My research work is motivated by topics in theoretical fluid dynamics. The two main areas are convective-diffusive heat and mass transfer, and flow of viscoelastic fluids.
We consider a statistical approach to simulate the movement of pedestrians. The virtual city is divided into nodes populated with avatars. Each node is associated with a pdf which dictates how long a pedestrian will "wander" in that node.
We consider the shape optimization problem associated with maximizing or minimizing diffusive transport. Is the cylinder an optimal shape? What is the shape that provides minimum drag? These are a few of the questions we hope to answer.
Diffusion in Lagrangian coordinates
We consider the convection-diffusion problem of a passive scalar in Lagrangian coordinates, i.e., in a coordinate system fixed on fluid particles. In the figure (left) we see a Brownian particle (thin line) jumping across fluid particles (thick lines).
Factors determining the stability of extruded polymers
We consider the problem of extrusion of a compressible fluid from a capillary rheometer and try to determine the origin of any instabilities.