The goal of this project was to observe and understand oscillating patterns in a large array of pendulums. This system provides a simple experimental model in which solitons, or something much like them, can be observed.
MATLAB Project 1: Complete the Onramp tutorial, due 1/28/2022 MATLAB Project 2: Slope Fields, due 2/11/2022 MATLAB Project 3a, due 3/4/2022 MATLAB Project 3: Euler’s Method, due Sunday, 3/11/2022 MATLAB Project 4: Computational Exploration of the SIR Model, due 5/5/2022
2005-2006 Project In a celebrated article in SIAM Review1, Diaconis, Holmes, and Montgomery show that under general conditions, a coin is inherently biased to land heads-up if it leaves the hand heads-up.
Everyone knows that objects falling under the influene of gravity near the surface of the earth experience constant acceleration of about 32 ft/s^2^, neglecting air resistance. Anyone who has taken elementary physics knows that the speed of a ball after it collides with the floor will be equal to its speed before impact, multiplied by ts coefficident of restitution.
In Spring 2010, the course featured several experiments in chaotic scattering, including, pictured above, the scattering of a laser beam off a system of three cylinders. The highlight of the class was an experiment to reproduce the chaotic dynamics of a soliton colliding with a localized defect (previously studied by Goodman and Haberman) in a simplified experimental setting: the motion of a ball rolling on a specially engineered surface.