(Georgia Institute of Technology, 2021-07-29)
Detal, Noah
In this thesis, two problems involving the macroscopic ordering of coupled nonlinear elements are studied. The first problem involves analyzing a synchronizing transition in a population of coupled oscillators. Synchronization of the oscillators in this model corresponds to coherent propagation of solitary waves in a nonlinear Schrödinger equation. The second problem concerns the elimination of chaotic fibrillatory dynamics in excitable cardiac tissue. In the fibrillatory state, reentrant spiral waves of electrical activity entrain the excitable cells and interrupt the healthy heart rhythm. By appealing to the topological structure of excitable dynamics, conditions are derived for the stimulated elimination of spiral waves and associated fibrillation. Insights from this topological framework are then applied to the optimization of a novel low-energy multi-pulse defibrillation scheme.