{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/49963"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/49963","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Multigroup transport equations with nondiagonal cross section matrices","abstract":"It is shown that multigroup transport equations with nondiagonal cross section matrices arise when the modal approximation is applied to energy dependent transport equations. This work is a study of such equations for the case that the cross section matrix is nondiagonalizable. For the special case of a two-group problem with a noninvertible scattering matrix, the problem is solved completely via the Wiener-Hopf method. For more general problems, generalized Chandrasekhar H equations are derived. A numerical method for their solution is proposed. Also, the exit distribution is written in terms of the H functions.","abstract_html":"It is shown that multigroup transport equations with nondiagonal cross section matrices arise when the modal approximation is applied to energy dependent transport equations. This work is a study of such equations for the case that the cross section matrix is nondiagonalizable. For the special case of a two-group problem with a noninvertible scattering matrix, the problem is solved completely via the Wiener-Hopf method. For more general problems, generalized Chandrasekhar H equations are derived. A numerical method for their solution is proposed. Also, the exit distribution is written in terms of the H functions.","abstract_has_math":false,"creators":["Willis, Barton L."],"institution":"Virginia Polytechnic Institute and State University","degree_name":"Ph. 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For the special case of a two-group problem with a noninvertible scattering matrix, the problem is solved completely via the Wiener-Hopf method. For more general problems, generalized Chandrasekhar H equations are derived. A numerical method for their solution is proposed. Also, the exit distribution is written in terms of the H functions."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. 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