{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/80579"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/80579","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Experimental Evidence for Mixed Reality States in an Interreality System, And, Generalized Resonant Forcing of Nonlinear Dynamics","abstract":"This work also explores resonances of nonlinear systems. This includes time-discrete chaotic maps as well as generalized systems of nonlinear first order differential equations. The calculus of variations is used to determine the minimal additive forcing function that induces a desired terminal response. In contrast to previous efforts, in this work only select degrees of freedom are forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. Certain Lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. The efficacy of this methodology is demonstrated with several examples.","abstract_html":"This work also explores resonances of nonlinear systems. This includes time-discrete chaotic maps as well as generalized systems of nonlinear first order differential equations. The calculus of variations is used to determine the minimal additive forcing function that induces a desired terminal response. In contrast to previous efforts, in this work only select degrees of freedom are forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. Certain Lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. The efficacy of this methodology is demonstrated with several examples.","abstract_has_math":false,"creators":["Gintautas, Vadas"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Hubler, Alfred"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T20:03:08Z","date_published":"2015-09-25T20:03:08Z","updated_at":"2026-07-22T22:26:14Z","subjects":["Physics, General"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3337760"],"render_values":[{"text":"(MiAaPQ)AAI3337760","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/80579","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hubler, Alfred"]},{"key":"dc:creator","label":"Author","values":["Gintautas, Vadas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T20:03:08Z","10000-01-01","2008"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"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":["Physics, General"]}]},{"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/2142/80579","(MiAaPQ)AAI3337760"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This work also explores resonances of nonlinear systems. This includes time-discrete chaotic maps as well as generalized systems of nonlinear first order differential equations. The calculus of variations is used to determine the minimal additive forcing function that induces a desired terminal response. In contrast to previous efforts, in this work only select degrees of freedom are forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. Certain Lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. The efficacy of this methodology is demonstrated with several examples.","Made available in DSpace on 2015-09-25T20:03:08Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3337760.pdf: 1082615 bytes, checksum: 264548094bd9b57482d719a06183624e (MD5) Previous issue date: 2008","Embargo set by: Seth Robbins for item 81861 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","77 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008."]},{"key":"dc:title","label":"Title","values":["Experimental Evidence for Mixed Reality States in an Interreality System, And, Generalized Resonant Forcing of Nonlinear Dynamics"]}]}],"canonical_facts":{"dc:contributor":["Hubler, Alfred"],"dc:creator":["Gintautas, Vadas"],"dc:date":["2015-09-25T20:03:08Z","10000-01-01","2008"],"dc:description":["This work also explores resonances of nonlinear systems. This includes time-discrete chaotic maps as well as generalized systems of nonlinear first order differential equations. The calculus of variations is used to determine the minimal additive forcing function that induces a desired terminal response. In contrast to previous efforts, in this work only select degrees of freedom are forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. Certain Lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. The efficacy of this methodology is demonstrated with several examples.","Made available in DSpace on 2015-09-25T20:03:08Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3337760.pdf: 1082615 bytes, checksum: 264548094bd9b57482d719a06183624e (MD5) Previous issue date: 2008","Embargo set by: Seth Robbins for item 81861 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","77 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008."],"dc:identifier":["http://hdl.handle.net/2142/80579","(MiAaPQ)AAI3337760"],"dc:language":["eng"],"dc:subject":["Physics, General"],"dc:title":["Experimental Evidence for Mixed Reality States in an Interreality System, And, Generalized Resonant Forcing of Nonlinear Dynamics"],"dc:type":["text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:14Z"}