I am interested in developing novel mathematical techniques for the analysis of physical phenomena, such as can be found in the realm of fluid dynamics. A good example of this is my summer work with Professor Divakar Viswanath of the Mathematics Department at the University of Michigan, in which we used Green's functions to develop a numerical algorithm capable of resolving turbulent solutions of the Navier-Stokes equations. In the future, I hope to develop new mathematics motivated by the analysis of micro-scale continuum mechanics, complex fluids, and turbulent flows. As such, I plan to focus on both the theoretical and computational analysis of partial differential equations while at the Courant Institute.
Navier-Stokes Solvers Using Green's Functions
Last summer, I worked with Professor Divakar Viswanath of the UofM Mathematics Department, where I was funded with a Mathematics REU. Our research concerned the numerical analysis of turbulent planar Couette flow; we developed a numerical algorithm which we believe is capable of resolving even the turbulent boundary layer for high Reynolds number situations. We plan on writing a journal paper in the coming semester.
A Probabilistic Approach to Inverse Convection-Diffusion
Starting in the summer of 2009, I worked with Professor Krzysztof Fidkowski of the UofM Aerospace Department on a computational method for atmospheric contaminant source inversion. Here is a video of me presenting the project as part of the 2009 UofM Summer Undergraduate Research Experience. I also presented the work at the 2010 AIAA Regional Student Conference, where I won first place in both the paper and presentation categories; I presented at the 2011 AIAA Aerospace Sciences Meeting as a result. Here is the paper and the presentation from the conference.