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 | |
| Publication status | Published - 2019 |
Keywords
- Asymptotics
- Effective properties
- Homogenization
- Operators
- Time-dispersive media
ASJC Scopus subject areas
- Applied Mathematics
Cite this
Time-dispersive behavior as a feature of critical-contrast media. / Cherednichenko, Kirill; Ershova, Yulia; Kiselev, Alexander V.
In: SIAM Journal on Applied Mathematics, Vol. 79, No. 2, 2019, p. 690-715.Research output: Contribution to journal › Article
}
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 -