" refers to the same pitch as A4; in other temperaments, these may be distinct pitches. Human perception of musical intervals is approximately logarithmic with respect to fundamental frequency: the perceived interval between the pitches "A220" and "A440" is the same as the perceived interval between the pitches A440 and A880. Motivated by this logarithmic perception, music theorists sometimes represent pitches using a numerical scale based on the logarithm of fundamental frequency. For example, one can adopt the widely used MIDI standard to map fundamental frequency, f, to a real number, p, as follows | eng_Latn | 10,800 |
How to mute notification sounds during a call on Samsung Galaxy 6 Edge? While on a call, if I receive a text message, the notification sound for text message plays during the call. How do I mute the notification sounds for text messages while I'm on a phone call? My device is Samsung Galaxy 6 Edge. | How to disable SMS notification during phone call? I call somebody, or somebody calls me, we are talking. Now, during the call I got SMS and I cannot hear anything because the SMS notification is playing. So how to disable this notification when call is active? Thank you in advance. Samsung Galaxy Ace 2, Android 2.3. Note: I am interested in setting this once and for good. Not something I have to remember to switch off each time I make/get a call. | Why can we distinguish different pitches in a chord but not different hues of light? In music, when two or more pitches are played together at the same time, they form a chord. If each pitch has a corresponding wave frequency (a pure, or fundamental, tone), the pitches played together make a , which is obtained by simple addition. This wave is no longer a pure sinusoidal wave. For example, when you play a low note and a high note on a piano, the resulting sound has a wave that is the mathematical sum of the waves of each note. The same is true for light: when you shine a 500nm wavelength (green light) and a 700nm wavelength (red light) at the same spot on a white surface, the reflection will be a superposition waveform that is the sum of green and red. My question is about our perception of these combinations. When we hear a chord on a piano, we’re able to discern the pitches that comprise that chord. We’re able to “pick out” that there are two (or three, etc) notes in the chord, and some of us who are musically inclined are even able to sing back each note, and even name it. It could be said that we’re able to decompose a Fourier Series of sound. But it seems we cannot do this with light. When you shine green and red light together, the reflection appears to be yellow, a “pure hue” of 600nm, rather than an overlay of red and green. We can’t “pick out” the individual colors that were combined. Why is this? Why can’t we see two hues of light in the same way we’re able to hear two pitches of sound? Is this a characteristic of human psychology? Animal physiology? Or is this due to a fundamental characteristic of electromagnetism? | eng_Latn | 10,801 |
What might be a flavor substitution for someone with an onion allergy? I can't eat onions of any kind, from shallots, green onions, red, white, yellow, or purple. What might I use as a subtitute for flavor? | Substitute for onions and garlic I love the taste of onions and garlic and it seems lots of other people do too. But they upset my stomach so much that I can't really cook with them. What can I use in their place to give my food a similar flavour? | Why can we distinguish different pitches in a chord but not different hues of light? In music, when two or more pitches are played together at the same time, they form a chord. If each pitch has a corresponding wave frequency (a pure, or fundamental, tone), the pitches played together make a , which is obtained by simple addition. This wave is no longer a pure sinusoidal wave. For example, when you play a low note and a high note on a piano, the resulting sound has a wave that is the mathematical sum of the waves of each note. The same is true for light: when you shine a 500nm wavelength (green light) and a 700nm wavelength (red light) at the same spot on a white surface, the reflection will be a superposition waveform that is the sum of green and red. My question is about our perception of these combinations. When we hear a chord on a piano, we’re able to discern the pitches that comprise that chord. We’re able to “pick out” that there are two (or three, etc) notes in the chord, and some of us who are musically inclined are even able to sing back each note, and even name it. It could be said that we’re able to decompose a Fourier Series of sound. But it seems we cannot do this with light. When you shine green and red light together, the reflection appears to be yellow, a “pure hue” of 600nm, rather than an overlay of red and green. We can’t “pick out” the individual colors that were combined. Why is this? Why can’t we see two hues of light in the same way we’re able to hear two pitches of sound? Is this a characteristic of human psychology? Animal physiology? Or is this due to a fundamental characteristic of electromagnetism? | eng_Latn | 10,802 |
How do I calculate my passive Wisdom (Perception) check? My 1st level Wizard has a Wisdom of 13 (modifier +1) and proficiency in Wisdom saving throws, but not proficiency in Perception. Does that mean my passive Wisdom (Perception) score equals 10+1 or 10+1+2 (adding my proficiency bonus). | Does a passive Perception (Wisdom) check add WIS mod + Perception skill? I'm new to D&D. There seems to be a discrepancy between the 5e Starter Set Rulebook and the associated character sheets. The Rulebook says that a passive wisdom (percep) score is "10 + the creature's wisdom modifier, as well as any bonuses." In the example they have a 1st-level character (with a proficiency bonus of +2) Wisdom of 15 (+2) and a proficiency in Perception, he or she has a passive Wisdom (Perception) of 14 (10+2+2). But the Human Fighter Folk hero character has a WIS mod of +1, and a +3 written beside perception, and a passive Wis percep of 13 (not 14?). The Dwarven Cleric has Wis mod of +3 and a +3 written beside perception, and only a 13 passive wisdom. I guess this has to do with proficiency in the skill, but I'm confused. Can someone explain these instances and maybe also when proficiency is used, vs when just the modifier or just the skill without proficiency? | Why can we distinguish different pitches in a chord but not different hues of light? In music, when two or more pitches are played together at the same time, they form a chord. If each pitch has a corresponding wave frequency (a pure, or fundamental, tone), the pitches played together make a , which is obtained by simple addition. This wave is no longer a pure sinusoidal wave. For example, when you play a low note and a high note on a piano, the resulting sound has a wave that is the mathematical sum of the waves of each note. The same is true for light: when you shine a 500nm wavelength (green light) and a 700nm wavelength (red light) at the same spot on a white surface, the reflection will be a superposition waveform that is the sum of green and red. My question is about our perception of these combinations. When we hear a chord on a piano, we’re able to discern the pitches that comprise that chord. We’re able to “pick out” that there are two (or three, etc) notes in the chord, and some of us who are musically inclined are even able to sing back each note, and even name it. It could be said that we’re able to decompose a Fourier Series of sound. But it seems we cannot do this with light. When you shine green and red light together, the reflection appears to be yellow, a “pure hue” of 600nm, rather than an overlay of red and green. We can’t “pick out” the individual colors that were combined. Why is this? Why can’t we see two hues of light in the same way we’re able to hear two pitches of sound? Is this a characteristic of human psychology? Animal physiology? Or is this due to a fundamental characteristic of electromagnetism? | eng_Latn | 10,803 |
Should buttons be illuminated, or darkened, upon hover? To most, this question might feel subjective... but there's really more than just opinion involved here. If you hover your hand over something in real life, most times a subtle shadow will appear above the object. Mimicking that same idea in the form of user-interface / experience could be more intuitive or natural... or not if the user perceives technology as something totally separate from real life. An example of the two: So again, what is more intuitive to the user, a button that is illuminated upon hover, or darkened upon hover? And why? | Should a button become lighter or darker on hover? We're having a discussion in the office about whether a button should become lighter or darker when a user hovers over it. Here are some examples from the field: Apple "Buy Now" button (Second is hover, third is depressed) - Twitter Bootstrap - (Unselected) (Hover) Github homepage - github.com The button on FogBugz homepage goes from yellow to slightly lighter yellow. The buttons on Optimizely and Visual Website Optimizer hardly change. Amazon's "Buy Now" button doesn't do anything when you hover over it (besides change to a pointer cursor). The colored buttons in Google's new interface (see Gmail or Calendar) go slightly darker when you hover over them. Finally here is our button: Should your button become lighter or darker when you hover over it? What else should you consider? Does anyone have data on whether the hover effect matters for conversions? | Why can we distinguish different pitches in a chord but not different hues of light? In music, when two or more pitches are played together at the same time, they form a chord. If each pitch has a corresponding wave frequency (a pure, or fundamental, tone), the pitches played together make a , which is obtained by simple addition. This wave is no longer a pure sinusoidal wave. For example, when you play a low note and a high note on a piano, the resulting sound has a wave that is the mathematical sum of the waves of each note. The same is true for light: when you shine a 500nm wavelength (green light) and a 700nm wavelength (red light) at the same spot on a white surface, the reflection will be a superposition waveform that is the sum of green and red. My question is about our perception of these combinations. When we hear a chord on a piano, we’re able to discern the pitches that comprise that chord. We’re able to “pick out” that there are two (or three, etc) notes in the chord, and some of us who are musically inclined are even able to sing back each note, and even name it. It could be said that we’re able to decompose a Fourier Series of sound. But it seems we cannot do this with light. When you shine green and red light together, the reflection appears to be yellow, a “pure hue” of 600nm, rather than an overlay of red and green. We can’t “pick out” the individual colors that were combined. Why is this? Why can’t we see two hues of light in the same way we’re able to hear two pitches of sound? Is this a characteristic of human psychology? Animal physiology? Or is this due to a fundamental characteristic of electromagnetism? | eng_Latn | 10,804 |
I ran into this situation. I had helped out a player by not placing the robber on them with my knight card. To sweeten the deal, she agreed to give me 1 wood + 1 hay in exchange for 1 wood. Is this legal? The board mentions that trading 1 wood for 2 wood is illegal, but is 1 wood + 1 hay considered legal? | Motivation: I once had one surplus card on my hand, and knew the robbers would come soon. So I gave it to someone for free, to avoid losing more cards when they hit. I was surprised by how badly this was received. Two of the three other players (the hosts of the game) acted upset, like I had tried to cheat. I had to take the card back, get robbed the next turn and 'giving cards away for free' was banned immediately. (Oh, how I hate mid-game additions to the rules. But that's beside the point.) So now the question: Is this really illegal in Settlers of Catan? Is it generally considered underhanded in any way? If so, why? My reasoning was like this: Consider players A and B. A wants to give B a sheep. A trades a sheep and one rock to B, in exchange for wheat. A trades the received wheat for the (formerly his) rock. A and B now both have the same resources they had in the beginning, only the sheep has moved from A to B. | In music, when two or more pitches are played together at the same time, they form a chord. If each pitch has a corresponding wave frequency (a pure, or fundamental, tone), the pitches played together make a , which is obtained by simple addition. This wave is no longer a pure sinusoidal wave. For example, when you play a low note and a high note on a piano, the resulting sound has a wave that is the mathematical sum of the waves of each note. The same is true for light: when you shine a 500nm wavelength (green light) and a 700nm wavelength (red light) at the same spot on a white surface, the reflection will be a superposition waveform that is the sum of green and red. My question is about our perception of these combinations. When we hear a chord on a piano, we’re able to discern the pitches that comprise that chord. We’re able to “pick out” that there are two (or three, etc) notes in the chord, and some of us who are musically inclined are even able to sing back each note, and even name it. It could be said that we’re able to decompose a Fourier Series of sound. But it seems we cannot do this with light. When you shine green and red light together, the reflection appears to be yellow, a “pure hue” of 600nm, rather than an overlay of red and green. We can’t “pick out” the individual colors that were combined. Why is this? Why can’t we see two hues of light in the same way we’re able to hear two pitches of sound? Is this a characteristic of human psychology? Animal physiology? Or is this due to a fundamental characteristic of electromagnetism? | eng_Latn | 10,805 |
