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Michael Brenner
Physical Mathematics

A major challenge for applied mathematics is to determine the extent to which simplified analytically tractable mathematical models, coupled with appropriate computational resources, can shed light on increasingly complex problems. Can something become sufficiently complicated that computation coupled with careful analysis cannot shed light on its essential features? And is it "just a matter of time" before a mathematical description of a given phenomenon provides an appropriately insightful description? We address these general problems by specific approaches in four main areas: fundamental conceptual issues related to hydrodynamics; development of first principles, quantitative models of interest to engineering (e.g. electrospinning); mathematical device design (e.g. what is the optimal mechanical device for performing a certain task?); and mathematical models for biophysics (e.g. colony-formation by growing yeast cells).

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Nguyen, B., Upadhyaya, A., van Oudenaarden, A., and Brenner, M.P. 2004. Elastic instability in growing yeast colonies. Biophys. J. 86: 2740-2747.

Brenner, M.P., Lang, J.H., Li J., Qui, J. and Slocum, A.H. 2003. Optimal design of a bistable switch. Proc. Natl. Acad. Sci. USA 100: 9663-9667.

Nikolaides, M.G., Bausch, A.R., Hsu, M.F., Dinsmore, A.D., Brenner, M.P., Gay, C. and Weitz, D.A. 2002. Electric-field-induced capillary attraction between like-charged particles at liquid interfaces. Nature 420: 299-301.

Betterton, M.D. and Brenner, M.P. 2001. Collapsing bacterial cylinders. Phys Rev E Stat. Nonlin Soft Matter Phys. 64: 061904.