1,721,031 research outputs found
Thermodynamic limit for isokinetic thermostats
No full textThermostat models in space dimension d=1,2,3 for nonequilibrium statistical mechanics are considered and it is shown that, in the thermodynamic limit, the motions of frictionless thermostats and isokinetic thermostats coincide. (C) 2010 American Institute of Physics. [doi:10.1063/1.3376659
Small deviations from local equilibrium for a process which exhibits hydrodynamical behavior. I
No full textThe symmetric simple exclusion process where infinitely many particles move
randomly on ~, jump with equal probability on nearest-neighbor sites, and
interact by simple exclusion is considered. It is known that the only extremal
invariant measures are Bernoulli, that each measure, in a suitable class, after a
"macroscopic" time is locally described, at a zero-order approximation, by a
Bernoulli measure with parameter depending on macroscopic space and time,
and that the so-defined equilibrium profile satisfies the heat equation. Small
deviations from local equilibrium in the hydrodynamical limit are investigated.
It is proven, under suitable assumptions, that at first order the state is Gibbs
with one- and two-body potentials whose strength depends only on macroscopic
space and time and on the equilibrium profile. More precisely, the one-body
potential is linear (on the microscopic positions of the particles) and proportional
to the macroscopic space gradient of the equilibrium parameter at that
time, so that Fourier law holds. The two-body potential varies on a macroscopic
scale and does not depend on the microscopic positions of the particles; it is
given by the value of the covariance of the Gaussian "macroscopic density
fluctuation field.
On the validity of the van der Waals theory in Ising systems with long range interactions
No full text
The weakly asymmetric simple exclusion process
No full textThe one dimensional n.n. simple exclusion process with generator \epsilon^{-2}L_0+\epsilon^{-1}1L_a, \epsilon > 0,
is considered, L_0 and L_a respectively the generators of the symmetric and totally asymmetric
simple exclusion processes. Propagation of chaos and convergence to the Burgers
equation with viscosity are proven in the limit when \epsilon goes to zero. The density fluctuation
field is shown to converge to a generalized Ornstein Uhlenbeck process with mean zero.
The time asymptotic covariance kernel is explicitly computed for traveling wave profiles
and the result indicates that the shock profile is stable while its space location fluctuates
around its average position like a brownian motion. Its diffusion coefficient is explicitly
computed
Spectral properties of integral operators in problems of interface dynamic and metastability
No full textIn this paper we study some integral operators that are obtained by linearizations of a
non local evolution equation for a non conserved order parameter which describes the phase of a fluid.
We prove a Perron-Frobenius theorem by showing that there is an isolated, simple, maximal eigenvalue
larger than 1 with a positive eigenvector and that the rest of the spectrum is strictly inside the unit
ball. Such properties are responsible for the existence of invariant, attractive unstable one dimensional
manifolds under the full, non linear evolution. This part of the analysis and the application to interface
dynamics and metastability will be carried out in separate papers
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