Morphology and dynamics in SOC universality classes

Abstract

Among the main issues about SOC models are the identification of universality classes and the relation with real systems. In this work we address the relationship between a sandpile and the slow advancement of a crack in a disordered medium. By means of extensive analyses in 1d, 2d and mean field, we show a strict and quantitative correspondence between the dynamics of a two-state Manna model and of a recently introduced Fiber Bundle model effectually describing the propagation of the crack front in a heterogeneous medium. We also demonstrate the ability of the Manna model itself to describe quantitatively the crack dynamical scaling, when supplied of the suited long range redistribution rule. On the other hand the Manna model looks hardly capable to yield the right crack front morphology. Specifically, no width saturation is observed, while the roughness displays at best a logarithmic scaling. These findings pose questions about definition and limits of universality classes in non equilibrium systems, and point out a lack of understanding of the interplay between dynamics and morphology in real and model systems.