Please use this identifier to cite or link to this item:
https://hdl.handle.net/11147/2232
Title: | Analysis of a corner layer problem in anisotropic interfaces | Authors: | Alikakos, N. D. Bates, P. W. Cahn, J. W. Fife, P. C. Fusco, G. Tanoğlu, Gamze |
Keywords: | Anisotropy Corner layers Crystalline structure Interfaces Nonlinear boundary value problems Singular perturbation |
Publisher: | Southwest Missouri State University | Source: | Alikakos, 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. | Abstract: | We 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. | URI: | http://hdl.handle.net/11147/2232 | ISSN: | 1531-3492 1531-3492 |
Appears in Collections: | Mathematics / Matematik Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
Show full item record
CORE Recommender
SCOPUSTM
Citations
14
checked on Dec 6, 2024
WEB OF SCIENCETM
Citations
12
checked on Nov 9, 2024
Page view(s)
3,368
checked on Dec 9, 2024
Download(s)
226
checked on Dec 9, 2024
Google ScholarTM
Check
Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.