U.S.-Western Europe Regional Cooperative Research: NumericalMethods in Particle Transport Theory

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This award supports Dr. Charles Siewert of North Carolina State University to collaborate in applied mathematics with Dr. J. Hovenier of the Free University of Amsterdam, Dr. V. Boffi of the University of Bologna, and Drs. C. Devaux and Y. Fouquart of the University of Lille. Using analytical and computational methods in particle transport theory, they are working on two basic problems in the general field of radiative transfer: the searchlight problem and the general polarization problem. In both cases, the F-N method, derived originally by Dr. Siewert in the context of neutron transport theory, is to be the basis of the numerical studies. The classical searchlight problem in radiative transfer will be studied as a first attempt to construct highly accurate numerical solutions to a class of multi-dimensional transport problems. In addition, exact analysis and highly accurate numerical methods are to be used to construct and implement computationally viable solutions to basic problems in radiative transfer models that include polarization effects. A general radiant energy transfer model that includes polarization effects will be used to study vector problems in transport theory where the computational difficulties encountered for non-azimuthally symmetric problems must be resolved. Dr. Siewert has a distinguished record of contributions to linear transport theory and a long history of productive international collaboration. The three foreign groups with which he is collaborating are major centers of research in radiative transfer and numerical transport theory and a basis for sharing new data and numerical results has been well established. The searchlight problem and polarization for multiply scattered radiation are two important problems first proposed over forty years ago by Chandrasekhar. They are particularly challenging in terms of numerical analysis methods. In light of their past work and the increasing power of computers, it is anticipated that Dr. Siewert's continued collaboration with his European colleagues will contribute significantly to the establishment of definitive solutions to these challenging problems in radiative transfer theory. In addition, the results of their work on the polarization problem may offer a useful diagnostic tool in inferring physical properties from observed intensity and polarization profiles.