Date of Award

5-2026

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematics

Thesis Sponsor/Dissertation Chair/Project Chair

Ashwin Vaidya

Committee Member

Deepak Bal

Committee Member

Bogdan Nita

Abstract

This thesis aims at understanding the phenomenon of of self-organization in complex dissipative systems, living and nonliving. Dissipative systems are characterized by their search for energy, interactions with their surroundings and the production of entropy, all of which result in the creation of stable structures or patterns, which persist as long as the initial environmental conditions are maintained. The two specific models that we chose to study here are (a) Futbol (or Soccer) and (b) a chemical system involving free-floating menthol crystals floating on a fluid surface to represent nonliving systems. Using experiments and mathematical models, we will try to understand the conditions that lead to the emergence of pattern formation and self-organization in these systems. We employ the tools of complexity theory, namely network theory and dynamical systems to examine the emergent patterns. Our larger, attempt is to seek commonalities and profiles that can be used to classify and categorize self-organization in physical versus biological systems and if possible, identify the physical basis for biology.

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