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 |
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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
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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
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Newton Mobility Grant -: Homogenisation of Degenerate Equations and Scattering for New Materials
1/02/17 → 31/01/19
Project: Research council
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Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council