Correlation of plastic events with local structure in jammed packings across spatial dimensions

TL;DR

This study demonstrates that local structural features, such as softness and coordination number, can predict rearrangements in jammed packings across dimensions 2 to 5, challenging the notion that local structure is irrelevant in high dimensions.

Contribution

The paper introduces machine learning-based identification of a local structural variable, softness, showing its predictive power in jammed packings across multiple dimensions.

Findings

Softness correlates with rearrangements in dimensions 2 to 5.

Coordination number $Z$ is predictive of rearrangements.

Local structure influences behavior even in high spatial dimensions.

Abstract

In jammed packings, it is usually thought that local structure only plays a significant role in specific regimes. The standard deviation of the relative excess coordination, $\sigma_Z/ Z_\mathrm{c}$, decays like $1/\sqrt{d}$, so that local structure should play no role in high spatial dimensions. Furthermore, in any fixed dimension $d \geq 2$, there are diverging length scales as the pressure vanishes approaching the unjamming transition, again suggesting that local structure should not be sufficient to describe response. Here we challenge the assumption that local structure does not matter in these cases. In simulations of jammed packings under athermal, quasistatic shear, we use machine learning to identify a local structural variable, softness, that correlates with rearrangements in dimensions $d=2$ to $d=5$. We find that softness - and even just the coordination number $Z$ - are quite predictive of rearrangements over a wide range of pressures, all the way down to unjamming, in all $d$ studied. This result provides direct evidence that local structure can play a role in higher spatial dimensions.