DYNAMICS OF SURFACE ROUGHENING IN DISORDERED MEDIA

We present results on the roughening of growing interfaces obtained from a Kardar-Parisi-Zhang (KPZ) type continuum equation with quenched additive noise, representing frozen in disorder. Close to the pinning transition, for the exponents describing respectively the temporal and the spatial scaling of the surface from numerical integration in 1 + 1 dimensions we obtain beta = 0.61 +/- 0.06 and alpha = 0.71 +/- 0.08 up to a crossover time. These estimates are in good agreement with the theoretical prediction beta = 3/5 and alpha = 3/4 we derive from a dimensional analysis of the equation.