Nonlinear Waves, Optics, and Coupled Oscillators

非线性波、光学和耦合振荡器

• 批准号: 9901897
• 负责人: Philip Holmes
• 金额: $ 7.1万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-09-01 至 2002-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9901897&HistoricalAwards=false
• 关键词: Nonlinear; Waves; Optics; Coupled; Oscillators

This project supports an NSF-Industrial Postdoctoral Fellow, Deborah Alterman, to carry out research jointly in the Program in Applied and Computational Mathematics at Princeton University and Lucent-Bell Laboratories, Murray Hill, NJ. The Faculty Mentor will be Philip Holmes, Professor of Mechanics and Applied Mathematics, and the Supervisor at Lucent Technologies will be Dr Michael Weinstein who has recently joined the Mathematical Sciences Research Center (Fundamental Mathematics Department). We envisage two principal areas of research: (1) Nonlinear wave theory applied to problems of optical communications, and (2) Coupled oscillators as models of neural networks. The mathematical tools to be used and developed include dynamical systems and bifurcation theory, ordinary and partial differential equations, asymptotics, and nonlinear wave and stability theory. A pervasive theme is the reduction of dynamical systems with infinite or high dimensional phase spaces, describing distributed phenomena, to simpler ``amplitude'' partial differential or ``modal'' ordinary differential equations. Such reduced models lead to improved understanding of the underlying physics, and offer shortcuts in predictions and design. This GOALI project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).

该项目支持美国国家科学基金会工业博士后Deborah Alterman在普林斯顿大学和新泽西州默里山的朗森-贝尔实验室的应用与计算数学项目中共同开展研究。教师导师将是力学与应用数学教授Philip Holmes，朗讯科技的导师将是最近加入数学科学研究中心（基础数学系）的Michael Weinstein博士。我们设想了两个主要的研究领域：(1)应用于光通信问题的非线性波动理论，以及(2)作为神经网络模型的耦合振荡器。要使用和发展的数学工具包括动力系统和分岔理论、常微分方程和偏微分方程、渐近学、非线性波动和稳定性理论。一个普遍的主题是将描述分布式现象的具有无限或高维相空间的动力系统简化为更简单的“振幅”偏微分或“模态”常微分方程。这种简化的模型可以提高对基本物理的理解，并为预测和设计提供捷径。该GOALI项目由MPS多学科活动办公室（OMA）和数学科学司（DMS）联合支持。