Scientific computing and numerical analysis: Efficient computational methods for complex fluids, plasma physics, electromagnetism and other physical applications.

Condensed Matter Physics, Soft materials, Colloids, Liquid Crystals, Computational Physics, Physics Education
Soft matter physics is the study of matter that is all around us in everyday life: soaps, oil, foods, sand, foams, and biological matter. All of these are readily deformable at room temperature and combine properties of both fluids and solids. Despite their ubiquity, these materials are extremely complicated. Unlike simple fluids like water, they have rich internal structure; unlike crystalline solids they are typically not periodically ordered. Moreover, they exist in long-lived metastable states far from equilibrium and respond to stimuli such as applied electric and magnetic fields, temperature and pressure. My work seeks to understand how these materials respond to shape: how they self-organize on curved surfaces or in complex geometries and how this knowledge can be used both to sculpt desirable shapes at the microscopic scale and create shape changing systems like soft robots. We use high performance computing to simulate and predict these behaviors and work closely with experimentalists at Tufts and beyond.

Applied dynamical systems, applied probability theory, kinetic theory, agent-based modeling, mathematical models of the economy, theoretical and computational fluid dynamics, complex systems science, quantum computation
Current research emphasis is on mathematical models of economics in general, and agent-based models of wealth distributions in particular. The group's work has shed new light on the tendency of wealth to concentrate, and has discovered new results for upward mobility, wealth autocorrelation, and the flux of agents and wealth. The group's mathematical description of the phenomenon of oligarchy has also shed new light on functional analysis in general and distribution theory in particular.
Secondary projects include new directions in lattice Boltzmann and lattice-gas models of fluid dynamics, kinetic theory, and quantum computation.