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Asymptotics of near-cloaking

OCKENDON, J. R.; OCKENDON, H.; SLEEMAN, B. D.; TEW, R. H.

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Authors

J. R. OCKENDON

H. OCKENDON

B. D. SLEEMAN

RICHARD TEW richard.tew@nottingham.ac.uk
Associate Professor



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.

Citation

OCKENDON, J. R., OCKENDON, H., SLEEMAN, B. D., & TEW, R. H. (2021). Asymptotics of near-cloaking. European Journal of Applied Mathematics, 32(6), 1106 - 1126. https://doi.org/10.1017/s0956792520000212

Journal Article Type Article
Acceptance Date Jun 22, 2020
Online Publication Date Jul 16, 2020
Publication Date 2021-12
Deposit Date Jun 30, 2020
Publicly Available Date Mar 29, 2024
Journal European Journal of Applied Mathematics
Print ISSN 0956-7925
Electronic ISSN 1469-4425
Publisher Cambridge University Press (CUP)
Peer Reviewed Peer Reviewed
Volume 32
Issue 6
Pages 1106 - 1126
DOI https://doi.org/10.1017/s0956792520000212
Keywords Applied Mathematics
Public URL https://nottingham-repository.worktribe.com/output/4741583
Publisher URL https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/abs/asymptotics-of-nearcloaking/A0B357234042F4C9455B835BE5D0A8DD
Additional Information Copyright: © The Author(s), 2020. Published by Cambridge University Press

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