Journal article

ON THE GENERAL RANDOM-WALK FORMULATION FOR DIFFUSION IN MEDIA WITH MULTIPLE DIFFUSIVITIES

JM HILL, BD HUGHES

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS | AUSTRALIAN MATHEMATICS PUBL ASSOC INC | Published : 1985

Abstract

AbstractA 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 diffe..

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