Date of Award

August 2020

Degree Type


Degree Name

Doctor of Philosophy (PhD)




Mary L. Manning

Second Advisor

James Henderson

Subject Categories

Physical Sciences and Mathematics


In this thesis, we investigate the relationships between the disorder, structure, and deformation in amorphous materials. First, to understand the surprising low-frequency vibrational modes in structural glasses, and how it arises from the microscopic disorder in the system, we study the spectra of a large ensemble of sparse random matrices where disorder is controlled by the distribution of bond weights and network coordination. When there is a finite probability density of infinitesimal bond weights, we find a region in the vibrational density of states that is consistent with the low-frequency behavior in structural glasses. Next, in order to investigate structural properties of active systems, we develop a novel method to generate static, finite packings in an artificial potential that reproduce the packing structures observed in a class of point-of-interest active self-propelled particle simulations. This allows us to compute structural measures, such as the vibrational modes, in an unstable active system. Finally, we evaluate the evolution of structure during strain-induced avalanches in athermal, amorphous systems using numerical simulation of soft spheres. We find that these avalanches can be decomposed into a series of bursts of localized deformations, and we develop an extension of persistent homology to isolate these bursts of localized deformations. Further, we extend existing tools for the structural evaluation of mechanically stable systems to generically unstable systems to identify how soft regions evolve and change throughout an avalanche.


Open Access