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On the general random walk formulation for diffusion in media with Diffusivities

Published online by Cambridge University Press:  17 February 2009

James M. Hill  and
Barry D. Hughes
James M. Hill
Affiliation:
Department of Mathematics, University of Wollongong, Wollongong, N.S.W.2500.
Barry D. Hughes
Affiliation:
Department of Mathematics, Faculty of Military Studies, University of New South Wales, RMC Duntroon, A.C.T. 2600. Department of Applied Mathematics, Research School of Physical Sciences, Australian National University, Canberra, A.C.T.2600.
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Abstract

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A general discrete multi-dimensional and multi-state random walk model is proposed to describe the phenomena of diffusion in media with multiple diffusivities. The model is a generalization of a two-state one-dimensional discrete random walk model (Hill [8]) which gives rise to the partial differential equations of double diffusion. The same partial differential equations are shown to emerge as a special case of the continuous version of the present general model. For two states a particular generalization of the model given in [8] is presented which is not restricted to nearest neighbour transitions. Under appropriate circumstances this two-state model still yields the partial differential equations of double diffusion in the continuum limit, but an example of circumstances leading to a radically different continuum limit is presented.

Type
Research Article
Information
The ANZIAM Journal , Volume 27 , Issue 1 , July 1985 , pp. 73 - 87
Copyright
Copyright © Australian Mathematical Society 1985

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