{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/72450"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/72450","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Differential and Integral Invariance of the Relativistic Vlasov-Boltzmann Equation and the Associated Invariant Variational Problem","abstract":"Relativistic Vlasov-Boltzmann kinetic equations are constructed from quantum field theory for scalar bosons and Dirac fermion fields. Lie's principle of differential invariance is extended to the case of non-linear integro-differential equations for both scalar and matrix distribution functions, corresponding to scalar and fermion kinetic equations respectively, and then is used to demonstrate the invariance of these equations under the action of the Poincare group. The invariant variational problem is then constructed for these equations, and is shown to yield the kinetic equations as Euler-Lagrange equations for the variational principle, as well as first integrals for the Euler-Lagrange, which are interpreted as conservation laws, for energy-linear momentum and angular momentum under the action of the Poincare group. Finally, macroscopic balance equations for particle and energy density, linear and angular momentum, and entropy production, appropriate for the description of non-ideal relativistic magnetohydrodynamics are obtained from moments of the relativistic kinetic equation.","abstract_html":"Relativistic Vlasov-Boltzmann kinetic equations are constructed from quantum field theory for scalar bosons and Dirac fermion fields. Lie's principle of differential invariance is extended to the case of non-linear integro-differential equations for both scalar and matrix distribution functions, corresponding to scalar and fermion kinetic equations respectively, and then is used to demonstrate the invariance of these equations under the action of the Poincare group. The invariant variational problem is then constructed for these equations, and is shown to yield the kinetic equations as Euler-Lagrange equations for the variational principle, as well as first integrals for the Euler-Lagrange, which are interpreted as conservation laws, for energy-linear momentum and angular momentum under the action of the Poincare group. Finally, macroscopic balance equations for particle and energy density, linear and angular momentum, and entropy production, appropriate for the description of non-ideal relativistic magnetohydrodynamics are obtained from moments of the relativistic kinetic equation.","abstract_has_math":false,"creators":["Burlet, Daniel John"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Nuclear Engineering","degree_department":null,"school":null,"contributors":["Axford, Roy A."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-17T22:36:17Z","date_published":"2014-12-17T22:36:17Z","updated_at":"2026-07-22T22:26:06Z","subjects":["Engineering, Nuclear","Physics, Fluid and Plasma","Physics, Elementary Particles and High Energy"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI9328983"],"render_values":[{"text":"(UMI)AAI9328983","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/72450","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Axford, Roy A."]},{"key":"dc:creator","label":"Author","values":["Burlet, Daniel John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-17T22:36:17Z","10000-01-01","1993"]},{"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","Physics, Fluid and Plasma","Physics, Elementary Particles and High Energy"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/72450","(UMI)AAI9328983"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Relativistic Vlasov-Boltzmann kinetic equations are constructed from quantum field theory for scalar bosons and Dirac fermion fields. Lie's principle of differential invariance is extended to the case of non-linear integro-differential equations for both scalar and matrix distribution functions, corresponding to scalar and fermion kinetic equations respectively, and then is used to demonstrate the invariance of these equations under the action of the Poincare group. The invariant variational problem is then constructed for these equations, and is shown to yield the kinetic equations as Euler-Lagrange equations for the variational principle, as well as first integrals for the Euler-Lagrange, which are interpreted as conservation laws, for energy-linear momentum and angular momentum under the action of the Poincare group. Finally, macroscopic balance equations for particle and energy density, linear and angular momentum, and entropy production, appropriate for the description of non-ideal relativistic magnetohydrodynamics are obtained from moments of the relativistic kinetic equation.","Made available in DSpace on 2014-12-17T22:36:17Z (GMT). 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Lie's principle of differential invariance is extended to the case of non-linear integro-differential equations for both scalar and matrix distribution functions, corresponding to scalar and fermion kinetic equations respectively, and then is used to demonstrate the invariance of these equations under the action of the Poincare group. The invariant variational problem is then constructed for these equations, and is shown to yield the kinetic equations as Euler-Lagrange equations for the variational principle, as well as first integrals for the Euler-Lagrange, which are interpreted as conservation laws, for energy-linear momentum and angular momentum under the action of the Poincare group. Finally, macroscopic balance equations for particle and energy density, linear and angular momentum, and entropy production, appropriate for the description of non-ideal relativistic magnetohydrodynamics are obtained from moments of the relativistic kinetic equation.","Made available in DSpace on 2014-12-17T22:36:17Z (GMT). No. of bitstreams: 1 9328983.pdf: 12273866 bytes, checksum: 65ab1e6d33cb89a55d63359b2ec16282 (MD5) Previous issue date: 1993","Embargo set by: Seth Robbins for item 72618 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","551 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1993."],"dc:identifier":["http://hdl.handle.net/2142/72450","(UMI)AAI9328983"],"dc:subject":["Engineering, Nuclear","Physics, Fluid and Plasma","Physics, Elementary Particles and High Energy"],"dc:title":["Differential and Integral Invariance of the Relativistic Vlasov-Boltzmann Equation and the Associated Invariant Variational Problem"],"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":"2026-07-22T22:26:06Z"}