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propagationThis项目地址的双曲守恒定律，如模型可压缩流体力学的理论的基本和知之甚少的问题。它还解决了不可压缩流体力学和广义相对论的问题，并将结果应用于各种重要的物理问题。一个共同的主题，许多拟议的工作是如何非线性导致的形成和传播的各种奇异性，如激波在可压缩流体，或时空奇点在广义相对论。建议研究的具体课题如下：激波反射;激波在随机介质中的传播;弹性力学和磁流体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量波、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（如声波、地震波、光波、量子力学波或引力波）是从原子到宇宙尺度的许多物理系统的核心特征。在较低的强度，波叠加，他们可以描述的线性理论，但在较高的强度非线性效应是显着的，导致定性的新现象（如冲击波和孤子）。非线性波比线性波更难进行数学分析，而且往往具有重要的实际意义。例如，冲击波在接近音速的飞行器周围形成。这个项目的一个目的是研究基本的，但还没有完全理解的冲击波现象，例如它们从墙壁上的反射。除其他课题外，该项目还包括非线性表面波的研究，如由地震产生并用于各种超声波设备的瑞利波，以及引力波时空奇异性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.