{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19813"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19813","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The role of topological defects and textures in the kinetics of phase ordering","abstract":"In this thesis, I present the results of a theoretical investigation of ordering processes induced by symmetry-breaking quenches in two physical systems. Both systems investigated possess a rich homotopy structure of the order-parameter space, which results in numerous topologically stable objects being generated during the quench, and influencing the properties of the system during the subsequent approach to equilibrium. The results reported are mostly computational in nature. The two systems investigated are (i) nematic liquid crystals, which support topologically stable abelian (in the uniaxial nematic case) and non-abelian (in the biaxial nematic case) singular defects, and (ii) the O(3)-symmetric vector (i.e., Heisenberg-type) system in 2 spatial dimensions, which supports topologically stable, but non-singular objects--topological textures.","abstract_html":"In this thesis, I present the results of a theoretical investigation of ordering processes induced by symmetry-breaking quenches in two physical systems. Both systems investigated possess a rich homotopy structure of the order-parameter space, which results in numerous topologically stable objects being generated during the quench, and influencing the properties of the system during the subsequent approach to equilibrium. The results reported are mostly computational in nature. The two systems investigated are (i) nematic liquid crystals, which support topologically stable abelian (in the uniaxial nematic case) and non-abelian (in the biaxial nematic case) singular defects, and (ii) the O(3)-symmetric vector (i.e., Heisenberg-type) system in 2 spatial dimensions, which supports topologically stable, but non-singular objects--topological textures.","abstract_has_math":false,"creators":["Zapotocky, Martin"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Goldbart, Paul M.","Oono, Yoshitsugu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:19:23Z","date_published":"2011-05-07T12:19:23Z","updated_at":"2026-07-22T22:25:14Z","subjects":["Engineering, Chemical","Physics, Condensed Matter","Biophysics, General"],"languages":["eng"],"rights":["Copyright 1996 Zapotocky, Martin"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["9780591199802","AAI9712498","(UMI)AAI9712498"],"render_values":[{"text":"9780591199802","href":null,"code":true},{"text":"AAI9712498","href":null,"code":true},{"text":"(UMI)AAI9712498","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19813","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Goldbart, Paul M.","Oono, Yoshitsugu"]},{"key":"dc:creator","label":"Author","values":["Zapotocky, Martin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:19:23Z","10000-01-01","1996"]},{"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":["Engineering, Chemical","Physics, Condensed Matter","Biophysics, 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 1996 Zapotocky, Martin"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["9780591199802","AAI9712498","(UMI)AAI9712498","http://hdl.handle.net/2142/19813"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis, I present the results of a theoretical investigation of ordering processes induced by symmetry-breaking quenches in two physical systems. Both systems investigated possess a rich homotopy structure of the order-parameter space, which results in numerous topologically stable objects being generated during the quench, and influencing the properties of the system during the subsequent approach to equilibrium. The results reported are mostly computational in nature. The two systems investigated are (i) nematic liquid crystals, which support topologically stable abelian (in the uniaxial nematic case) and non-abelian (in the biaxial nematic case) singular defects, and (ii) the O(3)-symmetric vector (i.e., Heisenberg-type) system in 2 spatial dimensions, which supports topologically stable, but non-singular objects--topological textures.","In the case of nematic systems, the numerical investigation concentrates on the phase-ordering process and point defect dynamics following a quench into both the uniaxial and biaxial nematic phases of a quasi-2-dimensional liquid crystalline system. By comparing the growth laws for the characteristic length scales extracted from the order-parameter correlations and from the total number of topological defects in the system, it is determined that weak violations of dynamical scaling occur in the system, even at the latest times studied. The observed scaling violations are attributed to the presence of a logarithmic correction to the asymptotic power-law growth of the average inter-defect separation. Following the quench to the biaxial nematic phase, there are four topologically distinct defect species present in the system, the populations of which are studied in detail.","In addition to the computational investigation of the phase ordering process in 2-dimensional nematic systems, analytical derivations of the singular (power-law) short-distance behavior of the contribution to the structure factor (i.e., the light scattering intensity) for all types of topologically stable defects encountered in 2- and 3-dimensional uniaxial and biaxial nematics are presented.","The second system studied--the Heisenberg-type model in 2 spatial dimensions--is first implemented numerically as the discretized O(3) nonlinear $\\sigma$-model with the standard form of free energy and with purely dissipative dynamics. Two distinct mechanisms for the decay of the order-parameter variations--single texture unwinding, and topological charge annihilation--are identified and characterized in this system. By examining the correlations in