and my radio is playing a tune you know... would you be able to tell which tune it is? | No, because the sonic boom would be deafening... | If you constantly listen to led zepplin more than an hour a day you have led poisoning.\n\nLead poisoning is a more serious medical condition that requires treatment and typing classes. The typing classes may be substituted by constantly using spellcheck. | eng_Latn | 10,806 |
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE \nLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL\nPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP | 13 signs of your soulmate\n\n13. When your on the phone with them late at night and they hang up but you miss them already when it was just five minutes ago...\n12. You read their texts over and over again...\n11. You walk really slow when you're with them...\n10. You feel shy whenever you're with them...\n9. When you think about them, your heart beats faster and faster...\n8. You smile when you hear their voice...\n7. When you look at them, you can't see the other people around\nyou... all you see is him/her...\n6. You start listening to slow songs, while thinking of them...\n5. They become all you think about...\n4. You get high just from their scent...\n3. You realize that you're always smiling to yourself when you think\nabout them...\n2. You would do anything for them...\n1. While reading this, there was one person on your mind the whole\ntime..... | Pentagons occur naturally when tying knots due to the same reason that when strings are pulled taut, and a fret is placed in the middle, that the pitch that it plays on either side of the fret is a 'perfect fifth.' The idea is that the knot is exactly half the distance away from its other side within the knot itself. If one wants to see how this happens naturally, all you have to do is draw a five-pointed star, turn the page 180 degrees, and then draw another five-pointed star the others middle. This can be done ad infinitum inward or outward until physics prevents it from occurring. \n\nThe irony is: the perfect fifth is not what makes music music per se, rather it is the diminished fifth, the tri-tone, or so called devil's tone that makes music capable of changing keys from one to the next. Though, the reason that this happens is due to the natural harmonics that occur in the environment, that make the diminished fifth the actual additive center (where the perfect fifth is its multiplicative one) from the root to the octave. Knowing these two sets of mathematics and where they overlap, eerily\ncan define pretty much any physical phenomena from the Relative to the Quantum. (Unfortunately, there are very peculiar rules that establish how the sets occur whose overtones include concepts such as inverses, opposites, paradigm, zero, and the infinite.) And chances are that disarming your knots will probably find us an answer to the Zeta function. Good luck!\n\nOn a side note: it was Pythagoras who (is ironically famous for someone anonymous' theorem) started a cult around the idea of the perfect fifth, which eventually made the pentagram the infamous symbol that it is today. But this was not until after, he was murdered by a band of math conscious rioters who decided his cult was evil because they had been hiding the existence of the irrational numbers, which exist due to the multiplicative tendencies of an additive system of measurement.\n\nThat's all for which I have time. | yue_Hant | 10,807 |
Why does the brain have waves? | What are brain waves and how can I simulate brain waves? | How do speakers produce sound waves? | eng_Latn | 10,808 |
vertex waves definition | The present study investigated the localization of the. vertex waves. Vertex waves are spike-shaped wave-. forms seen in the EEG leads located in the superior. parietal area during late stage 1 and stage 2 sleep. [1,10]. Vertex waves are thought to have numerous. generators [6] and possibly are secondary evoked po-. | In geometry, a vertex (plural vertices) is a special kind of point that describes the corners or intersections of geometric shapes. | eng_Latn | 10,809 |
intermission definition | Intermission definition, a short interval between the acts of a play or parts of a public performance, usually a period of approximately 10 or 15 minutes, allowing the performers and audience a rest. See more. | Neurotransmission (or synaptic transmission) is communication between neurons as accomplished by the movement of chemicals or electrical signals across a synapse. For any interneuron, its function is to receive INPUT information from other neurons through synapses, to process that information, then to send information as OUTPUT to other neurons through synapses. | eng_Latn | 10,810 |
what is responsible for the ability to read? | The temporal lobe is responsible for phonological awareness and decoding/discriminating sounds. The frontal lobe handles speech production, reading fluency, grammatical usage, and comprehension, making it possible to understand simple and complex grammar in our native language. | This couldnât be further from the truth. The ability to sight-read stems from all of the aspects of your musicianship and thus, can be improved on a daily basis with a little attention to detail. When you take an honest look at it, sight-reading is simply your ability to read music.o become a better sight-reader, you must do the complete opposite. You need to be looking at larger pieces of the music and feeling bigger chunks of time. Look at the music on the page as if you were going to read it in cut-time. | eng_Latn | 10,811 |
I just do not understand how myelination speeds up action potentials | Why is saltatory conduction in myelinated axons faster than continuous conduction in unmyelinated axons? | Case assignment rule is always executed in the test class | eng_Latn | 10,812 |
Observable-based parametrizations | Eigenvalues for unstable resonators with slightly misaligned strip mirrors. | Fully nonparametric estimation of scalar diffusion models | eng_Latn | 10,813 |
Stationary and slowly moving localised pulses in a singularly perturbed Brusselator model | Self-Organization in nonequilibrium systems | Completely Stale Transmitter Channel State Information is Still Very Useful | eng_Latn | 10,814 |
We experimentally generate different types of two-dimensional self-trapped photonic lattices in a photorefractive medium and analyze the induced refractive index change using two different methods. One method gives the first experimental Fourier space analysis of both linear and nonlinear self-trapped photonic lattices with periodic phase modulation using partially spatially incoherent multiband excitation of the lattice modes. The other method utilizes the waveguiding properties of the lattice to achieve a real space analysis of the induced refractive index change. The results of both methods are compared. | We review some of our recent results on experimental light-induced periodic structures and their role in controlling light ::: in discrete optics considering advanced features based on phase engineering and multiplexing of optically-induced lattices. ::: While in the past only rather simple geometries like diamond, square, or hexagonal lattices were studied, we focus ::: onto more complex photonic structures. Among them, we will present anisotropic triangular lattices, superlattices and ::: three-dimensional lattices. We also study the propagation and localization of light in these structures - from simple ::: waveforms to complex topological structures carrying phase dislocations. | ABSTRACTUNC-45A is an ubiquitously expressed protein highly conserved throughout evolution. Most of what we currently know about UNC-45A pertains to its role as a regulator of the actomyosin system... | eng_Latn | 10,815 |
M ay 2 00 2 Non-unitary observables in the 2 d critical Ising model | Critical percolation on the torus | Paper 320-2013 Reporting Tips for No Observations | eng_Latn | 10,816 |
On-site demonstration procedure for solid-state fluorescent ballast | LBL-11619 L-37 EEB-L-80-07 L bor tory ORNIA NVIR ENT Presented as an On-Site Demonstration Procedure for Solid-State Fluorescent Ballast, Lawrence Berkeley Laboratory, Berkeley, CA, September 11, 1980 ON-SITE DEMONSTRATION PROCEDURE FOR SOLID-STATE FLUORESCENT BALLAST Rudy Verderber and 01 i ver ~1orse September 1980 TWO-WEEK LOAN COPY . is a Library Circulating Copy k Th IS d for two wee s. which may be borrowe For a personal retention copy, call Tech. Info. Division, Ext 6782. Prepared for the U.S. Department of Energy under Contract W-7405-ENG-48 | We investigated the possible solutions of the higher order nonlinear Schrodinger (HNLS) equation describing femtosecond optical pulses in an optical fiber system. By using the Hirota direct method, we derived a fundamental solitary wave solution for arbitrary parameters and a N-soliton solution under some conditions. The significance of the soliton solution was discussed. | eng_Latn | 10,817 |
Characterizing heralded single photons with an all-fiber source of photon pairs | Abstract Based on the signal and idler photon pairs produced in a piece of high nonlinear fiber by a pulsed pump, we characterize the heralded single photon source from both the theoretical and experimental aspects. In the theory model, started from the derived expression of Bogoliubov transformation for a broadband pulsed pump, the second-order intensity correlation function g (2) c (0), heralding efficiency H, indistinguishability and brightness of the heralded single photons as a function of source parameters are analyzed and discussed. In the experiments, using several kinds of combinations of the source parameters, the values of g (2) c (0) and H are measured and compared. The experimental results are consistent with the theoretical predictions. The investigations are useful for optimizing the parameters and for developing a single photon source suitable for quantum information processing. | We study the behavior of interacting self-propelled particles, whose self-propulsion speed decreases with their local density. By combining direct simulations of the microscopic model with an analysis of the hydrodynamic equations obtained by explicitly coarse graining the model, we show that interactions lead generically to the formation of a host of patterns, including moving clumps, active lanes, and asters. This general mechanism could explain many of the patterns seen in recent experiments and simulations. | eng_Latn | 10,818 |
Time Evolution of Density Operator for Field Damping in Squeezed Bath Calculated by Squeezing Transformation and Entangled State Representation | We find that a squeezing transformation can efficiently simplify the density operator equation of field damping in a squeezed bath. Then the entangled state representation is introduced to solve the simplified equation and the time evolution of density operator, which turns out to be a mixed coherent squeezed state. | In the footsteps of our previous work \cite{RamatonBoschi} we generalize the Stefan-Boltzmann and Wien's displacement laws for the $ \textrm{AdS}_5 \times {\cal S}^5 $ spacetime, the background of the AdS/CFT correspondence foremost realization. Our results take into account the $ \textrm{AdS}_5 \times {\cal S}^5 $ full dimensionality in the electromagnetic field $A^{\mu}$ wave equation, which yields the higher-dimensional blackbody characteristic features suggested in literature. In particular, the total radiated power and the spectral radiancy match the original Stefan-Boltzmann and Wien's displacement laws in the low-energy regime up to available experimental data. | eng_Latn | 10,819 |
On the Ye Gongchuo's Conception of the Ci-poetry from "Quan Qing Ci-poetry Chao" | Ye Gongchuo is the editor-in-chief of "Quan Qing Ci-poetry Chao"-an election holding the largest amount of Qing Ci-poetry.Since it is an election;there,according to the editor,should be a standard.With skimming and scanning,it can be generalized that the following points can reflect the Ye's conception of the Ci-poetry: describing the real feeling in their heart of hearts;reflecting significant realistic events;advocating reforming the old rhythm of Ci-poetry,and proposing a new rhythm.Furthermore,In the editing process,the editor performed a rigorous document view. | We discuss Bose-Einstein condensation (BEC) in quasi-2D trapped gases and find that well below the transition temperature T(c) the equilibrium state is a true condensate, whereas at intermediate temperatures T<T(c) one has a quasicondensate (condensate with fluctuating phase). The mean-field interaction in a quasi-2D gas is sensitive to the frequency omega(0) of the (tight) confinement in the "frozen" direction, and one can switch the sign of the interaction by changing omega(0). Variation of omega(0) can also reduce the rates of inelastic processes. This offers promising prospects for tunable BEC in trapped quasi-2D gases. | eng_Latn | 10,820 |
Charge density wave formation accompanying ferromagnetic ordering in quasi-one-dimensional BaIrO3 | The magnetic, transport, optical, and structural properties of quasi-one-dimensional BaIrO 3 show evidence for the simultaneous onset of electronic density wave formation and ferromagnetism at Tc3a 175 K: Two additional features in the chain direction dc conductivity show a sudden change to metallic behavior below Tc2a 80 K and then a Mott-like transition at Tc1a 26 K: Highly non-linear dc conductivity, optical gap formation at <9kBTc3, additional phonon modes, and emergent X-ray satellite structure support density wave formation. Even at very high (30 T) fields the saturation Ir moment is very small, <0.04mB/Ir. q 2000 Elsevier Science Ltd. All rights reserved. | The main objective of this article is to study dynamic of the ::: three-dimensional Boussinesq equations with the periodic boundary ::: condition.We prove that when the Rayleigh number $R$ crosses the ::: first critical Rayleigh number $R_c$, the Rayleigh-Benard problem ::: bifurcates from the basic state to an global attractor $\Sigma$, which is homeomorphic to $S^3$. | eng_Latn | 10,821 |
