Related papers: Jamming of multiple persistent random walkers in a…
A new master equation to mimic the dynamics of a collection of interacting random walkers in an open system is proposed and solved numerically.In this model, the random walkers interact through excluded volume interaction (single-file…
We investigate the diffusion limited aggregation of particles executing persistent random walks. The scaling properties of both random walks and large aggregates are presented. The aggregates exhibit a crossover between ballistic and…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…
In this thesis, we study the diffusive and ballistic behaviors of random walk in random environment (RWRE) in an integer lattice with dimension at least 2. Our contributions are in three directions: a conditional law of large numbers and…
We consider the exclusion process on segments of the integers in a site-dependent random environment. We assume to be in the ballistic regime in which a single particle has positive linear speed. Our goal is to study the mixing time of the…
We study a two-lane driven lattice gas model with oppositely directed particles moving on two periodic lanes with correlated lane switching processes, so that particles can switch lanes with finite probability only when oppositely directed…
Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions, $\phi$, in the vicinity of the jamming transition at $\phi_{c}$. Various diffusion properties are computed…
A class of exclusion processes in which particles perform history-dependent random walks is introduced, stimulated by dynamic phenomena in some biological and artificial systems. The particles locally interact with the underlying substrate…
Given a discrete-time non-lattice supercritical branching random walk in $\mathbb{R}^d$, we investigate its first passage time to a shifted unit ball of a distance $x$ from the origin, conditioned upon survival. We provide precise…
Off-equilibrium dynamics of a three-dimensional lattice model with nearest- and next nearest-neighbors exclusions is studied. At equilibrium, the model undergoes a first-order fluid-solid transition. Non-equilibrium filling, through random…
We investigate the existence of random close and random loose packing limits in two-dimensional packings of monodisperse hard disks. A statistical mechanics approach-- based on several approximations to predict the probability distribution…
We study diffusive lattice gases with local injection of particles, namely we assume that whenever the origin becomes empty, a new particle is immediately injected into the origin. We consider two lattice gases: a symmetric simple exclusion…
We show that particle transport in a uniform, quantum multi-baker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semi-classical limit leads to diffusion. Random…
We study the first passage times of discrete-time branching random walks in ${\mathbb R}^d$ where $d\geq 1$. Here, the genealogy of the particles follows a supercritical Galton-Watson process. We provide asymptotics of the first passage…
We study persistent random walk with time dependent velocity reversal probabilities and identify a criterion for a non-equilibrium dynamical transition. As a representative example, we consider a power law reversal probability $p(t)\sim…
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is…
We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…
We study approach to the large-time jammed state of the deposited particles in the model of random sequential adsorption. The convergence laws are usually derived from the argument of Pomeau which includes the assumption of the dominance,…
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…
It has been well established that particulate systems show the jamming transition and critical scaling behaviors associated with it. However, our knowledge is limited to (nearly) monodisperse systems. Recently, a binary mixture of jammed…