phillip
O
pambuh
open heart
:::
open mind
:::
open door
home
resume
thesis - ms
Introduction
Abstract & t.o.c.
Abstract & t.o.c.
Abstract
Table of Contents
Chapter 1
Chapter 1
§ Motivations & Applications
§ Previous Work
§ Work in This Thesis
Chapter 2
Chapter 2
§ Introduction
§ General Coupling
§ Nearest-Neighbor Coupling
§ Overdamped Limit of the Coupled System
§ Observations from Simulation of Oscillators Interaction
Chapter 3
Chapter 3
§ Definition of the Winding Number
§ Observations from Simulation of Oscillators Interaction and Winding Number
Chapter 4
Chapter 4
§ Definition of Equilibrium
§ Location of Equilibrium Solutions
§ Energies of Equilibrium Solutions
§ Examples of Equilibrium Solutions for Unequally-Spaced Oscillators
Chapter 5
Chapter 5
§ Synchronization and the Case of Equally-Spaced Oscillators
§ Jacobian of a Network of Oscillators
§ The Circulant Matrix Form
§ Some Examples of Jacobians and Eigenvalues
§ The Eigenvalues of the Network
§ Analytical Verification of the Eigenvalue Formula
§ Computational Verification of the Eigenvalue Formula
§ Variations of the Eigenvalue Formula
Chapter 6
Chapter 6
§ Regions of Stability and Synchronization
§ Time-Evolution of Networks with Almost Equally-Spaced Oscillators
§ Summary
Appendix
Appendix
References
Kuramoto Model Simulator
portfolio / playground
Introduction
Simulators
Kuramoto Model - a Nonlinear System
Stadium Billiard - a Chaotic System
Calculators
Symmetrical Components - a SilverLight Demo (via WPF in C#)
contact
Stadium Billiards --
Collapse All
|
Expand All
A Stadium Billiard Simulator
Coming in Summer 2016.