A modified Jaynes-Cummings model for an atom interacting with a classical multifrequency field | Generation of sub-Poissonian light via the correlated absorption of photons by the dressed atom | Multi-modality in girls' game disputes | eng_Latn | 10,822 |
Special issue: Collisions in collisionless plasmas | Fast spectral methods for the Fokker-Planck-Landau collision operator | Spatial Interaction and the Statistical Analysis of Lattice Systems | eng_Latn | 10,823 |
Regularity of traveling periodic stratified water waves with vorticity | On stratified steady periodic water waves with linear density distribution and stagnation points | EXO0748−676 Rules out Soft Equations of State for Neutron Star Matter | eng_Latn | 10,824 |
Novel mechanism for superconductivity in the resonating-valence-bond ground state. | Loop condensation in the triangular lattice quantum dimer model | Lack of association of the renin-angiotensin system genes polymorphisms and left ventricular hypertrophy in hypertension. | eng_Latn | 10,825 |
SOLUTION OF THE GAP EQUATION FOR A SUPERCONDUCTOR | Mathematical laboratories: a new power for the physical and social sciences | Dissipative Chaos in Semiconductor Superlattices | yue_Hant | 10,826 |
Schroedinger Wheeler-DeWitt Equation In Multidimensional Cosmology | 1 Decoherence in Starobinsky Model | EXO0748−676 Rules out Soft Equations of State for Neutron Star Matter | kor_Hang | 10,827 |
Distinctive signatures of the lowest bottomonium hybrid | Progress in Particle and Nuclear Physics | Well-posedness results for the generalized Benjamin-Ono equation with arbitrary large initial data | eng_Latn | 10,828 |
Numerical Simulation of Two-color Stationary Light | Numerical analysis of stationary light for potential applications of a quantum interface | EXO0748−676 Rules out Soft Equations of State for Neutron Star Matter | eng_Latn | 10,829 |
Effect of nonlinear gain and filtering on soliton interaction | N-Soliton Train Interactions and Perturbed Complex Toda Chain in Nonlinear Optics. Adiabatic and non-adiabtic aspects. | Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires | eng_Latn | 10,830 |
Numerical Analysis of Quantum-Mechanical Non-Uniform E*B Drift | Handbook of mathematical functions | Numerical Quadrature and Solution of Ordinary Differential Equations | kor_Hang | 10,831 |
Symmetry-breaking for solutions of semilinear elliptic equations with general boundary conditions | Semilinear Elliptic Equations in General Domains | Strong Particle-Hole Symmetry Breaking in a 200 kelvin Superconductor | eng_Latn | 10,832 |
Critical dimensionality in the Anderson-Mott transition | Wave Localization Transitions in Complex Systems 1 | Dimensionless Analysis of Heat, Momentum and Mass Transfer in a Pool Fire | eng_Latn | 10,833 |
Non-Hermitian effective Hamiltonian and continuum shell model | Bound states in the continuum and exceptional points in dielectric waveguide equipped with a metal grating | An utter refutation of the ‘Fundamental Theorem of the HapMap’ | eng_Latn | 10,834 |
Experimental Results Related to Discrete Nonlinear Schr\"odinger Equations | Encyclopedia of Nonlinear Science | EXO0748−676 Rules out Soft Equations of State for Neutron Star Matter | eng_Latn | 10,835 |
Spectral incoherent solitons: a localized soliton behavior in the frequency domain. | Wave kinetic equation in a nonstationary and inhomogeneous medium with a weak quadratic nonlinearity | A coherent all-electrical interface between polar molecules and mesoscopic superconducting resonators | eng_Latn | 10,836 |
Global existence of diffusive-dispersive traveling waves for general flux functions | Existence of Traveling Waves of Conservation Laws with Singular Diffusion and Nonlinear Dispersion | Two-dimensional flexible high diffusive spin circuits | eng_Latn | 10,837 |
Adiabatic decay of internal solitons due to the Earth rotation within the framework of the Gardner-Ostrovsky equation. | Dynamics of Localized Waves with Large Amplitude in a Weakly Dispersive Medium with a Quadratic and Positive Cubic Nonlinearity | EXO0748−676 Rules out Soft Equations of State for Neutron Star Matter | eng_Latn | 10,838 |
Harmonically modulated complex solitary waves which are a generalized type of envelope soliton (herein coined oscillatory solitons) are studied for the two U(1)-invariant integrable generalizations of the modified Korteweg-de Vries equation, given by the Hirota equation and the Sasa-Satsuma equation. A bilinear formulation of these two equations is used to derive the oscillatory 1-soliton and 2-soliton solutions, which are then written out in a physical form parameterized in terms of their speed, modulation frequency, and phase. Depending on the modulation frequency, the speeds of oscillatory waves (1-solitons) can be positive, negative, or zero, in contrast to the strictly positive speed of ordinary solitons. When the speed is zero, an oscillatory wave is a time-periodic standing wave. Properties of the amplitude and phase of oscillatory 1-solitons are derived. Oscillatory 2-solitons are graphically illustrated to describe collisions between two oscillatory 1-solitons in the case when the speeds are distinct. In the special case of equal speeds, oscillatory 2-solitons are shown to reduce to harmonically modulated breather waves. | The Hirota equation and the Sasa-Satsuma equation are U(1)-invariant integrable generalizations of the modified Korteweg-de Vries equation. These two generalizations admit oscillatory solitons, which describe harmonically modulated complex solitary waves parameterized by their speed, modulation frequency, and phase. Depending on the modulation frequency, the speeds of oscillatory waves (1-solitons) can be positive, negative, or zero, in contrast to the strictly positive speed of ordinary solitons. When the speed is zero, an oscillatory wave is a time-periodic standing wave. Oscillatory 2-solitons with non-zero wave speeds are shown to describe overtake collisions of a fast wave and a slow wave moving in the same direction, or head-on collisions of two waves moving in opposite directions. When one wave speed is zero, oscillatory 2-solitons are shown to describe collisions in which a moving wave overtakes a standing wave. An asymptotic analysis using moving coordinates is carried out to show that, in all collisions, the speeds and modulation frequencies of the individual waves are preserved, while the phases and positions undergo a shift such that the center of momentum of the two waves moves at a constant speed. The primary constants of motion as well as some other features of the nonlinear interaction of the colliding waves are discussed. | The Hirota equation and the Sasa-Satsuma equation are U(1)-invariant integrable generalizations of the modified Korteweg-de Vries equation. These two generalizations admit oscillatory solitons, which describe harmonically modulated complex solitary waves parameterized by their speed, modulation frequency, and phase. Depending on the modulation frequency, the speeds of oscillatory waves (1-solitons) can be positive, negative, or zero, in contrast to the strictly positive speed of ordinary solitons. When the speed is zero, an oscillatory wave is a time-periodic standing wave. Oscillatory 2-solitons with non-zero wave speeds are shown to describe overtake collisions of a fast wave and a slow wave moving in the same direction, or head-on collisions of two waves moving in opposite directions. When one wave speed is zero, oscillatory 2-solitons are shown to describe collisions in which a moving wave overtakes a standing wave. An asymptotic analysis using moving coordinates is carried out to show that, in all collisions, the speeds and modulation frequencies of the individual waves are preserved, while the phases and positions undergo a shift such that the center of momentum of the two waves moves at a constant speed. The primary constants of motion as well as some other features of the nonlinear interaction of the colliding waves are discussed. | eng_Latn | 10,839 |
We employ the formal analogy between quadratic and nonlocal solitons to investigate analytically the properties of solitons and soliton bound states in second-harmonic generation in the regime of negative diffraction or dispersion of the second harmonic. We show that in the nonlocal description this regime corresponds to a periodic nonlocal response function. We then use the strongly nonlocal approximation to find analytical solutions of the families of single bright solitons and their bound states in terms of Mathieu functions. | A perturbation-iteration method is developed for the computation of the Hermite–Gaussian-like solitons with arbitrary peak numbers in nonlocal nonlinear media. This method is based on the perturbed model of the Schrodinger equation for the harmonic oscillator, in which the minimum perturbation is obtained by the iteration. This method takes a few tens of iteration loops to achieve enough high accuracy, and the initial condition is fixed to the Hermite–Gaussian function. The method we developed might also be extended to the numerical integration of the Schrodinger equations in any type of potentials. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,840 |
We present experimental evidence of non-instantaneous solitons within mid-IR supercontinuum spectra in anomalously dispersive liquid-core fibers. Simulations confirm two measured signatures of such states: inhibited broadening and fine spectral fringes. | Soliton-based MIR supercontinuum generation between 1.2 μm and 2.4 μm is presented using a highly nonlinear CS2-core optical fiber and a 430 fs Tm-based pump source. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,841 |
The Rayleigh-Taylor instability at the interface in an immiscible two-component Bose-Einstein condensate is investigated using the mean field and Bogoliubov theories. Rayleigh-Taylor fingers are found to grow from the interface and mushroom patterns are formed. Quantized vortex rings and vortex lines are then generated around the mushrooms. The Rayleigh-Taylor instability and mushroom-pattern formation can be observed in a trapped system. | In this paper we investigate the ground-state properties and related quantum phase transitions for the two-component Bose-Einstein condensate in a single-mode optical cavity. Apart from the usual normal and superradiant phases, multi-stable macroscopic quantum states are realized by means of the spin-coherent-state variational method. We demonstrate analytically the stimulated radiation from a collective state of atomic population inversion, which does not exist in the normal Dicke model with single-component atoms. It is also revealed that the stimulated radiation can be generated only from one component of atoms and the other remains in the ordinary superradiant state. However, the order of superradiant and stimulated-radiation states is interchangeable between two components of atoms by tuning the relative atom-field couplings and the frequency detuning as well. | We report enhancement of the mechanical stability of graphene through a one-step method to disperse gold nanoparticles on the pristine graphene without any added agent. | eng_Latn | 10,842 |
Properties of the linear eigenvalue problem associated to a hyperbolic non-linear Schrodinger equation are reviewed. The instability band of a deep-water soliton is shown to merge to the continuous spectrum of a linear Schrodinger operator. A new analytical approximation of the instability growth near a threshold is derived by means of a bifurcation theory of weakly localized wave functions. | The Hyperbolic Nonlinear Schrodinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrowband deep water gravity waves. In this study, the Petviashvili method is exploited to numerically compute bi-periodic time-harmonic solutions of the HypNLS equation. In physical space they represent non-localized standing waves. Non-trivial spatial patterns are revealed and an attempt is made to describe them using symbolic dynamics and the language of substitutions. Finally, the dynamics of a slightly perturbed standing wave is numerically investigated by means a highly acccurate Fourier solver. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,843 |
Maxwell–Bloch equations are widely used to model the dynamics due to coherent light-matter interaction in quantum cascade laser (QCL) structures, which plays an essential role especially for the generation of frequency combs and mode-locked pulses. While the modest numerical complexity of the Maxwell–Bloch system allows for a full spatiotemporal treatment, its main disadvantage is the inclusion of dissipation by empirical dephasing rates and electron lifetimes. We present a self-consistent multi-domain approach which couples the Maxwell–Bloch equations to advanced carrier transport simulations based on a density matrix Monte Carlo technique, yielding the scattering and dephasing rates. In this way, the compact spatiotemporal modeling of the carrier-light dynamics by the Maxwell–Bloch system can be combined with the versatility and reliability of self-consistent carrier transport approaches. Simulation results are shown for a QCL-based terahertz frequency comb source, and good agreement with experiment is obtained. | We present long-term dynamic simulations of the optical and carrier dynamics in quantum cascade lasers, obtained by numerically solving the Maxwell-Bloch equations without invoking the rotating wave approximation. We discuss the applied numerical methods and parallelization techniques used to obtain the required numerical efficiency and accuracy, and show results for a mode-locked terahertz quantum cascade laser. | Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights. | eng_Latn | 10,844 |
