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Counting Holes in Physical Systems - Applications of Computational Homology to Systems in Physics -

Stanish, Sage
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.
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2022-05-01
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Undergraduate Honors Theses
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The_Homology_of_Phase_Transitions_in_Physical_Systems.pdf
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Advisor
Day, Sarah
Mordijck, Saskia
Dudson, Benjamin
Li, Chi-Kwong
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Mathematics
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https://scholarworks.wm.edu/handle/internal/11227
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