Asymptotics of near-cloaking

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

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: Jan 17, 2021
• Journal: European Journal of Applied Mathematics
• Print ISSN: 0956-7925
• Electronic ISSN: 1469-4425
• Publisher: Cambridge University Press
• 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