Propagation of short laser pulses governing by a vector type 3D+1 non-linear Schrodinger equation in Kerr-type medium ::: with anomalous dispersion and spatial dependence of the nonlinear refractive index is investigated. Finite energy ::: analytical soliton solutions in spherical coordinates are found. Conditions for experimental observation are discussed. | L. M. Kovachev, N. I. Kaymakanova, D. Y. Dakova, L. I. Pavlov, R. A. Rousev, S. G. Donev, R. L. Pavlov Institute of Electronics, Bulgarian Academy of Sciences, Tsarigradcko Chaussee 72,1784 Sofia, Bulgaria, Plovdiv University, 24 Tsar Asen Str., 4000 Plovdiv,Bulgaria, Institute for Nuclear Research and Nuclear Energy, 72 Tsarigradsko Chaussee, 1784, Bulgaria (Received January 17, 2003; received in final form June 5, 2003) | In this paper we prove that every nonlinear ∗ -Lie derivation from a factor von Neumann algebra into itself is an additive ∗ -derivation. | eng_Latn | 10,845 |
Evolution of an oscillatory wide-band pulse in a sparse medium composed of randomly distributed, uncorrelated, discrete scatterers (such as atmospheric clouds, dust, or other aerosols) is studied. The frequency-dependent (dispersive) losses are evaluated by taking into account energy absorption in the medium constituents as well as scattering itself. A reduced, algebraic attenuation of the pulse energy is observed, provided the pulse contains a significant frequency content in the region of strongly varying medium dispersive properties. These frequencies can be provided by pulse carrier frequency selection, short rise and fall times of the pulse, or pulse chirping. It is shown that different types of algebraic attenuation, over the range of penetration depth corresponding to several orders of mean-free path, can be present depending on the inter-relations between characteristic frequencies of the pulse spectrum and the medium dispersive properties. A simple analytical model is constructed that captures relevant features of the propagating pulse energy decay, as well as ranges of penetration depths, and hence may serve as a useful tool in designing and analyzing various scenarios of wide-band pulse propagation in dispersive media in the context of, e.g., signal transmission, imaging, or target detection. | It is shown that the scattered field and the field inside the body can be expressed formally as power series in the above ratio, the calculation of successive terms in the series requiring the solution of standard problems in potential theory, together with the evaluation of certain potential integrals, so that the process can be carried as far as desired if Laplace's equation can be solved in the coordinate system appropriate for the body. The convergence of the series for the scattered field becomes progressively worse as we recede from the body, but an alternative expression for the field, also proceeding in powers of the same parameter, gives a representation which is valid everywhere except in the immediate neighborhood of the body (in particular, in the wave zone) and which does not suffer from this defect. The case of a perfect conductor, or diffraction through a hole in a perfectly conducting screen, can be treated as particular cases of the general theory. The paper can be regarded as an extensio... | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,846 |
In current Bose-Einstein condensate experiments, the shot-to-shot variation of atom number fluctuates up to 10%. In here, we present a procedure to suppress such fluctuations by using a nonlinear p-pi-pbar matter wave interferometer for a Bose-Einstein condensate with two internal states and a high beam-splitter asymmetry (p, pbar not-equal 0.5). We analyze the situation for an inhomogeneous trap within the Gross-Pitaevskii mean-field theory, as well as a quantum mechanical Josephson model, which addresses complementary aspects of the problem and agrees well otherwise. | Classical Models of Light Experiments with Photons Quantum Models of Light Basic Optical Components Photo-currents: Generation and Detection The Laser Quantum Noise: Basic Measurements Sub-Poissonian Light Squeezing Experiments Quantum Non-demolition Experiments Applications of Quantum Optics Summary and Outlook Appendices Index. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,847 |
In this article, we report on the curious phenomena of anomalous spreading in a system of coupled Fisher-KPP equations. When a single parameter is set to zero, the system consists of two uncoupled Fisher-KPP equations which give rise to traveling fronts propagating with the unique, minimal KPP speed. When the coupling parameter is nonzero various behaviors can be observed. Anomalous spreading occurs when one component of the system spreads at a speed significantly faster in the coupled system than it does in isolation, while the speed of the second component remains unchanged. We study these anomalous spreading speeds and show that they arise due to poles of the pointwise Green's function corresponding to the linearizion about the unstable homogeneous state. These poles lead to anomalous spreading in the linearized system and come in two varieties -- one that persists and leads to anomalous spreading for the nonlinear system and one that does not. We describe the mechanisms leading to these two behaviors and prove that one class of poles are irrelevant as far as nonlinear wavespeed selection is concerned. Finally, we show that the same mechanism can give rise to anomalous spreading even when the slower component does not spread. | Range expansions are a ubiquitous phenomenon, leading to the spatial spread of genetic, ecological, and cultural traits. While some of these traits are advantageous (and hence selected), other, nonselected traits can also spread by hitchhiking on the wave of population expansion. This requires us to understand how the spread of a hitchhiking trait is coupled to the wave of advance of its host population. Here, we use a system of coupled Fisher-Kolmogorov-Petrovsky-Piskunov (F-KPP) equations to describe the spread of a horizontally transmitted hitchhiking trait within a population as it expands. We extend F-KPP wave theory to the system of coupled equations to predict how the hitchhiking trait spreads as a wave within the expanding population. We show that the speed of this trait wave is controlled by an intricate coupling between the tip of the population and trait waves. Our analysis yields a new speed selection mechanism for coupled waves of advance and reveals the existence of previously unexpected speed transitions. | Every function of n inputs can be efficiently computed by a complete network of n processors in such a way that: If no faults occur, no set of size t n /2 of players gets any additional information (other than the function value), Even if Byzantine faults are allowed, no set of size t n /3 can either disrupt the computation or get additional information. Furthermore, the above bounds on t are tight! | eng_Latn | 10,848 |
The emergence of a non-equilibrium Bose-Einstein-like condensation of magnons in rf-pumped magnetic thin films has recently been experimentally observed. We present here a complete theoretical description of the non-equilibrium processes involved. It is demonstrated that the phenomenon is another example of the presence of a Bose-Einstein-like condensation in non-equilibrium many-boson systems embedded in a thermal bath, better referred-to as Frohlich-Bose-Einstein condensation. The complex behavior emerges after a threshold of the exciting intensity is attained. It is inhibited at higher intensities when the magnon-magnon interaction drives the magnons to internal thermalization. The observed behavior of the relaxation to equilibrium after the end of the pumping pulse is also accounted for and the different processes fully described. | A statistical-thermodynamic theory of the phenomenon of stimulated amplification of the population of excitons which lie at the bottom of their lowest-energy band is presented. The experimentally detected "packet" of excitons flowing ballistically is shown to consist of a Schrodinger-Davydov solitary wave, dressed with a cloud of incoherent excitons. Moreover, a secondary excitation by a c.w. laser beam promotes a Frohlich-Bose-Einstein–like condensation, which is responsible for the relevant phenomenon that the lifetime of the soliton is largely increased with increasing pumping power. | Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights. | eng_Latn | 10,849 |
An innovative and novel quartz-enhanced photoacoustic spectroscopy (QEPAS) sensor for highly sensitive and selective breath gas analysis is introduced. The QEPAS sensor consists of two acoustically coupled micro- resonators (mR) with an off-axis 20 kHz quartz tuning fork (QTF). The complete acoustically coupled mR system is optimized based on finite element simulations and experimentally verified. Due to the very low fabrication costs the QEPAS sensor presents a clear breakthrough in the field of photoacoustic spectroscopy by introducing novel disposable gas chambers in order to avoid cleaning after each test. The QEPAS sensor is pumped resonantly by a nanosecond pulsed single-mode mid-infrared optical parametric oscillator (MIR OPO). Spectroscopic measurements of methane and methanol in the 3.1 μm to 3.7 μm wavelength region is conducted. Demonstrating a resolution bandwidth of 1 cm -1 . An Allan deviation analysis shows that the detection limit at optimum integration time for the QEPAS sensor is 32 ppbv@190s for methane and that the background noise is solely due to the thermal noise of the QTF. Spectra of both individual molecules as well as mixtures of molecules were measured and analyzed. The molecules are representative of exhaled breath gasses that are bio-markers for medical diagnostics. | The Morse-Ingard equations of thermoacoustics are a system of coupled time-harmonic equations for the temperature and pressure of an excited gas. They form a critical aspect of modeling trace gas sensors. In this paper, we analyze a reformulation of the system that has a weaker coupling between the equations than the original form. We give a G{\aa}rding-type inequality for the system that leads to optimal-order asymptotic finite element error estimates. We also develop preconditioners for the coupled system. These are derived by writing the system as a 2x2 block system with pressure and temperature unknowns segregated into separate blocks and then using either the block diagonal or block lower triangular part of this matrix as a preconditioner. Consequently, the preconditioner requires inverting smaller, Helmholtz-like systems individually for the pressure and temperature. Rigorous eigenvalue bounds are given for the preconditioned system, and these are supported by numerical experiments. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,850 |
Workshop on Mathematical Methods in Quantum Molecular Dynamics 28 April – 3 May 2013 MEALS | The multi-configurational time-dependent Hartree approach | Chemistry and Quantum Mechanics in 2019: Give Us Insight and Numbers | yue_Hant | 10,851 |
Dynamics of high-order solitons in the nonlocal nonlinear Schr\"{o}dinger equations | Complete integrability of Nonlocal Nonlinear Schr\"odinger equation | EXO0748−676 Rules out Soft Equations of State for Neutron Star Matter | eng_Latn | 10,852 |
From Classical to Quantum Glasses with Ultracold Polar Molecules | Anisotropic blockade using pendular long-range Rydberg molecules | BUAP: Polarity Classification of Short Texts | eng_Latn | 10,853 |
The Fokker-Planck Equation for Lattice Vibration: Stochastic Dynamics and Thermal Conductivity | Thermal Conductivity: Theory, Properties, and Applications | EXO0748−676 Rules out Soft Equations of State for Neutron Star Matter | eng_Latn | 10,854 |
LECTURES ON NONLINEAR DISPERSIVE EQUATIONS II | Well-posedness results for the generalized Benjamin-Ono equation with arbitrary large initial data | EXO0748−676 Rules out Soft Equations of State for Neutron Star Matter | yue_Hant | 10,855 |
On relation between discrete Frenet frames and the bi-Hamiltonian structure of the discrete nonlinear Schr\"odinger equation | Hamiltonian methods in the theory of solitons | Evidence against a role for platelet-derived molecules in liver regeneration after partial hepatectomy in humans | eng_Latn | 10,856 |
Searching for Entropically Stabilized Phases: The Case of Silver Iodide | Path collective variables without paths | Completely Stale Transmitter Channel State Information is Still Very Useful | eng_Latn | 10,857 |
Decoherence-free propagation and ramification of a solitary pulse | The Theory of Open Quantum Systems | Another Weakness of “ Determinacy ” as a Selection Criterion for Rational Expectations Models | eng_Latn | 10,858 |
Strong-field ionization of He by elliptically polarized light in attoclock configuration | Attoclock revisited on electron tunnelling time | Weak Solutions for SPDEs and Backward Doubly Stochastic Differential Equations | eng_Latn | 10,859 |
On Decay of Solutions to Nonlinear Schrödinger Equations | Exponential Decay Of Two-Body Eigenfunctions: A Review | Improved Measurement of the Pseudoscalar Decay Constant | eng_Latn | 10,860 |
On Choices of Discrepancy for Randomly-Shifted Lattice Rules | Quasi-Monte Carlo Methods with Applications in Finance | Dissipative Chaos in Semiconductor Superlattices | eng_Latn | 10,861 |
Nonequilibrium Statistical Mechanics of Classical Lattice φ4 Field Theory | On the Boltzmann Equation for Weakly Nonlinear Wave Equations | Nonequilibrium evolution of strong-field anisotropic ionized electrons towards a delayed plasma-state | eng_Latn | 10,862 |
