Time-dispersive behavior as a feature of critical-contrast media

Kirill Cherednichenko; Yulia Ershova; Alexander V. Kiselev

doi:10.1137/18M1187167

Time-dispersive behavior as a feature of critical-contrast media

Kirill Cherednichenko, Yulia Ershova, Alexander V. Kiselev

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

42 Downloads (Pure)

Abstract

Motivated by the need to attribute a rigorous mathematical meaning to the term ``metamaterial,"" we propose a novel approach to the homogenization of critical-contrast composites. This is based on the asymptotic analysis of the Dirichlet-to-Neumann map on the interface between different components (``stiff"" and ``soft"") of the medium, which leads to an asymptotic approximation of eigenmodes. This allows us to see that the presence of the soft component makes the stiff one behave as a class of time-dispersive media. By an inversion of this argument, we also offer a recipe for the construction of such media with prescribed dispersive properties from periodic composites.

Original language	English
Pages (from-to)	690-715
Number of pages	26
Journal	SIAM Journal on Applied Mathematics
Volume	79
Issue number	2
Early online date	16 Apr 2019
DOIs	https://doi.org/10.1137/18M1187167
Publication status	Published - 2019

Keywords

Asymptotics
Effective properties
Homogenization
Operators
Time-dispersive media

ASJC Scopus subject areas

Applied Mathematics

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10.1137/18M1187167

Cher_Yer_Kis_18_SIAP
(C) Society for Industrial and Applied Mathematics, 2019.
Accepted author manuscript, 640 KB

3 Finished

Newton Mobility Grant -: Homogenisation of Degenerate Equations and Scattering for New Materials
Cherednichenko, K.
The Royal Society
1/02/17 → 31/01/19
Project: Research council
Bath-UNAM-CIMAT (BUC) workshop series -- BUC VI-IX
Cherednichenko, K., Shaddick, G., Kyprianou, A., Milewski, P. & Majumdar, A.
1/09/16 → 1/09/18
Project: Research-related funding
Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Cherednichenko, K.
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council

Cite this

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KW - Asymptotics

KW - Effective properties

KW - Homogenization

KW - Operators

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Time-dispersive behavior as a feature of critical-contrast media

Abstract

Keywords

ASJC Scopus subject areas

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Projects

Newton Mobility Grant -: Homogenisation of Degenerate Equations and Scattering for New Materials

Bath-UNAM-CIMAT (BUC) workshop series -- BUC VI-IX

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this