Mean Field Theory of Sandpile Avalanches: from the Intermittent to the Continuous Flow Regime

TL;DR

This paper models granular avalanches in rotating cylinders using mean-field theory, revealing a hysteresis cycle between intermittent and continuous flow regimes, with critical slowing down and power-law avalanche durations near the transition.

Contribution

It introduces a mean-field model capturing the hysteresis and avalanche statistics in granular flow, aligning with experimental observations.

Findings

Hysteresis cycle between flow regimes identified

Avalanche durations exhibit power-law distribution near transition

Critical slowing down observed as system approaches transition

Abstract

We model the dynamics of avalanches in granular assemblies in partly filled rotating cylinders using a mean-field approach. We show that, upon varying the cylinder angular velocity $\omega$, the system undergoes a hysteresis cycle between an intermittent and a continuous flow regimes. In the intermittent flow regime, and approaching the transition, the avalanche duration exhibits critical slowing down with a temporal power-law divergence. Upon adding a white noise term, and close to the transition, the distribution of avalanche durations is also a power-law. The hysteresis, as well as the statistics of avalanche durations, are in good qualitative agreement with recent experiments in partly filled rotating cylinders.