Particles flowing in square microchannels at finite Reynolds number experience an inertial lift force. This force is used to sort particles and cells in bioengineering. Using numerics and asymptotics, we develop a theory for the scaling of this lift force with particle radius. My slides from DFD 2012.

Theory of Orthogonal Polynomials on the Sierpinski Gasket. We developed a three-term recursion relation for the Orthogonal Polynomials, and investigate the asymptotics of the coefficients in this recurrence relation. We also study the zero sets of the OP, as well as the dynamics of the values of the OP at fixed points in SG. My website from the Cornell REU, and the preprint.

Quantum turbulance in superfluid helium produces a tangle of vortices. Previous studies investigated vortex recconnection. This is a continuing study in vortex ring collapse. See Lathrop Lab at the University of Maryland, especially Quantum Turbulance.

Frames are a generalization of bases for vector spaces. The advantage of frames over bases is redundancy. In signal and image processing, this redundancy can provide resilience to noise and robustness to erasures. Tight frames are a particular computationally efficient class of frames. I worked on the problem of scaling frames to be tight frames. Preprint.