{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/18954"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/18954","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Approach to equilibrium in systems with continuous symmetries","abstract":"In this thesis, we consider the approach to equilibrium of quenched systems with continuous symmetry, whose relaxational dynamics is dominated by topological defects. The general aspects of the problem are discussed in chapter 1. In chapters 2 and 3, we report the results of two and three dimensional simulations of a simple model with non-conserved order parameter and the symmetry of a planar ferromagnet. A transient behavior is observed at early times in two dimensions. Finite-size scaling of the scattering function is demonstrated and it is shown that dynamical scaling is satisfied not only by the correlation functions of the order parameter but also by the correlation functions of the defects (point-vortices in two dimensions and vortex-strings in three dimensions). In the three dimensional case, the effect of a bias in the initial conditions is considered. The introduction of a bias (or external field) leads to exponential relaxation and the break-down of dynamical scaling. In chapter 4, we consider a system with conserved order parameter, which is proposed as a model of crystal surface relaxation. Multiscaling behavior for the scattering function is investigated, with negative results. A comparison of the correlation functions in the conserved and non-conserved case indicates that the conservation constraint significantly affects the vortex dynamics. In chapter 5, we discuss a model of the superconducting transition. A linear stability analysis of the normal-superconductor interface for type I superconductors indicates the presence of an instability, analogous to that responsible for dendritic patterns in solidification. A simple mean-field picture of the transition kinetics of type II superconductors suggests the existence of two dynamical regimes, characterized by a power-law and a logarithmic growth of ordered (superconducting) domains in the system. Numerical simulations of type II superconductors in the spinodal regime bear out this prediction. Selected computer programs are given in the appendices.","abstract_html":"In this thesis, we consider the approach to equilibrium of quenched systems with continuous symmetry, whose relaxational dynamics is dominated by topological defects. The general aspects of the problem are discussed in chapter 1. In chapters 2 and 3, we report the results of two and three dimensional simulations of a simple model with non-conserved order parameter and the symmetry of a planar ferromagnet. A transient behavior is observed at early times in two dimensions. Finite-size scaling of the scattering function is demonstrated and it is shown that dynamical scaling is satisfied not only by the correlation functions of the order parameter but also by the correlation functions of the defects (point-vortices in two dimensions and vortex-strings in three dimensions). In the three dimensional case, the effect of a bias in the initial conditions is considered. The introduction of a bias (or external field) leads to exponential relaxation and the break-down of dynamical scaling. In chapter 4, we consider a system with conserved order parameter, which is proposed as a model of crystal surface relaxation. Multiscaling behavior for the scattering function is investigated, with negative results. A comparison of the correlation functions in the conserved and non-conserved case indicates that the conservation constraint significantly affects the vortex dynamics. In chapter 5, we discuss a model of the superconducting transition. A linear stability analysis of the normal-superconductor interface for type I superconductors indicates the presence of an instability, analogous to that responsible for dendritic patterns in solidification. A simple mean-field picture of the transition kinetics of type II superconductors suggests the existence of two dynamical regimes, characterized by a power-law and a logarithmic growth of ordered (superconducting) domains in the system. Numerical simulations of type II superconductors in the spinodal regime bear out this prediction. Selected computer programs are given in the appendices.","abstract_has_math":false,"creators":["Mondello, Maurizio"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Goldenfeld, Nigel D."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T11:52:32Z","date_published":"2011-05-07T11:52:32Z","updated_at":"2026-07-22T22:25:12Z","subjects":["Physics, General"],"languages":["eng"],"rights":["Copyright 1991 Mondello, Maurizio"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9210923","(UMI)AAI9210923"],"render_values":[{"text":"AAI9210923","href":null,"code":true},{"text":"(UMI)AAI9210923","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/18954","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Goldenfeld, Nigel D."]