Dynamics of Local Surface Fluctuations in Growth Models With Power-Law Noise

We study one-dimensional surface growth models with power-law noise. We focus on the time behavior of the models to show that the surfaces behave anomalously in the sense that the local surface fluctuations scale with time as tβ* for t > lz, where the time exponent β* is in excellent agreement with a recent theory for anomalous roughening. According to the anomalous roughening picture, we also find that the local fluctuations of the height in the stationary regime scale with a local roughness exponent w(l) ~ lα loc that is different from the global exponent α, which is obtained from the scaling of the saturated width as W(L)~ Lα. Our results suggest that, despite initial hopes, these types of model are not a plausible explanation for the values of the exponents observed in experiments of two-phase flow in disordered media.