9733030 Brenner This work is supported by a National Science Foundation Faculty Early Career Development Award. The research component will focus on an array of problems applying techniques of nonlinear dynamics to fluid dynamics, acoustics, and biophysics. The uniting theme is the mathematics of nonlinear partial differential equations. Specific projects include the breaking of fluid drops as an example of singularity formation in partial differential equations; the dynamical mechanisms behind electrosprays; a theoretical investigation of single bubble sonoluminescence, the conversion of acoustic energy into light; and a study of experiments in bacterial chemotaxis, done in collaboration with biologists. The educational component of this activity aims both to improve the learning environment in applied mathematics at MIT, as well as provide concrete mechanisms for using teaching opportunities to extend the principal investigator's research program to new areas. These are several specific points: There will be an initiative to involve undergraduate students in the research program by carrying out simple experiments to test theories and extend research directions. To identify and train undergraduate students for this research, it is proposed to develop a short course during the Independent Activities Period on the application of mathematics to physical experiments. The undergraduate course in basic fluid dynamics will also be revamped. For graduate students, several new courses will be developed that describe important mathematical techniques in the context of current research. Finally, a special student seminar series for informal discussion of topics of current research interest has been established. The National Science Foundation strongly encourages the early development of academic faculty as both educators and researchers. The Faculty Early Career Development (CAREER) Program is a Foundation-wide program that provides for the support of junior faculty within the context of their overall career development. It combines in a single program the support of quality research and education in the broadest sense and the full participation of those traditionally underrepresented in science and engineering. This program enhances and emphasizes the importance the Foundation places on the development of full, balanced academic careers which include both research and education.
