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Asymptotics of near-cloaking

Published online by Cambridge University Press:  16 July 2020

J. R. OCKENDON
Affiliation:
Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK emails: [email protected]; [email protected]
H. OCKENDON
Affiliation:
Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK emails: [email protected]; [email protected]
B. D. SLEEMAN
Affiliation:
School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK Division of Mathematics, University of Dundee, Dundee, DD1 4HN, UK email: [email protected]
R. H. TEW
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK email: [email protected]

Abstract

This paper describes how asymptotic analysis can be used to gain new insights into the theory of cloaking of spherical and cylindrical targets within the context of acoustic waves in a class of linear elastic materials. In certain cases, these configurations allow solutions to be written down in terms of eigenfunction expansions from which high-frequency asymptotics can be extracted systematically. These asymptotics are compared with the predictions of ray theory and are used to describe the scattering that occurs when perfect cloaking models are regularised.

Type
Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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