Related papers: Void formation in diffusive lattice gases
We investigate the fluctuations around the average density profile in the weakly asymmetric exclusion process with open boundaries in the steady state. We show that these fluctuations are given, in the macroscopic limit, by a centered…
We study the position of a biased tracer particle (TP) in a bath of hardcore particles moving on a lattice of arbitrary dimension and in contact with a reservoir. Starting from the master equation satisfied by the joint probability of the…
We study Langevin dynamics with stochastic diffusivity arising from fluctuations of the surrounding medium. The diffusivity is modeled as Ornstein-Uhlenbeck process driven by symmetric dichotomous noise, which confines it to a finite…
This paper is a continuation of the works in \cite{Euler} and \cite{NS}, where the authors have established the global existence of smooth compressible flows in infinitely expanding balls for inviscid gases and viscid gases, respectively.…
We consider first passage percolation with i.i.d. weights on edges of the d-dimensional cubic lattice. Under the assumptions that a weight is equal to zero with probability smaller than the critical probability of bond percolation in the…
We concern with the global existence and large time behavior of compressible fluids (including the inviscid gases, viscid gases, and Boltzmann gases) in an infinitely expanding ball. Such a problem is one of the interesting models in…
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a…
The second law of thermodynamics posits that in closed macroscopic systems the rate of entropy production must be positive. However, small systems can exhibit negative entropy production over short timescales, seemingly in contradiction…
Maximum-density dimer packings (maximum matchings) of non-bipartite site-diluted lattices, such as the triangular and Shastry-Sutherland lattices in $d=2$ dimensions and the stacked-triangular and corner-sharing octahedral lattices in…
The fluctuation-dissipation theory is grounded on the Langevin condition expressing the local independence between the thermal force and the particle velocity history. Upon hydrodynamic grounds, it is reasonable to relax this condition in…
The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in non--equilibrium, namely for non reversible systems. In this paper we consider a simple example of…
We study, using numerical simulations, the dynamical evolution of self-gravitating point particles in static euclidean space, starting from a simple class of infinite ``shuffled lattice'' initial conditions. These are obtained by applying…
The authors in a previous paper proved the hydrodynamic incompressible limit in $d\ge 3$ for a thermal lattice gas, namely a law of large numbers for the density, velocity field and energy. In this paper the equilibrium fluctuations for…
We define a transverse correlation length suitable to discuss the finite-size-scaling behavior of an out-of-equilibrium lattice gas, whose correlation functions decay algebraically with the distance. By numerical simulations we verify that…
Exact results are obtained for random walks on finite lattice tubes with a single source and absorbing lattice sites at the ends. Explicit formulae are derived for the absorption probabilities at the ends and for the expectations that a…
This paper investigates the exit-time problem for time-inhomogeneous diffusion processes. The focus is on the small-noise behavior of the exit time from a bounded positively invariant domain. We demonstrate that, when the drift and…
To seek for a possible origin of fractal pattern in nature, we perform a molecular dynamics simulation for a fragmentation of an infinite fcc lattice. The fragmentation is induced by the initial condition of the model that the lattice…
What is the probability that all the gas in a box accumulates in the same half of this box? Though amusing, this question underlies the fundamental problem of density fluctuations at equilibrium, which has profound implementations in many…
We study the nucleation and dynamics of vortices in rotating lattice potentials where weakly linked condensates are formed with each condensate exhibiting an almost axial symmetry. Due to such a symmetry, the on-site phases acquire a linear…
We investigate the validity of fluctuation theorems for an asymmetric rotor experiment in a granular gas. A first state, with a Gaussian distribution of the angular velocity, is found to be well described by a first order Langevin equation.…