Radiative Transport Theory for Waves

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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.