},{"key":"dc:creator","label":"Author","values":["Mondello, Maurizio"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T11:52:32Z","10000-01-01","1991"]},{"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"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1991 Mondello, Maurizio"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9210923","(UMI)AAI9210923","http://hdl.handle.net/2142/18954"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis, we consider the approach to equilibrium of quenched systems with continuous symmetry, whose relaxational dynamics is dominated by topological defects. The general aspects of the problem are discussed in chapter 1. In chapters 2 and 3, we report the results of two and three dimensional simulations of a simple model with non-conserved order parameter and the symmetry of a planar ferromagnet. A transient behavior is observed at early times in two dimensions. Finite-size scaling of the scattering function is demonstrated and it is shown that dynamical scaling is satisfied not only by the correlation functions of the order parameter but also by the correlation functions of the defects (point-vortices in two dimensions and vortex-strings in three dimensions). In the three dimensional case, the effect of a bias in the initial conditions is considered. The introduction of a bias (or external field) leads to exponential relaxation and the break-down of dynamical scaling. In chapter 4, we consider a system with conserved order parameter, which is proposed as a model of crystal surface relaxation. Multiscaling behavior for the scattering function is investigated, with negative results. A comparison of the correlation functions in the conserved and non-conserved case indicates that the conservation constraint significantly affects the vortex dynamics. In chapter 5, we discuss a model of the superconducting transition. A linear stability analysis of the normal-superconductor interface for type I superconductors indicates the presence of an instability, analogous to that responsible for dendritic patterns in solidification. A simple mean-field picture of the transition kinetics of type II superconductors suggests the existence of two dynamical regimes, characterized by a power-law and a logarithmic growth of ordered (superconducting) domains in the system. Numerical simulations of type II superconductors in the spinodal regime bear out this prediction. Selected computer programs are given in the appendices.","Made available in DSpace on 2011-05-07T11:52:32Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9210923.pdf: 5559720 bytes, checksum: faac10b2dab13930774f9687b3c648fc (MD5) Previous issue date: 1991","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:33:40Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:12:31-05:00 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":["Approach to equilibrium in systems with continuous symmetries"]}]}],"canonical_facts":{"dc:contributor":["Goldenfeld, Nigel D."],"dc:creator":["Mondello, Maurizio"],"dc:date":["2011-05-07T11:52:32Z","10000-01-01","1991"],"dc:description":["In this thesis, we consider the approach to equilibrium of quenched systems with continuous symmetry, whose relaxational dynamics is dominated by topological defects. The general aspects of the problem are discussed in chapter 1. In chapters 2 and 3, we report the results of two and three dimensional simulations of a simple model with non-conserved order parameter and the symmetry of a planar ferromagnet. A transient behavior is observed at early times in two dimensions. Finite-size scaling of the scattering function is demonstrated and it is shown that dynamical scaling is satisfied not only by the correlation functions of the order parameter but also by the correlation functions of the defects (point-vortices in two dimensions and vortex-strings in three dimensions). In the three dimensional case, the effect of a bias in the initial conditions is considered. The introduction of a bias (or external field) leads to exponential relaxation and the break-down of dynamical scaling. In chapter 4, we consider a system with conserved order parameter, which is proposed as a model of crystal surface relaxation. Multiscaling behavior for the scattering function is investigated, with negative results. A comparison of the correlation functions in the conserved and non-conserved case indicates that the conservation constraint significantly affects the vortex dynamics. In chapter 5, we discuss a model of the superconducting transition. A linear stability analysis of the normal-superconductor interface for type I superconductors indicates the presence of an instability, analogous to that responsible for dendritic patterns in solidification. A simple mean-field picture of the transition kinetics of type II superconductors suggests the existence of two dynamical regimes, characterized by a power-law and a logarithmic growth of ordered (superconducting) domains in the system. Numerical simulations of type II superconductors in the spinodal regime bear out this prediction. Selected computer programs are given in the appendices.","Made available in DSpace on 2011-05-07T11:52:32Z (GMT). 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