{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/67793"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/67793","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The Asymptotic Development of The Equations of Nuclear Reactor Theory","abstract":"The solutions to various forms of the diffusion equation are shown to correspond to the leading term of an asymptotic expansion of the solution to the neutron transport equation for large near-homogeneous systems which are close to critical. The product of the fundamental unit-cell transport theory eigenfunction and the fundamental cell-homogenized diffusion theory eigenfunction is shown to correspond to the leading asymptotic solution to the transport equation for large near-critical heterogeneous systems comprised of periodic or near-periodic lattices. The generalized point kinetics equations and a consistent theory of lattice homogenization are simultaneously developed for the same kinds of systems. Finally, an asymptotic approximation to the energy-dependent (omega)-mode transport equation is developed for large near-homogeneous systems which need not be close to critical.","abstract_html":"The solutions to various forms of the diffusion equation are shown to correspond to the leading term of an asymptotic expansion of the solution to the neutron transport equation for large near-homogeneous systems which are close to critical. The product of the fundamental unit-cell transport theory eigenfunction and the fundamental cell-homogenized diffusion theory eigenfunction is shown to correspond to the leading asymptotic solution to the transport equation for large near-critical heterogeneous systems comprised of periodic or near-periodic lattices. The generalized point kinetics equations and a consistent theory of lattice homogenization are simultaneously developed for the same kinds of systems. Finally, an asymptotic approximation to the energy-dependent (omega)-mode transport equation is developed for large near-homogeneous systems which need not be close to critical.","abstract_has_math":false,"creators":["Chiang, Ren-Tai"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Nuclear Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"10000-01-01","date_published":"10000-01-01","updated_at":"2026-07-22T22:25:58Z","subjects":["Engineering, Nuclear","Energy"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8108463"],"render_values":[{"text":"(UMI)AAI8108463","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/67793","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Chiang, Ren-Tai"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["10000-01-01","2014-12-14T06:26:16Z","1980"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Nuclear Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Nuclear","Energy"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/67793","(UMI)AAI8108463"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The solutions to various forms of the diffusion equation are shown to correspond to the leading term of an asymptotic expansion of the solution to the neutron transport equation for large near-homogeneous systems which are close to critical. The product of the fundamental unit-cell transport theory eigenfunction and the fundamental cell-homogenized diffusion theory eigenfunction is shown to correspond to the leading asymptotic solution to the transport equation for large near-critical heterogeneous systems comprised of periodic or near-periodic lattices. The generalized point kinetics equations and a consistent theory of lattice homogenization are simultaneously developed for the same kinds of systems. Finally, an asymptotic approximation to the energy-dependent (omega)-mode transport equation is developed for large near-homogeneous systems which need not be close to critical.","Made available in DSpace on 2014-12-14T06:26:16Z (GMT). No. of bitstreams: 1 8108463.pdf: 4054342 bytes, checksum: 61826cb21c9e069af30e5986fec43f9d (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 67971 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","142 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."]},{"key":"dc:title","label":"Title","values":["The Asymptotic Development of The Equations of Nuclear Reactor Theory"]}]}],"canonical_facts":{"dc:creator":["Chiang, Ren-Tai"],"dc:date":["10000-01-01","2014-12-14T06:26:16Z","1980"],"dc:description":["The solutions to various forms of the diffusion equation are shown to correspond to the leading term of an asymptotic expansion of the solution to the neutron transport equation for large near-homogeneous systems which are close to critical. The product of the fundamental unit-cell transport theory eigenfunction and the fundamental cell-homogenized diffusion theory eigenfunction is shown to correspond to the leading asymptotic solution to the transport equation for large near-critical heterogeneous systems comprised of periodic or near-periodic lattices. The generalized point kinetics equations and a consistent theory of lattice homogenization are simultaneously developed for the same kinds of systems. Finally, an asymptotic approximation to the energy-dependent (omega)-mode transport equation is developed for large near-homogeneous systems which need not be close to critical.","Made available in DSpace on 2014-12-14T06:26:16Z (GMT). No. of bitstreams: 1 8108463.pdf: 4054342 bytes, checksum: 61826cb21c9e069af30e5986fec43f9d (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 67971 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","142 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."],"dc:identifier":["http://hdl.handle.net/2142/67793","(UMI)AAI8108463"],"dc:language":["eng"],"dc:subject":["Engineering, Nuclear","Energy"],"dc:title":["The Asymptotic Development of The Equations of Nuclear Reactor Theory"],"dc:type":["text"],"thesis:degree_discipline":["Nuclear Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:58Z"}