Nonlinear wave propagation

非线性波传播

• 批准号: 0072343
• 负责人: John Hunter
• 金额: $ 10.8万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2004-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072343&HistoricalAwards=false
• 关键词: Nonlinear; wave; propagation

NSF Award Abstract - DMS-0072343Mathematical Sciences: Nonlinear Wave PropagationAbstract0072343 HunterThis project studies a number of problems in nonlinear wave propagation. The first problem is the reflection of weak shock waves, where there have been longstanding discrepancies between theory and experiment. There are close relationships between this problem and transonic aerodynamics. The second problem is the study of nonlinear effects on gravitational waves in the Einstein field equations of general relativity, an issue of fundamental scientific significance. The third problem is the study of nonlocal, nonlinear equations for hyperbolic surface waves in elasticity and magnetohydrodynamics. Such waves arise, for example, in surface acoustic wave devices used in signal processing. The fourth problem is the study of the interaction of high frequency vorticity waves and mean flows in incompressible fluids. This research will describe the nonlinear development of vorticity instabilities, and is relevant to the closure problem for turbulent flows. The fifth problem is the propagation of fronts in a bistable oscillatory system of reaction-diffusion equation that provides a simplified model of the collective behavior of beta-cells in the pancreas, which produce insulin. The sixth problem is the study of surfactant deposition by a spreading liquid drop. This problem has industrial applications in the use of droplets for the deposition of surface films. Waves, such as sound waves, elastic waves, and gravitational waves, are an important feature of many physical and biological systems. Large amplitude waves may behave nonlinearly, and this leads to new effects not seen in linear waves: for example, the generation of shock waves by an aircraft traveling at speeds close to or above the speed of sound. A detailed analysis of the equations that describe nonlinear waves is often very difficult. The aim of this research is an increased understanding of nonlinear waves in the context of a variety of applications that involve qualitatively interesting and poorly understood phenomena, and that are related to problems of current scientific and technological interest.

美国国家科学基金会奖摘要- DMS-0072343数学科学：非线性波传播摘要0072343亨特这个项目研究非线性波传播中的一些问题。 第一个问题是弱冲击波的反射，长期以来理论和实验之间一直存在差异。 这个问题与跨音速空气动力学有着密切的关系。 第二个问题是研究广义相对论爱因斯坦场方程中引力波的非线性效应，这是一个具有基础科学意义的问题。 第三个问题是弹性力学和磁流体力学中双曲表面波的非局部非线性方程的研究。 例如，这种波出现在用于信号处理的表面声波装置中。 第四个问题是研究不可压缩流体中高频涡量波与平均流的相互作用。 这项研究将描述涡不稳定性的非线性发展，并与湍流的封闭问题有关。 第五个问题是反应扩散方程的振荡系统中的前沿传播，该方程提供了胰腺中产生胰岛素的β细胞的集体行为的简化模型。 第六个问题是研究表面活性剂通过铺展液滴沉积。 这个问题在使用液滴沉积表面膜方面具有工业应用。波，如声波，弹性波和引力波，是许多物理和生物系统的重要特征。 大振幅波可能表现为非线性，这导致了线性波中看不到的新效应：例如，以接近或高于声速的速度行驶的飞机产生冲击波。 对描述非线性波的方程进行详细的分析通常是非常困难的。 这项研究的目的是增加对非线性波的理解，在各种应用的背景下，涉及定性有趣和了解甚少的现象，并与当前科学和技术感兴趣的问题。