Nonlinear Dynamics in Models of Wave Propagation and Domain Coarsening

波传播和域粗化模型中的非线性动力学

• 批准号: 0072609
• 负责人: Robert Pego
• 金额: $ 15.69万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-15 至 2003-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072609&HistoricalAwards=false
• 关键词: Nonlinear; Dynamics; Models; Wave; Propagation

The aim of this work is to understand significant aspects of wave phenomena through developing and applying the methods of nonlinear dynamics --- the mathematics of systems that change in time and space. A main goal is to explain the robustness or stability of solitons, an important class of waves which exhibit particle-like properties and are capable of a remarkably deep and explicit mathematical description. The mathematics of wave dynamics is also unexpectedly important for prograss concerning a fundamental problem in materials science. To understand how an alloy's microscopic structure coarsens in time, the investigator is developing a new mathematical understanding of wave-like transport for singular mass distributions.This work seeks to explain mathematically a number of poorly understood characteristics of waves of various kinds, surface waves on fluids being a prime example. Such characteristics include: the extraordinary stability of solitons (waves that persist in isolation); the tsunami-like qualities of wakes produced in certain conditions by modern fast car ferries; and the nature of the powerful forces created when waves focus and break simultaneously. The common thread that runs through these investigations is the effective understanding of physical phenomena through the development of new mathematical methods for analyzing dynamic change.

这项工作的目的是通过开发和应用非线性动力学方法（随时间和空间变化的系统数学）来理解波动现象的重要方面。主要目标是解释孤子的鲁棒性或稳定性，孤子是一类重要的波，具有类似粒子的特性，并且能够进行非常深入和明确的数学描述。波动力学的数学对于材料科学基本问题的进展也出乎意料地重要。为了了解合金的微观结构如何随着时间的推移而变粗，研究人员正在开发一种对奇异质量分布的波状输运的新数学理解。这项工作旨在从数学上解释各种波、表面波的一些鲜为人知的特征。流体就是一个典型的例子。这些特性包括： 孤子（孤立存在的波）的非凡稳定性；现代快速汽车渡轮在某些条件下产生的类似海啸的尾流；以及波浪同时聚集和破碎时产生的强大力量的本质。贯穿这些研究的共同点是通过开发分析动态变化的新数学方法来有效理解物理现象。