Extreme events driven glassy behaviour in granular media

TL;DR

This paper presents a simple model linking microscopic dynamics to macroscopic rearrangements in granular media, explaining experimental observations of jamming and relaxation times through extreme event statistics.

Contribution

It introduces a novel model that connects microscopic rearrangements to macroscopic behavior in granular media, incorporating extreme-value statistics to explain experimental findings.

Findings

The control parameter is the spatial amplitude of perturbation.

Relaxation time follows a Vogel-Fulcher-Tammann-like form.

The model successfully relates microscopic events to macroscopic relaxation.

Abstract

Motivated by recent experiments on the approach to jamming of a weakly forced granular medium using an immersed torsion oscillator [Nature 413 (2001) 407], we propose a simple model which relates the microscopic dynamics to macroscopic rearrangements and accounts for the following experimental facts: (1) the control parameter is the spatial amplitude of the perturbation and not its reduced peak acceleration; (2) a Vogel-Fulcher-Tammann-like form for the relaxation time. The model draws a parallel between macroscopic rearrangements in the system and extreme events whose probability of occurrence (and thus the typical relaxation time) is estimated using extreme-value statistics. The range of validity of this description in terms of the control parameter is discussed as well as the existence of other regimes.