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会早期职业发展奖的支持。 研究组件将集中于对等效动力学系统的数学方法的进一步发展，以应用于特定的物理问题。 其中包括旋转对流和磁反射的流体动力模型，约瑟夫森交界阵列的模型以及适用于各种二维和三维几何形状中的燃烧或凝固问题的模型。 在每种情况下，重点是有明确证据表明对称性起着核心作用的不稳定性。 拟议研究的一个重要组成部分是基于模型独立组理论/动力学系统方法比较理论结果，并通过直接数值模拟来处理差分方程来比较理论结果。 该教育组成部分将包括在本科层面应用动力学系统的课程开发，研究生一级的课程发展，研究生咨询，指导和组织研究生研讨会。 国家科学基金会强烈鼓励学术教师作为教育者和研究人员的早期发展。 教师早期职业发展（职业）计划是一个基础范围的计划，在整体职业发展的背景下为初级教师提供了支持。 它结合了一个计划，以最广泛的意义将优质研究和教育的支持结合在一起，并且传统上代表性不足在科学和工程中的人的全部参与。 该计划增强并强调了基础对包括研究和教育在内的全面，平衡学术职业发展的重要性。