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Numerical Solution for a Non-Fickian Diffusion in a Periodic Potential

Published online by Cambridge University Press:  03 June 2015

Adérito Araújo ,
Amal K. Das ,
Cidália Neves  and
Ercília Sousa
Adérito Araújo*
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal
Amal K. Das*
Affiliation:
Department of Physics, Dalhousie University, Halifax, Nova Scotia B3H3J5, Canada
Cidália Neves*
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal ISCAC, Polytechnic Institute of Coimbra, 3040-316 Coimbra, Portugal
Ercília Sousa*
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal
*
Email:alma@mat.uc.pt
Email:akdas@dal.ca
Email:cneves@iscac.pt
Corresponding author.Email:ecs@mat.uc.pt
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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.

Keywords

35L1560K4060J6565R1065M0665M1202.60.Lj05.40.JcNumerical methodsLaplace transformtelegraph equationperiodic potentialnon-Fickian diffusion

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 2 , February 2013 , pp. 502 - 525
Copyright
Copyright © Global Science Press Limited 2013

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