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

2 Citations (Scopus)

31 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

Access to Document

10.1137/18M1187167

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

Projects

2 Finished

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

Cherednichenko, K., Ershova, Y., & Kiselev, A. V. (2019). Time-dispersive behavior as a feature of critical-contrast media. SIAM Journal on Applied Mathematics, 79(2), 690-715. https://doi.org/10.1137/18M1187167

@article{4a208efa6bd947fcb2ddcb14234033aa,

title = "Time-dispersive behavior as a feature of critical-contrast media",

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.",

keywords = "Asymptotics, Effective properties, Homogenization, Operators, Time-dispersive media",

author = "Kirill Cherednichenko and Yulia Ershova and Kiselev, {Alexander V.}",

year = "2019",

doi = "10.1137/18M1187167",

language = "English",

volume = "79",

pages = "690--715",

journal = "SIAM Journal on Applied Mathematics",

issn = "0036-1399",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "2",

}

TY - JOUR

T1 - Time-dispersive behavior as a feature of critical-contrast media

AU - Cherednichenko, Kirill

AU - Ershova, Yulia

AU - Kiselev, Alexander V.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Asymptotics

KW - Effective properties

KW - Homogenization

KW - Operators

KW - Time-dispersive media

UR - http://www.scopus.com/inward/record.url?scp=85068803393&partnerID=8YFLogxK

U2 - 10.1137/18M1187167

DO - 10.1137/18M1187167

M3 - Article

AN - SCOPUS:85068803393

VL - 79

SP - 690

EP - 715

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 2

ER -