1,957 research outputs found
An expression for stationary distribution in nonequilibrium steady state
We study the nonequilibrium steady state realized in a general stochastic
system attached to multiple heat baths and/or driven by an external force.
Starting from the detailed fluctuation theorem we derive concise and suggestive
expressions for the corresponding stationary distribution which are correct up
to the second order in thermodynamic forces. The probability of a microstate
is proportional to where
is the excess entropy change.
Here is the difference between two kinds of conditioned
path ensemble averages of excess heat transfer from the -th heat bath whose
inverse temperature is . Our expression may be verified experimentally
in nonequilibrium states realized, for example, in mesoscopic systems.Comment: 4 pages, 2 figure
Breakdown of hydrodynamics in the inelastic Maxwell model of granular gases
Both the right and left eigenfunctions and eigenvalues of the linearized
homogeneous Boltzmann equation for inelastic Maxwell molecules corresponding to
the hydrodynamic modes are calculated. Also, some non-hydrodynamic modes are
identified. It is shown that below a critical value of the parameter
characterizing the inelasticity, one of the kinetic modes decays slower than
one of the hydrodynamic ones. As a consequence, a closed hydrodynamic
description does not exist in that regime. Some implications of this behavior
on the formally computed Navier-Stokes transport coefficients are discussed.Comment: Submitted to PRL (13/04/10
Chapman-Enskog expansion about nonequilibrium states: the sheared granular fluid
The Chapman-Enskog method of solution of kinetic equations, such as the
Boltzmann equation, is based on an expansion in gradients of the deviations fo
the hydrodynamic fields from a uniform reference state (e.g., local
equilibrium). This paper presents an extension of the method so as to allow for
expansions about \emph{arbitrary}, far-from equilibrium reference states. The
primary result is a set of hydrodynamic equations for studying variations from
the arbitrary reference state which, unlike the usual Navier-Stokes
hydrodynamics, does not restrict the reference state in any way. The method is
illustrated by application to a sheared granular gas which cannot be studied
using the usual Navier-Stokes hydrodynamics.Comment: 23 pages, no figures. Submited to PRE Replaced to correct misc.
errors Replaced to correct misc. errors, make notation more consistant,
extend discussio
Kinetic Theory of Response Functions for the Hard Sphere Granular Fluid
The response functions for small spatial perturbations of a homogeneous
granular fluid have been described recently. In appropriate dimensionless
variables, they have the form of stationary state time correlation functions.
Here, these functions are expressed in terms of reduced single particle
functions that are expected to obey a linear kinetic equation. The functional
assumption required for such a kinetic equation, and a Markov approximation for
its implementation are discussed. If, in addition, static velocity correlations
are neglected, a granular fluid version of the linearized Enskog kinetic theory
is obtained. The derivation makes no a priori limitation on the density, space
and time scale, nor degree of inelasticity. As an illustration, recently
derived Helfand and Green-Kubo expressions for the Navier-Stokes order
transport coefficients are evaluated with this kinetic theory. The results are
in agreement with those obtained from the Chapman-Enskog solution to the
nonlinear Enskog kinetic equation.Comment: Submitted to J. Stat. Mec
Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
The revised Enskog approximation for a fluid of hard spheres which lose
energy upon collision is discussed for the case that the energy is lost from
the normal component of the velocity at collision but is otherwise arbitrary.
Granular fluids with a velocity-dependent coefficient of restitution are an
important special case covered by this model. A normal solution to the Enskog
equation is developed using the Chapman-Enskog expansion. The lowest order
solution describes the general homogeneous cooling state and a generating
function formalism is introduced for the determination of the distribution
function. The first order solution, evaluated in the lowest Sonine
approximation, provides estimates for the transport coefficients for the
Navier-Stokes hydrodynamic description. All calculations are performed in an
arbitrary number of dimensions.Comment: 27 pages + 1 figur
Phase diagram and universality of the Lennard-Jones gas-liquid system
The gas-liquid phase transition of the three-dimensional Lennard-Jones
particles system is studied by molecular dynamics simulations. The gas and
liquid densities in the coexisting state are determined with high accuracy. The
critical point is determined by the block density analysis of the Binder
parameter with the aid of the law of rectilinear diameter. From the critical
behavior of the gas-liquid coexsisting density, the critical exponent of the
order parameter is estimated to be . Surface tension is
estimated from interface broadening behavior due to capillary waves. From the
critical behavior of the surface tension, the critical exponent of the
correlation length is estimated to be . The obtained values of
and are consistent with those of the Ising universality class.Comment: 8 pages, 8 figures, new results are adde
A dynamical theory of homogeneous nucleation for colloids and macromolecules
Homogeneous nucleation is formulated within the context of fluctuating
hydrodynamics. It is shown that for a colloidal or macromolecular system in the
strong damping limit the most likely path for nucleation can be determined by
gradient descent in density space governed by a nontrivial metric fixed by the
dynamics. The theory provides a justification and extension of more heuristic
equilibrium approaches based solely on the free energy. It is illustrated by
application to liquid-vapor nucleation where it is shown that, in contrast to
most free energy-based studies, the smallest clusters correspond to long
wavelength, small amplitude perturbations.Comment: final version; 4 pages, 2 figure
The law of action and reaction for the effective force in a nonequilibrium colloidal system
We study a nonequilibrium Langevin many-body system containing two 'test'
particles and many 'background' particles. The test particles are spatially
confined by a harmonic potential, and the background particles are driven by an
external driving force. Employing numerical simulations of the model, we
formulate an effective description of the two test particles in a
nonequilibrium steady state. In particular, we investigate several different
definitions of the effective force acting between the test particles. We find
that the law of action and reaction does not hold for the total mechanical
force exerted by the background particles, but that it does hold for the
thermodynamic force defined operationally on the basis of an idea used to
extend the first law of thermodynamics to nonequilibrium steady states.Comment: 13 page
Mass transport of an impurity in a strongly sheared granular gas
Transport coefficients associated with the mass flux of an impurity immersed
in a granular gas under simple shear flow are determined from the inelastic
Boltzmann equation. A normal solution is obtained via a Chapman-Enskog-like
expansion around a local shear flow distribution that retains all the
hydrodynamic orders in the shear rate. Due to the anisotropy induced by the
shear flow, tensorial quantities are required to describe the diffusion process
instead of the conventional scalar coefficients. The mass flux is determined to
first order in the deviations of the hydrodynamic fields from their values in
the reference state. The corresponding transport coefficients are given in
terms of the solutions of a set of coupled linear integral equations, which are
approximately solved by considering the leading terms in a Sonine polynomial
expansion. The results show that the deviation of these generalized
coefficients from their elastic forms is in general quite important, even for
moderate dissipation.Comment: 6 figure
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