Structure, Dynamics, and Elasticity in Amorphous Systems

In amorphous systems, the connection between local structure and the dynamics is far from understood. Here we address several aspects of these systems, particularly in supercooled liquids and jammed packings. We study the connection between mean-field theory and finite-dimensional jammed packings, both by studying the correlation between local structure and rearrangements as a function of spatial dimension, and by studying the predictions of elastic models in mean-field theory and more ad-hoc mean-field-like calculations. We also study how local structural variables identified by machine learning can be used to develop models of dynamics, both in athermal and thermal systems. In Chapter 2, we discover that rearrangement events under athermal quasistatic shear remain localized and well-correlated with local structure in any spatial dimension. This suggests a modification of the conventionally-understood picture relating mean-field theory to finite-dimensional jammed packings. In Chapter 3, we elucidate the relationship between local structural softness, elastic strain, and plastic events during avalanches in athermal systems. In Chapter 4, we identify how the underlying requirement of time-reversal invariance constraints the type of model that can be constructed for dynamical facilitation using machine-learned softness in thermal systems, and construct such a model. In Chapter 5 we turn instead to the defense of mean-field theory, showing that it predicts not only the exponents of scaling laws near unjamming but also the dependence of the amplitudes on dimension. We reproduce one of these scalings with dimension using a simple theoretical calculation outside of mean-field. In Chapter 6, we study the linear elastic response to two different kinds of random or local deformation. For one of these definitions we are able to produce theoretical predictions of the moduli, demonstrating a strong system-size dependence not reported in previous numerical work. For the other, we demonstrate a surprising similarity between the theoretically-predicted distribution of elastic moduli for a random deformation, and that of the shear modulus. Collectively, our results represent progress in two quite different directions: the understanding of amorphous systems using machine learning to identify a relevant local structural variable, and understanding the connection between real jammed packings and mean-field theory