Correlations in the shear flow of athermal amorphous solids: A principal component analysis

TL;DR

This paper uses principal component analysis to identify key features of particle displacements in sheared amorphous solids, revealing elastic and plastic deformation modes and their relation to soft vibrational modes.

Contribution

It demonstrates the application of PCA to characterize deformation modes and links principal directions to soft elastic modes in athermal amorphous solids.

Findings

PCA reveals dominant elastic and plastic deformation features.

Principal directions correspond to soft modes of elastic propagator.

Projections relate to displacement structure factors at specific wavevectors.

Abstract

We apply principal component analysis, a method frequently used in image processing and unsupervised machine learning, to characterize particle displacements observed in the steady shear flow of amorphous solids. PCA produces a low-dimensional representation of the data and clearly reveals the dominant features of elastic (i.e. reversible) and plastic deformation. We show that the principal directions of PCA in the plastic regime correspond to the soft (i.e. zero energy) modes of the elastic propagator that governs the redistribution of shear stress due to localized plastic events. Projections onto these soft modes also correspond to components of the displacement structure factor at the first nonzero wavevectors, in close analogy to PCA results for thermal phase transitions in conserved Ising spin systems. The study showcases the ability of PCA to identify physical observables related to the broken symmetry in a dynamical nonequilibrium transition.