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Title
DISTORTION-CONTROLLED ISOTROPIC SWELLING AND SELF-ASSEMBLY OF TRIPLY-PERIODIC MINIMAL SURFACES
Author ORCID Identifier
http://orcid.org/0000-0003-0567-4664
AccessType
Open Access Dissertation
Document Type
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.
DOI
https://doi.org/10.7275/19190548
Recommended Citation
Duque, Carlos M., "DISTORTION-CONTROLLED ISOTROPIC SWELLING AND SELF-ASSEMBLY OF TRIPLY-PERIODIC MINIMAL SURFACES" (2020). Doctoral Dissertations. 2011.
https://doi.org/10.7275/19190548
https://scholarworks.umass.edu/dissertations_2/2011