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

9502266 Silber 这项工作得到了美国国家科学基金会的支持 教师早期 职业发展奖。 研究部分将侧重于 上 等变数学方法的进一步发展 动力学 系统应用于特定的物理问题。 这些包括 旋转对流的水动力学模型和 磁对流， 约瑟夫森结阵列的模型和适用模型 燃烧 或固化问题，在各种二，三， 维 几何学 在每一种情况下，重点是不稳定性， 存在 对称性起着核心作用。 一个 重要组成部分 的建议研究是比较理论结果， 基于模型- 独立群论/动力系统方法， 那些 通过直接数值模拟得到的控制 微分 方程 教育部分将包括课程 发展 在本科阶段学习应用动力系统， 课程 研究生水平的发展，研究生 提供建议指导 组织研究生研讨会。 美国国家科学基金会强烈鼓励 早期 发展学术教师作为教育工作者和 研究人员 的 教师早期职业发展（CAREER）计划是一个 基金会- 一项广泛的计划，为青少年提供支持 学院内部 在整体职业发展的背景下。 它结合了 单个 计划支持高质量的研究和教育， 最广泛意义 以及那些传统上 在科学领域代表性不足 与工程学 该计划增强并强调了 重要性 基金会致力于发展全面、均衡的 学术 包括研究和教育的职业。

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.