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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
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.

Abstract

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
Copyright
Copyright © Australian Mathematical Society 1985

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