CAREER PROPOSAL IN PHYSICAL MATHEMATICS

9733030 Brenner这项工作得到了国家科学基金教师早期职业发展奖的支持。研究部分将集中于将非线性动力学技术应用于流体动力学、声学和生物物理学的一系列问题。统一的主题是非线性偏微分方程的数学。具体项目包括作为偏微分方程奇点形成的一个例子的液滴破裂；电喷雾背后的动力学机制；单泡声致发光的理论研究——声能转化为光还有一项关于细菌趋化性的实验研究，是与生物学家合作完成的。这项活动的教育部分旨在改善麻省理工学院应用数学的学习环境，并提供具体的机制，利用教学机会将首席研究员的研究计划扩展到新的领域。这是几个具体的点：将有一个倡议，让本科生参与研究计划，通过进行简单的实验来检验理论和扩展研究方向。为了确定和培养本研究的本科生，建议在独立活动期开设一门关于数学在物理实验中的应用的短期课程。基础流体力学的本科课程也将进行改革。对于研究生，将开发几门新课程，描述当前研究背景下的重要数学技术。最后，建立了一个特别的学生研讨会系列，以非正式讨论当前研究感兴趣的主题。美国国家科学基金会强烈鼓励教师作为教育工作者和研究人员的早期发展。教师早期职业发展（Career）计划是一个基金会范围内的计划，为初级教师的整体职业发展提供支持。它在一个项目中结合了对最广泛意义上的高质量研究和教育的支持，以及那些传统上在科学和工程领域代表性不足的人的充分参与。该计划加强并强调了基金会对包括研究和教育在内的全面，平衡的学术生涯发展的重要性。

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.