Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

On anomalous localized resonance for the elastostatic system

Language

English

Abstract

We consider the anomalous localized resonance due to a plasmonic structure for the elastostatic system in $\mathbb{R}^2$. The plasmonic structure takes a general core-shell-matrix form with the metamaterial located in the shell. If there is no core, we show that resonance occurs for a very broad class of sources. If the core is nonempty and of an arbitrary shape, we show that there exists a critical radius such that resonance occurs for a certain class of sources lying within the critical radius, whereas resonance does not occur for a certain class of sources lying outside the critical radius. Our argument is based on a variational technique by making use of the primal and dual variational principles for the elastostatic system, along with the construction of suitable test functions.

Keywords

anomalous localized resonance, plasmonic material, elastostatics

Publication Date

9-2016

Source Publication Title

SIAM Journal on Mathematical Analysis

Volume

48

Issue

5

Start Page

3322

End Page

3344

Publisher

Society for Industrial and Applied Mathematics

Peer Reviewed

1

Funder

The work of the authors was supported by FRG grants from Hong Kong Baptist University, Hong Kong RGC General Research Funds, 12302415 and 405513, and NSF of China grant 11371115.

DOI

10.1137/16M1059023

Link to Publisher's Edition

http://dx.doi.org/10.1137/16M1059023

ISSN (print)

00361410

ISSN (electronic)

10957154

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