Related papers: Lattice gases with a point source
Stochastic particle--based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of…
We discuss the approximate phenomenological description of the motion of a single second-class particle in a two-species totally asymmetric simple exclusion process (TASEP) on a 1D lattice. Initially, the second class particle is located at…
In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the…
We study the effect of a single excluded site on the diffusion of a particle undergoing random walk in a d-dimensional lattice. The determination of the characteristic function allows to find explicitly the asymptotical behaviour of…
We study the steady-state behavior of a driven non-equilibrium lattice gas of hard-core particles with next-nearest-neighbor interaction. We calculate the exact stationary distribution of the periodic system and for a particular line in the…
We investigate the dynamics of continuous-time two-particle quantum walks on a one-dimensional noisy lattice. Depending on the initial condition, we show how the interplay between particle indistinguishability and interaction determines…
We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect…
We study a model of self propelled particles exhibiting run and tumble dynamics on lattice. This non-Brownian diffusion is characterised by a random walk with a finite persistence length between changes of direction, and is inspired by the…
We study three basic diffusion-controlled reaction processes -- annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a half-line is uniformly filled by…
We study one-dimensional hardcore lattice gases, with nearest-neighbor interactions, in the presence of an external potential barrier, that moves on the periodic lattice with a constant speed. We investigate how the nature of the…
We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a $d$-dimensional cubic lattice in the presence…
We study the interaction between a pair of particles suspended in a uniform oscillatory flow. The time-averaged behavior of particles under these conditions, driven by inertial and viscous effects, is explored through a theoretical…
With the help of Monte Carlo simulations and a mean-field theory, we investigate the ordered steady-state structures resulting from the motion of a single vacancy on a periodic lattice which is filled with two species of oppositely…
We consider an infinite system of particles in one dimension, each particle performs independant Sinai's random walk in random environment. Considering an instant $t$, large enough, we prove a result in probability showing that the…
Branching random walks on multidimensional lattice with heavy tails and a constant branching rate are considered. It is shown that under these conditions (heavy tails and constant rate), the front propagates exponentially fast, but the…
It is known that the stochastic generators of effective processes associated with the unconditioned dynamics of rare events might consist of non-local interactions; however, it can be shown that there are special cases for which these…
We define a new class of random walk processes which maximize entropy. This maximal entropy random walk is equivalent to generic random walk if it takes place on a regular lattice, but it is not if the underlying lattice is irregular. In…
We study three different lattice models in which two species of diffusing particles are driven in opposite directions by an electric field. We focus on dynamical phase transitions that involve phase separation into domains that may be…
Nonequilibrium collective motion is ubiquitous in nature and often results in a rich collection of intringuing phenomena, such as the formation of shocks or patterns, subdiffusive kinetics, traffic jams, and nonequilibrium phase…
We study the motion of a particle on the two-dimensional honeycomb lattice, whose sites are occupied by either flipping rotators or flipping mirrors, which scatter the particle according to a deterministic rule. For both types of scatterers…