Derivation and Simulation in Radiative Transfer Theory

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NSF Award Abstract - DMS-0072008Mathematical Sciences: Derivation and Simulation in Radiative Transfer TheoryAbstract0072008 BalThis project studies the propagation of high frequency waves in highly heterogeneous media. Radiative transport theory provides an accurate macroscopic description of the microscopicinteractions between the propagating waves and the rapidly-fluctuating underlying medium. The objectives of the research are threefold. First, extend radiative transport theory to include boundary conditions and surface and volume wave interaction. Second, solve the volume and surface equations numerically using a Monte Carlo method based on a probabilistic representation of radiative transfer with polarization. Finally, assess the domain of validity of radiative transfer by setting up suitable inverse problems that allow determination of statisticalparameters characterizing the underlying medium from boundary measurements.A major recent success of radiative transport theory is the modeling of the propagation of seismic waves in the earth's crust. Numerical study of seismic wave propagation over hundreds of kilometers remains prohibitive with a microscopic model, but simulations are now accessibleusing radiative transfer theory and suitable statistical methods. Results promise to yield better understanding and prediction of earthquakes. Another application of radiative transport and its diffusion approximation is near-infrared spectroscopy. This novel method is increasinglyused in medical imaging for monitoring properties of human tissues. Numerical simulation of forward and inverse transport problems remains an active field of research. The project provides the mathematical and numerical analysis to address these issues.