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Volume 13, Issue 2
Numerical Solution for a Non-Fickian Diffusion in a Periodic Potential

Adérito Araújo, Amal K. Das, Cidália Neves & Ercília Sousa

Commun. Comput. Phys., 13 (2013), pp. 502-525.

Published online: 2013-02

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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.

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@Article{CiCP-13-502, author = {}, title = {Numerical Solution for a Non-Fickian Diffusion in a Periodic Potential}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {2}, pages = {502--525}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.280711.010312a}, url = {http://global-sci.org/intro/article_detail/cicp/7233.html} }
TY - JOUR T1 - Numerical Solution for a Non-Fickian Diffusion in a Periodic Potential JO - Communications in Computational Physics VL - 2 SP - 502 EP - 525 PY - 2013 DA - 2013/02 SN - 13 DO - http://doi.org/10.4208/cicp.280711.010312a UR - https://global-sci.org/intro/article_detail/cicp/7233.html KW - AB -

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.

Adérito Araújo, Amal K. Das, Cidália Neves & Ercília Sousa. (2020). Numerical Solution for a Non-Fickian Diffusion in a Periodic Potential. Communications in Computational Physics. 13 (2). 502-525. doi:10.4208/cicp.280711.010312a
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