Related papers: Diffusional Relaxation in Random Sequential Deposi…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
In this article we investigate the asymptotic behavior of a new class of multi-dimensional diffusions in random environment. We introduce cut times in the spirit of the work done by Bolthausen, Sznitman and Zeitouni, see [4], in the…
In this paper we analyze the relaxation to steady-state of intracellular diffusion in a pair of cells with gap-junction coupling. Gap junctions are prevalent in most animal organs and tissues, providing a direct diffusion pathway for both…
Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…
A dynamic scaling of a diffusion process involving the Langmuir type adsorption is studied. We find dynamic scaling functions in one and two dimensions and compare them with direct numerical simulations, and we further study the dynamic…
This paper is concerned with the connection between the properties of dielectric relaxation and ac (alternating-current) conduction in disordered dielectrics. The discussion is divided between the classical linear-response theory and a…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
We study discrete linear divergence-form operators with random coefficients, also known as the random conductance model. We assume that the conductances are bounded, independent and stationary; the law of a conductance may depend on the…
We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial…
The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed…
We consider diffusion processes in media with pockets of large diffusivity. The asymptotic behavior of such processes is described when the diffusion coefficients in the pockets tend to infinity. The limiting process is identified as a…
Stochastic resetting has been a subject of considerable interest within statistical physics, both as means of improving completion times of complex processes such as searches and as a paradigm for generating nonequilibrium stationary…
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
In this paper we analyze a coupling between the very large jumps in physical and operational times as applied to anomalous diffusion. The approach is based on subordination of a skewed Levy-stable process by its inverse to get two types of…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
In this paper we study the randomized non-autonomous complete linear differential equation. The diffusion coefficient and the source term in the differential equation are assumed to be stochastic processes and the initial condition is…
We simulate a relaxation process of non-brownian particles in a sheared viscous medium; the small shear strain is initially applied to a system, which then undergoes relaxation. The relaxation time and the correlation length are estimated…
Numerical diffusion is introduced by any numerical scheme as soon as small scales fluctuations, generated during the dynamical evolution of a collisionless plasma, become comparable to the grid size. Here we investigate the role of…
The distribution function for the intensity of radiation propagating in a random medium is analyzed for arbitrary multiplicity of scattering (for arbitrary relation between the distance of propagation and mean free path), including as…
Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…