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Author ORCID Identifier

http://orcid.org/0000-0003-0567-4664

Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Physics

Year Degree Awarded

2020

Month Degree Awarded

September

First Advisor

Christian D. Santangelo

Second Advisor

Gregory Grason

Third Advisor

Narayanan Menon

Fourth Advisor

Ryan Hayward

Subject Categories

Statistical, Nonlinear, and Soft Matter Physics

Abstract

In the first part of this thesis, I propose a method that allows us to construct optimal swelling patterns that are compatible with experimental constraints. This is done using a greedy algorithm that systematically increases the perimeter of the target surface with the help of minimum length cuts. This reduces the areal distortion that comes from the changing Gaussian curvature of the sheet. The results of our greedy cutting algorithm are tested on surfaces of constant and varying Gaussian curvature, and are additionally validated with finite thickness simulations using a modified Seung-Nelson model.

In the second part of the thesis, we focus on self-assembly methods as an alternate approach to program specific desired structures. More specifically, we develop theoretical design rules for triply-periodic minimal surfaces (TPMS) and show how their symmetry properties can be used to program a minimum number triangular particle-types that successfully coalesce into the TPMS shape. We finally simulate our design rules with Monte Carlo methods and study the robustness of the self-assembled structures upon changing different system parameters like elastic moduli.

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