Growing fractal interfaces in the presence of self-similar hopping surface diffusion

We propose and study an analytic model for growing interfaces in the presence of Brownian diffusion and hopping transport. The model is based on a continuum formulation of mass conservation at the interface, including reactions. The Burgers-KPZ equation for the rate of elevation change emerges after a number of approximations are invoked. We add to the model the possibility that surface transport may be by a hopping mechanism of a Lévy flight, which leads to the (multi)fractal Burgers-KPZ model. The issue how to incorporate experimental data on the jump length distribution in our model is discussed and controlled algorithms for numerical solutions of such fractal Burgers-KPZ equations are provided.