Mathematical Sciences: Asymptotic Pertubation and Numerical Studies of Wave Propagation

数学科学：渐近摄动和波传播的数值研究

• 批准号: 8700794
• 负责人: Edward Reiss
• 金额: $ 17.03万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8700794&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Asymptotic; Pertubation; Numerical

This project is concerned with mathematical methods in the studies of acoustic waves. Wave propagation is a means of moving energy from one region to another. When the wave amplitudes are sufficiently small, as occurs in many problems, then the motion is adequately described by a linearized theory of wave propagation. Thus, the classical theories of wave propagation in acoustics,optics, electromagnetics, elastic solids, etc. are linearized theories. When the geometry, material properties and source structures are simple it may then be possible to solve wave propagation problems explicitly. However, for realistic situations and hence more complicated problems it is necessary to employ asymptotic, perturbation, numerical and other approximate methods to solve wave propagation problems. The purposes of this research project are to develop and apply asymptotic, perturbation and numerical methods to wave propagation problems of scientific and engineering significance, and to study specific physical problems that are basic to future progress in wave propagation. Some of the present effort represents a continuation and elaboration on past work. Professor Reiss is a well known authority on wave propagation and Professor Kriegsmann is his younger talented partner. They constitute an excellent, very productive team. This research falls into the general area of asymptotic methods and perturbation theory in applied mathematics, which constitute an active and practical trend in applied mathematics research. Many of the results obtained by these researchers have direct engineering applications in acoustics, radar, sonar and in the studies of electromagnetic wave propagation.

这个项目是关于数学方法在 声波的研究。波的传播是一种移动的手段 能量从一个地区转移到另一个地区。 当波的振幅 足够小，就像在许多问题中发生的那样，那么运动 可以用线性波理论来描述 传播 因此，经典的波传播理论， 声学、光学、电磁学、弹性固体等， 线性理论 当几何形状、材料属性和 源结构很简单，然后就有可能解决 波的传播问题。 然而，对于现实 情况，因此更复杂的问题，有必要 采用渐近、扰动、数值和其他近似 解决波传播问题的方法。 该研究项目的目的是开发和 将渐近法、摄动法和数值法应用于波动 科学和工程意义的传播问题， 研究特定的物理问题， 波传播的进展。 目前的一些努力 是对过去工作的继续和阐述。 赖斯教授是波传播方面的著名权威 克里格斯曼教授是他年轻的搭档 他们 组成了一个优秀的，非常有成效的团队。本研究 福尔斯属于渐近方法的一般领域， 微扰理论在应用数学中，构成了一个 应用数学研究的积极性和实用性。许多 这些研究人员获得的结果直接 声学、雷达、声纳和 电磁波传播的研究。