Related papers: Cattaneo--type subdiffusion--reaction equation
The unified description of diffusion processes that cross over from a ballistic behavior at short times to normal or anomalous diffusion (sub- or superdiffusion) at longer times is constructed on the basis of a non-Markovian generalization…
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…
We consider a continuous random walk model for describing normal as well as anomalous diffusion of particles subjected to an external force when these particles diffuse in a uniformly expanding (or contracting) medium. A general equation…
Levy walks define a fundamental concept in random walk theory which allows one to model diffusive spreading that is faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a…
Continuous-time random walks combining diffusive scattering and ballistic propagation on lattices model a class of L\'evy walks. The assumption that transitions in the scattering phase occur with exponentially-distributed waiting times…
We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two dimensional potential. The potential may be either periodic or random. Depending…
We consider the coagulation dynamics A+A -> A and A+A <-> A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems,…
We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided…
We develop a microscopic theory for reaction-difusion (R-D) processes based on a generalization of Einstein's master equation with a reactive term and we show how the mean field formulation leads to a generalized R-D equation with…
We consider scaled Brownian motion (sBm), a random process described by a diffusion equation with explicitly time-dependent diffusion coefficient $D(t) = D_0 t^{\alpha - 1}$ (Batchelor's equation) which, for $\alpha < 1$, is often used for…
We consider an irreversible autocatalytic conversion reaction A+B -> 2A under subdiffusion described by continuous time random walks. The reactants' transformations take place independently on their motion and are described by constant…
The long range movement of certain organisms in the presence of a chemoattractant can be governed by long distance runs, according to an approximate Levy distribution. This article clarifies the form of biologically relevant model…
The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…
We study a variation of the trapping reaction, A+B->A, in which both the traps (A) and the particles (B) undergo diffusion, and the traps upon meeting react according to A+A->0 or A. This two-species reaction-diffusion system is known to…
A physical-mathematical approach to anomalous diffusion may be based on fractional diffusion equations and related random walk models. The fundamental solutions of these equations can be interpreted as probability densities evolving in time…
This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the…
We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random…
Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement $\overline{\delta^2}$ of individual particles remains a random variable while indicating that the particle…
Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…
Based on the non-Markov diffusion equation taking into account the spatial fractality and modeling for the generalized coefficient of particle diffusion…