Elementary Excitation Modes in a Granular Glass above Jamming

TL;DR

This study uses PCA to analyze collective excitation modes in granular glasses near jamming, revealing large fluctuation modes and linking soft modes to rearrangements, with implications for understanding jamming dynamics.

Contribution

It introduces a PCA-based approach to identify collective modes in granular glasses and explores their connection to rearrangements near jamming.

Findings

Large collective fluctuation modes are observed at high densities.

Soft modes can predict rearrangements during quiet periods.

The relevance of mode-based descriptions diminishes as the system unjams.

Abstract

The dynamics of granular media in the jammed, glassy region is described in terms of "modes", by applying a Principal Component Analysis (PCA) to the covariance matrix of the position of individual grains. We first demonstrate that this description is justified and gives sensible results in a regime of time/densities such that a metastable state can be observed on long enough timescale to define the reference configuration. For small enough times/system sizes, or at high enough packing fractions, the spectral properties of the covariance matrix reveals large, collective fluctuation modes that cannot be explained by a Random Matrix benchmark where these correlations are discarded. We then present a first attempt to find a link between the softest modes of the covariance matrix during a certain "quiet" time interval and the spatial structure of the rearrangement event that ends this quiet period. The motion during these cracks is indeed well explained by the soft modes of the dynamics before the crack, but the number of cracks preceded by a "quiet" period strongly reduces when the system unjams, questioning the relevance of a description in terms of modes close to the jamming transition, at least for frictional grains.