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Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors

Paul Ledger, W.R.B. Lionheart, Alan Amad Orcid Logo

Mathematical Methods in the Applied Sciences, Volume: 42, Issue: 3, Pages: 830 - 860

Swansea University Authors: Paul Ledger, Alan Amad Orcid Logo

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DOI (Published version): 10.1002/mma.5387

Abstract

Realistic applications in metal detection involve multiple inhomogeneous‐conducting permeable objects, and the aim of this paper is to characterise such objects by polarizability tensors. We show that, for the eddy current model, the leading order terms for the perturbation in the magnetic field, du...

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Published in: Mathematical Methods in the Applied Sciences
ISSN: 0170-4214 1099-1476
Published: 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa45292
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spelling 2021-01-14T12:54:06.5915938 v2 45292 2018-10-30 Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors 068dd31af167bcda33878951b2a01e97 Paul Ledger Paul Ledger true false fe2123481afa7460a369317354cba4ec 0000-0001-7709-5536 Alan Amad Alan Amad true false 2018-10-30 FGSEN Realistic applications in metal detection involve multiple inhomogeneous‐conducting permeable objects, and the aim of this paper is to characterise such objects by polarizability tensors. We show that, for the eddy current model, the leading order terms for the perturbation in the magnetic field, due to the presence of N small conducting permeable homogeneous inclusions, comprises of a sum of N terms with each containing a complex symmetric rank 2 polarizability tensor. Each tensor contains information about the shape and material properties of one of the objects and is independent of its position. The asymptotic expansion we obtain extends a previously known result for a single isolated object and applies in situations where the object sizes are small and the objects are sufficiently well separated. We also obtain a second expansion that describes the perturbed magnetic field for inhomogeneous and closely spaced objects, which again characterises the objects by a complex symmetric rank 2 tensor. The tensor's coefficients can be computed by solving a vector valued transmission problem, and we include numerical examples to illustrate the agreement between the asymptotic formula describing the perturbed fields and the numerical prediction. We also include algorithms for the localisation and identification of multiple inhomogeneous objects. Journal Article Mathematical Methods in the Applied Sciences 42 3 830 860 0170-4214 1099-1476 28 2 2019 2019-02-28 10.1002/mma.5387 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University RCUK, EP/R002134/1 2021-01-14T12:54:06.5915938 2018-10-30T08:57:41.3421293 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Paul Ledger 1 W.R.B. Lionheart 2 Alan Amad 0000-0001-7709-5536 3 45292__17879__52a04951023a42d7a1b004e7b49efd67.pdf ledger2018(5).pdf 2020-08-06T16:27:22.6489855 Output 2417111 application/pdf Version of Record true Released under the terms of a Creative Commons Attribution License (CC-BY). true eng http://creativecommons.org/licenses/by/4.0/
title Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors
spellingShingle Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors
Paul Ledger
Alan Amad
title_short Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors
title_full Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors
title_fullStr Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors
title_full_unstemmed Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors
title_sort Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors
author_id_str_mv 068dd31af167bcda33878951b2a01e97
fe2123481afa7460a369317354cba4ec
author_id_fullname_str_mv 068dd31af167bcda33878951b2a01e97_***_Paul Ledger
fe2123481afa7460a369317354cba4ec_***_Alan Amad
author Paul Ledger
Alan Amad
author2 Paul Ledger
W.R.B. Lionheart
Alan Amad
format Journal article
container_title Mathematical Methods in the Applied Sciences
container_volume 42
container_issue 3
container_start_page 830
publishDate 2019
institution Swansea University
issn 0170-4214
1099-1476
doi_str_mv 10.1002/mma.5387
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
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description Realistic applications in metal detection involve multiple inhomogeneous‐conducting permeable objects, and the aim of this paper is to characterise such objects by polarizability tensors. We show that, for the eddy current model, the leading order terms for the perturbation in the magnetic field, due to the presence of N small conducting permeable homogeneous inclusions, comprises of a sum of N terms with each containing a complex symmetric rank 2 polarizability tensor. Each tensor contains information about the shape and material properties of one of the objects and is independent of its position. The asymptotic expansion we obtain extends a previously known result for a single isolated object and applies in situations where the object sizes are small and the objects are sufficiently well separated. We also obtain a second expansion that describes the perturbed magnetic field for inhomogeneous and closely spaced objects, which again characterises the objects by a complex symmetric rank 2 tensor. The tensor's coefficients can be computed by solving a vector valued transmission problem, and we include numerical examples to illustrate the agreement between the asymptotic formula describing the perturbed fields and the numerical prediction. We also include algorithms for the localisation and identification of multiple inhomogeneous objects.
published_date 2019-02-28T03:57:02Z
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score 11.012678

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