Alexander has recently completed a bachelor of science in applied mathematics with a focus on optimization, and a bachelor of science in physics with a focus in cosmology/astrophysics, both at the University of Rhode Island. His academic interests lie in the regions of astrophysics, accelerator physics and plasma physics (depending on which day you ask). Alex is starting a master of science in mathematics, with the hope of studying the local and global stability of differential equations, particularly those that govern electrodynamics.
Project: Machine Learning for Control of Chaotic Systems
The goal of this project is to extend the control system for the single inverted pendulum to an inverted double pendulum. I will proceed by discovering the equations of motion for a double pendulum, then implementing a proportional-derivative controller on the first link. From there, I will research how the single pendulum control affects the second link, and modulate the controller accordingly. Once this has been completed, I will create a large training set of position and velocity data, and teach a neural network how to respond to many possible initial conditions for the double pendulum.
Favorite 3-Color 2D Totalistic Cellular Automaton
I've chosen cellular automaton 16365 from this space. It exhibits some interesting growth behavior: there are some slightly enlarged structures at the corners of the CA initialized with one cell. They grow with progressing time, then grow again. They meet in the center of each side, and the 2D symmetric representation seems to have a jump in growth. Below is a Manipulate of the 2D automaton.
This is primarily interesting because the corner structures meet at irregular intervals.