Related papers: Random walk diffusion simulations in semi-permeabl…
We consider subdiffusion in a system which consists of two media separated by a thin membrane. The subdiffusion parameters may be different in each of the medium. Using the new method presented in this paper we derive the probabilities (the…
This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the…
Chirality in active and passive fluids gives rise to odd transport properties, most notably the emergence of robust edge currents that defy standard dissipative dynamics. While these phenomena are well-described by continuum hydrodynamics,…
Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium. However, in many practical cases the medium is highly irregular due to…
In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…
In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a…
We consider random walks in a random environment which are generalized versions of well-known effective models for Mott variable-range hopping. We study the homogenized diffusion constant of the random walk in the one-dimensional case. We…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
We present the results of a numerical investigation of charged-particle transport across a synthesized magnetic configuration composed of a constant homogeneous background field and a multiscale perturbation component simulating an effect…
The integration of Diffusion Models into Intelligent Transportation Systems (ITS) is a substantial improvement in the detection of accidents. We present a novel hybrid model integrating guidance classification with diffusion techniques. By…
We introduce a continuous-time random walk model on an infinite multilayer structure inspired by transportation networks. Each layer is a copy of $\mathbb{R}^d$, indexed by a non-negative integer. A walker moves within a layer by means of…
In a cellular medium, the plasmic membrane is a place of interactions between the cell and its direct external environment. A classic model describes it as a fluid mosaic. The fluid phase of the membrane allows a lateral degree of freedom…
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…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
The purpose of this paper is to implement a random death process into a persistent random walk model which produces subballistic superdiffusion (L\'{e}vy walk). We develop a Markovian model of cell motility with the extra residence variable…
The run-and-tumble (RT) dynamics followed by bacterial swimmers gives rise first to a ballistic motion due to their persistence, and later, through consecutive tumbles, to a diffusive process. Here we investigate how long it takes for a…
In this article, we generalize the recent Discrete Time Random Walk (DTRW) algorithm, which was introduced for the computation of probability densities of fractional diffusion. Although it has the same computational complexity and shares…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…