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Asymptotics of near-cloaking

Published online by Cambridge University Press:  16 July 2020

J. R. OCKENDON ,
H. OCKENDON ,
B. D. SLEEMAN  and
R. H. TEW Open the ORCID record for R. H. TEW [Opens in a new window]
J. R. OCKENDON
Affiliation:
Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK emails: ock@maths.ox.ac.uk; Hilary.Ockendon@maths.ox.ac.uk
H. OCKENDON
Affiliation:
Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK emails: ock@maths.ox.ac.uk; Hilary.Ockendon@maths.ox.ac.uk
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: B.D.Sleeman@leeds.ac.uk
R. H. TEW
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK email: richard.tew@nottingham.ac.uk
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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.

Keywords

Cloakingray theoryelastic wavesasymptotics
Type
Papers
Information
European Journal of Applied Mathematics , Volume 32 , Special Issue 6: Special issue featuring papers on Professor Sam Howison , December 2021 , pp. 1106 - 1126
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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