Cohesion induced deepening transition of avalanches

TL;DR

This paper introduces a directed avalanche model with a control parameter to study the transition from cohesive to noncohesive granular materials, revealing a continuous phase transition with specific scaling behaviors.

Contribution

It establishes a novel connection between avalanche dynamics and interface growth models, identifying a phase transition and analyzing its critical properties.

Findings

Identifies a continuous phase transition between deep and shallow avalanches.

Shows scaling exponents match those of interface growth models.

Reveals breakdown of mass hyperscaling at the transition due to fractal avalanches.

Abstract

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.