Exact traveling wave solutions of some nonlinear evolution equations | Soliton solutions of some nonlinear evolution equations with time-dependent coefficients | EXO0748−676 Rules out Soft Equations of State for Neutron Star Matter | eng_Latn | 10,863 |
Breather-Type Periodic Soliton Solutions for (1+1)-Dimensional Sinh-Poisson Equation | Generalized Kudryashov method for nonlinear fractional double sinh--Poisson equation | EXO0748−676 Rules out Soft Equations of State for Neutron Star Matter | eng_Latn | 10,864 |
Canonical structure of soliton equations. I | An integrable decomposition of the Manakov equation | EXO0748−676 Rules out Soft Equations of State for Neutron Star Matter | eng_Latn | 10,865 |
Transient oscillations in electric wave-filters | Pure mathematics applied in early twentieth-century America: The case of T.H. Gronwall, consulting mathematician | Completely Stale Transmitter Channel State Information is Still Very Useful | eng_Latn | 10,866 |
2004 A Hamiltonian formulation for long internal waves | Hamiltonian Formulation for Water Wave Equation | EXO0748−676 Rules out Soft Equations of State for Neutron Star Matter | eng_Latn | 10,867 |
The relationship between the atomic coherent-state representation of Arecchi et al. [Phys. Rev. A 6, 2211 (1972)] and the state multipoles is established. The state multipoles are used to develop a theory of generalized phase-space distributions for angular momentum (collective atomic) systems. The general theory for angular momentum systems is shown to have many features in common with the general theory for boson systems [Phys. Rev. D 2, 2161 (1970)]. These generalized phase-space distributions contain as a special case the coherent-state representation of Arecchi et al. The applications of the generalized phase-space distributions and state multipoles to the dynamical problems and to the calculation of multitime correlations are given. State-multipole techniques are used to give a brief discussion of the master equation describing cooperative resonance fluorescence. | Due to the weak absorption of H2O in the near infra red region, the frequency modulation (FM) is one of good technologies to increase the sensitivity of detection. This method is used to study the absorption spectra of water-vapor in the region around 814.65 nm. Compared to direct absorption method, the signal-to-noise of spectral signal is enhanced. Therefore, the laser FM is a good potential spectroscopic technology in the application of laser sensor for trace gas. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,868 |
We consider dynamically generated spin squeezing in interacting bimodal condensates. We show that particle losses and non-zero temperature effects in a multimode theory completely change the scaling of the best squeezing for large atom numbers. We present the new scalings and we give approximate analytical expressions for the squeezing in the thermodynamic limit. Besides reviewing our recent theoretical results, we give here a simple physical picture of how decoherence acts to limit the squeezing. We show in particular that under certain conditions the decoherence due to losses and non-zero temperatureacts as a simple dephasing. | We consider the problem of quantum phase estimation with access to arbitrary measurements in a single suboptimal basis. The achievable sensitivity limit in this case is determined by the classical Cram\'{e}r-Rao bound with respect to the fixed basis. Here we show that the sensitivity can be enhanced beyond this limit if knowledge about the energy expectation value is available. The combined information is shown to be equivalent to a direct measurement of an optimal linear combination of the basis projectors and the phase-imprinting Hamiltonian. Application to an atomic clock with oversqueezed spin states yields a sensitivity gain that scales linearly with the number of atoms. Our analysis further reveals that small modifications of the observable can have a strong impact on the sensitivity. | The temporal behavior of squeezing parameters and second order correlation function is investigated for a two atom dissipative model. The analytic expressions for considering parameters are obtained on the basis of master equation solution for coherent input. An influence of different dissipation mechanisms onto statistics and squeezing are considered.© (2008) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only. | eng_Latn | 10,869 |
The dynamics of driven-dissipative systems is shown to be well-fitted for achieving efficient combinatorial optimization. The proposed method can be applied to solve any combinatorial optimization problem that is equivalent to minimizing an Ising Hamiltonian. Moreover, the dynamics considered can be implemented using various physical systems as it is based on generic dynamics-the normal form of the supercritical pitchfork bifurcation. The computational principle of the proposed method relies on an hybrid analog-digital representation of the binary Ising spins by considering the gradient descent of a Lyapunov function that is the sum of an analog Ising Hamiltonian and archetypal single or double-well potentials. By gradually changing the shape of the latter potentials from a single to double well shape, it can be shown that the first nonzero steady states to become stable are associated with global minima of the Ising Hamiltonian, under the approximation that all analog spins have the same amplitude. In the more general case, the heterogeneity in amplitude between analog spins induces the stabilization of local minima, which reduces the quality of solutions to combinatorial optimization problems. However, we show that the heterogeneity in amplitude can be reduced by setting the parameters of the driving signal near a regime, called the dynamic phase transition, where the analog spins' DC components map more accurately the global minima of the Ising Hamiltonian which, in turn, increases the quality of solutions found. Last, we discuss the possibility of a physical implementation of the proposed method using networks of degenerate optical parametric oscillators. | We will discuss the basic concept, operational principle and implementation of a coherent Ising/XY/recurrent neural network machines based on degenerate optical parametric oscillators. The coherent Ising machine with 2048 spins with all-to-all connections demonstrated already competitive performance against the state of art classical digital computers. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,870 |
We survey mathematical properties of quasicrystals, first from the point of view of harmonic analysis, then from the point of view of morphic and automatic sequences. | We review the recent developments in the theory of the one-dimensional tight-binding Schrodinger equation for a class of deterministic ergodic potentials. In the typical examples the potentials are generated by substitutional sequences, like the Fibonacci or the Thue-Morse sequence. We concentrate on rigorous results which will be explained rather than proved. The necessary mathematical background is provided in the text. | Thank you very much for reading analysis in classes of discontinuous functions and equations of mathematical physics. As you may know, people have look hundreds times for their favorite books like this analysis in classes of discontinuous functions and equations of mathematical physics, but end up in malicious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they cope with some harmful virus inside their laptop. | eng_Latn | 10,871 |
The self-consistent field method utilized for solving the Hartree-Fock (HF) problem and the closely related Kohn-Sham problem is typically thought of as one of the cheapest methods available to quantum chemists. This intuition has been developed from the numerous applications of the self-consistent field method to a large variety of molecular systems. However, as characterized by its worst-case behavior, the HF problem is NP-complete. In this work, we map out boundaries of the NP-completeness by investigating restricted instances of HF. We have constructed two new NP-complete variants of the problem. The first is a set of Hamiltonians whose translationally invariant Hartree-Fock solutions are trivial, but whose broken symmetry solutions are NP-complete. Second, we demonstrate how to embed instances of spin glasses into translationally invariant Hartree-Fock instances and provide a numerical example. These findings are the first steps towards understanding in which cases the self-consistent field method is computationally feasible and when it is not. | Obtaining exact solutions to the Schrödinger equation for atoms, molecules, and extended systems continues to be a "Holy Grail" problem which the fields of theoretical chemistry and physics have been striving to solve since inception. Recent breakthroughs have been made in the development of hardware-efficient quantum optimizers and coherent Ising machines capable of simulating hundreds of interacting spins with an Ising-type Hamiltonian. One of the most vital questions pertaining to these new devices is, "Can these machines be used to perform electronic structure calculations?" Within this work, we review the general procedure used by these devices and prove that there is an exact mapping between the electronic structure Hamiltonian and the Ising Hamiltonian. Additionally, we provide simulation results of the transformed Ising Hamiltonian for H2 , He2 , HeH+, and LiH molecules, which match the exact numerical calculations. This demonstrates that one can map the molecular Hamiltonian to an Ising-type Hamiltonian which could easily be implemented on currently available quantum hardware. This is an early step in developing generalized methods on such devices for chemical physics. | The liquid drop model the shell model rotation and single-particle motion nuclear forces the Hartree-Fock method pairing correlations and superfluid nuclei the generalized single-particle model (HFB theory) harmonic vibrations boson expansion methods the generator coordinate method restoration of broken symmetries the time dependent Hartree-Fock method (TDHF) semiclassical methods in nuclear physics. Appendices: angular momentum algebra in the laboratory and the body-fixed system electromagnetic moments and transitions second quantization density matrices theorems concerning product wave functions many-body green's functions. | eng_Latn | 10,872 |
Bright and dark spatial gap solitons are demonstrated in waveguide arrays. These gap solitons travel across the array at zero transverse velocity, in complete analogy with stationary (immobile) temporal gap solitons. Furthermore, the launching configuration for observing these stationary gap solitons is shown to be the analog of an "ideal experiment" for observing stationary temporal gap solitons, never observed so far. A clear distinction is established between the family of Floquet-Bloch solitons in general and discrete solitons in particular, and the limiting case of gap solitons. | We report on the stabilization of inherently unstable counterpropagating photorefractive spatial solitons by the use of one- and two-dimensional photonic lattices. We numerically investigate the dependence of the instability dynamics on period and amplitude of the lattice and present experimental verification for the dynamic stabilization of the bi-directional soliton state. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,873 |
The Aharonov-Bohm, and its dual, the Aharonov-Casher effects have been extremely fruitful in physics and, nowadays, they are of central importance for quantum technologies. Here, we study the Aharonov-Bohm effect for a Bose-Einstein condensate propagating out of equilibrium along a mesoscopic ring-shaped laser light potential, pierced by an effective magnetic flux. We found how the system experiences a subtle crossover between physical regimes dominated by pronounced interference patterns and others in which the Aharonov-Bohm effect is effectively washed out. We propose various applications for this system. | Mott insulators provide stable quantum states and long coherence times to due to small number fluctuations, making them good candidates for quantum memory and atomic circuits. We propose a proof-of-principle for a 1D Mott switch using an ultracold Bose gas and optical lattice. With time-evolving block decimation simulations -- efficient matrix product state methods -- we design a means for transient parameter characterization via a local excitation for ease of engineering into more complex atomtronics. We perform the switch operation by tuning the intensity of the optical lattice, and thus the interaction strength through a conductance transition due to the confined modifications of the"wedding cake"Mott structure. We demonstrate the time-dependence of Fock state transmission and fidelity of the excitation as a means of tuning up the device in a double well and as a measure of noise performance. Two-point correlations via the $g^{(2)}$ measure provide additional information regarding superfluid fragments on the Mott insulating background due to the confinement of the potential. | Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights. | eng_Latn | 10,874 |
