Kirill Cherednichenko
Homogenization of the system of high-contrast Maxwell equations
Cherednichenko, Kirill; Cooper, Shane
Authors
Shane Cooper
Abstract
We study the system of Maxwell equations for a periodic composite dielectric medium with components whose dielectric permittivities ε have a high degree of contrast between each other. We assume that the ratio between the permittivities of the components with low and high values of ε is of the order η2, where η > 0 is the period of the medium. We determine the asymptotic behaviour of the electromagnetic response of such a medium in the “homogenization limit”, as η → 0, and derive the limit system of Maxwell equations in R3. Our results extend a number of conclusions of a paper by Zhikov [On gaps in the spectrum of some divergent elliptic operators with periodic coefficients. St. Petersburg Math. J. 16(5) (2004), 719–773] to the case of the full system of Maxwell equations.
Citation
Cherednichenko, K., & Cooper, S. (2015). Homogenization of the system of high-contrast Maxwell equations. Mathematika, 61(02), 475-500. https://doi.org/10.1112/s0025579314000424
Journal Article Type | Article |
---|---|
Online Publication Date | Feb 27, 2015 |
Publication Date | May 1, 2015 |
Deposit Date | Oct 31, 2017 |
Publicly Available Date | Apr 23, 2018 |
Journal | Mathematika |
Print ISSN | 0025-5793 |
Electronic ISSN | 2041-7942 |
Publisher | Wiley |
Peer Reviewed | Peer Reviewed |
Volume | 61 |
Issue | 02 |
Pages | 475-500 |
DOI | https://doi.org/10.1112/s0025579314000424 |
Public URL | https://durham-repository.worktribe.com/output/1372704 |
Files
Published Journal Article
(322 Kb)
PDF
Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
Copyright Statement
© University College London 2015 This article is distributed with Open Access under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided that the original work is properly cited.
You might also like
On the existence of high-frequency boundary resonances in layered elastic media
(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