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dc.contributor.authorAlikakos, N. D.
dc.contributor.authorBates, P. W.
dc.contributor.authorCahn, J. W.
dc.contributor.authorFife, P. C.
dc.contributor.authorFusco, G.
dc.contributor.authorTanoğlu, Gamze
dc.date.accessioned2016-10-13T12:16:53Z
dc.date.available2016-10-13T12:16:53Z
dc.date.issued2006-03
dc.identifier.citationAlikakos, N. D., Bates, P. W., Cahn, J. W., Fife, P. C., Fusco, G., & Tanoglu, G. (2006). Analysis of a corner layer problem in anisotropic interfaces. Discrete and Continuous Dynamical Systems - Series B, 6(2), 237-255.en_US
dc.identifier.issn1531-3492
dc.identifier.urihttp://hdl.handle.net/11147/2232
dc.description.abstractWe investigate a model of anisotropic diffuse interfaces in ordered FCC crystals introduced recently by Braun et al and Tanoglu et al [3, 18, 19], focusing on parametric conditions which give extreme anisotropy. For a reduced model, we prove existence and stability of plane wave solutions connecting the disordered FCC state with the ordered Cu3Au state described by solutions to a system of three equations. These plane wave solutions correspond to planar interfaces. Different orientations of the planes in relation to the crystal axes give rise to different surface energies. Guided by previous work based on numerics and formal asymptotics, we reduce this problem in the six dimensional phase space of the system to a two dimensional phase space by taking advantage of the symmetries of the crystal and restricting attention to solutions with corresponding symmetries. For this reduced problem a standing wave solution is constructed that corresponds to a transition that, in the extreme anisotropy limit, is continuous but not differentiable. We also investigate the stability of the constructed solution by studying the eigenvalue problem for the linearized equation. We find that although the transition is stable, there is a growing number 0(1/ε), of critical eigenvalues, where 1/ε ≫ 1 is a measure of the anisotropy. Specifically we obtain a discrete spectrum with eigenvalues λn = ε2/3 μn with μn ∼ Cn2/3, as n → +∞. The scaling characteristics of the critical spectrum suggest a previously unknown microstructural instability.en_US
dc.description.sponsorshipUniversity of North Texas and the University of Athensen_US
dc.language.isoengen_US
dc.publisherSouthwest Missouri State Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectAnisotropyen_US
dc.subjectCorner layersen_US
dc.subjectCrystalline structureen_US
dc.subjectInterfacesen_US
dc.subjectNonlinear boundary value problemsen_US
dc.subjectSingular perturbationen_US
dc.titleAnalysis of a corner layer problem in anisotropic interfacesen_US
dc.typearticleen_US
dc.contributor.authorIDTR103234en_US
dc.contributor.institutionauthorTanoğlu, Gamze
dc.relation.journalDiscrete and Continuous Dynamical Systems - Series Ben_US
dc.contributor.departmentIzmir Institute of Technology. Mathematicsen_US
dc.identifier.volume6en_US
dc.identifier.issue2en_US
dc.identifier.startpage237en_US
dc.identifier.endpage255en_US
dc.identifier.wosWOS:000233123800002
dc.identifier.scopusSCOPUS:2-s2.0-33644518267
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US


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