We investigate the entanglement and nonlocality properties of two random XX spin-1/2 critical chains, in order to better understand the role of breaking translational invariance to achieve nonlocal states in critical systems. We show that breaking translational invariance is a necessary but not sufficient condition for nonlocality, as the random chains remain in a local ground state up to a small degree of randomness. Furthermore, we demonstrate that the random dimer model does not have the same nonlocality properties of the translationally invariant chain, even though they share the same universality class for a certain range of randomness. | The Strong Disorder RG approach for random systems has been extended in many new directions since our previous review of 2005 [Phys. Rep. 412, 277]. The aim of the present colloquium paper is thus to give an overview of these various recent developments. In the field of quantum disordered models, recent progress concern Infinite Disorder Fixed Points for short-ranged models in higher dimensions $d>1$, Strong Disorder Fixed Points for long-ranged models, scaling of the entanglement entropy in critical ground-states and after quantum quenches, the RSRG-X procedure to construct the whole set excited stated and the RSRG-t procedure for the unitary dynamics in Many-Body-Localized Phases, the Floquet dynamics of periodically driven chains, the dissipative effects induced by the coupling to external baths, and Anderson Localization models. In the field of classical disordered models, new applications include the contact process for epidemic spreading, the strong disorder renormalization procedure for general master equations, the localization properties of random elastic networks and the synchronization of interacting non-linear dissipative oscillators. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,875 |
We theoretically investigate properties of magnetostatic traps for cold atoms that are subject to externally applied uniform fields. We show that Ioffe-Pritchard traps and other stationary points of B are confined to a two-dimensional curved surface, or manifold M, defined by det({partial_derivative}B{sub i}/{partial_derivative}x{sub j})=0. We describe how stationary points can be moved over the manifold by applying external uniform fields. The manifold also plays an important role in the behavior of points of zero field. Field zeroes occur in two distinct types, in separate regions of space divided by the manifold. Pairs of zeroes of opposite type can be created or annihilated on the manifold. Finally, we give examples of the manifold for cases of practical interest. | We review recent developments in the use of magnetic lattices as a complementary tool to optical lattices for trapping periodic arrays of ultracold atoms and degenerate quantum gases. Recent advances include the realisation of Bose–Einstein condensation in multiple sites of a magnetic lattice of one-dimensional microtraps, the trapping of ultracold atoms in square and triangular magnetic lattices, and the fabrication of magnetic lattice structures with sub-micron period suitable for quantum tunnelling experiments. Finally, we describe a proposal to utilise long-range interacting Rydberg atoms in a large spacing magnetic lattice to create interactions between atoms on neighbouring sites. | In this short note we prove that if X is a separably rationally connected variety over an algebraically closed field of positive characteristic, then H^1(X, O_X)=0. | eng_Latn | 10,876 |
In solving the problem of finding a temperature distribution which, at zero temperature, corresponds to superfluidity, i.e., to nonzero energy, the author tried to quantize free energy. This was done on the basis of supersecondary quantization whose special case is the usual secondary quantization for bosons and with the help of which new representations of the Schr\"odinger equation were obtained. The supersecondary quantization allowed the author to construct a variational method whose zero approximation are the Hartree-Fock and Bogolyubov-BCSch variational principles. This method works especially well in the case of not a large number of particles. The new quantization and the variational method are of general character and can be used in the quantum field theory. | The Principle of Complementarity of Probabilities based on of noncommutative probability is introduced. | Recently, S. Reich and S. Simons provided a novel proof of the Kirszbraun-Valentine extension theorem using Fenchel duality and Fitzpatrick functions. In the same spirit, we provide a new proof of an extension result for firmly nonexpansive mappings with an optimally localized range. | eng_Latn | 10,877 |
In this paper, we study an integro-differential equation based on the generalized KdV equation with a convolution term which introduces a time delay in the nonlinearity. Special attention is paid to the existence of solitary wave solutions. Motivated by [M.J. Ablowitz, H. Seger, Soliton and Inverse Scattering Transform, SIAM, Philadelphia, 1981; C.K.R.T. Jones, Geometrical singular perturbation theory, in: R. Johnson (Ed.), Dynamical Systems, in: Lecture Notes in Math., vol. 1609, Springer, New York, 1995; T. Ogawa, Travelling wave solutions to perturbed Korteweg–de Vries equations, Hiroshima Math. J. 24 (1994) 401–422], we prove, using the linear chain trick and geometric singular perturbation analysis, that the solitary wave solutions persist when the average delay is suitably small, for a special convolution kernel. | We consider a fifth-order singularly perturbed KdV equation. The direct perturbation method for solving it is investigated in the first order approximation for the travelling wave case. The application of the method leads to a general soliton of the first-order equation, which describes some arrays of wave crests. Analysis of the solution shows that the perturbation makes the soliton lower and narrower than an unperturbed KdV soliton. | A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory. The subjects addressed include: solitary waves and solitons, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation, and the inverse method for the isospectral Schroedinger equation and the general solution of the solvable nonlinear equations. Also considered are: isolation of the Korteweg-de Vries equation in some physical examples, the Zakharov-Shabat/AKNS inverse method, kinks and the sine-Gordon equation, the nonlinear Schroedinger equation and wave resonance interactions, amplitude equations in unstable systems, and numerical studies of solitons. 45 references. | eng_Latn | 10,878 |
The adiabatic dynamics of a two level atom with spontaneous decay is studied. The existence of a complex adiabatic phase shift is established: The real part being the usual Berry’s phase. A closed‐form expression for this phase and the adiabatic transition amplitudes is obtained. Incorporation of a finite preparation time for the initial state yields a new asymptotic form for the adiabatic transition amplitudes which is significantly different from the standard Landau–Zener–Dykhne formula. | We consider the adiabatic regime of two parameters evolution semigroups generated by linear operators that are analytic in time and satisfy the following gap condition for all times: the spectrum of the generator consists in finitely many isolated eigenvalues of finite algebraic multiplicity, away from the rest of the spectrum. The restriction of the generator to the spectral subspace corresponding to the distinguished eigenvalues is not assumed to be diagonalizable. | We demonstrated adiabatic sum-frequency generation with 92 % photon conversion efficiency between a white-light continuum and a strong pump at 1030 nm to cover the spectral range of 405-500 nm by using an aperiodically-poled nonlinear crystal. | eng_Latn | 10,879 |
We study analytically the existence and uniqueness of the ground state of the nonlinear Schr\"{o}dinger equation (NLSE) with a general power nonlinearity described by the power index $\sigma\ge0$. For the NLSE under a box or a harmonic potential, we can derive explicitly the approximations of the ground states and their corresponding energy and chemical potential in weak or strong interaction regimes with a fixed nonlinearity $\sigma$. Besides, we study the case where the nonlinearity $\sigma\to\infty$ with a fixed interaction strength. In particular, a bifurcation in the ground states is observed. Numerical results in 1D and 2D will be reported to support our asymptotic results. | In this paper, we mainly review recent results on mathematical theory and ::: numerical methods for Bose-Einstein condensation (BEC), ::: based on the Gross-Pitaevskii equation (GPE). Starting from the simplest case with one-component BEC of the weakly interacting bosons, we study the reduction of GPE to lower dimensions, the ground states of BEC including the existence and uniqueness as well as nonexistence results, and the dynamics of GPE including dynamical laws, well-posedness of the Cauchy problem as well as the finite time blow-up. To compute the ground state, the gradient flow with discrete normalization (or imaginary time) method is reviewed and various full discretization methods are presented and compared. To simulate the dynamics, both finite difference methods and time splitting spectral methods are reviewed, and their error estimates are briefly outlined. When the GPE has symmetric properties, we show how to simplify the numerical methods. Then we compare two widely used scalings, i.e. physical scaling (commonly used) and semiclassical scaling, for BEC in strong repulsive interaction regime (Thomas-Fermi regime), and discuss semiclassical limits of the GPE. Extensions of these results for one-component BEC are then ::: carried out for rotating BEC by GPE with an angular momentum rotation, dipolar BEC by GPE with long range dipole-dipole interaction, and two-component BEC by coupled GPEs. Finally, as a perspective, we show briefly the mathematical models for ::: spin-1 BEC, Bogoliubov excitation and BEC at finite temperature. | Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights. | eng_Latn | 10,880 |
We discuss various methods and problems pertaining to that part of Random Dynamical Systems which deals with real noise processes. We consider the theory of random orthogonal polynomials, and show how methods applied to the study of the random Schrodinger operator can be generalized to study them. We further discuss certain questions in the area of random bifurcation theory; we formulate and illustrate a “robustness” criterion pertaining to bifurcation in the presence of real noise. Finally, we give a brief survey of some other recent advances in the field. | We study bifurcations in dynamical systems with bounded random perturbations. Such systems, which arise quite naturally, have been nearly ignored in the literature, despite a rich body of work on systems with unbounded, usually normally distributed, noise. In systems with bounded random perturbations, new kinds of bifurcations that we call ‘hard’ may happen and in fact do occur in many situations when the unperturbed deterministic systems experience elementary, codimension-one bifurcations such as saddle-node and homoclinic bifurcations. A hard bifurcation is defined as discontinuous change in the density function or support of a stationary measure of the system. | Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights. | eng_Latn | 10,881 |
We consider a complete study of the influence of the cavity size on the spontaneous decay of an atom excited state, roughly approximated by a harmonic oscillator. We confine the oscillator-field system in a spherical cavity of radius $R$, perfectly reflective, and work in the formalism of dressed coordinates and states, which allows to perform non-perturbative calculations for the probability of the atom to decay spontaneously from the first excited state to the ground state. In free space, $R\to\infty$, we obtain known exact results an for sufficiently small $R$ we have developed a power expansion calculation in this parameter. Furthermore, for arbitrary cavity size radius, we developed numerical computations and showed complete agreement with the exact one for $R\to\infty$ and the power expansion results for small cavities, in this way showing the robustness of our results. We have found that in general the spontaneous decay of an excited state of the atom increases with the cavity size radius and vice versa. For sufficiently small cavities the atom practically does not suffers spontaneous decay, whereas for large cavities the spontaneous decay approaches the free-space $R\to\infty$ value. On the other hand, for some particular values of the cavity radius, in which the cavity is in resonance with the natural frequency of the atom, the spontaneous decay transition probability is increased compared to the free-space case. Finally, we showed how the probability spontaneous decay go from an oscillatory time behaviour, for finite cavity radius, to an almost exponential decay, for free space. | Fundamentals Survey of the Various Approaches Path Integral Description of Open Quantum Systems Imaginary-Time and Real-Time Approaches Influence Functional Method Phenomenological and Microscopic System-Plus-Reservoir Models Linear and Nonlinear Quantum Environments Ohmic, Super-Ohmic, and Sub-Ohmic Dissipation Quantum Decoherence and Relaxation Correlation Functions, Response Functions, and Fluctuation-Dissipation Theorem Damped Quantum Mechanical Harmonic Oscillator Quantum Brownian Motion Thermodynamic Variational Approach and Effective Potential Method Unified Approach to Quantum-Statistical Metastability: From Thermal Activation to Quantum Tunneling Electron Transfer and Incoherent Tunneling Macroscopic Quantum Effects in Josephson Systems Spin-Boson Model and Qubit Dissipative Two-State System: Thermodynamics and Dynamics Single-Charge and Cooper-Pair Tunneling Magnetic and Spin Tunneling Driven Quantum Tunneling Nonequilibrium Quantum Transport Full Counting Statistics Charge Transport in Quantum Impurity Systems Duality and Self-Duality. | Private charity has often been modelled as a pure public good. The results reported in this paper, however, suggest that this model of altruism fails to confirm even the broadest empirical observations about charity. In particular, as the size of the economy grows, the fraction contributing to the public good diminishes to zero. This and other results imply that this approach leads to a very limited model with little, if any, predictive power. A truly descriptive model of privately provided public goods must be generalized to include other non-altruistic motives for giving. | eng_Latn | 10,882 |
