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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, we study
simple discrete ``forest fire'' lattice models through Monte Carlo simulations
in two and three spatial dimensions. An interface generated in the models is
found to display complex behavior. Away from the percolation transition, the
interface is self-affine with asymptotic dynamics consistent with the
Kardar-Parisi-Zhang universality class. However, in the vicinity of the
percolation transition, there is a different behavior at earlier times. By
scaling arguments we show that the global scaling exponents associated with the
kinetic roughening of the interface can be obtained from the properties of the
underlying percolation cluster. Our numerical results are in good agreement
with theory. However, we demonstrate that at the depinning transition, the
interface as defined in the models is no longer self-affine. Finally, we
compare these results to those obtained from a more realistic
reaction-diffusion model of slow combustion.Comment: 7 pages, 9 figures, to appear in Phys. Rev. E (1998