MICROSCOPIC EQUATION FOR GROWING INTERFACES IN QUENCHED DISORDERED MEDIA

We present a microscopic equation for a growing interface with quenched noise of the Tang and Leschhorn model (Tang L H and Leschhorn H 1992 Phys. Rev. A 45 R8309). Evolution equations for the height, the mean height, and the roughness are reached in a simple way. An equation for the interface activity density (or free sites density) as a function of time is obtained. The microscopic equation allows us to express these equations in terms of two contributions: the diffusion and the substratum contributions. All these equations shows the strong interplay between the diffusion and the substratum contribution in the dynamics.