CAREER PROPOSAL IN PHYSICAL MATHEMATICS

9733030布伦纳这项工作得到了国家科学基金会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：作为偏微分方程式中奇点形成的例子的液滴破裂；电喷雾背后的动力学机制；单泡声致发光的理论研究，即声能到光的转换；以及与生物学家合作完成的细菌趋化性实验研究。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。这些是几个具体的要点：将主动让本科生参与研究计划，通过开展简单的实验来检验理论和扩展研究方向。为了确定和培训本研究的本科生，建议在自主活动期间开设一门关于数学在物理实验中的应用的短期课程。基础流体力学本科课程也将进行改革。对于研究生，将开发几门新课程，在当前研究的背景下描述重要的数学技术。最后，建立了一个专门的学生研讨会系列，用于非正式讨论当前研究感兴趣的主题。国家科学基金会强烈鼓励学术人员的早期发展，既是教育工作者，也是研究者。学院早期职业发展(Career)计划是一个基础范围的计划，为初级教师在其整体职业发展的背景下提供支持。它在一个单一的计划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。这一计划加强并强调了基金会对充分、平衡的学术事业发展的重视，包括研究和教育。

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.