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

基本信息

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

项目摘要

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运用非线性动力学方法来理解波浪现象的重要方面---在时间和空间上改变的系统的数学。一个主要目标是解释孤子的鲁棒性或稳定性，孤子的稳健性或稳定性是一种重要的波浪，具有类似粒子的特性，并且能够具有非常深而明确的数学描述。波动动力学的数学对于关于材料科学中的基本问题的促进性也很重要。为了了解合金的显微镜结构如何及时散发，研究者正在对奇异质量分布的波浪样转运进行新的数学理解。这项工作旨在在数学上解释许多多种波浪的特征，而流体上的表面波是一个很好的例子。这样的特征包括：孤子的特殊稳定性（孤立的波浪）；现代快速汽车渡轮在某些条件下产生的像海啸一样的唤醒品质；当波浪同时集中并折断时，强大力量的本质就产生了。通过这些研究进行的共同线程是通过开发新的数学方法来分析动态变化的有效理解物理现象。