This multifaceted research project addresses issues in fluid dynamics, nonlinear optics, coupled rigid body dynamics, and infinite dimensional dynamics. The fluid dynamics work is related to transport and mixing phenomena which arise in fluid flows due to chaotic advection. This effort will focus on two distinct topics, specifically, feedback control of transport and mixing, and flows with more general time dependence. The optics research deals with the polarization dynamics of optical pulses propagating in nonlinear media. This work has applications to fiber optical devices. The rigid body dynamics effort studies the global dynamics of coupled rigid body dynamics systems with viscous damping and external forcing. The intent of the final research topic is to bring the geometrical theory of dynamical systems to bear on problems in infinite dimensions.
