Date Thesis Awarded

5-2022

Access Type

Honors Thesis -- Access Restricted On-Campus Only

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Sarah Day

Committee Members

Saskia Mordijck

Benjamin Dudson

Chi-Kwong Li

Abstract

Visual patterns are everywhere in nature and often give insight into the underlying physical systems that generate them. When the dynamics of these physical systems change, the visual patterns mirror that change. We quantify these visual changes by studying the homology of these patterns (a measure of `holes'). In particular, we study the homology of two systems. The first are phase transitions like boiling water, and the second are turbulent to zonal flow transitions like those found in the jet stream. In both cases, we simulate these patterns and show that their homology describes the behavior around either transition. This technique generalizes to arbitrary dimensions and may be useful in studying physical systems in 3 or more dimensions where our visual intuition breaks down.

Recommended Citation

Stanish, Sage, "Counting Holes in Physical Systems - Applications of Computational Homology to Systems in Physics -" (2022). Undergraduate Honors Theses. William & Mary. Paper 1785.
https://scholarworks.wm.edu/honorstheses/1785