Published online by Cambridge University Press: 17 February 2009
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 ) 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  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.
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