We introduce a novel class of higher-order, three-mode states called K-dimensional trio coherent states. We study their mathematical properties and prove that they form a complete set in a truncated Fock space. We also study their physical content by explicitly showing that they exhibit nonclassical features such as oscillatory number distribution, sub-Poissonian statistics, Cauchy–Schwarz inequality violation and phase-space quantum interferences. Finally, we propose an experimental scheme to realize the state with K = 2 in the quantized vibronic motion of a trapped ion. | In this contribution we study a superposition of two finite dimensional trio coherent states (FTCS). The state is regarded as a correlated three-mode state in finite dimensional bases. The framework of Pegg and Barnett formalism, and the phase distribution in addition to the Poissonian distribution are examined. It is shown that the eigenvalue of the difference of the photon number (the q-parameter) is responsible for the non-classical phenomenon. Furthermore, the quasi-probability distribution functions (the Wigner and Q-functions) are also discussed. In this case and for the Wigner function the non-classical behavior is only reported for the odd values of the q-parameter. | ABSTRACTUNC-45A is an ubiquitously expressed protein highly conserved throughout evolution. Most of what we currently know about UNC-45A pertains to its role as a regulator of the actomyosin system... | eng_Latn | 10,883 |
The collision between two counterpropagating dust acoustic solitary waves in a strongly coupled dusty plasma has been observed. The measured velocity and width of the solitary wave agree with the solution of the Korteweg-de Vries equation derived by using the generalized hydrodynamic model. The two counterpropagating solitary waves of equal amplitude merge into a single pulse with twice the individual soliton amplitude and then pass through each other. The solitons suffer a small time delay in propagation after collision. The measured delay time obtained from their trajectories is also presented. | The rarefactive KdV solitary waves in a dusty plasma have been extensively studied analytically and found experimentally in the previous works. Though the envelope solitary wave described by a nonlinear Schrödinger equation (NLSE) has been proposed by using the reductive perturbation method, it is first verified by using the particle-in-cell (PIC) numerical method in this paper. Surprisingly, there is no phase shift after the head on collision between two envelope solitary waves, while it is sure that there are phase shifts of two colliding KdV solitary waves after head on collision. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,884 |
We realize an experimental control over the topological stability of three-lobe discrete vortex solitons by modifying the symmetry of a hexagonal photonic lattice optically induced in a photorefractive crystal. By continuously deforming the lattice wave in one transverse direction, we manipulate the coupling between lattice sites and induce or inhibit the reversal of soliton vorticity. | In this work we study quantum signatures of charge flipping vortices[1], found in the classical discrete nonlinear Schrodinger trimer[2], by use of the Bose-Hubbard model. We are able to identify s ... | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,885 |
The phenomenon of wave tails has attracted much attention over the years from both physicists and mathematicians. However, our understanding of this fascinating phenomenon is not complete yet. In particular, most former studies of the tail phenomenon have focused on scattering potentials which approach zero asymptotically ($x\to\infty$) faster than $x^{-2}$. It is well-known that for these (rapidly decaying) scattering potentials the late-time tails are determined by the first Born approximation and are therefore {\it linear} in the amplitudes of the scattering potentials (there are, however, some exceptional cases in which the first Born approximation vanishes and one has to consider higher orders of the scattering problem). In the present study we analyze in detail the late-time dynamics of the Klein-Gordon wave equation with a ({\it slowly} decaying) Coulomb-like scattering potential: $V(x\to\infty)=\alpha/x$. In particular, we write down an explicit solution (that is, an exact analytic solution which is not based on the first Born approximation) for this scattering problem. It is found that the asymptotic ($t\to\infty$) late-time behavior of the fields depends {\it non}-linearly on the amplitude $\alpha$ of the scattering potential. This non-linear dependence on the amplitude of the scattering potential reflects the fact that the late-time dynamics associated with this slowly decaying scattering potential is dominated by {\it multiple} scattering from asymptotically far regions. | The main aim of this paper is twofold. (1) Exact solutions of a scalar field in the Schwarzschild spacetime are presented. The exact wave functions of scattering states and bound-states are presented. Besides the exact solution, we also provide explicit approximate expressions for bound-state eigenvalues and scattering phase shifts. (2) By virtue of the exact solutions, we give a direct calculation for the discontinuous jump on the horizon for massive scalar fields, while in literature such a jump is obtained from an asymptotic solution by an analytic extension treatment. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,886 |
The Kibble–Zurek mechanism is applied to the spontaneous formation of vortices in a harmonically trapped thermal gas following a temperature quench through the critical value for Bose–Einstein condensation. Whereas in the homogeneous scenario, vortex nucleation is always expected, we show that it can be completely suppressed in the presence of the confinement potential whenever the speed of the spatial front undergoing condensation is lower than a threshold velocity. Otherwise, the interplay between the geometry and the causality leads to different scaling laws for the density of vortices as a function of the quench rate, as we also illustrate for the case of a toroidal trapping potential. | The Kibble–Zurek scaling describes the driven critical dynamics starting with an equilibrium state far away from the critical point. Recently, it has been shown that scaling behaviors also exist when the fluctuation term changes starting near the critical point. In this case, the relevant initial conditions should be included in the scaling theory as additional scaling variables. Here, we study the driven quantum critical dynamics in which a symmetry-breaking field is linearly changed starting from the vicinity of the critical point. We find that, similar to the case of changing the fluctuation term, scaling behaviors in the driven dynamics can be described by the Kibble–Zurek scaling with the initial symmetry-breaking field being included as its additional scaling variable. Both the cases of zero and finite temperatures are considered, and the scaling forms of the order parameter and the entanglement entropy are obtained. We numerically verify the scaling theory by taking the quantum Ising model as an example. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,887 |
In the Memory of Shlomo Alexander.- Topological Considerations in Superconductivity.- The de Gennes-Alexander Theory of Superconducting Micronetworks.- Nodal Sets, Multiplicity and Superconductivity in Non-simply Connected Domains.- Connectivity and Flux Confinement Phenomena in Nanostructured Superconductors.- Zero Set of the Order Parameter, Especially in Rings.- Persistent Currents in Ginzburg-Landau Models.- On the Normal/Superconducting Phase Transition in the Presence of Large Magnetic Fields.- On the Numerical Solution of the Time-Dependent Ginzburg-Landau Equations in Multiply Connected Domains.- Formation of Vortex-Antivortex Pairs.- The Order Parameter as a Macroscopic Quantum Wavefunction.- The Ehrenberg-Siday-Aharonov-Bohm Effect.- Connectivity and Superconductivity in Inhomogeneous Structures. | Many analyses based on the time-dependent Ginzburg--Landau model are not consistent with statistical mechanics, because thermal fluctuations are not taken correctly into account. We use the fluctuation-dissipation theorem in order to establish the appropriate size of the Langevin terms, and thus ensure the required consistency. Fluctuations of the electromagnetic potential are essential, even when we evaluate quantities that do not depend directly on it. Our method can be cast in gauge-invariant form. We perform numerous tests, and all the results are in agreement with statistical mechanics. We apply our method to evaluate paraconductivity of a superconducting wire. The Aslamazov--Larkin result is recovered as a limiting situation. Our method is numerically stable and the nonlinear term is easily included. We attempt a comparison between our numerical results and the available experimental data. Within an appropriate range of currents, phase slips occur, but we found no evidence for thermally activated phase slips. We studied the behavior of a moderate constriction. A constriction pins and enhances the occurrence of phase slips. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,888 |
We study many-body systems in $d$ dimensions interacting with a purely attractive pair potential $\ensuremath{\sim}|{\mathbf{x}}_{i}\ensuremath{-}{\mathbf{x}}_{j}{|}^{\ensuremath{\nu}}$, where ${\mathbf{x}}_{i}$ is the position vector of particle $i$, and $\ensuremath{\nu}$ is a positive parameter. We derive the temperature in microcanonical equilibrium for arbitrary $\ensuremath{\nu}$ and $d$ and, for $d=1$, the corresponding velocity distribution for a finite number $N$ of particles. The latter reduces to the Maxwell-Boltzmann distribution in the infinite-particle limit. The one-dimensional particle distribution of the equilibrium cluster in the mean-field limit is computed numerically for various potential parameters $\ensuremath{\nu}$. We test these theoretical expressions by comparing them to extensive computer simulation results of one-dimensional systems and find close agreement for $\ensuremath{\nu}=1$ (the sheet model) and $\ensuremath{\nu}=4.5$. In similar simulations for $\ensuremath{\nu}=1.5$ the macroscopic relaxation time exceeded the length of our simulation runs and the system did not relax towards the known microcanonical equilibrium state. We also compute full Lyapunov spectra for the linear sheet model and find that the Kolmogorov-Sinai entropy starts to increase linearly with $N$ for $Ng10$. | Dedicated to Yakov Sinai and David Ruelle on the occasion of their 65th birthday ABSTRACT. We propose a definition of microcanonical and canonical statistical ensem- bles based on the concept of density of states. This definition applies both to the classical and the quantum case. For the microcanonical case this allows for a definition of a temper- ature and its fluctuation, which might be useful in the theory of mesoscopic systems. In the quantum case the concept of density of states applies to one-particle Schr ¨ odinger operators, in particular to operators with a periodic potential or to random Anderson type models. In the case of periodic potentials we show that for the resulting n-particle system the density of states is ((n - 1)/2) times differentiable, such that like for classical microcanonical en- sembles a (positive) temperature may be defined whenever n ≥ 5. We expect that a similar result should also hold for Anderson type models. We also provide the first terms in as- ymptotic expansions of thermodynamic quantities at large energies for the microcanonical ensemble and at large temperatures for the canonical ensemble. A comparison shows that then both formulations asymptotically give the same results. | We report enhancement of the mechanical stability of graphene through a one-step method to disperse gold nanoparticles on the pristine graphene without any added agent. | eng_Latn | 10,889 |
This paper presents collective variable approach for super-sech soliton dynamics in optical metamaterials. The soliton dynamics is governed by the generalized nonlinear Schrodinger's equation. The numerical simulations of pulse width, amplitude, chirp and frequency are given. | Employing collective variable approach, femtosecond pulse propagation has been investigated in optical fibers using the higher order nonlinear Schrodinger equation. In order to view the pulse dynamics along the propagation distance, variation of different pulse parameters, called collective variables, such as pulse amplitude, width, chirp, pulse center and frequency has been investigated by numerically solving the set of ordinary equations obtained from collective variable approach. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,890 |
Motivated by recent experiments, we investigate the system of isotropically-interacting bosons with Rashba spin-orbit coupling. At the non-interacting level, there is a macroscopic ground-state degeneracy due to the many ways bosons can occupy the Rashba spectrum. Interactions treated at the mean-field level restrict the possible ground-state configurations, but there remains an accidental degeneracy not corresponding to any symmetry of the Hamiltonian, indicating the importance of fluctuations. By finding analytical expressions for the collective excitations in the long-wavelength limit and through numerical solution of the full Bogoliubov- de Gennes equations, we show that the system condenses into a single momentum state of the Rashba spectrum via the mechanism of order by disorder. We show that in 3D the quantum depletion for this system is small, while the thermal depletion has an infrared logarithmic divergence, which is removed for finite-size systems. In 2D, on the other hand, thermal fluctuations destabilize the system. | Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonian are required for suppressing the condensation. Here, we show that ultra cold atoms with synthetic spin-orbit coupling provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where the single-particle ground state shrinks to a point from a circle in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,891 |
