Date of Award

5-10-2026

Date Published

June 2026

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics

Advisor(s)

Christian Santangelo

Keywords

bifurcations;hysterons;memory;soft matter

Subject Categories

Physical Sciences and Mathematics | Physics

Abstract

The primary focus of this dissertation is the development of a geometric framework for understanding memory formation in systems composed of interacting hysteretic elements, or hysterons. Using tools from bifurcation and catastrophe theory, this work provides a description of how complex memory behaviors emerge from the structure of the system's configuration space and the system bifurcations under external driving. As a concrete model system, we study networks of connected rubber balloons subjected to different inflation protocols. Under pressure control, the system maps naturally onto a Preisach-type system of non-interacting hysterons and exhibits return point memory. In contrast, under volume control, interactions between balloons lead to avalanches, scrambling of switching order, and violations of return point memory. By explicitly constructing and analyzing the configuration space of the system, we show how these behaviors arise from bifurcations that change the topology of configuration space, which corresponds to qualitative changes in system behavior. This approach provides a direct geometric route from configuration space to transition graphs. Building on these insights, the dissertation introduces a catastrophe-theoretic description of interacting hysterons in dissipative systems, linking fold and higher-codimension bifurcations to modifications of transition graphs and memory behavior. This framework clarifies how tuning system parameters can systematically alter accessible states. The second part of the dissertation examines thin membranes with patterned rigidity as soft pneumatic actuators. A theoretical model for membrane deformations is developed and combined with experimental measurements and machine learning based modeling to characterize and predict actuator performance. Together, these studies demonstrate how nonlinearities and geometric structure, often viewed as complications, can instead be harnessed to design soft systems with programmable and rich responses.

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Open Access

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