{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23900"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23900","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Some problems in the dynamics of spatially extended systems","abstract":"\"In this thesis, we study some representative problems in the dynamics of systems which have a non-trivial spatial dependence. In the first chapter, we study the perturbed sine-Gordon equation and the \"\"Painleve test of integrability.\"\" We present results of our numerical studies of the d.c. driven, damped sine-Gordon equation. We also present a nonperturbative proof of the persistence of soliton-like (\"\"soliton\"\") and antisoliton-like (\"\"antisoliton\"\") solutions of the d.c. driven, damped sineGordon equation. Subsequently, we describe the so-called \"\"Painleve test of integrability.\"\" We apply this test to the d.c. driven, damped sine-Gordon equation, which is shown to be nonintegrable in the Painleve sense. In the second chapter, we present computationally efficient Cell-Dynamical System (CDS) models of phase ordering dynamics. We present results of our numerical studies on these models for (a) The nonconserved order parameter case without and with noise; (b) The conserved order parameter case with a critical quench (without and with noise), an off-critical quench in the unstable regime (without noise), and the nucleation regime (without noise). Results on these systems have been obtained inexpensively in terms of computer time usage. Consequently, we have been able to see stages in the process which have not been numerically accessed so far. Specifically, we demonstrate that the scaled form factor appears to approach an asymptotic regime in which the effects of noise are irrelevant, in accordance with the generally held theoretical view.\"","abstract_html":""In this thesis, we study some representative problems in the dynamics of systems which have a non-trivial spatial dependence. In the first chapter, we study the perturbed sine-Gordon equation and the ""Painleve test of integrability."" We present results of our numerical studies of the d.c. driven, damped sine-Gordon equation. We also present a nonperturbative proof of the persistence of soliton-like (""soliton"") and antisoliton-like (""antisoliton"") solutions of the d.c. driven, damped sineGordon equation. Subsequently, we describe the so-called ""Painleve test of integrability."" We apply this test to the d.c. driven, damped sine-Gordon equation, which is shown to be nonintegrable in the Painleve sense. In the second chapter, we present computationally efficient Cell-Dynamical System (CDS) models of phase ordering dynamics. We present results of our numerical studies on these models for (a) The nonconserved order parameter case without and with noise; (b) The conserved order parameter case with a critical quench (without and with noise), an off-critical quench in the unstable regime (without noise), and the nucleation regime (without noise). Results on these systems have been obtained inexpensively in terms of computer time usage. Consequently, we have been able to see stages in the process which have not been numerically accessed so far. Specifically, we demonstrate that the scaled form factor appears to approach an asymptotic regime in which the effects of noise are irrelevant, in accordance with the generally held theoretical view."","abstract_has_math":false,"creators":["Puri, Sanjay"],"institution":null,"degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Oono, Yoshitsugu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-16T21:12:05Z","date_published":"2011-05-16T21:12:05Z","updated_at":"2026-07-22T22:25:22Z","subjects":["dynamics of spatially extended systems","non-trivial spatial dependence","perturbed sine-Gordon equation"],"languages":["en"],"rights":["1988 Sanjay Puri"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["3471834"],"render_values":[{"text":"3471834","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23900","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Oono, Yoshitsugu"]},{"key":"dc:creator","label":"Author","values":["Puri, Sanjay"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-16T21:12:05Z","10000-01-01","1988"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation / Thesis","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."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["dynamics of spatially extended systems","non-trivial spatial dependence","perturbed sine-Gordon equation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["1988 Sanjay Puri"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["3471834","http://hdl.handle.net/2142/23900"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"In this thesis, we study some representative problems in the dynamics of systems which have a non-trivial spatial dependence. In the first chapter, we study the perturbed sine-Gordon equation and the \"\"Painleve test of integrability.