Nonlinear Wave Propagation

摘要，提案 0309648，亨特，加州大学戴维斯分校标题：非线性波传播该项目解决了双曲守恒定律理论中的基本问题和人们不太了解的问题，例如模拟可压缩流体力学的问题。它还解决了不可压缩流体力学和广义相对论中的问题，并将结果应用于各种重要的物理问题。所提出的大部分工作的一个共同主题是非线性如何导致各种奇点的形成和传播，例如可压缩流体中的冲击波或广义相对论中的时空奇点。提出的具体研究课题如下：冲击波反射；随机介质中的冲击波传播；弹性和磁流体动力学中的非线性双曲表面波；不可压缩流体力学中的普朗特边界层方程和涡度波、平均流相互作用；以及广义相对论中非线性对引力波的影响。波（例如声波、地震波、光波、量子力学波或引力波）是从原子尺度到宇宙尺度的许多物理系统的核心特征。在较低强度下，波叠加，并且可以用线性理论来描述，但在较高强度下，非线性效应变得显着，导致性质上的新现象（如冲击波和孤子）。非线性波比线性波更难以进行数学分析，并且通常具有重要的实际意义。例如，飞机周围形成的冲击波以接近音速的速度传播。该项目的目标之一是研究基本但尚未完全理解的冲击波现象，例如墙壁的反射。除其他主题外，该项目还包括非线性表面波的研究，例如地震产生的瑞利波，用于各种超声波设备，以及引力波中时空奇点的形成和传播的研究。

Abstract, Proposal 0309648, Hunter, University of California-DavisTitle: Nonlinear wave propagationThis project addresses fundamental and poorly understood issues in thetheory of hyperbolic conservation laws,such as the ones that modelcompressible fluid mechanics. It also addresses problems inincompressible fluid mechanics and general relativity, and applies theresults to a variety of important physical problems. A common theme ofmuch of the proposed work is how nonlinearity leads to the formationand propagation of various kinds of singularities, such as shock wavesin compressible fluids, or space-time singularities in generalrelativity. Specific topics proposed for study are the following:shock wave reflection; shock wave propagation in random media;nonlinear hyperbolic surface waves in elasticity andmagnetohydrodynamics; the Prandtl boundary layer equations andvorticity wave, mean flow interactions in incompressible fluidmechanics; and the effect of nonlinearity on gravitational waves ingeneral relativity.Waves (such as sound waves, seismic waves, light waves, quantummechanical waves,or gravitational waves) are a central feature of manyphysical systems, from the atomic to the cosmological scales. At lowerintensities, waves superpose and they may be described by lineartheories, but at higher intensities nonlinear effects becomessignificant, leading to qualitatively new phenomena (like shock wavesand solitons). Nonlinear waves are much more difficult to analysemathematically than linear waves, and are often of great practicalimportance. For example, shock waves form around aircraft that travelclose to the speed of sound. One aim of this project is to studybasic, but not fully understood, shock wave phenomena, such as theirreflection from walls. Among other topics, the project also includes astudy of nonlinear surface waves, such as the Rayleigh waves which aregenerated by earthquakes and are used in a variety of ultrasonicdevices, and a study of the formation and propagation of space-timesingularities in gravitational waves.