Linear and Non-Linear Waves

线性和非线性波

• 批准号: 9322146
• 负责人: Walter Strauss
• 金额: $ 9万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9322146&HistoricalAwards=false
• 关键词: Linear; Non; Waves

9322146 Strauss Stability and instability phenomena will be investigated in the kinetic theory of charged particles both with and without collisions. Also to be studied are harmonic maps in Minkowski space, and the stability theory of time- dependent ground states of scalar fields, including the effects of boundaries. A further focus of research is the smoothing phenomenon for linear and nonlinear dispersive waves.Advanced semiconductor devices, used for computer chips, are made of materials whose properties derive from the movements of negative electrons and positive "holes". Such movements form a type of nonlinear wave and are described by certain mathematical equations. We study how these movements change and how they are sensitive to initial variations. The same kinds of equations describe many other wave phenomena in science and engineering, such as in energy research and space research. The sensitivity of nonlinear waves is studied in a variety of contexts. The purpose is to determine the fundamental reasons for the unstable behavior of waves.Walter Strauss

小行星9322146 稳定性和不稳定性现象将在带电粒子的动力学理论中进行研究，包括碰撞和不碰撞。也要研究的是闵可夫斯基空间中的调和映射，以及标量场含时基态的稳定性理论，包括边界的影响。研究的另一个焦点是线性和非线性色散波的平滑现象。用于计算机芯片的先进半导体器件是由负电子和正“空穴”的运动产生特性的材料制成的。 这种运动形成一种非线性波，并由某些数学方程描述。我们研究这些运动是如何变化的，以及它们对初始变化是如何敏感的。同样的方程描述了科学和工程中的许多其他波动现象，例如能源研究和空间研究。非线性波的灵敏度在各种情况下进行了研究。其目的是确定波的不稳定行为的根本原因。