Front propagation in a random medium with a power-law distribution of transit times.

Abstract

We perform Monte Carlo simulations of front propagation in a two-dimensional random medium in which a fraction 1-p of the bonds have infinite transit time and the remainder have finite transit times t drawn from a probability distribution f(t). We take f(t) to be zero for t1 and to decay as ${\mathit{t}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\tau}}}$ for t\ensuremath{\ge}1. At the percolation threshold, we recover the usual values for the kinetic critical exponents when \ensuremath{\tau}>2, but these exponents vary continuously with \ensuremath{\tau} for \ensuremath{\tau}\ensuremath{\in}(1,2]. For p=1, the kinetics of the front appear to be correctly described by the Kardar-Parisi-Zhang equation when \ensuremath{\tau}>2. In contrast, we find anomalous scaling behavior for \ensuremath{\tau}=1.75.