Related papers: Phase transitions for the long-time behavior of in…
We analyze the role of the interplay between on-site interaction and inhomogeneous diffusion on the phenomenon of condensation in the zero-range process. We predict a universal phase diagram in the plane of two exponents, respectively…
We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their…
A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…
Spatiotemporal disorder has been recently associated to the occurrence of anomalous nonergodic diffusion of molecular components in biological systems, but the underlying microscopic mechanism is still unclear. We introduce a model in which…
In this article we address the problem of the nonlinear interaction of subdiffusive particles. We introduce the random walk model in which statistical characteristics of a random walker such as escape rate and jump distribution depend on…
We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…
Starting from a simple animal-biology example, a general, somewhat counter-intuitive property of diffusion random walks is presented. It is shown that for any (non-homogeneous) purely diffusing system, under any isotropic uniform incidence,…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…
We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior.…
This paper studies long range random walks on ${\mathbb{Z}_q}^d$. $X_{t+1} = X_t + Z_t \mod q$, with $(Z_t)$ independent and identically distributed. Multiple entries of $Z_t$ can be non-zero in a transition. An emphasis is on finding the…
We determine the phase diagrams of conservative diffusive contact processes by means of numerical simulations. These models are versions of the ordinary diffusive single-creation, pair-creation and triplet-creation contact processes in…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
Brownian particles in random potentials show an extended regime of subdiffusive dynamics at intermediate times. The asymptotic diffusive behavior is often established at very long times and thus cannot be accessed in experiments or…
A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to non-analytic behavior of the free energy density at the critical temperature: The knowledge of the…
A noncolliding diffusion process is a conditional process of $N$ independent one-dimensional diffusion processes such that the particles never collide with each other. This process realizes an interacting particle system with long-ranged…
We examine a two-dimensional system of sterically repulsive interacting disks where each particle runs in a random direction. This system is equivalent to a run-and-tumble dynamics system in the limit where the run time is infinite. At low…
In the present work, we explore homogenization techniques for a class of switching diffusion processes whose drift and diffusion coefficients, and jump intensities are smooth, spatially periodic functions; we assume full coupling between…
In this work we present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a…
We study the dynamics of the quantum phase distribution associated with the reduced density matrix of a system for a number of situations of practical importance, as the system evolves under the influence of its environment, interacting via…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…