1,131 research outputs found
Front propagation techniques to calculate the largest Lyapunov exponent of dilute hard disk gases
A kinetic approach is adopted to describe the exponential growth of a small
deviation of the initial phase space point, measured by the largest Lyapunov
exponent, for a dilute system of hard disks, both in equilibrium and in a
uniform shear flow. We derive a generalized Boltzmann equation for an extended
one-particle distribution that includes deviations from the reference phase
space point. The equation is valid for very low densities n, and requires an
unusual expansion in powers of 1/|ln n|. It reproduces and extends results from
the earlier, more heuristic clock model and may be interpreted as describing a
front propagating into an unstable state. The asymptotic speed of propagation
of the front is proportional to the largest Lyapunov exponent of the system.
Its value may be found by applying the standard front speed selection mechanism
for pulled fronts to the case at hand. For the equilibrium case, an explicit
expression for the largest Lyapunov exponent is given and for sheared systems
we give explicit expressions that may be evaluated numerically to obtain the
shear rate dependence of the largest Lyapunov exponent.Comment: 26 pages REVTeX, 1 eps figure. Added remarks, a reference and
corrected some typo
Kinetic Theory Estimates for the Kolmogorov-Sinai Entropy and the Largest Lyapunov Exponents for Dilute, Hard-Ball Gases and for Dilute, Random Lorentz Gases
The kinetic theory of gases provides methods for calculating Lyapunov
exponents and other quantities, such as Kolmogorov-Sinai entropies, that
characterize the chaotic behavior of hard-ball gases. Here we illustrate the
use of these methods for calculating the Kolmogorov-Sinai entropy, and the
largest positive Lyapunov exponent, for dilute hard-ball gases in equilibrium.
The calculation of the largest Lyapunov exponent makes interesting connections
with the theory of propagation of hydrodynamic fronts. Calculations are also
presented for the Lyapunov spectrum of dilute, random Lorentz gases in two and
three dimensions, which are considerably simpler than the corresponding
calculations for hard-ball gases. The article concludes with a brief discussion
of some interesting open problems.Comment: 41 pages (REVTEX); 7 figs., 4 of which are included in LaTeX source.
(Fig.7 doesn't print well on some printers) This revised paper will appear in
"Hard Ball Systems and the Lorentz Gas", D. Szasz ed., Encyclopaedia of
Mathematical Sciences, Springe
Controlling Molecular Scattering by Laser-Induced Field-Free Alignment
We consider deflection of polarizable molecules by inhomogeneous optical
fields, and analyze the role of molecular orientation and rotation in the
scattering process. It is shown that molecular rotation induces spectacular
rainbow-like features in the distribution of the scattering angle. Moreover, by
preshaping molecular angular distribution with the help of short and strong
femtosecond laser pulses, one may efficiently control the scattering process,
manipulate the average deflection angle and its distribution, and reduce
substantially the angular dispersion of the deflected molecules. We provide
quantum and classical treatment of the deflection process. The effects of
strong deflecting field on the scattering of rotating molecules are considered
by the means of the adiabatic invariants formalism. This new control scheme
opens new ways for many applications involving molecular focusing, guiding and
trapping by optical and static fields
Constructing smooth potentials of mean force, radial, distribution functions and probability densities from sampled data
In this paper a method of obtaining smooth analytical estimates of
probability densities, radial distribution functions and potentials of mean
force from sampled data in a statistically controlled fashion is presented. The
approach is general and can be applied to any density of a single random
variable. The method outlined here avoids the use of histograms, which require
the specification of a physical parameter (bin size) and tend to give noisy
results. The technique is an extension of the Berg-Harris method [B.A. Berg and
R.C. Harris, Comp. Phys. Comm. 179, 443 (2008)], which is typically inaccurate
for radial distribution functions and potentials of mean force due to a
non-uniform Jacobian factor. In addition, the standard method often requires a
large number of Fourier modes to represent radial distribution functions, which
tends to lead to oscillatory fits. It is shown that the issues of poor sampling
due to a Jacobian factor can be resolved using a biased resampling scheme,
while the requirement of a large number of Fourier modes is mitigated through
an automated piecewise construction approach. The method is demonstrated by
analyzing the radial distribution functions in an energy-discretized water
model. In addition, the fitting procedure is illustrated on three more
applications for which the original Berg-Harris method is not suitable, namely,
a random variable with a discontinuous probability density, a density with long
tails, and the distribution of the first arrival times of a diffusing particle
to a sphere, which has both long tails and short-time structure. In all cases,
the resampled, piecewise analytical fit outperforms the histogram and the
original Berg-Harris method.Comment: 14 pages, 15 figures. To appear in J. Chem. Phy
An Extension of the Fluctuation Theorem
Heat fluctuations are studied in a dissipative system with both mechanical
and stochastic components for a simple model: a Brownian particle dragged
through water by a moving potential. An extended stationary state fluctuation
theorem is derived. For infinite time, this reduces to the conventional
fluctuation theorem only for small fluctuations; for large fluctuations, it
gives a much larger ratio of the probabilities of the particle to absorb rather
than supply heat. This persists for finite times and should be observable in
experiments similar to a recent one of Wang et al.Comment: 12 pages, 1 eps figure in color (though intelligible in black and
white
Electric Deflection of Rotating Molecules
We provide a theory of the deflection of polar and non-polar rotating
molecules by inhomogeneous static electric field. Rainbow-like features in the
angular distribution of the scattered molecules are analyzed in detail.
Furthermore, we demonstrate that one may efficiently control the deflection
process with the help of short and strong femtosecond laser pulses. In
particular the deflection process may by turned-off by a proper excitation, and
the angular dispersion of the deflected molecules can be substantially reduced.
We study the problem both classically and quantum mechanically, taking into
account the effects of strong deflecting field on the molecular rotations. In
both treatments we arrive at the same conclusions. The suggested control scheme
paves the way for many applications involving molecular focusing, guiding, and
trapping by inhomogeneous fields
Effective pair potentials for spherical nanoparticles
An effective description for spherical nanoparticles in a fluid of point
particles is presented. The points inside the nanoparticles and the point
particles are assumed to interact via spherically symmetric additive pair
potentials, while the distribution of points inside the nanoparticles is taken
to be spherically symmetric and smooth. The resulting effective pair
interactions between a nanoparticle and a point particle, as well as between
two nanoparticles, are then given by spherically symmetric potentials. If
overlap between particles is allowed, the effective potential generally has
non-analytic points, but for each effective potential the expressions for
different overlapping cases can be written in terms of one analytic auxiliary
potential. Effective potentials for hollow nanoparticles (appropriate e.g. for
buckyballs) are also considered, and shown to be related to those for solid
nanoparticles. Finally, explicit expressions are given for the effective
potentials derived from basic pair potentials of power law and exponential
form, as well as from the commonly used London-Van der Waals, Morse,
Buckingham, and Lennard-Jones potential. The applicability of the latter is
demonstrated by comparison with an atomic description of nanoparticles with an
internal face centered cubic structure.Comment: 27 pages, 12 figures. Unified description of overlapping and
nonoverlapping particles added, as well as a comparison with an idealized
atomic descriptio
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