Radiative Transport Theory for Waves

研究者使用解析和数值技术研究复杂介质中的波传播问题。研究了地震波和其他波在具有不同特征的随机介质之间既有外部边界又有尖锐界面的域中的长距离传播。从第一原理（波动方程）出发，分析了光滑和随机界面的正确边界条件和界面条件。它们用于推导扩散近似中的界面条件，使其更易于数值模拟。提出了极化波的矩阵值辐射输运方程的解析和数值分析方法。本文还讨论了非均匀湍流对声波传播的影响以及其他一些问题（燃烧前传播问题）。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、地震波在地球上的传播等基本现象。即使是现在最快的计算机也无法直接应用波动方程来解决这类问题。辐射输运理论是描述波在具有材料性质快速波动的复杂介质中的能量传播的有价值的近似方法。最有希望的应用之一是地震波传播，该理论在过去十年中已经成功地应用于地震波传播，特别是地震引起的扰动传播模型。

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.