Date of Award

2019

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Physics & Astronomy

First Advisor

Randall D. Kamien

Abstract

Transitions between various states of matter occur everywhere and are integral in the processes that make life, as we know it, possible. Given such importance in everyday life, it makes sense that considerable time has been spent looking for theories of these transitions. What makes our modern theories of phase transitions so powerful is their predictive ability despite ignoring the essential granularity of matter. Success in this manner has made field theory an indispensable tool. There are ordered states of matter, generally spoken of as having broken symmetries of the Euclidean group: broken translations for crystals and broken rotations for vector-like order. There are even more exotic states of matter such as smectic liquid crystals and diblock copolymers which manifest states that have fewer broken translations in a given dimension than would be necessary for the formation of crystalline structure. These exotic states are variously called striped or lamellar phases. We start with some general facts and features of transitions to these striped phases and discuss what may happen when these transitions occur on the surface of a sphere. Next we identify pollen cell surface patterning as an instance of this transition from disorder to a patterned state of matter on the surface of a sphere. The character of the transition is found to be first-order, which leads us to study the nucleation process and its kinetics on spherical surfaces. Lastly, we show how fluctuations lower the surface tension of nucleated droplets on a sphere relative to their flat space counterpart.

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