Cohesion-induced deepening transition of avalanches

A directed avalanche model with a control parameter is introduced to describe the transition between cohesive and noncohesive granular material. The underlying dynamics of the process can be mapped to interface growth model. In that representation, a continuous phase transition separates the rough phase and the flat phase. In the avalanche formulation, this corresponds to a transition from deep to shallow avalanches. The scaling exponents of the avalanches indeed follow those of the underlying interface growth in both phases and at the transition point. However, the mass hyperscaling relation is broken at the transition point due to the fractal nature of the avalanche and a hierarchy of critical directed percolation processes.