FRONT PROPAGATION IN A RANDOM MEDIUM WITH A POWER-LAW DISTRIBUTION OFTRANSIT TIMES

We perform Monte Carlo simulations of front propagation in a two-dimen sional random medium in which a fraction 1-p of the bonds have infinit e transit time and the remainder have finite transit times t drawn fro m a probability distribution f(t). We take f(t) to be zero for t <1 an d to decay as t(-tau) for t greater than or equal to 1. At the percola tion threshold, we recover the usual values for the kinetic critical e xponents when tau > 2, but these exponents vary continuously with tau for tau is an element of(1,2]. For p = 1, the kinetics of the front ap pear to be correctly described by the Kardar-Parisi-Zhang equation whe n tau > 2. In contrast, we find anomalous scaling behavior for tau = 1 .75.