Research
In my time at the University of Arizona, I have had occasion to work on many interesting projects with many fine advisors. Contained in this page are links and some brief explanations of what I have been working on and what my current interests are.
My thesis research is under Dr. Joceline Lega in the dynamics of disk systems. Of particular interest are the Lyapunov exponents and modes of these systems for various aspect ratios and number of disks. This problem has a great many applications in biology, fluid dynamics and statistical mechanics. Here is the presentation I gave a few semesters back giving a brief overview of the problem. Also, here is a high-level paper written for my MATH599 independent research project explaining Lyapunov exponents in greater detail. At right are a few images from my research. The movie is courtesy of Dr. Lega and shows how two different sets of nearly identical initial conditions have phase space trajectories that diverge over time. The lower plot shows how the Lorenz system can move from a chaotic regime to a non-chaotic one as the parameter 'rho' is varied.
I am also interested in agent-based simulation techniques to model simple "real world-like" networks of interacting automata. I have applied such techniques to healthcare (paper, presentation) and numerical solution of PDEs (paper). A really handy tool with a lot of pre-compiled examples for immediate use is NetLogo. The work on numerical solution of PDEs was done with Dr. Miklos Szilagyi of the Electrical and Computer Engineering Department.
Previously for a semester term project, I worked on the problem of swimming at low Reynold's number with Dr. Shankar Venkataramani. This problem is pretty fascinating: think about a human being trying to move through a pool full of peanut butter! (paper, presentation).
As an undergraduate, I participated in the Summer 2005 REU at the University of Illinois, Urbana-Champaign under the advisement of Dr. Joseph Rosenblatt. The topic was phase retrieval algorithms.
