Mathematical Sciences: Fundamental Aspects of Nonlinear Dynamics

数学科学：非线性动力学的基本方面

• 批准号: 9001629
• 负责人: Melvyn Berger
• 金额: $ 14.79万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001629&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Fundamental; Aspects; Nonlinear

This project will cover three basic interrelated areas of applied mathematics. The first is concerned with large amplitude motions both quasi periodic and almost periodic in dynamical systems of many degrees of freedom. The principal investigator will develop new methods of study, going beyond the KAM theory for small perturbations, that utilize a novel nonlinear p.d.e. approach. The second related topic involves vortex dynamics of an ideal inviscid fluid. Here the principal investigator will research the outstanding problems of leapfrogging of vortex rings, classes of vortex cores, and vortex breakdown of bubble and spiral type. Finally, the principal investigator will study of "flux phenomenon" in the new theories of high Tc superconductivity, an area of prime importance in high technology. All these areas require deep understanding of nonlinear science and its associated mathematical structures. This has been the central focus of the investigator's research for over two decades.

这个项目将涵盖应用数学的三个相互关联的基本领域。第一类是关于多自由度动力系统中的大振幅运动，包括准周期运动和几乎周期运动。首席研究员将开发新的研究方法，超越小扰动的KAM理论，利用新的非线性p.d.e.方法。第二个相关主题涉及理想无粘流体的涡旋动力学。主要研究涡旋环的跨越式、涡旋核的种类、气泡型和螺旋型涡旋的破碎等突出问题。最后，首席研究员将研究高Tc超导新理论中的“通量现象”，这是高科技领域的一个重要领域。所有这些领域都需要对非线性科学及其相关的数学结构有深刻的理解。二十多年来，这一直是研究者研究的中心焦点。