1,458 research outputs found
Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases II: Open Systems
We calculate the spectrum of Lyapunov exponents for a point particle moving
in a random array of fixed hard disk or hard sphere scatterers, i.e. the
disordered Lorentz gas, in a generic nonequilibrium situation. In a large
system which is finite in at least some directions, and with absorbing boundary
conditions, the moving particle escapes the system with probability one.
However, there is a set of zero Lebesgue measure of initial phase points for
the moving particle, such that escape never occurs. Typically, this set of
points forms a fractal repeller, and the Lyapunov spectrum is calculated here
for trajectories on this repeller. For this calculation, we need the solution
of the recently introduced extended Boltzmann equation for the nonequilibrium
distribution of the radius of curvature matrix and the solution of the standard
Boltzmann equation. The escape-rate formalism then gives an explicit result for
the Kolmogorov Sinai entropy on the repeller.Comment: submitted to Phys Rev
Evolution of collision numbers for a chaotic gas dynamics
We put forward a conjecture of recurrence for a gas of hard spheres that
collide elastically in a finite volume. The dynamics consists of a sequence of
instantaneous binary collisions. We study how the numbers of collisions of
different pairs of particles grow as functions of time. We observe that these
numbers can be represented as a time-integral of a function on the phase space.
Assuming the results of the ergodic theory apply, we describe the evolution of
the numbers by an effective Langevin dynamics. We use the facts that hold for
these dynamics with probability one, in order to establish properties of a
single trajectory of the system. We find that for any triplet of particles
there will be an infinite sequence of moments of time, when the numbers of
collisions of all three different pairs of the triplet will be equal. Moreover,
any value of difference of collision numbers of pairs in the triplet will
repeat indefinitely. On the other hand, for larger number of pairs there is but
a finite number of repetitions. Thus the ergodic theory produces a limitation
on the dynamics.Comment: 4 pages, published versio
Ultralow-power local laser control of the dimer density in alkali-metal vapors through photodesorption
Ultralow-power diode-laser radiation is employed to induce photodesorption of
cesium from a partially transparent thin-film cesium adsorbate on a solid
surface. Using resonant Raman spectroscopy, we demonstrate that this
photodesorption process enables an accurate local optical control of the
density of dimer molecules in alkali-metal vapors.Comment: 4 pages, 4 figure
Relating chaos to deterministic diffusion of a molecule adsorbed on a surface
Chaotic internal degrees of freedom of a molecule can act as noise and affect
the diffusion of the molecule on a substrate. A separation of time scales
between the fast internal dynamics and the slow motion of the centre of mass on
the substrate makes it possible to directly link chaos to diffusion. We discuss
the conditions under which this is possible, and show that in simple atomistic
models with pair-wise harmonic potentials, strong chaos can arise through the
geometry. Using molecular-dynamics simulations, we demonstrate that a realistic
model of benzene is indeed chaotic, and that the internal chaos affects the
diffusion on a graphite substrate
Rectification of thermal fluctuations in ideal gases
We calculate the systematic average speed of the adiabatic piston and a
thermal Brownian motor, introduced in [Van den Broeck, Kawai and Meurs,
\emph{Microscopic analysis of a thermal Brownian motor}, to appear in Phys.
Rev. Lett.], by an expansion of the Boltzmann equation and compare with the
exact numerical solution.Comment: 18 page
Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases I: Equilibrium Systems
We compute the Lyapunov spectrum and the Kolmogorov-Sinai entropy for a
moving particle placed in a dilute, random array of hard disk or hard sphere
scatterers - i.e. the dilute Lorentz gas model. This is carried out in two
ways: First we use simple kinetic theory arguments to compute the Lyapunov
spectrum for both two and three dimensional systems. In order to provide a
method that can easily be generalized to non-uniform systems we then use a
method based upon extensions of the Lorentz-Boltzmann (LB) equation to include
variables that characterize the chaotic behavior of the system. The extended LB
equations depend upon the number of dimensions and on whether one is computing
positive or negative Lyapunov exponents. In the latter case the extended LB
equation is closely related to an "anti-Lorentz-Boltzmann equation" where the
collision operator has the opposite sign from the ordinary LB equation. Finally
we compare our results with computer simulations of Dellago and Posch and find
very good agreement.Comment: 48 pages, 3 ps fig
Aging to non-Newtonian hydrodynamics in a granular gas
The evolution to the steady state of a granular gas subject to simple shear
flow is analyzed by means of computer simulations. It is found that, regardless
of its initial preparation, the system reaches (after a transient period
lasting a few collisions per particle) a non-Newtonian (unsteady) hydrodynamic
regime, even at strong dissipation and for states where the time scale
associated with inelastic cooling is shorter than the one associated with the
irreversible fluxes. Comparison with a simplified rheological model shows a
good agreement.Comment: 6 pages, 4 figures; v2: improved version to be published in EP
Fluctuations and correlations in an individual-based model of biological coevolution
We extend our study of a simple model of biological coevolution to its
statistical properties. Staring with a complete description in terms of a
master equation, we provide its relation to the deterministic evolution
equations used in previous investigations. The stationary states of the
mutationless model are generally well approximated by Gaussian distributions,
so that the fluctuations and correlations of the populations can be computed
analytically. Several specific cases are studied by Monte Carlo simulations,
and there is excellent agreement between the data and the theoretical
predictions.Comment: 25 pages, 2 figure
Phase-Space Metric for Non-Hamiltonian Systems
We consider an invariant skew-symmetric phase-space metric for
non-Hamiltonian systems. We say that the metric is an invariant if the metric
tensor field is an integral of motion. We derive the time-dependent
skew-symmetric phase-space metric that satisfies the Jacobi identity. The
example of non-Hamiltonian systems with linear friction term is considered.Comment: 12 page
Transport coefficients for dense hard-disk systems
A study of the transport coefficients of a system of elastic hard disks,
based on the use of Helfand-Einstein expressions is reported. The
self-diffusion, the viscosity, and the heat conductivity are examined with
averaging techniques especially appropriate for the use in event-driven
molecular dynamics algorithms with periodic boundary conditions. The density
and size dependence of the results is analyzed, and comparison with the
predictions from Enskog's theory is carried out. In particular, the behavior of
the transport coefficients in the vicinity of the fluid-solid transition is
investigated and a striking power law divergence of the viscosity in this
region is obtained, while all other examined transport coefficients show a drop
in that density range.Comment: submitted to PR
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