We demonstrate that a site-dependent driving of a periodic potential allows for the controlled manipulation of a quantum particle on length scales of the lattice spacing. Specifically we observe for distinct driving frequencies a near depletion of certain sites which is explained by a resonant mixing of the involved Floquet-Bloch modes occurring at these frequencies. Our results could be exploited as a scheme for a site-selective loading of e.g. ultracold atoms into an optical lattices. | Part I: Pictures And Concepts The Time Dependent Schrodinger Equation The Free Particle Wave Packet The Gaussian Wavepacket Classical-quantum Correspondence The Wigner Representation Correlation Functions and Spectra One Dimensional Barrier Scattering Part II: Formal Theory And Methods Of Approximation Linear Algebra and Quantum Mechanics Approximate Solutions Semiclassical Mechanics Numerical Methods Part III: Applications Introduction to Molecular Dynamics Femtosecond Pulse Pair Excitation One- and Two-Photon Electronic Spectroscopy Strong Field Excitation Design of Femtosecond Pulse Sequences to Control Reactions Wavepacket Approach to Photodissociation Wavepacket Approach to Reactive Scattering Projects Index | Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights. | eng_Latn | 10,892 |
The interaction between two two-level atoms via photon exchange is simulated. The language of qubits is used with the aim of possible application of this model to the construction of quantum processors based on the interaction of several atoms with unit photons. The study involves a qubit form of the Jaynes-Cummings-Hubbard model with two-photon excitations and its polariton modification, in which any displacement of photons between cavities is associated with a photon absorbed or emitted by an atom. Relaxation is described by the Kossakowski-Lindblad equation for the density matrix of electron and photon states. The relaxation time is obtained as a function of the photon transition probability between atoms and of the amplitude of the photon interaction with an atom. Additionally, the degree of agreement between the density matrices in both models is calculated. An artifact of incomplete relaxation is described in the case of fuzzy qubit semantics, when the description of photons depends on their number. | We describe computer methods of simulation of Tavis-Cummings based quantum models, and apply those methods to specific tasks, conductivity measurements of atomic excitations in short chains of optical cavities with two-level atoms, C-Sign optical model, and dark states. For the conductivity measurements, we reproduce the dephasing assisted transport and quantum bottleneck effects and show their relation, and study the "which way?" problem. For the C-Sign optical model, we use the model to find optimal parameters of the system to minimize the error. For dark states, we study their collapse due to dephasing noise. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,893 |
We give a simple derivation of the perturbed Boussinesq and Korteweg--de Vries equations which take into account the effects of the interaction between ion-sound waves and resonance particles. We obtain for the perturbation terms explicit expressions which describe the resonance interaction of solitons with plasma particles in cases which are of real interest from the point of view of laboratory and numerical experiments. We obtain the equations which describe the change in the soliton parameters due to their interaction with resonance particles in a form which is suitable for comparisons with experiments. | A simple model of ion fluctuations (ion acoustic and ion cyclotron fluctuations for example) driven by an elec- tron current which leads to intermittent fluctuations when the linear growth rate exceeds the wave packet dispersion rate is analized. The normalized fluctuation amplitude e 0/T can be much larger than the mass ratio (me/mi) level predicted by the conventional quasilinear theory or Manheimer's the- ory (see references in this document), and where 0 repre- sents the amplitude of the main peak of the ion fluctuations. Although the ion motion is linear, intermittency is produced by the strong nonlinear electron response, which causes the electron momentum input to the ion fluctuations to be spa- tially localized. We treat the 1-D case because it is espe- cially simple from an intuitive and analytical point of view, but it is readily apparent and one can put forward the conjec- ture that the effect occurs in a three dimensional magnetized plasma. The 1-D analysis, as shown in this manuscript will clearly help identify the subtle difference between turbulence as conventionally understood and intermittency as it occurs in space and laboratory plasmas. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,894 |
We consider systems, which conserve the particle number and are described by Schr\"odinger equations containing complex nonlinearities. In the case of canonical systems, we study their main symmetries and conservation laws. We introduce a Cole-Hopf like transformation both for canonical and noncanonical systems, which changes the evolution equation into another one containing purely real nonlinearities, and reduces the continuity equation to the standard form of the linear theory. This approach allows us to treat, in a unifying scheme, a wide variety of canonical and noncanonical nonlinear systems, some of them already known in the literature. pacs{PACS number(s): 02.30.Jr, 03.50.-z, 03.65.-w, 05.45.-a, 11.30.Na, 11.40.Dw | A large class of physically important nonlinear and nonhomogeneous evolution problems, characterized by advection-like and diffusion-like processes, can be usefully studied by a time-differential form of Kolmogorov's solution of the backward-time Fokker-Planck equation. The differential solution embodies an integral representation theorem by which any physical or mathematical entity satisfying a generalized nonhomogeneous advection-diffusion equation can be calculated incrementally in time. The utility of the approach for tackling nonlinear problems is illustrated via solution of the noise-free Burgers and related Kardar-Parisi-Zhang (KPZ) equations where it is shown that the differential Kolmogorov solution encompasses, and allows derivation of, the classical Cole-Hopf and KPZ transformations and solutions. A second example, illustrating application of this approach to nonhomogeneous evolution problems, derives the Feynman-Kac formula appropriate to a Schrodinger-like equation. | We describe a direct method for solving sparse linear least squares problems. The storage required for the method is no more than that needed for the conventional normal equations approach. However, the normal equations are not computed; orthogonal transformations are applied to the coefficient matrix, thus avoiding the potential numerical instability associated with computing the normal equations. Our approach allows full exploitation of sparsity, and permits the use of a fixed (static) data structure during the numerical computation. Finally, the method processes the coefficient matrix one row at a time, allowing for the convenient use of auxiliary storage and updating operations. | eng_Latn | 10,895 |
We present a laser beam shaping method using acousto-optic deflection of light and discuss its application to dipole trapping of ultracold atoms. By driving the acousto-optic deflector with multiple frequencies, we generate an array of overlapping diffraction-limited beams that combine to form an arbitrary-shaped smooth and continuous trapping potential. Confinement of atoms in a flat-bottomed potential formed by a laser beam with uniform intensity over its central region confers numerous advantages over the harmonic confinement intrinsic to Gaussian beam dipole traps and many other trapping schemes. We demonstrate the versatility of this beam shaping method by generating potentials with large flat-topped regions as well as intensity patterns that compensate for residual external potentials to create a uniform background to which the trapping potential of experimental interest can be added. | We have created a Bose-Einstein condensate (BEC) of ${}^{87}\mathrm{Rb}$ atoms directly in an optical trap. We employ a quasielectrostatic dipole force trap formed by two crossed ${\mathrm{CO}}_{2}$ laser beams. Loading directly from a sub-Doppler laser-cooled cloud of atoms results in initial phase space densities of $\ensuremath{\sim}1/200$. Evaporatively cooling through the BEC transition is achieved by lowering the power in the trapping beams over $\ensuremath{\sim}2\mathrm{s}$. The resulting condensates are $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ spinors with $3.5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ atoms distributed between the ${m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(\ensuremath{-}1,0,1)$ states. | Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights. | eng_Latn | 10,896 |
We present first steps toward understanding the ultracold scattering properties of polar molecules in strong electric field-seeking states. We have found that the elastic cross section displays a quasiregular set of potential resonances as a function of the electric field, which potentially offers intimate details about the intermolecular interaction. We illustrate these resonances in a ``toy'' model composed of pure dipoles, and in more physically realistic systems. To analyze these resonances, we use a simple WKB approximation to the eigenphase, which proves both reasonably accurate and meaningful. A general treatment of the Stark effect and dipolar interactions is also presented. | In this review chapter we focus on the many-body dynamics of cold polar molecules in the strongly interacting regime. In particular, we discuss a toolbox for engineering many-body Hamiltonians based on the manipulation of the electric dipole moments of the molecules, and thus of molecular interactions, using external static and microwave fields. This forms the basis for the realization of novel quantum phases in these systems. | Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights. | eng_Latn | 10,897 |
We introduce the one-dimensional PT-symmetric Schrodinger equation, with complex potentials in the form of the canonical superoscillatory and suboscillatory functions known in quantum mechanics and optics. While the suboscillatory-like potential always generates an entirely real eigenvalue spectrum, its counterpart based on the superoscillatory wave function gives rise to an intricate pattern of PT-symmetry-breaking transitions, controlled by the parameters of the superoscillatory function. One scenario of the transitions proceeds smoothly via a set of threshold values, while another one exhibits a sudden jump to the broken PT symmetry. Another noteworthy finding is the possibility of restoration of the PT symmetry, following its original loss, in the course of the variation of the parameters. | The spectral, dynamical and topological properties of physical systems described by non-Hermitian (including $\mathcal{PT}$-symmetric) Hamiltonians are deeply modified by the appearance of exceptional points and spectral singularities. Here we show that exceptional points in the continuum can arise in non-Hermitian (yet admitting and entirely real-valued energy spectrum) optical lattices with engineered defects. At an exceptional point, the lattice sustains a bound state with an energy embedded in the spectrum of scattered states, similar to the von-Neumann Wigner bound states in the continuum of Hermitian lattices. However, the dynamical and scattering properties of the bound state at an exceptional point are deeply different from those of ordinary von-Neumann Wigner bound states in an Hermitian system. In particular, the bound state in the continuum at an exceptional point is an unstable state that can secularly grow by an infinitesimal perturbation. Such properties are discussed in details for transport of discretized light in a $\mathcal{PT}$-symmetric array of coupled optical waveguides, which could provide an experimentally accessible system to observe exceptional points in the continuum. | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,898 |
We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schr\"odinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic field, and confined in a strong optical lattice. When the nonlinear coupling strengths are equal, we use a unitary transformation to remove the linear coupling terms, and show that the existing soliton solutions oscillate from one species to the other. When the nonlinear coupling strengths are different, the soliton dynamics is numerically investigated and the findings are compared to the results of an effective two-mode model. The case of two linearly coupled Ablowitz-Ladik equations is also investigated. | 1. The Birth of a Paradigm 2. Linear Wave Theory 3. The Classical Soliton Equations 4. Reaction-Diffusion Systems 5. Nonlinear Lattices 6. Inverse Scattering Methods 7. Peturbation Theory 8. Quantum Lattice Solitons 9. Looking Ahead Bibliography Index | We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero. | eng_Latn | 10,899 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.