346 research outputs found
More ergodic billiards with an infinite cusp
In a previous paper (nlin.CD/0107041) the following class of billiards was
studied: For convex,
sufficiently smooth, and vanishing at infinity, let the billiard table be
defined by , the planar domain delimited by the positive -semiaxis, the
positive -semiaxis, and the graph of .
For a large class of we proved that the billiard map was hyperbolic.
Furthermore we gave an example of a family of that makes this map ergodic.
Here we extend the latter result to a much wider class of functions.Comment: 13 pages, 4 figure
Escape Orbits for Non-Compact Flat Billiards
It is proven that, under some conditions on , the non-compact flat
billiard
has no orbits going {\em directly} to . The relevance of such
sufficient conditions is discussed.Comment: 9 pages, LaTeX, 3 postscript figures available at
http://www.princeton.edu/~marco/papers/ . Minor changes since previously
posted version. Submitted to 'Chaos
Nonlinear wave interactions in quantum magnetoplasmas
Nonlinear interactions involving electrostatic upper-hybrid (UH),
ion-cyclotron (IC), lower-hybrid (LH), and Alfven waves in quantum
magnetoplasmas are considered. For this purpose, the quantum hydrodynamical
equations are used to derive the governing equations for nonlinearly coupled
UH, IC, LH, and Alfven waves. The equations are then Fourier analyzed to obtain
nonlinear dispersion relations, which admit both decay and modulational
instabilities of the UH waves at quantum scales. The growth rates of the
instabilities are presented. They can be useful in applications of our work to
diagnostics in laboratory and astrophysical settings.Comment: 15 pages, to appear in Physics of Plasma
The comparative analysis of statistics, based on the likelihood ratio criterion, in the automated annotation problem
<p>Abstract</p> <p>Background</p> <p>This paper discusses the problem of automated annotation. It is a continuation of the previous work on the A<sup>4</sup>-algorithm (Adaptive algorithm of automated annotation) developed by Leontovich and others.</p> <p>Results</p> <p>A number of new statistics for the automated annotation of biological sequences is introduced. All these statistics are based on the likelihood ratio criterion.</p> <p>Conclusion</p> <p>Some of the statistics yield a prediction quality that is significantly higher (up to 1.5 times higher) in comparison with the results obtained with the A<sup>4</sup>-procedure.</p
Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics
Stochastic thermodynamics of chemical reaction systems has recently gained
much attention. In the present paper, we consider such an issue for a system
with both oscillatory and excitable dynamics, using catalytic oxidation of
carbon monoxide on the surface of platinum crystal as an example. Starting from
the chemical Langevin equations, we are able to calculate the stochastic
entropy production P along a random trajectory in the concentration state
space. Particular attention is paid to the dependence of the time averaged
entropy productionP on the system sizeN in a parameter region close to the
deterministic Hopf bifurcation.In the large system size (weak noise) limit, we
find that P N^{\beta} with {\beta}=0 or 1 when the system is below or abovethe
Hopf bifurcation, respectively. In the small system size (strong noise) limit,
P always increases linearly with N regardless of the bifurcation parameter.
More interestingly,P could even reach a maximum for some intermediate system
size in a parameter region where the corresponding deterministic system shows
steady state or small amplitude oscillation. The maximum value of P decreases
as the system parameter approaches the so-called CANARD point where the maximum
disappears.This phenomenon could be qualitativelyunderstood by partitioning the
total entropy production into the contributions of spikes and of small
amplitude oscillations.Comment: 13 pages, 6 figure
Collisional Energy Loss of Fast Charged Particles in Relativistic Plasmas
Following an argument by Kirzhnits we rederive an exact expression for the
energy loss of a fast charged particle in a relativistic plasma using the
quantum field theoretical language. We compare this result to perturbative
calculations of the collisional energy loss of an energetic electron or muon in
an electron-positron plasma and of an energetic parton in the quark-gluon
plasma.Comment: 9 pages, LATEX, 2 PostScript figure
Magnetic Force Exerted by the Aharonov-Bohm Line
The problem of the scattering of a charge by the Aharonov-Bohm (AB) flux line
is reconsidered in terms of finite width beams. It is shown that despite the
left-right symmetry in the AB scattering cross-section, the charge is scattered
asymmetrically. The asymmetry (i.e. magnetic force) originates from almost
forward scattering within the angular size of the incident wave. In the
paraxial approximation, the real space solution to the scattering problem of a
beam is found as well as the scattering S-matrix. The Boltzmann kinetics and
the Landau quantization in a random AB array are considered.Comment: 5 pages, RevTeX. Discussions of paraxial approximation to the
Aharonov-Bohm solution (Cornu spiral) and S-matrix, are extended. References
are adde
Nonlinear interaction of light with Bose-Einstein condensate: new methods to generate subpoissonian light
We consider -type model of the Bose-Einstein condensate of sodium
atoms interacting with the light. Coefficients of the Kerr-nonlinearity in the
condensate can achieve large and negative values providing the possibility for
effective control of group velocity and dispersion of the probe pulse. We find
a regime when the observation of the "slow" and "fast" light propagating
without absorption becomes achievable due to strong nonlinearity. An effective
two-level quantum model of the system is derived and studied based on the su(2)
polynomial deformation approach. We propose an efficient way for generation of
subpoissonian fields in the Bose-Einstein condensate at time-scales much
shorter than the characteristic decay time in the system. We show that the
quantum properties of the probe pulse can be controlled in BEC by the classical
coupling field.Comment: 13 pages, 6 figures, 1 tabl
Landau Damping and Coherent Structures in Narrow-Banded 1+1 Deep Water Gravity Waves
We study the nonlinear energy transfer around the peak of the spectrum of
surface gravity waves by taking into account nonhomogeneous effects. In the
narrow-banded approximation the kinetic equation resulting from a
nonhomogeneous wave field is a Vlasov-Poisson type equation which includes at
the same time the random version of the Benjamin-Feir instability and the
Landau damping phenomenon. We analytically derive the values of the Phillips'
constant and the enhancement factor for which the
narrow-banded approximation of the JONSWAP spectrum is unstable. By performing
numerical simulations of the nonlinear Schr\"{o}dinger equation we check the
validity of the prediction of the related kinetic equation. We find that the
effect of Landau damping is to suppress the formation of coherent structures.
The problem of predicting freak waves is briefly discussed.Comment: 4 pages, 3 figure
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