DYNAMICS OF DRIVEN INTERFACES NEAR ISOTROPIC PERCOLATION TRANSITION

We consider the dynamics and kinetic roughening of interfaces embedded in uniformly random media near percolation treshold. In particular, w e study simple discrete ''forest fire'' lattice models through Monte C arlo simulations in two and three spatial dimensions. An interface gen erated in the models is found to display complex behavior. Away from t he percolation transition, the interface is self-affine with asymptoti c dynamics consistent with the Kardar-Parisi-Zhang universality class. However, in the vicinity of the percolation transition, there is a di fferent behavior at earlier times. By scaling arguments we show that t he global scaling exponents associated with the kinetic roughening of the interface can be obtained from the properties of the underlying pe rcolation cluster. Our numerical results are in good agreement with th eory. However, we demonstrate that at the depinning transition, the in terface as defined in the models is no longer self-affine. Finally, we compare these results with those obtained from a more realistic react ion-diffusion model of slow combustion.