Electronic Theses and Dissertations

Date

2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Computer Science

Committee Chair

Max Garzon

Committee Member

Russell Deaton

Committee Member

Thomas Watson

Committee Member

Ching-Chi Yang

Abstract

Self-assembly is a pervasive process in natural phenomena that builds complex structures from very simple components. These processes are central to nanoscale manufacturing and crystallography and rely on stochastic self-assembly to bring order out of molecular chaos. In particular, the algorithmic models of self-assembly (for example, the aTAM) employ highly nondeterministic dynamics in an attempt to emulate the massively parallel physical feats effected by DNA {\it in vivo} to support life. In this work, we define a new object in algorithmic self-assembly called the synoptic pattern to explore structural properties and the long-term behavior of algorithmic self-assembly systems. The synoptic pattern is analogous to the computation tree of a nondeterministic Turing machine, which are known to be computational universal and hence unpredictable algorithmically. We show that synoptic patterns are a robust and useful framework for self-assembly processes at large and enable analysis of their behavior. In particular, they afford a useful analytical tool to understand structural properties of and a nontrivial probabilistic analysis of the long-term behavior of self-assembly processes in large families of 1D and some 2D aTAM self-assembly systems, including systems generating infinite families of patterns describable by regular and linear languages in the Chomsky hierarchy. Finally, we also introduce probabilistic definitions of the efficiency of assembly processes and expand on previous work to show how one assembler can efficiently probabilistically approximate a given target assembler by mostly producing patterns that match closely patterns produced by the target assembler, even in the presence of assembly errors.

Comments

Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to ProQuest

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