the order parameter and in the topological charge density, it is shown that dynamical scaling is strongly violated during the phase-ordering process, and multiple characteristic length-scales growing as distinct power-laws in time are identified.","In order to study in detail the origins of the observed multi-scaling behavior, the phase-ordering process is then studied within a modified O(3) nonlinear $\\sigma$-model with an additional free energy term (analogous to the so-called Skyrme term, familiar in high-energy physics) that stabilizes the textures against shrinking and unwinding. It is found that this modification influences the multi-scaling properties of the system in a dramatic way, and that with single-texture unwindings suppressed, the form of the spectrum of exponents characterizing the decay of the moments of the topological charge density distribution can be predicted successfully by a simple two-length-scale argument.","Made available in DSpace on 2011-05-07T12:19:23Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9712498.pdf: 7646563 bytes, checksum: d070aa17e498b11d71a23ac32b80fd56 (MD5) Previous issue date: 1996","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:39:36Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:16:44-05:00 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":["The role of topological defects and textures in the kinetics of phase ordering"]}]}],"canonical_facts":{"dc:contributor":["Goldbart, Paul M.","Oono, Yoshitsugu"],"dc:creator":["Zapotocky, Martin"],"dc:date":["2011-05-07T12:19:23Z","10000-01-01","1996"],"dc:description":["In this thesis, I present the results of a theoretical investigation of ordering processes induced by symmetry-breaking quenches in two physical systems. Both systems investigated possess a rich homotopy structure of the order-parameter space, which results in numerous topologically stable objects being generated during the quench, and influencing the properties of the system during the subsequent approach to equilibrium. The results reported are mostly computational in nature. The two systems investigated are (i) nematic liquid crystals, which support topologically stable abelian (in the uniaxial nematic case) and non-abelian (in the biaxial nematic case) singular defects, and (ii) the O(3)-symmetric vector (i.e., Heisenberg-type) system in 2 spatial dimensions, which supports topologically stable, but non-singular objects--topological textures.","In the case of nematic systems, the numerical investigation concentrates on the phase-ordering process and point defect dynamics following a quench into both the uniaxial and biaxial nematic phases of a quasi-2-dimensional liquid crystalline system. By comparing the growth laws for the characteristic length scales extracted from the order-parameter correlations and from the total number of topological defects in the system, it is determined that weak violations of dynamical scaling occur in the system, even at the latest times studied. The observed scaling violations are attributed to the presence of a logarithmic correction to the asymptotic power-law growth of the average inter-defect separation. Following the quench to the biaxial nematic phase, there are four topologically distinct defect species present in the system, the populations of which are studied in detail.","In addition to the computational investigation of the phase ordering process in 2-dimensional nematic systems, analytical derivations of the singular (power-law) short-distance behavior of the contribution to the structure factor (i.e., the light scattering intensity) for all types of topologically stable defects encountered in 2- and 3-dimensional uniaxial and biaxial nematics are presented.","The second system studied--the Heisenberg-type model in 2 spatial dimensions--is first implemented numerically as the discretized O(3) nonlinear $\\sigma$-model with the standard form of free energy and with purely dissipative dynamics. Two distinct mechanisms for the decay of the order-parameter variations--single texture unwinding, and topological charge annihilation--are identified and characterized in this system. By examining the correlations in the order parameter and in the topological charge density, it is shown that dynamical scaling is strongly violated during the phase-ordering process, and multiple characteristic length-scales growing as distinct power-laws in time are identified.","In order to study in detail the origins of the observed multi-scaling behavior, the phase-ordering process is then studied within a modified O(3) nonlinear $\\sigma$-model with an additional free energy term (analogous to the so-called Skyrme term, familiar in high-energy physics) that stabilizes the textures against shrinking and unwinding. It is found that this modification influences the multi-scaling properties of the system in a dramatic way, and that with single-texture unwindings suppressed, the form of the spectrum of exponents characterizing the decay of the moments of the topological charge density distribution can be predicted successfully by a simple two-length-scale argument.","Made available in DSpace on 2011-05-07T12:19:23Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9712498.pdf: 7646563 bytes, checksum: d070aa17e498b11d71a23ac32b80fd56 (MD5) Previous issue date: 1996","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:39:36Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:16:44-05:00 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":["9780591199802","AAI9712498","(UMI)AAI9712498","http://hdl.handle.net/2142/19813"],"dc:language":["eng"],"dc:rights":["Copyright 1996 Zapotocky, Martin"],"dc:subject":["Engineering, Chemical","Physics, Condensed Matter","Biophysics, General"],"dc:title":["The role of topological defects and textures in the kinetics of phase ordering"],"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":"2026-07-22T22:25:14Z"}