How to simulate anisotropic diffusion processes on curved surfaces

A general method for simulating diffusive processes in inhomogeneous, anisotropic media or in spaces with non-trivial geometry, such as on irregular metallic surfaces or cellular membranes, is derived through the diffusion approximation leading from the Master equation to the Fokker–Planck equation. The method is of the Monte Carlo type, and it can be applied to multi-particle systems and even coupled to internal dynamics, for example the quantum mechanical development of spin states. The correctness of the algorithm is proved and optimization issues discussed. As an illustration, recombination processes on a curved surface is treated.