1,477 research outputs found
Chaotic Scattering Theory of Transport and Reaction-Rate Coefficients
The chaotic scattering theory is here extended to obtain escape-rate
expressions for the transport coefficients appropriate for a simple classical
fluid, or for a chemically reacting system. This theory allows various
transport coefficients such as the coefficients of viscosity, thermal
conductivity, etc., to be expressed in terms of the positive Lyapunov exponents
and Kolmogorov-Sinai entropy of a set of phase space trajectories that take
place on an appropriate fractal repeller. This work generalizes the previous
results of Gaspard and Nicolis for the coefficient of diffusion of a particle
moving in a fixed array of scatterers.Comment: 27 pages LaTeX, no figure
Fractal Dimensions of the Hydrodynamic Modes of Diffusion
We consider the time-dependent statistical distributions of diffusive
processes in relaxation to a stationary state for simple, two dimensional
chaotic models based upon random walks on a line. We show that the cumulative
functions of the hydrodynamic modes of diffusion form fractal curves in the
complex plane, with a Hausdorff dimension larger than one. In the limit of
vanishing wavenumber, we derive a simple expression of the diffusion
coefficient in terms of this Hausdorff dimension and the positive Lyapunov
exponent of the chaotic model.Comment: 20 pages, 6 figures, submitted to Nonlinearit
Transport Properties of the Lorentz Gas in Terms of Periodic Orbits
We establish a formula relating global diffusion in a space periodic
dynamical system to cycles in the elementary cell which tiles the space under
translations.Comment: 8 pages, Postscript, A
Transport and Helfand moments in the Lennard-Jones fluid. II. Thermal Conductivity
The thermal conductivity is calculated with the Helfand-moment method in the
Lennard-Jones fluid near the triple point. The Helfand moment of thermal
conductivity is here derived for molecular dynamics with periodic boundary
conditions. Thermal conductivity is given by a generalized Einstein relation
with this Helfand moment. We compute thermal conductivity by this new method
and compare it with our own values obtained by the standard Green-Kubo method.
The agreement is excellent.Comment: Submitted to the Journal of Chemical Physic
Viscosity in the escape-rate formalism
We apply the escape-rate formalism to compute the shear viscosity in terms of
the chaotic properties of the underlying microscopic dynamics. A first passage
problem is set up for the escape of the Helfand moment associated with
viscosity out of an interval delimited by absorbing boundaries. At the
microscopic level of description, the absorbing boundaries generate a fractal
repeller. The fractal dimensions of this repeller are directly related to the
shear viscosity and the Lyapunov exponent, which allows us to compute its
values. We apply this method to the Bunimovich-Spohn minimal model of viscosity
which is composed of two hard disks in elastic collision on a torus. These
values are in excellent agreement with the values obtained by other methods
such as the Green-Kubo and Einstein-Helfand formulas.Comment: 16 pages, 16 figures (accepted in Phys. Rev. E; October 2003
Chaos properties and localization in Lorentz lattice gases
The thermodynamic formalism of Ruelle, Sinai, and Bowen, in which chaotic
properties of dynamical systems are expressed in terms of a free energy-type
function - called the topological pressure - is applied to a Lorentz Lattice
Gas, as typical for diffusive systems with static disorder. In the limit of
large system sizes, the mechanism and effects of localization on large clusters
of scatterers in the calculation of the topological pressure are elucidated and
supported by strong numerical evidence. Moreover it clarifies and illustrates a
previous theoretical analysis [Appert et al. J. Stat. Phys. 87,
chao-dyn/9607019] of this localization phenomenon.Comment: 32 pages, 19 Postscript figures, submitted to PR
The Fractality of the Hydrodynamic Modes of Diffusion
Transport by normal diffusion can be decomposed into the so-called
hydrodynamic modes which relax exponentially toward the equilibrium state. In
chaotic systems with two degrees of freedom, the fine scale structure of these
hydrodynamic modes is singular and fractal. We characterize them by their
Hausdorff dimension which is given in terms of Ruelle's topological pressure.
For long-wavelength modes, we derive a striking relation between the Hausdorff
dimension, the diffusion coefficient, and the positive Lyapunov exponent of the
system. This relation is tested numerically on two chaotic systems exhibiting
diffusion, both periodic Lorentz gases, one with hard repulsive forces, the
other with attractive, Yukawa forces. The agreement of the data with the theory
is excellent
Thermodynamic time asymmetry in nonequilibrium fluctuations
We here present the complete analysis of experiments on driven Brownian
motion and electric noise in a circuit, showing that thermodynamic entropy
production can be related to the breaking of time-reversal symmetry in the
statistical description of these nonequilibrium systems. The symmetry breaking
can be expressed in terms of dynamical entropies per unit time, one for the
forward process and the other for the time-reversed process. These entropies
per unit time characterize dynamical randomness, i.e., temporal disorder, in
time series of the nonequilibrium fluctuations. Their difference gives the
well-known thermodynamic entropy production, which thus finds its origin in the
time asymmetry of dynamical randomness, alias temporal disorder, in systems
driven out of equilibrium.Comment: to be published in : Journal of Statistical Mechanics: theory and
experimen
Quantum fingerprints of classical Ruelle-Pollicot resonances
N-disk microwave billiards, which are representative of open quantum systems,
are studied experimentally. The transmission spectrum yields the quantum
resonances which are consistent with semiclassical calculations. The spectral
autocorrelation of the quantum spectrum is shown to be determined by the
classical Ruelle-Pollicot resonances, arising from the complex eigenvalues of
the Perron-Frobenius operator. This work establishes a fundamental connection
between quantum and classical correlations in open systems.Comment: 6 pages, 2 eps figures included, submitted to PR
Kinetics and thermodynamics of first-order Markov chain copolymerization
We report a theoretical study of stochastic processes modeling the growth of
first-order Markov copolymers, as well as the reversed reaction of
depolymerization. These processes are ruled by kinetic equations describing
both the attachment and detachment of monomers. Exact solutions are obtained
for these kinetic equations in the steady regimes of multicomponent
copolymerization and depolymerization. Thermodynamic equilibrium is identified
as the state at which the growth velocity is vanishing on average and where
detailed balance is satisfied. Away from equilibrium, the analytical expression
of the thermodynamic entropy production is deduced in terms of the Shannon
disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is
recovered in the fully irreversible growth regime. The theory also applies to
Bernoullian chains in the case where the attachment and detachment rates only
depend on the reacting monomer
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