\"\" We present results of our numerical studies of the d.c. driven, damped sine-Gordon equation. We also present a nonperturbative proof of the persistence of soliton-like (\"\"soliton\"\") and antisoliton-like (\"\"antisoliton\"\") solutions of the d.c. driven, damped sineGordon equation. Subsequently, we describe the so-called \"\"Painleve test of integrability.\"\" We apply this test to the d.c. driven, damped sine-Gordon equation, which is shown to be nonintegrable in the Painleve sense. In the second chapter, we present computationally efficient Cell-Dynamical System (CDS) models of phase ordering dynamics. We present results of our numerical studies on these models for (a) The nonconserved order parameter case without and with noise; (b) The conserved order parameter case with a critical quench (without and with noise), an off-critical quench in the unstable regime (without noise), and the nucleation regime (without noise). Results on these systems have been obtained inexpensively in terms of computer time usage. Consequently, we have been able to see stages in the process which have not been numerically accessed so far. Specifically, we demonstrate that the scaled form factor appears to approach an asymptotic regime in which the effects of noise are irrelevant, in accordance with the generally held theoretical view.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-16T21:12:05Z No. of bitstreams: 1 1988_puri.pdf: 6534913 bytes, checksum: 68c339a81867e33c45f15caf944f3752 (MD5)","Made available in DSpace on 2011-05-16T21:12:05Z (GMT). No. of bitstreams: 1 1988_puri.pdf: 6534913 bytes, checksum: 68c339a81867e33c45f15caf944f3752 (MD5) Previous issue date: 1988","Restriction data tranferred 2014-07-01T11:13:59-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-16T21:12:05Z Item is restricted indefinitely.","Thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["Some problems in the dynamics of spatially extended systems"]}]}],"canonical_facts":{"dc:contributor":["Oono, Yoshitsugu"],"dc:creator":["Puri, Sanjay"],"dc:date":["2011-05-16T21:12:05Z","10000-01-01","1988"],"dc:description":["\"In this thesis, we study some representative problems in the dynamics of systems which have a non-trivial spatial dependence. In the first chapter, we study the perturbed sine-Gordon equation and the \"\"Painleve test of integrability.\"\" We present results of our numerical studies of the d.c. driven, damped sine-Gordon equation. We also present a nonperturbative proof of the persistence of soliton-like (\"\"soliton\"\") and antisoliton-like (\"\"antisoliton\"\") solutions of the d.c. driven, damped sineGordon equation. Subsequently, we describe the so-called \"\"Painleve test of integrability.\"\" We apply this test to the d.c. driven, damped sine-Gordon equation, which is shown to be nonintegrable in the Painleve sense. In the second chapter, we present computationally efficient Cell-Dynamical System (CDS) models of phase ordering dynamics. We present results of our numerical studies on these models for (a) The nonconserved order parameter case without and with noise; (b) The conserved order parameter case with a critical quench (without and with noise), an off-critical quench in the unstable regime (without noise), and the nucleation regime (without noise). Results on these systems have been obtained inexpensively in terms of computer time usage. Consequently, we have been able to see stages in the process which have not been numerically accessed so far. Specifically, we demonstrate that the scaled form factor appears to approach an asymptotic regime in which the effects of noise are irrelevant, in accordance with the generally held theoretical view.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-16T21:12:05Z No. of bitstreams: 1 1988_puri.pdf: 6534913 bytes, checksum: 68c339a81867e33c45f15caf944f3752 (MD5)","Made available in DSpace on 2011-05-16T21:12:05Z (GMT). No. of bitstreams: 1 1988_puri.pdf: 6534913 bytes, checksum: 68c339a81867e33c45f15caf944f3752 (MD5) Previous issue date: 1988","Restriction data tranferred 2014-07-01T11:13:59-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-16T21:12:05Z Item is restricted indefinitely.","Thesis","U of I Only"],"dc:identifier":["3471834","http://hdl.handle.net/2142/23900"],"dc:language":["en"],"dc:rights":["1988 Sanjay Puri"],"dc:subject":["dynamics of spatially extended systems","non-trivial spatial dependence","perturbed sine-Gordon equation"],"dc:title":["Some problems in the dynamics of spatially extended systems"],"dc:type":["Dissertation / Thesis","text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."]},"updated_at":"2026-07-22T22:25:22Z"}