These are some of my current and past research interests and projects.
Passive tracer problems. My PhD research is
on transport of passive scalars in shear flow, working with Roberto Camassa and Rich McLaughlin.
The broad research question is essentially, "when a dye gets pushed by a fluid flow in a pipe, what
influence does the shape of the pipe have in shaping the dye?" Our approach is to both apply techniques in
mathematical analysis to the advection-diffusion equation to gain quantitative predictions at both
short and long times, and use numerical simulations for validatation. The short answer is that the cross section
does play an important role. We have published papers at both
Physical Review Letters and
Science covering different aspects of this question.
Stability problems. I spent the summer of 2013 at Los Alamos National Lab,
working with Balu Nadiga
on a stability problem in geophysical fluid dynamics. The broad goal here is to be able to understand the mechanism
for, and size of, instabilities in ocean flows. My project was to develop a numerical code for one such scenario.
Spectral image segmentation. In my undergraduate, I worked with Andrew Knyazev
on a project on spectral image segmentation. The goal is to develop a black-box method for identifying the salient
features of an image. I also briefly assisted on a code for optimal polynomial fitting
in the sup-norm, that is, finding an optimal n-th degree polynomial to minimize the sup-norm of
the error function f(x) - pn(x) on an interval.