{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23930"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23930","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. 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): aS phase which seems to contain solitons and aT 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 GinzburgLandau equations and show that the scaling hypothesis restricts the asymptotic growth rate of the length-scale of the patterns and the small wavevector behavior ofthe form factor. Specifically, if the form factor Sk(t) grows as k8 for small 6, then 6 ~ 4 (for the CHC dynamics). We find that experimental data indicates 6 = 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.\"","abstract_html":""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): aS phase which seems to contain solitons and aT 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 GinzburgLandau equations and show that the scaling hypothesis restricts the asymptotic growth rate of the length-scale of the patterns and the small wavevector behavior ofthe form factor. Specifically, if the form factor Sk(t) grows as k8 for small 6, then 6 ~ 4 (for the CHC dynamics). We find that experimental data indicates 6 = 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."","abstract_has_math":false,"creators":["Yeung, Chuck"],"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":"2011-05-17T18:40:58Z","date_published":"2011-05-17T18:40:58Z","updated_at":"2026-07-22T22:25:22Z","subjects":["spatial patterns","nonequilibrium systems","1-d cellular automata (CA) model","chemical turbulence","dynamical scaling hypothesis","phase ordering dynamics"],"languages":["en"],"rights":["1989 Chuck Yeung"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["3473705"],"render_values":[{"text":"3473705","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23930","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":["2011-05-17T18:40:58Z","10000-01-01","1989"]},{"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":["spatial patterns","nonequilibrium systems","1-d cellular automata (CA) model","chemical turbulence","dynamical scaling hypothesis","phase ordering dynamics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["1989 Chuck Yeung"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["3473705","http://hdl.handle.net/2142/23930"]}]},{"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): aS phase which seems to contain solitons and aT 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 GinzburgLandau equations and show that the scaling hypothesis restricts the asymptotic growth rate of the length-scale of the patterns and the small wavevector behavior ofthe form factor. Specifically, if the form factor Sk(t) grows as k8 for small 6, then 6 ~ 4 (for the CHC dynamics). We find that experimental data indicates 6 = 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.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-17T18:40:58Z No. of bitstreams: 1 1989_yeung.pdf: 10827908 bytes, checksum: fb13fe0b3646cac2051bee019fdc3d92 (MD5)","Made available in DSpace on 2011-05-17T18:40:58Z (GMT). No. of bitstreams: 1 1989_yeung.pdf: 10827908 bytes, checksum: fb13fe0b3646cac2051bee019fdc3d92 (MD5) Previous issue date: 1989","Restriction data tranferred 2014-07-01T11:16:33-05:00 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 2011-05-17T18:40:58Z Item is restricted indefinitely.","Thesis","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":["2011-05-17T18:40:58Z","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): aS phase which seems to contain solitons and aT 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 GinzburgLandau equations and show that the scaling hypothesis restricts the asymptotic growth rate of the length-scale of the patterns and the small wavevector behavior ofthe form factor. Specifically, if the form factor Sk(t) grows as k8 for small 6, then 6 ~ 4 (for the CHC dynamics). We find that experimental data indicates 6 = 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.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-17T18:40:58Z No. of bitstreams: 1 1989_yeung.pdf: 10827908 bytes, checksum: fb13fe0b3646cac2051bee019fdc3d92 (MD5)","Made available in DSpace on 2011-05-17T18:40:58Z (GMT). No. of bitstreams: 1 1989_yeung.pdf: 10827908 bytes, checksum: fb13fe0b3646cac2051bee019fdc3d92 (MD5) Previous issue date: 1989","Restriction data tranferred 2014-07-01T11:16:33-05:00 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 2011-05-17T18:40:58Z Item is restricted indefinitely.","Thesis","U of I Only"],"dc:identifier":["3473705","http://hdl.handle.net/2142/23930"],"dc:language":["en"],"dc:rights":["1989 Chuck Yeung"],"dc:subject":["spatial patterns","nonequilibrium systems","1-d cellular automata (CA) model","chemical turbulence","dynamical scaling hypothesis","phase ordering dynamics"],"dc:title":["Some problems on spatial patterns in nonequilibrium 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"}