## Sigma Xi Poster Competition

## Academic Level at Time of Presentation

Senior

## Major

Engineering Physics

## Minor

Math

## 2nd Student Academic Level at Time of Presentation

Senior

## 2nd Student Major

Engineering Physics

## 2nd Student Minor

Math

## List all Project Mentors & Advisor(s)

Matthew Williams

## Presentation Format

Poster Presentation

## Abstract/Description

The purpose of our work is to analyze the results of a two-dimensional parallel tempering Monte Carlo simulation of a coarse-grained helical homopolymer. The two-dimensional simulation allows Hamiltonian exchanges across both temperature and torsion values, while the one-dimensional simulation exclusively exchanges across temperature values. The genesis of each simulation is defined by a randomly configured polymer; as time progresses, randomly generated movements of monomers decrease the structure’s energy until equilibrium is reached. Equilibrium is determined by finding the absolute minimum of the data series, computing the mean of all remaining data, and finding the intersection between the rolling average and the post-minimum mean. Data collected after equilibration is used to understand polymer behavior for each model and simulated temperature. This data aids in constructing a hyperphase diagram to visualize phase transitions of the simulated polymers. Simulation efficiencies as a function of both equilibration time and steps per new structure are calculated to compare the efficacy of the 2D parallel exchange scheme versus the 1D. Incorporating the two-dimensional Hamiltonian exchange into parallel tempering simulations lead to an average seven-fold increase in the rate at which new structures are generated in this model and a decrease in the equilibration time by as much as 95%.

## Spring Scholars Week 2023 Event

Sigma Xi Poster Competition

One-Dimensional and Two-Dimensional Simulations of Helical Homopolymers: A Comparative Analysis of Energy Stabilization and Efficiency

The purpose of our work is to analyze the results of a two-dimensional parallel tempering Monte Carlo simulation of a coarse-grained helical homopolymer. The two-dimensional simulation allows Hamiltonian exchanges across both temperature and torsion values, while the one-dimensional simulation exclusively exchanges across temperature values. The genesis of each simulation is defined by a randomly configured polymer; as time progresses, randomly generated movements of monomers decrease the structure’s energy until equilibrium is reached. Equilibrium is determined by finding the absolute minimum of the data series, computing the mean of all remaining data, and finding the intersection between the rolling average and the post-minimum mean. Data collected after equilibration is used to understand polymer behavior for each model and simulated temperature. This data aids in constructing a hyperphase diagram to visualize phase transitions of the simulated polymers. Simulation efficiencies as a function of both equilibration time and steps per new structure are calculated to compare the efficacy of the 2D parallel exchange scheme versus the 1D. Incorporating the two-dimensional Hamiltonian exchange into parallel tempering simulations lead to an average seven-fold increase in the rate at which new structures are generated in this model and a decrease in the equilibration time by as much as 95%.