Program in Nonlinear Waves, Kinetic Theory and Hamiltonian Partial Differential Equations-Fields Institute, Spg 04

非线性波、运动理论和哈密顿偏微分方程项目-场研究所，Spg 04

• 批准号: 0352061
• 负责人: Nicholas Ercolani
• 金额: $ 4.5万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-05-01 至 2005-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0352061&HistoricalAwards=false
• 关键词: Program; Nonlinear; Waves; Kinetic; Theory

AbstractAward: DMS-0352061Principal Investigator: Nicholas M. ErcolaniThis proposal is for support of junior US based mathematicians toparticipate in scientific activities at the Fields Instituteduring the thematic program semester in Nonlinear Waves, KineticTheory and Hamiltonian Partial Differential Equations (PDE) thatwill take place during the Spring semester of 2004. The focus ofthe semester will concern areas of research on PDE that aremotivated by nonlinear wave theory, kinetic theory, andHamiltonian systems. Hamiltonian PDE form a class of linear andnonlinear partial differential equations which share the propertythat they can be written in the form of a Hamiltonian system withinfinitely many degrees of freedom, using various and sometimesnonclassical symplectic structures. Principal examples includenonlinear wave equations, nonlinear Schroedinger equations andEuler's equations for water waves. The analogy with dynamicalsystems raises a number of basic questions, which form a part ofthe motivation for this semester of focus on Hamiltonian PDE. Ofparticular note is the connection that has been establishedbetween the theory of kinetic equations coming from statisticalmechanics, and the nonlinear systems of PDE which arise in theirmacroscopic limits. The paradigm is the fluid dynamical scalinglimit of the Boltzmann equation, but there are numerous emergingareas of relevance for this analysis, including the beginnings ofa mathematically rigorous foundation for the theory of nonlinearwave turbulence.The organizers are expecting this thematic program to be a verydynamic focus of research on Partial Differential Equations thatmodel a variety of physical phenomena, such as planetary motions,lasers and optical fiber systems, ocean waves and fluidturbulence. The character of the program is broadlyinternational, and it represents an opportunity for exposure foryoung mathematicians. The short course series, the four workshopsand the symposia are especially appropriate for participation bydeveloping research mathematicians or physicists early in theircareer. The organizing committee believes that the program willengender further interaction and lasting collaboration amongparticipants from various disciplines. Additionally, theparticipation of women and under-represented minorities will beactively encouraged.

AbstractAward：DMS-0352061原理研究者：Nicholas M. Ercolanithis提议的建议是支持美国初级数学家在田野上的科学活动，以非线性浪潮，动力学理论和汉密尔顿的部分差分方程（PDE）在春季中的范围（PDE）进行了表达。非线性波理论，动力学理论，Andhamiltonian系统引起的PDE研究领域。 Hamiltonian PDE构成了一类线性和non线性偏微分方程，它们共享属性，这些属性可以在最终的自由度内以哈密顿系统的形式编写，并使用各种且有时的典型符号结构。主要示例包括烯键波方程，非线性Schroedinger方程和水波方程。与动力系统的类比提出了许多基本问题，这构成了本学期关注汉密尔顿PDE的动机的一部分。特有的注意是在来自统计学的动力学方程理论与在其宏观界限中产生的非线性PDE系统之间建立的联系。范式是玻尔兹曼方程的流体动态缩放限制，但是有许多与此分析相关的出现，包括在数学上对非线性波湍流理论的开始，组织者期望这种卑鄙的程序是对偏见的偏重的焦点。以及光纤系统，海浪和流体扰动。该计划的特征是广泛的，它代表了曝光数学家的机会。简短的课程系列，四个研讨会和座谈会特别适合参与拜托研究数学家或物理学家的参与。组织委员会认为，该计划将进一步互动，并在各个学科的参与者之间进行持久的合作。此外，妇女和代表性不足的少数民族的参与将受到战斗的鼓励。