Depinning transition in disorder media: a fractional approach

We introduce a fractional stochastic equation for driven interfaces in random media, in which the normal diffusion term is replaced by a fractional Laplacian for exhibiting long-range interaction through quenched disorder. The critical exponents are obtained numerically at the depinning transition. Our results show that the model displays a family of continuously changing universality classes. The fractional Laplacian affects evidently the depinning transition in disorder media. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012