{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/18868"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/18868","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Asymptotic behavior in spinodal decomposition","abstract":"\"In this Thesis, we study the kinetics of systems undergoing spinodal decomposition, using computational and semi-analytical methods. We use a Cell Dynamical System (CDS) to build effective computational models of spinodal decomposition in a large 3-space isotropic ideal binary alloy system and a well matched binary fluid system. Use of a CDS allows us to greatly increase the size of system we may study and allows us to reach late stages of development. At late times, the coarsening spinodal decomposition pattern appears to have a statistically similar structure independent of the time. This gives rise to simple scaling arguments for quantities such as the scattering form factor which are motivated by analogies to critical phenomena. We study the nature of scaling for the observable scattering form factor in the late, but pre-asymptotic regime using a simple \"\"hardening\"\" analysis. From this, we extract out the best available information on the true asymptotic behavior of spinodal decomposition at critical composition for the binary alloy and binary fluid case. Next, we study a simpler problem which give us insight into the late but preasymptotic growth law in the binary alloy and binary fluid system at critical composition. Using the equilibrium kink solution of the binary alloy and binary fluid model, we study the dispersion relation, or relaxation rate, of small perturbations of the kink or wall solution. We find that the relaxation rate depends on the wavevector of the perturbation. This gives rise to a growth law for the binary alloy and binary fluid system. These growth laws demonstrate the crossover to the asymptotic growth exponents as predicted by dimensional analysis, and a subtle effect in the binary 111 fluid model which appears to lead to computationally demonstrable but unexpected behavior.\"","abstract_html":""In this Thesis, we study the kinetics of systems undergoing spinodal decomposition, using computational and semi-analytical methods. We use a Cell Dynamical System (CDS) to build effective computational models of spinodal decomposition in a large 3-space isotropic ideal binary alloy system and a well matched binary fluid system. Use of a CDS allows us to greatly increase the size of system we may study and allows us to reach late stages of development. At late times, the coarsening spinodal decomposition pattern appears to have a statistically similar structure independent of the time. This gives rise to simple scaling arguments for quantities such as the scattering form factor which are motivated by analogies to critical phenomena. We study the nature of scaling for the observable scattering form factor in the late, but pre-asymptotic regime using a simple ""hardening"" analysis. From this, we extract out the best available information on the true asymptotic behavior of spinodal decomposition at critical composition for the binary alloy and binary fluid case. Next, we study a simpler problem which give us insight into the late but preasymptotic growth law in the binary alloy and binary fluid system at critical composition. Using the equilibrium kink solution of the binary alloy and binary fluid model, we study the dispersion relation, or relaxation rate, of small perturbations of the kink or wall solution. We find that the relaxation rate depends on the wavevector of the perturbation. This gives rise to a growth law for the binary alloy and binary fluid system. These growth laws demonstrate the crossover to the asymptotic growth exponents as predicted by dimensional analysis, and a subtle effect in the binary 111 fluid model which appears to lead to computationally demonstrable but unexpected behavior."","abstract_has_math":false,"creators":["Shinozaki, Aritomo"],"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":"2011-04-25T15:32:04Z","date_published":"2011-04-25T15:32:04Z","updated_at":"2026-07-22T22:25:11Z","subjects":["kinetics","spinodal decomposition","computational physics","semi-analytical","Cell Dynamical System (CDS)","Asymptotic"],"languages":["en"],"rights":["1993 Aritomo Shinozaki"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["3644336"],"render_values":[{"text":"3644336","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/18868","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":["Shinozaki, Aritomo"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-04-25T15:32:04Z","10000-01-01","1993-10"]},{"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":["kinetics","spinodal decomposition","computational physics","semi-analytical","Cell Dynamical System (CDS)","Asymptotic"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["1993 Aritomo