151 research outputs found
Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog
We study the diffusion of tracers (self-diffusion) in a homogeneously cooling
gas of dissipative particles, using the Green-Kubo relation and the
Chapman-Enskog approach. The dissipative particle collisions are described by
the coefficient of restitution which for realistic material
properties depends on the impact velocity. First, we consider self-diffusion
using a constant coefficient of restitution, const, as frequently
used to simplify the analysis. Second, self-diffusion is studied for a
simplified (stepwise) dependence of on the impact velocity. Finally,
diffusion is considered for gases of realistic viscoelastic particles. We find
that for const both methods lead to the same result for the
self-diffusion coefficient. For the case of impact-velocity dependent
coefficients of restitution, the Green-Kubo method is, however, either
restrictive or too complicated for practical application, therefore we compute
the diffusion coefficient using the Chapman-Enskog method. We conclude that in
application to granular gases, the Chapman-Enskog approach is preferable for
deriving kinetic coefficients.Comment: 15 pages, 1 figur
A simple measure of memory for dynamical processes described by the generalized Langevin equation
Memory effects are a key feature in the description of the dynamical systems
governed by the generalized Langevin equation, which presents an exact
reformulation of the equation of motion. A simple measure for the estimation of
memory effects is introduced within the framework of this description.
Numerical calculations of the suggested measure and the analysis of memory
effects are also applied for various model physical systems as well as for the
phenomena of ``long time tails'' and anomalous diffusion
Simple model for transport phenomena : Microscopic construction of Maxwell Demon like engine
We present a microscopic Hamiltonian framework to develop Maxwell demon like
engine. Our model consists of a equilibrium thermal bath and a non-equilibrium
bath; latter generated by driving with an external stationary, Gaussian noise.
The engine we develop, can be considered as a device to extract work by
modifying internal fluctuations. Our theoretical analysis focusses on finding
the essential ingredients necessary for generating fluctuation induced
transport under non-equilibrium condition. An important outcome of our model is
that the net motion occurs when the non-linear bath is modulated by the
external noise, creating the non-zero effective temperature even when the
temperature of both the baths are same.Comment: 6 pages, RevTex
Transport and bistable kinetics of a Brownian particle in a nonequilibrium environment
A system reservoir model, where the associated reservoir is modulated by an
external colored random force, is proposed to study the transport of an
overdamped Brownian particle in a periodic potential. We then derive the
analytical expression for the average velocity, mobility, and diffusion rate.
The bistable kinetics and escape rate from a metastable state in the overdamped
region are studied consequently. By numerical simulation we then demonstrate
that our analytical escape rate is in good agreement with that of numerical
result.Comment: 10 pages, 2 figures, RevTex4, minor correction
Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic and conservative interactions
We present a generalization of the Green-Kubo expressions for thermal
transport coefficients in complex fluids of the generic form, , i.e.
a sum of an instantaneous transport coefficient , and a time
integral over a time correlation function in a state of thermal equilibrium
between a current and a transformed current . The streaming
operator generates the trajectory of a dynamical variable
when used inside the thermal average . These
formulas are valid for conservative, impulsive (hard spheres), stochastic and
dissipative forces (Langevin fluids), provided the system approaches a thermal
equilibrium state. In general and ,
except for the case of conservative forces, where the equality signs apply. The
most important application in the present paper is the hard sphere fluid.Comment: 14 pages, no figures. Version 2: expanded Introduction and section II
specifying the classes of fluids covered by this theory. Some references
added and typos correcte
Stochastic thermodynamics under coarse-graining
A general formulation of stochastic thermodynamics is presented for open
systems exchanging energy and particles with multiple reservoirs. By
introducing a partition in terms of "macrostates" (e.g. sets of "microstates"),
the consequence on the thermodynamic description of the system is studied in
detail. When microstates within macrostates rapidly thermalize, the entire
structure of the microscopic theory is recovered at the macrostate level. This
is not the case when these microstates remain out of equilibrium leading to
additional contributions to the entropy balance. Some of our results are
illustrated for a model of two coupled quantum dots.Comment: 12 pages, 3 figure
Dynamics of a metastable state nonlinearly coupled to a heat bath driven by an external noise
Based on a system-reservoir model, where the system is nonlinearly coupled to
a heat bath and the heat bath is modulated by an external stationary Gaussian
noise, we derive the generalized Langevin equation with space dependent
friction and multiplicative noise and construct the corresponding Fokker-Planck
equation, valid for short correlation time, with space dependent diffusion
coefficient to study the escape rate from a metastable state in the moderate to
large damping regime. By considering the dynamics in a model cubic potential we
analyze the result numerically which are in good agreement with the theoretical
prediction. It has been shown numerically that the enhancement of rate is
possible by properly tuning the correlation time of the external noise.Comment: 13 pages, 5 figures, Revtex4. To appear in Physical Review
Fractional Fokker-Planck Equation for Fractal Media
We consider the fractional generalizations of equation that defines the
medium mass. We prove that the fractional integrals can be used to describe the
media with noninteger mass dimensions. Using fractional integrals, we derive
the fractional generalization of the Chapman-Kolmogorov equation (Smolukhovski
equation). In this paper fractional Fokker-Planck equation for fractal media is
derived from the fractional Chapman-Kolmogorov equation. Using the Fourier
transform, we get the Fokker-Planck-Zaslavsky equations that have fractional
coordinate derivatives. The Fokker-Planck equation for the fractal media is an
equation with fractional derivatives in the dual space.Comment: 17 page
The Fokker-Planck equation, and stationary densities
The most general local Markovian stochastic model is investigated, for which
it is known that the evolution equation is the Fokker-Planck equation. Special
cases are investigated where uncorrelated initial states remain uncorrelated.
Finally, stochastic one-dimensional fields with local interactions are studied
that have kink-solutions.Comment: 10 page
Transport coefficients for an inelastic gas around uniform shear flow: Linear stability analysis
The inelastic Boltzmann equation for a granular gas is applied to spatially
inhomogeneous states close to the uniform shear flow. A normal solution is
obtained via a Chapman-Enskog-like expansion around a local shear flow
distribution. The heat and momentum fluxes are determined to first order in the
deviations of the hydrodynamic field gradients from their values in the
reference state. The corresponding transport coefficients are determined from a
set of coupled linear integral equations which are approximately solved by
using a kinetic model of the Boltzmann equation. The main new ingredient in
this expansion is that the reference state (zeroth-order
approximation) retains all the hydrodynamic orders in the shear rate. In
addition, since the collisional cooling cannot be compensated locally for
viscous heating, the distribution depends on time through its
dependence on temperature. This means that in general, for a given degree of
inelasticity, the complete nonlinear dependence of the transport coefficients
on the shear rate requires the analysis of the {\em unsteady} hydrodynamic
behavior. To simplify the analysis, the steady state conditions have been
considered here in order to perform a linear stability analysis of the
hydrodynamic equations with respect to the uniform shear flow state. Conditions
for instabilities at long wavelengths are identified and discussed.Comment: 7 figures; previous stability analysis modifie
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