Growing fractal interfaces in the presence of self-similar hopping surfacediffusion

We propose and study an analytic model for growing interfaces in the presen ce of Brownian diffusion and hopping transport. The model is based on a con tinuum formulation of mass conservation at the interface, including reactio ns. The Burgers-KPZ equation for the rate of elevation change emerges after a number of approximations are invoked. We add to the model the possibilit y that surface transport may be by a hopping mechanism of a Levy flight, wh ich leads to the (multi)fractal Burgers-KPZ model. The issue how to incorpo rate experimental data on the jump length distribution in our model is disc ussed and controlled algorithms for numerical solutions of such fractal Bur gers-KPZ equations are provided. (C) 2001 Elsevier Science B.V. All rights reserved.