Many diffusion problems span widely different length and time scales. In this presentation we show how lattice-based random walks of virtual particles can be used to address a variety of complex phenomenologically conceived diffusion problems. Examples include the determination of grain boundary depth profiles in the presence of grain boundary slabs, the determination of the effective diffusivity (and thermal conductivity) in the presence of various shapes of grains with and without solute segregation, the determination of time-dependent concentration profiles of solute that segregates at metal-ceramic oxide interfaces and the effective electrical conductivity of composite electrolytes. In some examples we also show how the finite element method can also be used. Comparison is made of the results of these two methods where possible.

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