Mathematical Sciences: Analytical and Numerical Methods in Radiative Transfer

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This is a proposal that continues the principal investigator's efforts to construct accurate numerical solutions of two problems in radiative transfer theory: the searchlight problem for an obliquely incident beam and a general nonhomogeneous problem that describes internal emission. The basic numerical method is the so-called FN-method, and there is genuine hope that the research on its application to the above two problems will lead to robust numerical methods for more general nonhomogeneous linear transport models. One of the many important problems that modern technology has created is involved with the transmission of light waves and radio waves through the earth's atmosphere. For example, the shuttle astronauts have to worry about their communication with the earth because the earth's atmosphere very often interferes with their radio signals. The same problems arise in satellite communications as well. Rather than tackle a problem as large as the earth's atmosphere some scientists, like the principal investigator, study simpler mathematical models for the transmission of waves through inhomogeneous media like the atmosphere. In this case the principal investigator will study such problems numerically.