Related papers: Estimating the Steady State Diffusion Coefficient …
A method-of-moments scheme is invoked to compute the asymptotic, long-time mean (or composite) velocity and dispersivity (effective diffusivity) of a two-state particle undergoing one-dimensional convective-diffusive motion accompanied by a…
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…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
For a one dimensional diffusion process $X=\{X(t) ; 0\leq t \leq T \}$, we suppose that $X(t)$ is hidden if it is below some fixed and known threshold $\tau$, but otherwise it is visible. This means a partially hidden diffusion process. The…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation…
A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that active bath transfer to the tracer, thus the model…
We study diffusion in ratchet systems. As a particular experimental realization we consider an asymmetric SQUID subjected to an external ac current and a constant magnetic flux. We analyze mean-square displacement of the Josephson phase and…
A Langevin process diffusing in a periodic potential landscape has a time dependent diffusion constant which means that its average mean squared displacement (MSD) only becomes linear at late times. The long time, or effective diffusion…
Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…
We consider the particle current in the asymmetric avalanche process on a ring. It is known to exhibit a transition from the intermittent to continuous flow at the critical density of particles. The exact expressions for the first two…
We consider diffusive lattice gases on a ring and analyze the stability of their density profiles conditionally to a current deviation. Depending on the current, one observes a phase transition between a regime where the density remains…
Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and…
The chronoamperometric measurements performed with rotating ring-disc electrode become a one of the standard techniques for the diffusion coefficient determination. However, the theoretical estimation of the transit time on which the…
We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
Fluids confined to quasi-one-dimensional channels exhibit a dynamic crossover from single file diffusion to normal diffusion as the channel becomes wide enough for particles to hop past each other. In the crossover regime, where hopping…
We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with mean squared displacement <r^2(t)>~t^{2/3}. Long-ranged correlations of the waiting…
Chemical master equation plays an important role to describe the time evolution of homogeneous chemical system. In addition to the reaction process, it is also accompanied by physical diffusion of the reactants in complex system that is…
It has been noticed that when the waiting time distribution exhibits a transition from an intermediate time power law decay to a long-time exponential decay in the continuous time random walk model, a transition from anomalous diffusion to…