{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/37568"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/37568","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Functional analytic treatment of linear transport equations in kinetic theory and neutron transport theory","abstract":"The temperature-density equation of Kinetic Theory and the conservative neutron transport equation are studied. In both cases a modified version of the Larsen-Habetler resolvent integration technique is applied to obtain full-range and half-range expansions. For the neutron transport equation the method applied is seen to have notational advantages over previous approaches. In the case of the temperature-density equation this development extends previous results by enlarging the class of expandable functions and has the added advantage of rigor and simplicity. As a natural extension of the Kinetic Theory results, an integral equation for the surface density is derived for half-space problems involving the boundary condition of arbitrary accommodation.","abstract_html":"The temperature-density equation of Kinetic Theory and the conservative neutron transport equation are studied. In both cases a modified version of the Larsen-Habetler resolvent integration technique is applied to obtain full-range and half-range expansions. For the neutron transport equation the method applied is seen to have notational advantages over previous approaches. In the case of the temperature-density equation this development extends previous results by enlarging the class of expandable functions and has the added advantage of rigor and simplicity. As a natural extension of the Kinetic Theory results, an integral equation for the surface density is derived for half-space problems involving the boundary condition of arbitrary accommodation.","abstract_has_math":false,"creators":["Cameron, William Lyle"],"institution":"Virginia Tech","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Physics","degree_department":"Physics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Zweifel, Paul F."],"committee_members":["Bowden, Robert L.","Teplitz, V. L.","Greenburg, William","Garbanati, Linda F."],"year":1978,"date_issued":"1978-01-08","date_published":"1978-01-08","updated_at":"2026-07-22T22:19:56Z","subjects":["surface density"],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-04072010-020227"],"render_values":[{"text":"etd-04072010-020227","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/37568","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Zweifel, Paul F."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Bowden, Robert L.","Teplitz, V. 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In both cases a modified version of the Larsen-Habetler resolvent integration technique is applied to obtain full-range and half-range expansions. For the neutron transport equation the method applied is seen to have notational advantages over previous approaches. In the case of the temperature-density equation this development extends previous results by enlarging the class of expandable functions and has the added advantage of rigor and simplicity. As a natural extension of the Kinetic Theory results, an integral equation for the surface density is derived for half-space problems involving the boundary condition of arbitrary accommodation."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. 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