Radiative Transport Theory for Waves

研究人员研究复杂介质中的波传播问题，使用分析和数值技术，研究地震波和其他波在包含外部边界和具有不同特性的随机介质之间的尖锐界面的区域中的长距离传播。 本文从第一性原理（波动方程）出发，分析了光滑界面和随机界面的正确边界条件和界面条件，并将它们用于导出扩散近似中的界面条件，使之更易于数值模拟，发展了分析偏振波矩阵值辐射输运方程的解析和数值方法。 本文还讨论了非均匀湍流对声波传播和其它一些问题（燃烧中的前向传播问题）的影响。 波的传播是最基本的物理过程之一。 许多物理应用需要考虑高度不均匀介质中的波。 这些包括声波在大气中的传播、地震波在地球中的传播等基本现象。 直接将波动方程应用于这类问题，即使是当今可用的快速计算机也达不到。 辐射输运理论是一种描述波在复杂介质中的能量传播的有价值的近似方法，它具有材料性质的快速波动。 最有前途的应用之一是在地震波传播中，在过去的十年里，这一理论已经成功地应用于地震引起的扰动的传播模型。

The investigator studies problems of wave propagation incomplex media, using both analytical and numerical techniques.Long range propagation of seismic and other waves in domains thatinvolve both external boundaries and sharp interfaces betweenrandom media with different characteristics are studied. Thecorrect boundary and interface conditions are analyzed from firstprinciples (wave equations) for smooth and random interfaces.They are used to derive the interface conditions in the diffusionapproximation that is more tractable for numerical simulations.Analytical and numerical methods for the analysis of the matrixvalued radiative transport equations for polarized waves aredeveloped. Effects of inhomogeneous turbulent flows on acousticwave propagation and in some other problems (front propagation incombustion problems) are also addressed. Wave propagation is one of the most fundamental physicalprocesses. Many physical applications require consideration ofwaves in highly inhomogeneous media. These include such basicphenomena as acoustic wave propagation in the atmosphere, seismicwaves in the Earth, and many others. Direct application of waveequations to such problems is beyond reach of even the fastcomputers available today. The radiative transport theory is avaluable approximation that describes energy propagation of wavesin complex media with rapid fluctuations of the materialproperties. One of the most promising applications is in seismicwave propagation, where this theory has been successfully appliedin the last ten years, in particular to model propagation ofdisturbances caused by earthquakes.