{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23272"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23272","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Some problems on spatial patterns in nonequilibrium systems","abstract":"In this thesis, we study the evolution of spatial patterns in two nonequilibrium systems.","abstract_html":"In this thesis, we study the evolution of spatial patterns in two nonequilibrium systems.","abstract_has_math":false,"creators":["Yeung, Chuck"],"institution":"University of Illinois at Urbana-Champaign","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":"2011-05-07T14:08:14Z","date_published":"2011-05-07T14:08:14Z","updated_at":"2026-07-22T22:25:21Z","subjects":["Physics, Condensed Matter"],"languages":["eng"],"rights":["Copyright 1989 Yeung, Chuck"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8916323","(UMI)AAI8916323"],"render_values":[{"text":"AAI8916323","href":null,"code":true},{"text":"(UMI)AAI8916323","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23272","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":["Yeung, Chuck"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T14:08:14Z","10000-01-01","1989"]},{"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, Condensed Matter"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1989 Yeung, Chuck"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8916323","(UMI)AAI8916323","http://hdl.handle.net/2142/23272"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis, we study the evolution of spatial patterns in two nonequilibrium systems.","\"In Chapter 1, we study the steady state of a 1-d cellular automata (CA) model of chemical turbulence. Empirically there are two interesting types of space-time patterns (depending on model parameters): a S phase which seems to contain solitons and a T phase which seems to be turbulent. We show that the macroscopic phases can be predicted from the microscopic dynamics. We define the thermodynamic limit of the steady state of CAs and show that the steady state of the S phase is trivial and the T phase exhibits a Gibbs state. We explicitly calculate the T phase steady state and find an approximate form for the energy functional which generates the Gibbs state. We show that there is no adequate characterization of turbulent behavior in CAs and introduce a quantity the \"\"P-entropy\"\" which is positive if the CA patterns are turbulent and zero otherwise. We show the P-entropy for the T phase is positive.\"","In Chapter 2, we consider the consequences of the dynamical scaling hypothesis in phase ordering dynamics. We assume that the dynamics are governed by the Cahn-Hilliard-Cook (CHC) and time-dependent Ginzburg-Landau equations and show that the scaling hypothesis restricts the asymptotic growth rate of the length-scale of the patterns and the small wavevector behavior of the form factor. Specifically, if the form factor $S\\sb{k}$($t$) grows as $k\\sp{\\delta}$ for small $\\delta$, then $\\delta\\geq$ 4 (for the CHC dynamics). We find that experimental data indicates $\\delta$ = 4. We also show that the CHC equation is sometimes inadequate for describing phase ordering dynamics. An alternative to the CHC model by Oono, Kitahara and Jasnow is examined. We find that many features of phase ordering dynamics are robust with respect to changing the dynamics.","Made available in DSpace on 2011-05-07T14:08:14Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8916323.pdf: 6658164 bytes, checksum: c2e40e85713ffdb340486374a9619d5c (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:03:21Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:30:11-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Some problems on spatial patterns in nonequilibrium systems"]}]}],"canonical_facts":{"dc:contributor":["Oono, Yoshitsugu"],"dc:creator":["Yeung, Chuck"],"dc:date":["2011-05-07T14:08:14Z","10000-01-01","1989"],"dc:description":["In this thesis, we study the evolution of spatial patterns in two nonequilibrium systems.","\"In Chapter 1, we study the steady state of a 1-d cellular automata (CA) model of chemical turbulence. Empirically there are two interesting types of space-time patterns (depending on model parameters): a S phase which seems to contain solitons and a T phase which seems to be turbulent. We show that the macroscopic phases can be predicted from the microscopic dynamics. We define the thermodynamic limit of the steady state of CAs and show that the steady state of the S phase is trivial and the T phase exhibits a Gibbs state. We explicitly calculate the T phase steady state and find an approximate form for the energy functional which generates the Gibbs state. We show that there is no adequate characterization of turbulent behavior in CAs and introduce a quantity the \"\"P-entropy\"\" which is positive if the CA patterns are turbulent and zero otherwise. We show the P-entropy for the T phase is positive.\"","In Chapter 2, we consider the consequences of the dynamical scaling hypothesis in phase ordering dynamics. We assume that the dynamics are governed by the Cahn-Hilliard-Cook (CHC) and time-dependent Ginzburg-Landau equations and show that the scaling hypothesis restricts the asymptotic growth rate of the length-scale of the patterns and the small wavevector behavior of the form factor. Specifically, if the form factor $S\\sb{k}$($t$) grows as $k\\sp{\\delta}$ for small $\\delta$, then $\\delta\\geq$ 4 (for the CHC dynamics). We find that experimental data indicates $\\delta$ = 4. We also show that the CHC equation is sometimes inadequate for describing phase ordering dynamics. An alternative to the CHC model by Oono, Kitahara and Jasnow is examined. We find that many features of phase ordering dynamics are robust with respect to changing the dynamics.","Made available in DSpace on 2011-05-07T14:08:14Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8916323.pdf: 6658164 bytes, checksum: c2e40e85713ffdb340486374a9619d5c (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:03:21Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:30:11-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI8916323","(UMI)AAI8916323","http://hdl.handle.net/2142/23272"],"dc:language":["eng"],"dc:rights":["Copyright 1989 Yeung, Chuck"],"dc:subject":["Physics, Condensed Matter"],"dc:title":["Some problems on spatial patterns in nonequilibrium systems"],"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":"2026-07-22T22:25:21Z"}