Date on Honors Thesis

Spring 4-20-2023

Major

Engineering Physics

Minor

Math

Examining Committee Member

Matthew Williams, PhD, Advisor

Examining Committee Member

Dr. James Rogers, PhD, Committee Member

Examining Committee Member

Dr. Kevin Miller, PhD, Committee Member

Abstract/Description

The purpose of my work is to analyze the results of Monte Carlo simulations of various types of polymers: a helical homopolymer and a flexible homopolymer. Specific applications of Monte Carlo polymer simulations and parallel tempering replica exchanges are presented. Using temporal analysis, I aim to measure the efficiency of each type of simulation as it relates to equilibration time. For the helical homopolymer model, equilibration time is expanded upon to analyze the rate of structure generation and relevant hyper-phase diagram. Stable states for helical homopolymers will use data generated from parallel tempering replica exchange Monte Carlo simulations created by Dr. Matthew Williams. The stable states for flexible polymers will be analyzed and generated using a simulation created by myself. Each simulation begins with a polymer in a random configuration; as time progresses, changes to polymer structure are randomly induced to decrease the energy of each structure until equilibrium is reached. Data collected after equilibrium is reached is used to understand polymer behavior for each model and simulated temperature. Canonical analysis of post-equilibration data yields a specific heat plot for the flexible polymer model and a hyper-phase diagram for the helical polymer model. Analysis of equilibration data shows up to a 95% decrease in equilibration time for the 2D replica exchange scheme over the 1D. Additionally, the incorporation of Hamiltonian exchange into parallel tempering simulations for the helical homopolymer model leads to an average of a seven-fold increase in the rate of unique structure generation. Future research steps involve expanding the application of the 2D replica exchange scheme to differing Monte Carlo simulations as well as the addition of measurable physical and thermodynamic parameters to my simulation.

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