Numerical solution for a nonFickian diffusion in a periodic potential
Abstract
Numerical solutions of a nonFickian 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 meansquaredisplacement (covering both inertial and diffusive regimes) are presented.
 Publication:

arXiv eprints
 Pub Date:
 September 2011
 arXiv:
 arXiv:1109.2344
 Bibcode:
 2011arXiv1109.2344A
 Keywords:

 Physics  Computational Physics;
 Condensed Matter  Statistical Mechanics;
 Mathematics  Numerical Analysis;
 35L15;
 60K40;
 60J65;
 65R10;
 65M06;
 65M12
 EPrint:
 Communications in Computational Physics, 13 (2), (2013), 502525