{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/67790"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/67790","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Performance Characteristics of Specified Power Reactors in Multidimensional Neutron Diffusion Problems","abstract":"The multigroup neutron diffusion equations with the constraint of specified power distributions are investigated by the application of the straight-line method which can be considered as the limiting case of zero mesh space in the finite difference method. The standard partial differential form of the diffusion equation is reduced to sets of ordinary differential equations and then converted into sets of integral equations by using Green's functions defined on the pseudo straight lines. Coupling of each straight line to the adjacent lines arises from the application of a three-point central difference formula. The interfaces encountered between two regions are taken into account by imposing the continuity conditions for the group fluxes and net currents with Taylor expansions of internal fluxes at the interface positions.","abstract_html":"The multigroup neutron diffusion equations with the constraint of specified power distributions are investigated by the application of the straight-line method which can be considered as the limiting case of zero mesh space in the finite difference method. The standard partial differential form of the diffusion equation is reduced to sets of ordinary differential equations and then converted into sets of integral equations by using Green's functions defined on the pseudo straight lines. Coupling of each straight line to the adjacent lines arises from the application of a three-point central difference formula. The interfaces encountered between two regions are taken into account by imposing the continuity conditions for the group fluxes and net currents with Taylor expansions of internal fluxes at the interface positions.","abstract_has_math":false,"creators":["Kim, Moon Gil"],"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":"2014-12-14T06:26:15Z","date_published":"2014-12-14T06:26:15Z","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)AAI8026537"],"render_values":[{"text":"(UMI)AAI8026537","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/67790","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Kim, Moon Gil"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-14T06:26:15Z","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/2142/67790","(UMI)AAI8026537"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The multigroup neutron diffusion equations with the constraint of specified power distributions are investigated by the application of the straight-line method which can be considered as the limiting case of zero mesh space in the finite difference method. The standard partial differential form of the diffusion equation is reduced to sets of ordinary differential equations and then converted into sets of integral equations by using Green's functions defined on the pseudo straight lines. Coupling of each straight line to the adjacent lines arises from the application of a three-point central difference formula. The interfaces encountered between two regions are taken into account by imposing the continuity conditions for the group fluxes and net currents with Taylor expansions of internal fluxes at the interface positions.","A few sample problems are selected to test the validity of the method. It is found that the proposed method of solution is similar to the finite Fourier sine transform.","Numerical results for the solutions obtained by the method of straight lines are compared with the results of the exact analytical solutions for simple geometries. These comparisons indicate that the proposed method is compatible with the analytical method, and in some problems considered the straight-line solutions are much more efficient than the exact solutions.","The method is also extended to the reactor kinetics problem by expressing the kinetics parameters in tems of the basis functions which are used to obtain the solutions of the steady-state neutron diffusion equations.","Made available in DSpace on 2014-12-14T06:26:15Z (GMT). No. of bitstreams: 1 8026537.pdf: 4659281 bytes, checksum: 324b4e314057fbbbabfe0a620c65d9af (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 67968 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","172 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."]},{"key":"dc:title","label":"Title","values":["Performance Characteristics of Specified Power Reactors in Multidimensional Neutron Diffusion Problems"]}]}],"canonical_facts":{"dc:creator":["Kim, Moon Gil"],"dc:date":["2014-12-14T06:26:15Z","10000-01-01","1980"],"dc:description":["The multigroup neutron diffusion equations with the constraint of specified power distributions are investigated by the application of the straight-line method which can be considered as the limiting case of zero mesh space in the finite difference method. The standard partial differential form of the diffusion equation is reduced to sets of ordinary differential equations and then converted into sets of integral equations by using Green's functions defined on the pseudo straight lines. Coupling of each straight line to the adjacent lines arises from the application of a three-point central difference formula. The interfaces encountered between two regions are taken into account by imposing the continuity conditions for the group fluxes and net currents with Taylor expansions of internal fluxes at the interface positions.","A few sample problems are selected to test the validity of the method. It is found that the proposed method of solution is similar to the finite Fourier sine transform.","Numerical results for the solutions obtained by the method of straight lines are compared with the results of the exact analytical solutions for simple geometries. These comparisons indicate that the proposed method is compatible with the analytical method, and in some problems considered the straight-line solutions are much more efficient than the exact solutions.","The method is also extended to the reactor kinetics problem by expressing the kinetics parameters in tems of the basis functions which are used to obtain the solutions of the steady-state neutron diffusion equations.","Made available in DSpace on 2014-12-14T06:26:15Z (GMT). No. of bitstreams: 1 8026537.pdf: 4659281 bytes, checksum: 324b4e314057fbbbabfe0a620c65d9af (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 67968 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","172 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."],"dc:identifier":["http://hdl.handle.net/2142/67790","(UMI)AAI8026537"],"dc:language":["eng"],"dc:subject":["Engineering, Nuclear","Energy"],"dc:title":["Performance Characteristics of Specified Power Reactors in Multidimensional Neutron Diffusion Problems"],"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"}