Random walk to describe diffusion phenomena in three-dimensional discontinuous media: Extension to anisotropic phases and nonplane interfaces.

ABSTRACT

We extend the step-balanced random walk [Y. Maruyama, Phys. Rev. E 96, 032135 (2017)2470-004510.1103/PhysRevE.96.032135], which was proposed for diffusion phenomena in three-dimensional discontinuous media, to systems that contain anisotropic phase zones with nonplane interfaces. What is key is threefold For each interstep transition at discontinuous interfaces to be equilibrated by its reverse transition, incident and penetration steps are in one-to-one correspondence; at each incidence, penetration probability is determined by the normal components of an incident step and the corresponding penetration step with respect to an incident tangential plane, and for reflection, the reverse of an incident step, which satisfies the conditions for time reversibility at any interface, is used as a reflection step.