A generalized stochastically-motivated gauge procedure was used to introduce the geometry of a material space which described the effect of dislocations upon the free diffusion process. The dependence of diffusion processes and their steady states upon the curvature of the material space of edge dislocations, upon the scalar density of the dislocations and upon the interaction energy between dislocations and a diffusing atom, was analyzed. An equation which defined the interaction energy was deduced, using statistical arguments, from the material space geometry.

On the Geometry of Diffusion Processes in Continuum Dislocated Crystals. A.Trzesowski: Fortschritte der Physik, 1995, 43[6], 565-84