Inhomogeneous media spatially varying

A spatially varying diffusivity can model not only inhomogeneities in the medium but also hydro-dynamic interactions between the Brownian particles and channel walls. The diffusivity is then replaced by a diffusion tensor D(r), and instead of Eq. 1, one obtains... 

Analogous considerations apply to spatially distributed reacting media where diffusion is tire only mechanism for mixing chemical species. Under equilibrium conditions any inhomogeneity in tire system will be removed by diffusion and tire system will relax to a state where chemical concentrations are unifonn tliroughout tire medium. However, under non-equilibrium conditions chemical patterns can fonn. These patterns may be regular, stationary variations of high and low chemical concentrations in space or may take tire fonn of time-dependent stmctures where chemical concentrations vary in botli space and time witli complex or chaotic fonns. 

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