Professor of Applied Mathematics and Applied Physics
Pierce Hall, Room 313
29 Oxford Street
Cambridge, MA 02138
Tel: 617-495 3336
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.
Current research projects range from efforts to understand the limitations of self assembly (e.g. what can be reliably assembled with spherically symmetric building blocks), to algorithm development for atmospheric chemistry (the development o algorithms to accelerate simulations of global pollution), to fluid mechanics (e.g. the aerodynamics of whale flippers, the splashing of droplets and the ejection of fungal spores), to material science (pattern formation on ion sputtered surfaces) to studies of the connection between evolution and physiology, targeted to specific protein families (voltage gated ion channels and hemoglobin).
Broadly speaking, our work is moving more and more towards the interfaces between engineering and biology, as well as towards biology itself. This is both because contemporary sociology has created much opportunity for finding new ways of applying mathematics to contribute to biology, and also because we are fascinated by the possibility that understanding the mechanistic principles of biology can be used to develop novel directions in engineering.
Most of 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), the interactions between colloidal spheres, etc.
E. A. van Nierop , S. Alben and M.P. Brenner, “ “How bumps on whale flippers delay stall: an aerodynamic model”, Phys. Rev. Lett., 100, 054502 (2008).
S.Tee, P.J. Mucha, M.P. Brenner and D.A. Weitz, “Velocity fluctuations in a low Reynolds Number Fluidized Bed”, J. Fluid Mech,, 596, 467-475 (2008).
M. Roper, R. Pepper, M.P. Brenner and A.Pringle, “Explosively launched spores of ascomycete fungi have drag minimizing shapes”, to appear in Proc. Natl. Acad. Sci (2008)
* M. Roper, T.M. Squires and M.P. Brenner, “Symmetry un-breaking in the shapes of perfect projectiles”, Phys. Fluids, 20, 0923606 (2008).
* M. Roper and M. P. Brenner, “A nonperturbative approximation to the Moderate Reynolds Number Navier Stokes Equation”, to appear in Proc. Natl. Acad. Sci