Our research uses methods and ideas of applied mathematics to address problems in science and engineering. We are first and foremost problem solvers, and search widely to find problems where mathematics (simple or complicated, with large computer simulations or without) can answer scientific questions.

Over the past decade our research has focused essentially primarily on theoretical modeling in the physical sciences and engineering. Much of the work has arisen out of close contact with experimentalists, and efforts to develop quantitative descriptions of phenomena and experiments. Problems addressed have included the breaking of fluid droplets; sonoluminescence (the production of light from small bubbles); the sedimentation of small particles; device design in engineering; electrospinning (a materials technique for producing small fibers), etc.

Current projects in the physical sciences include problems in microfluidics (such as mechanisms for producing small fibers in microfluidic devices), fluid mechanics (such as the aerodynamics of whale flippers), the rheology of colloidal suspensions (such the mechanisms underlying shear banding), self assembly, as well as various problems in material science (ion beam sputtering), and atmospheric chemistry (algorithm development for speeding up current atmospheric transport codes, as well as fundamental research into nonlinear chemical plumes in the atmosphere).

In recent years more and more of our work has been moving to biological questions and biological phenomena. We are interested in this both because the problems themselves are of interest and have much opportunity, and also because we feel strongly that the principles of biology can be used to develop novel directions in engineering. Current projects range from the connection between evolution and physiology (primarily in voltage gated ion channels, and hemoglobin), to the mechanism of transport in the nuclear pore, to issues having to do with understanding the very large systems of differential equations that commonly arise in biological modeling.