Projects per year
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 |
Funding
\ast Received by the editors May 14, 2018; accepted for publication (in revised form) January 28, 2019; published electronically April 16, 2019. http://www.siam.org/journals/siap/79-2/M118716.html Funding: The work of the first and second authors was supported by the Engineering and Physical Sciences Research Council: grant EP/L018802/2 ``Mathematical Foundations of Metama-terials: Homogenisation, Dissipation and Operator Theory."" The work of the second author was also supported by RFBR grant 19-01-00657-a. The work of the third author was partially supported by RFBR grant 16-01-00443-a.
Keywords
- Asymptotics
- Effective properties
- Homogenization
- Operators
- Time-dispersive media
ASJC Scopus subject areas
- Applied Mathematics
Fingerprint
Dive into the research topics of 'Time-dispersive behavior as a feature of critical-contrast media'. Together they form a unique fingerprint.Projects
- 2 Finished
-
Newton Mobility Grant -: Homogenisation of Degenerate Equations and Scattering for New Materials
Cherednichenko, K. (PI)
1/02/17 → 31/01/19
Project: Research council
-
Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Cherednichenko, K. (PI)
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council