Date of Award

5-10-2026

Date Published

June 2026

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics

Advisor(s)

M. Manning

Subject Categories

Physical Sciences and Mathematics | Physics

Abstract

Biological systems are able to exhibit remarkable and exotic mechanical properties by tuning their microscopic internal degrees of freedom in order to accomplish global functions. One of the most interesting mechanical behaviors of some such materials is the ability to transition between stiff solid-like states and soft fluid-like states in order to initiate specific flow patterns or tune their mechanical response. Not only this, but they are able to selectively cross this transition while also being optimized for other functions. In this dissertation I explore numerical and analytical methods for mapping the landscapes of states on the edge of rigidity in several mechanical models of amorphous materials, as a starting point towards understanding how biological systems are able to "learn" on these landscapes as well as how one might think about designing materials with specific functions. First I discuss the mathematical theory that governs the rigidity transitions observed in commonly studied models. Then, I describe a method for defining and locating structural defects in amorphous active solids by a nonlinear analysis of the force landscape, and show numerical evidence that the resulting quasilocalized excitations are highly predictive of plastic events that facilitate large scale flows and rearrangement in such materials. Finally, I consider the space of all rigid states of disordered central force networks and show that this can be naturally parameterized as a smooth manifold, then use this to numerically locate special optimal rigid configurations at the rigidity transition. I also discuss some preliminary results extending this formalism to networks with bending interactions. Overall, this work extends our understanding of the underlying mechanisms governing the mechanical properties of disordered and non-equilibrium matter.

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Open Access

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