Dynamics of Interfaces in Random Media

Abstract

One of the essential consequences of non-linear equations of motion is the possibility of several stable stationary states /1/. As a result, for a d-dimension system many configurations exist, where regions in which the system is in one of its stable states are separated by thin transition layers. As the non-linearity increases, the widths of these layers decrease, so that they can be described as (d-1)-dimensional hypersurfaces. The time evolution of the system is then determined by the dynamics of these phase-separating interfaces. Situations of this type arise in a variety of physical systems. Well-known examples are equilibrium phase transitions of first order as, e.g., liquid-vapour systems/2/. Of great practical importance are furthermore systems quenched into the phase region of distinct multistability /3–6/. After a very quick local relaxation process, a complicated pattern of domains separated by interfaces emerge. These domains coarsen with time, as can be verified experimentally by scattering techniques. Since the coarsening process is determined by the dynamics of the existing interfaces, comparison between theory and experiment becomes possible /5/. Of interest for practical purpose are in particular metallurgical systems as, e.g., binary alloys /3/.