{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/67781"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/67781","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Reactor Static Optimization With Integral System Equations","abstract":"An algorithm is developed for the optimality analysis of thermal reactor assemblies with a mathematical programming method. The neutron balances of the systems under consideration are transformed into integral equations by using Green's functions. Two-group, two-dimensional Green's functions for the neutron diffusion equations have been derived.","abstract_html":"An algorithm is developed for the optimality analysis of thermal reactor assemblies with a mathematical programming method. The neutron balances of the systems under consideration are transformed into integral equations by using Green's functions. Two-group, two-dimensional Green's functions for the neutron diffusion equations have been derived.","abstract_has_math":false,"creators":["Sheen, Yu-Min"],"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":2014,"date_issued":"2014-12-14T06:26:11Z","date_published":"2014-12-14T06:26:11Z","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)AAI8017982"],"render_values":[{"text":"(UMI)AAI8017982","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/67781","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Sheen, Yu-Min"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-14T06:26:11Z","10000-01-01","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/2142/67781","(UMI)AAI8017982"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["An algorithm is developed for the optimality analysis of thermal reactor assemblies with a mathematical programming method. The neutron balances of the systems under consideration are transformed into integral equations by using Green's functions. Two-group, two-dimensional Green's functions for the neutron diffusion equations have been derived.","A nodal method has been used to transform integral system equations into equivalent matrix eigenvalue problems. A benchmark problem solved with both the nodal method and a finite difference code "CITATION" establishes the validity of the integral system equations. Possible ways of improving computed results are discussed. Only 50 mesh points are required in nodal method to obtain one percent error in the eigenvalue in the benchmark calculation. The same accuracy requires 2500 mesh points in the "CITATION" code.","With the nodal method described above, a two-dimensional maximum power problem for a thermal reactor is solved by treating the fissile material concentration as the controller. Two numerical examples are given.","Made available in DSpace on 2014-12-14T06:26:11Z (GMT). No. of bitstreams: 1 8017982.pdf: 3392631 bytes, checksum: 7884cef29b2e83c89e8d86d9e7042a5e (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 67959 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","141 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."]},{"key":"dc:title","label":"Title","values":["Reactor Static Optimization With Integral System Equations"]}]}],"canonical_facts":{"dc:creator":["Sheen, Yu-Min"],"dc:date":["2014-12-14T06:26:11Z","10000-01-01","1980"],"dc:description":["An algorithm is developed for the optimality analysis of thermal reactor assemblies with a mathematical programming method. The neutron balances of the systems under consideration are transformed into integral equations by using Green's functions. Two-group, two-dimensional Green's functions for the neutron diffusion equations have been derived.","A nodal method has been used to transform integral system equations into equivalent matrix eigenvalue problems. A benchmark problem solved with both the nodal method and a finite difference code "CITATION" establishes the validity of the integral system equations. Possible ways of improving computed results are discussed. Only 50 mesh points are required in nodal method to obtain one percent error in the eigenvalue in the benchmark calculation. The same accuracy requires 2500 mesh points in the "CITATION" code.","With the nodal method described above, a two-dimensional maximum power problem for a thermal reactor is solved by treating the fissile material concentration as the controller. Two numerical examples are given.","Made available in DSpace on 2014-12-14T06:26:11Z (GMT). No. of bitstreams: 1 8017982.pdf: 3392631 bytes, checksum: 7884cef29b2e83c89e8d86d9e7042a5e (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 67959 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","141 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."],"dc:identifier":["http://hdl.handle.net/2142/67781","(UMI)AAI8017982"],"dc:language":["eng"],"dc:subject":["Engineering, Nuclear","Energy"],"dc:title":["Reactor Static Optimization With Integral System Equations"],"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"}