Spatiotemporal Chaotic unjamming and jamming in granular avalanches

TL;DR

This study explores the complex spatiotemporal chaotic behavior of particles during avalanches in a rotating drum, measuring Lyapunov vectors and velocities to understand unjamming and jamming dynamics.

Contribution

It provides the first direct measurement of Lyapunov vectors in granular avalanches and links their spatial correlation to unjamming and jamming transitions.

Findings

Stronger spatial correlation near unjamming

Weaker correlation near jamming

Velocity growth and decay patterns in avalanches

Abstract

We have investigated the spatiotemporal chaotic dynamics of unjamming and jamming of particles in a toy-model system -- a rotating drum partially filled with bidisperse disks to create avalanches. The magnitudes of the first Lyapunov vector $\delta u(t)$ and velocity $v(t)$ of particles are directly measured for the first time to yield insights into their spatial correlation $C_{\delta u,v}$, which is stronger near the unjamming but is weaker near the jamming transition, consistent with the recent work of Banigan et al., Nature Phys. $\bf{9}$, 288, (2013). $v(t)$ shows rich dynamics: it grows exponentially for unstable particles and keeps increasing despite stochastic interactions; after the maximum, it decays with large fluctuations. Hence the spatiotemporal chaotic dynamics of avalanche particles are entangled, causing temporal correlations of macroscopic quantities of the system. We propose a simple model for these observations.