Shinozaki"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["3644336","http://hdl.handle.net/2142/18868"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"In this Thesis, we study the kinetics of systems undergoing spinodal decomposition, using computational and semi-analytical methods. We use a Cell Dynamical System (CDS) to build effective computational models of spinodal decomposition in a large 3-space isotropic ideal binary alloy system and a well matched binary fluid system. Use of a CDS allows us to greatly increase the size of system we may study and allows us to reach late stages of development. At late times, the coarsening spinodal decomposition pattern appears to have a statistically similar structure independent of the time. This gives rise to simple scaling arguments for quantities such as the scattering form factor which are motivated by analogies to critical phenomena. We study the nature of scaling for the observable scattering form factor in the late, but pre-asymptotic regime using a simple \"\"hardening\"\" analysis. From this, we extract out the best available information on the true asymptotic behavior of spinodal decomposition at critical composition for the binary alloy and binary fluid case. Next, we study a simpler problem which give us insight into the late but preasymptotic growth law in the binary alloy and binary fluid system at critical composition. Using the equilibrium kink solution of the binary alloy and binary fluid model, we study the dispersion relation, or relaxation rate, of small perturbations of the kink or wall solution. We find that the relaxation rate depends on the wavevector of the perturbation. This gives rise to a growth law for the binary alloy and binary fluid system. These growth laws demonstrate the crossover to the asymptotic growth exponents as predicted by dimensional analysis, and a subtle effect in the binary 111 fluid model which appears to lead to computationally demonstrable but unexpected behavior.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-04-25T15:32:04Z No. of bitstreams: 1 1993_shinozaki.pdf: 8009574 bytes, checksum: 5776a4b1916df607157f411d0e7caebc (MD5)","Made available in DSpace on 2011-04-25T15:32:04Z (GMT). No. of bitstreams: 1 1993_shinozaki.pdf: 8009574 bytes, checksum: 5776a4b1916df607157f411d0e7caebc (MD5) Previous issue date: 1993-10","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-04-25T15:32:04Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:12:10-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis","Thesis","U of I Only"]},{"key":"dc:title","label":"Title","values":["Asymptotic behavior in spinodal decomposition"]}]}],"canonical_facts":{"dc:contributor":["Oono, Yoshitsugu"],"dc:creator":["Shinozaki, Aritomo"],"dc:date":["2011-04-25T15:32:04Z","10000-01-01","1993-10"],"dc:description":["\"In this Thesis, we study the kinetics of systems undergoing spinodal decomposition, using computational and semi-analytical methods. We use a Cell Dynamical System (CDS) to build effective computational models of spinodal decomposition in a large 3-space isotropic ideal binary alloy system and a well matched binary fluid system. Use of a CDS allows us to greatly increase the size of system we may study and allows us to reach late stages of development. At late times, the coarsening spinodal decomposition pattern appears to have a statistically similar structure independent of the time. This gives rise to simple scaling arguments for quantities such as the scattering form factor which are motivated by analogies to critical phenomena. We study the nature of scaling for the observable scattering form factor in the late, but pre-asymptotic regime using a simple \"\"hardening\"\" analysis. From this, we extract out the best available information on the true asymptotic behavior of spinodal decomposition at critical composition for the binary alloy and binary fluid case. Next, we study a simpler problem which give us insight into the late but preasymptotic growth law in the binary alloy and binary fluid system at critical composition. Using the equilibrium kink solution of the binary alloy and binary fluid model, we study the dispersion relation, or relaxation rate, of small perturbations of the kink or wall solution. We find that the relaxation rate depends on the wavevector of the perturbation. This gives rise to a growth law for the binary alloy and binary fluid system. These growth laws demonstrate the crossover to the asymptotic growth exponents as predicted by dimensional analysis, and a subtle effect in the binary 111 fluid model which appears to lead to computationally demonstrable but unexpected behavior.\"","Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-04-25T15:32:04Z No. of bitstreams: 1 1993_shinozaki.pdf: 8009574 bytes, checksum: 5776a4b1916df607157f411d0e7caebc (MD5)","Made available in DSpace on 2011-04-25T15:32:04Z (GMT). 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