K.D. Cherednichenko
Spectral Analysis of One-Dimensional High-Contrast Elliptic Problems with Periodic Coefficients
Cherednichenko, K.D.; Cooper, S.; Guenneau, S.
Authors
S. Cooper
S. Guenneau
Abstract
We study the behavior of the spectrum of a family of one-dimensional operators with periodic high-contrast coefficients as the period goes to zero, which may represent, e.g., the elastic or electromagnetic response of a two-component composite medium. Compared to the standard operators with moderate contrast, they exhibit a number of new effects due to the underlying nonuniform ellipticity of the family. The effective behavior of such media in the vanishing period limit also differs notably from that of multidimensional models investigated thus far by other authors, due to the fact that neither component of the composite forms a connected set. We then discuss a modified problem, where the equation coefficient is set to a positive constant on an interval that is independent of the period. Formal asymptotic analysis and numerical tests with finite elements suggest the existence of localized eigenfunctions (``defect modes''), whose eigenvalues are situated in the gaps of the limit spectrum for the unperturbed problem.
Citation
Cherednichenko, K., Cooper, S., & Guenneau, S. (2015). Spectral Analysis of One-Dimensional High-Contrast Elliptic Problems with Periodic Coefficients. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 13(1), 72-98. https://doi.org/10.1137/130947106
Journal Article Type | Article |
---|---|
Acceptance Date | Aug 15, 2014 |
Online Publication Date | Jan 8, 2015 |
Publication Date | Jan 8, 2015 |
Deposit Date | Oct 31, 2017 |
Publicly Available Date | Apr 23, 2018 |
Journal | Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal |
Print ISSN | 1540-3459 |
Electronic ISSN | 1540-3467 |
Publisher | Society for Industrial and Applied Mathematics |
Peer Reviewed | Peer Reviewed |
Volume | 13 |
Issue | 1 |
Pages | 72-98 |
DOI | https://doi.org/10.1137/130947106 |
Public URL | https://durham-repository.worktribe.com/output/1345459 |
Files
Published Journal Article
(723 Kb)
PDF
Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
Copyright Statement
© 2015, Society for Industrial and Applied Mathematics. Published by SIAM under the terms of the Creative Commons 4.0 license.
You might also like
On the existence of high-frequency boundary resonances in layered elastic media
(2015)
Journal Article
Resolvent Estimates for High-Contrast Elliptic Problems with Periodic Coefficients
(2015)
Journal Article
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search