Numerical solution for a non-Fickian diffusion in a periodic potential
Computational Physics
2013-02-27 v1 Statistical Mechanics
Numerical Analysis
Abstract
Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension. The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter. We consider a numerical method which consists of applying Laplace transform in time; we then obtain an elliptic diffusion equation which is discretized using a finite difference method. We analyze some aspects of the convergence of the method. Numerical results for particle density, flux and mean-square-displacement (covering both inertial and diffusive regimes) are presented.
Cite
@article{arxiv.1109.2344,
title = {Numerical solution for a non-Fickian diffusion in a periodic potential},
author = {Adérito Araújo and Amal K. Das and Cidália Neves and Ercília Sousa},
journal= {arXiv preprint arXiv:1109.2344},
year = {2013}
}