Dynamical scaling and kinetic roughening of single valued fronts propagating in fractal media

We consider the dynamical scaling and kinetic roughening of single-valued interfaces propagating in 2D fractal media. Assuming that the nearest-neighbor height difference distribution function of the fronts obeys Lévy statistics with a well-defined algebraic decay exponent, we consider the generalized scaling forms and derive analytic expressions for the local scaling exponents. We show that the kinetic roughening of the interfaces displays intrinsic anomalous scaling and multiscaling in the relevant correlation functions. We test the predictions of the scaling theory with a variety of well-known models which produce fractal growth structures. Results are in excellent agreement with theory. For some models, we find interesting crossover behavior related to large-scale structural instabilities of the growing aggregates