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 research directions range from figuring out the nature of the turbulent cascade, to understanding the rules for building materials that assemble themselves, possibly with life-like properties, to efforts to use recent advances in machine learning to facilitate scientific discovery.