Fractal-type relations and extensions suitable for systems of evolving polycrystalline microstructures

We report on two possible physically justified situations concerning the ev olution of polycrystalline microstructures. The first is an observation tha t a polycrystalline microstructure formation process, considered as a rando m walk in the space of the crystallites' sizes, can be equivalent to the an omalous kinetic problem in a continuum percolation space. The second, in tu rn, regards some extension of the random walk process while occurring on a fractal substrate and/or when a single grain boundary can presumably be tre ated as a random walk trajectory, i.e. a situation quite acceptable when de aling with, e.g. quasicrystals. One may find possible applications of the m odeling offered in the areas of biophysics and physical metallurgy. (C) 199 9 Elsevier Science B.V. All rights reserved.