TY - JOUR

T1 - A lattice-model representation of continuous-time random walks

AU - Campos, Daniel

AU - Méndez, Vicenç

PY - 2008/2/29

Y1 - 2008/2/29

N2 - We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied. © 2008 IOP Publishing Ltd.

AB - We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied. © 2008 IOP Publishing Ltd.

U2 - 10.1088/1751-8113/41/8/085101

DO - 10.1088/1751-8113/41/8/085101

M3 - Article

VL - 41

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 8

M1 - 085101

ER -