Bubble Dynamics

• Currently I'm studying a PDE model of symmetric and nonsymmetric oscillations of bubbles in a compressible fluid.

The Lamb model

• Lamb model paper
• This classical model of an oscillator coupled to a wave was studied numerically and analytically. Special attention was paid to energy conserving numerics.

Previous graduate work -- mostly for my own reference

• Symmetry breaking.
• Hyperbolic Geometry.

Cornell University REU (Summer 2003)

• Calculus on a Sierpinski Gasket II (with Nitsan Ben-Gal, Robert Strichartz, and Clint Young)
• I worked with Dr. Bob Strichartz on fractal differential equations. The work I and other students did was recently published in Transactions of the American Mathematical Society. You can also check out the website I made about my research. It has some data files and pictures for later work.

UCLA Institute for Pure and Applied Mathematics RIPS (Summer 2002)

• I worked with Dr. Luminita Vese and three students on an image processing project sponsored by Areté Associates. We used a level set algorithm to filter vehicles from foliage and image noise in 3D image data. We used the results to modify software.