This github repository contains all of the code used to produce the figures from my dissertation at the University of Delaware, titled "Microscale Interactions Lead to Macroscopic Dyanmics: An Analysis of Various Flocking Mechanisms."
The work in Chapters 3-5 was conducted under the direction of Dr. Louis Rossi from the University of Delaware. The work in Chapter 6 was conducted under the direction of Drs. Michael Mayo and Kevin Pilkewicz from the Army Corps of Engineers.
Here is the abstract of the dissertation:
Collective behavior and pattern formation occur in all organisms, and researchers have searched for answers as to why these formations occur. In this dissertation, we utilize mathematical techniques to gain insight into two pressing questions in this field. In the first question, a specific species of phytoplankton, Heterosigma akashiwo , has been the cause of harmful algal blooms (HABs) in waterways around the world causing millions of dollars in damage to farmed animals and destroying ecosystems. Developing a fundamental understanding of their movements and interactions through phototaxis and chemotaxis is vital to comprehending why these HABs start to form and how they can be prevented. We develop a novel one- and two-dimensional mathematical and computational model reflecting the movement of an ecology of plankton, incorporating both run-and-tumble motion and autochemotaxis. We present a succession of complex and biologically meaningful models combined with a sequence of laboratory and computational experiments that inform the ideas underlying the model. By analyzing the dynamics and pattern formation which are similar to experimental observations, we identify parameters that are significant in plankton's pattern formation in the absence of bulk fluid flow. We numerically analyze variations on how might plankton deposit chemical and connect the outcomes with features observed in experimental observations. In the second research question, we find applicable metrics and tools scientists can use to differentiate between flocking mechanisms such as schools of fish and flocks of birds. Motivated by the hydrodynamic character of flocks, we repurpose metrics from liquid theory to characterize both the structural and mechanistic properties of the classic Vicsek model. We show how varying certain parameters affects the structural development of the flock, and we show that these metrics are able to identify, for the first time, indelible marks on its structure.