Mathematical Sciences: Dynamical Systems with Symmetry: Applications to Physical Problems

数学科学：对称动力系统：在物理问题中的应用

• 批准号: 9502266
• 负责人: Mary Silber
• 金额: $ 13.75万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 2000-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9502266&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamical; Systems; Symmetry

9502266 Silber This work is supported by a National Science Foundation Faculty Early Career Development Award. The research component will focus on the further development of mathematical methods of equivariant dynamical systems for application to specific physical problems. These include hydrodynamic models of rotating convection and of magnetoconvection, models of Josephson junction arrays, and models applicable to combustion or solidification problems in various two- and three- dimensional geometries. In each case, the focus is on instabilities for which there is clear evidence that symmetry plays a central role. An essential component of the proposed research is to compare theoretical results, based on model- independent group theoretic/dynamical systems methods, with those obtained by direct numerical simulation of the governing differential equations. The education component will include course development in applied dynamical systems at the undergraduate level, curriculum development at the graduate level, graduate student advising, mentoring, and organizing graduate seminars. 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.

9502266 Silber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。研究部分将集中于进一步发展等变动力系统的数学方法，以应用于具体的物理问题。这些包括旋转对流和磁对流的流体动力学模型，约瑟夫森结阵列模型，以及适用于各种二维和三维几何形状的燃烧或凝固问题的模型。在每种情况下，重点都是不稳定性，有明确的证据表明对称性起着核心作用。所提出的研究的一个重要组成部分是将基于模型无关的群论/动力系统方法的理论结果与直接数值模拟控制微分方程得到的结果进行比较。教育部分将包括本科阶段应用动力系统课程开发、研究生阶段课程开发、研究生咨询、指导和组织研究生研讨会。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。