Flowing sand - a physical realization of Directed Percolation

TL;DR

This paper presents a simple model of flowing sand that reproduces experimental avalanche behavior and predicts a crossover from compact to directed percolation, providing the first experimental realization of directed percolation phenomena.

Contribution

The authors introduce a minimal model capturing flowing sand dynamics and demonstrate a crossover to directed percolation, bridging experimental observations with theoretical models.

Findings

Model reproduces avalanche angles observed experimentally.

Identifies a crossover from compact to directed percolation.

Predicts conditions for observing true directed percolation behavior.

Abstract

We introduce and investigate a simple model to describe recent experiments by Douady and Daerr on flowing sand. The model reproduces experimentally observed compact avalanches, whose opening angle decreases linearly as a threshold is approached. On large scales the model exhibits a crossover from compact directed percolation to directed percolation; we predict similar behavior for the experimental system. We estimate the regime where "true" directed percolation morphology and exponents will be observed, providing the first experimental realization for this class of models.