Propagação de frentes em meios heterogêneos

Abstract

We develop a study about one-dimensional propagation of fronts, with calculation of roughness, correlation length, etc.. In our model, the minimum value of a combination between the second and fourth derivative of the front h(x) is the parameter decision for the position x where the next random slide h will occur. We observe critical exponents that characterize long-range correlations. The model is a simplification for Rice's formulation, in which the minimized parameter is an integral along the entire front. Thus, the long-range feature is already built into the recipe. In our case, the combination of the second and fourth derivatives is local, so the long-range correlations emerge naturally from the dynamics.