Mathematical Sciences: Symmetry-Breaking Bifurcations and Pattern Formation

数学科学：对称破缺分岔和模式形成

• 批准号: 9404266
• 负责人: Mary Silber
• 金额: $ 7.5万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404266&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Symmetry; Breaking; Bifurcations

9404266 SILBER The goal of the project is to develop equivariant bifurcation theory for applications to pattern formation and for applications to globally coupled oscillator arrays. The proposed research will be carried out within the framework of finite-dimensional center manifold normal forms of bifurcation problems. The symmetries of these bifurcation problems will be exploited in their analysis and in the interpretation of the results. Special attention will also be given to developing geometric methods that exploit integrable Hamiltonian limits of the bifurcation problems. Symmetries play a central role in the evolution of pattern-forming instabilities in hydrodynamic systems. The primary goal of the proposed research is to develop mathematical methods that exploit their presence. The research on pattern formation will aid the interpretation of large-scale numerical studies of three-dimensional magnetoconvection, and laboratory studies of electroconvection in nematic liquid crystals. The research on globally coupled oscillators will contribute to our understanding of the dynamics of series arrays of Josephson junctions.

9404266 SILBER项目的目标是开发对模式形成的应用以及应用于全球耦合振荡器阵列的应用。拟议的研究将在有限维中心歧管歧管的法线形式的分叉问题的框架内进行。这些分叉问题的对称性将在它们的分析和结果解释中得到利用。还将特别关注开发几何方法，以利用可分叉问题的可综合性哈密顿限制。 对称性在流体动力系统中形成模式不稳定性的演变中起着核心作用。拟议的研究的主要目标是开发利用其存在的数学方法。关于模式形成的研究将有助于解释三维磁反看的大规模数值研究，以及列液晶体中电交流的实验室研究。关于全球耦合振荡器的研究将有助于我们对约瑟夫森连接系列阵列动态的理解。