Dynamics at the angle of repose: jamming, bistability, and collapse

TL;DR

This paper models the complex dynamics of sandpiles under vibration, explaining phenomena like bistability, jamming, and collapse through coupled stochastic equations that incorporate density fluctuations and external noise.

Contribution

It introduces a coupled stochastic model linking density fluctuations and the angle of repose, providing a unified explanation for various sandpile behaviors.

Findings

Describes sandpile collapse as an activated process influenced by an effective temperature.

Explains bistability and jamming phenomena through density fluctuation dynamics.

Provides a theoretical framework connecting external noise to sandpile stability.

Abstract

When a sandpile relaxes under vibration, it is known that its measured angle of repose is bistable in a range of values bounded by a material-dependent maximal angle of stability; thus, at the same angle of repose, a sandpile can be stationary or avalanching, depending on its history. In the nearly jammed slow dynamical regime, sandpile collapse to a zero angle of repose can also occur, as a rare event. We claim here that fluctuations of {\it dilatancy} (or local density) are the key ingredient that can explain such varied phenomena. In this work, we model the dynamics of the angle of repose and of the density fluctuations, in the presence of external noise, by means of coupled stochastic equations. Among other things, we are able to describe sandpile collapse in terms of an activated process, where an effective temperature (related to the density as well as to the external vibration intensity) competes against the configurational barriers created by the density fluctuations.