{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/80547"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/80547","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Scaling and Pattern Formation in Condensed Matter Systems","abstract":"Finally, I study multiscale patterns in polycrystalline materials, with the phase field crystal (PFC) model. I first show that the complex amplitudes representation incorporates the correct form of nonlinear elasticity. I then analyze the plastic properties of the model by applying a shearing force. Dislocation avalanches, which resembling the scaling behavior in driven ferromagnetic, are observed. Critical exponents are extracted from power laws extending over 5 decades. I extend the PFC model to accommodate actual atomic configurations and vacancies. I use the extended PFC model to simulate a liquid and reproduce the correct form of the two-point correlation functions. Finally, I extend the PFC model to describing binary systems. The resulting theory describes both atomic hopping events on microscopic scales and diffusion on macroscopic scales. It also reproduces the activated Arrhenius form of the diffusion coefficient.","abstract_html":"Finally, I study multiscale patterns in polycrystalline materials, with the phase field crystal (PFC) model. I first show that the complex amplitudes representation incorporates the correct form of nonlinear elasticity. I then analyze the plastic properties of the model by applying a shearing force. Dislocation avalanches, which resembling the scaling behavior in driven ferromagnetic, are observed. Critical exponents are extracted from power laws extending over 5 decades. I extend the PFC model to accommodate actual atomic configurations and vacancies. I use the extended PFC model to simulate a liquid and reproduce the correct form of the two-point correlation functions. Finally, I extend the PFC model to describing binary systems. The resulting theory describes both atomic hopping events on microscopic scales and diffusion on macroscopic scales. It also reproduces the activated Arrhenius form of the diffusion coefficient.","abstract_has_math":false,"creators":["Chan, Pak Yuen"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Nigel Goldenfeld"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T20:03:00Z","date_published":"2015-09-25T20:03:00Z","updated_at":"2026-07-22T22:26:14Z","subjects":["Geophysics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3290194"],"render_values":[{"text":"(MiAaPQ)AAI3290194","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/80547","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Nigel Goldenfeld"]},{"key":"dc:creator","label":"Author","values":["Chan, Pak Yuen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T20:03:00Z","10000-01-01","2007"]},{"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":["Geophysics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/80547","(MiAaPQ)AAI3290194"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Finally, I study multiscale patterns in polycrystalline materials, with the phase field crystal (PFC) model. 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I first show that the complex amplitudes representation incorporates the correct form of nonlinear elasticity. I then analyze the plastic properties of the model by applying a shearing force. Dislocation avalanches, which resembling the scaling behavior in driven ferromagnetic, are observed. Critical exponents are extracted from power laws extending over 5 decades. I extend the PFC model to accommodate actual atomic configurations and vacancies. I use the extended PFC model to simulate a liquid and reproduce the correct form of the two-point correlation functions. Finally, I extend the PFC model to describing binary systems. The resulting theory describes both atomic hopping events on microscopic scales and diffusion on macroscopic scales. It also reproduces the activated Arrhenius form of the diffusion coefficient.","Made available in DSpace on 2015-09-25T20:03:00Z (GMT). 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