Flowing sand - a possible physical realization of Directed Percolation

TL;DR

This paper introduces a simple model for flowing sand on an inclined plane, demonstrating its relation to experiments and showing it can serve as a physical realization of directed percolation with a crossover in critical behavior.

Contribution

It presents a new model linking flowing sand to directed percolation, capturing experimental features and revealing a crossover from compact to ordinary directed percolation.

Findings

Model reproduces experimental avalanche features

Avalanches are compact at intermediate scales

Large-scale avalanches break into multiple branches

Abstract

A simple model for flowing sand on an inclined plane is introduced. The model is related to recent experiments by Douady and Daerr [Nature 399, 241 (1999)] and reproduces some of the experimentally observed features. Avalanches of intermediate size appear to be compact, placing the critical behavior of the model into the universality class of compact directed percolation. On very large scales, however, the avalanches break up into several branches leading to a crossover from compact to ordinary directed percolation. Thus, systems of flowing granular matter on an inclined plane could serve as a first physical realization of directed percolation.