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

James M. Hill, Barry D. Hughes
1985 The Journal of the Australian Mathematical Society Series B Applied Mathematics  
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
more » ... tes 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.
doi:10.1017/s033427000000477x fatcat:72eg56qdxvde5ncb7ab4qry76a