SINGULARITIES AND AVALANCHES IN INTERFACE GROWTH WITH QUENCHED DISORDER

A simple model for an interface moving in a disordered medium is prese nted. The model exhibits a transition between the two universality cla sses of interface growth in the presence of quenched disorder. Using t his model, it is shown that the application of constraints to the loca l slopes of the interface produces avalanches of growth that become re levant in the vicinity of the depinning transition. The study of these avalanches reveals a singular behavior at the depinning transition th at explains a recently observed divergency in the equation of motion o f the interface. The anisotropy in the medium is also studied as a pos sible source of the divergency in the equation of motion.