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Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors / Paul, Ledger

Mathematical Methods in the Applied Sciences

Swansea University Author: Paul, Ledger

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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: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa45292
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spelling 2019-10-13T11:08:42.5942525 v2 45292 2018-10-30 Characterisation of multiple conducting permeable objects in metal detection by polarizability tensors 068dd31af167bcda33878951b2a01e97 0000-0002-2587-7023 Paul Ledger Paul Ledger true false 2018-10-30 EEN 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 0170-4214 1099-1476 1 1 2018 2018-01-01 10.1002/mma.5387 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University RCUK, EP/R002134/1 2019-10-13T11:08:42.5942525 2018-10-30T08:57:41.3421293 College of Engineering Engineering P.D. Ledger 1 W.R.B. Lionheart 2 A.A.S. Amad 3 Paul Ledger 0000-0002-2587-7023 4 0045292-13122018120118.pdf ledger2018(5).pdf 2018-12-13T12:01:18.6770000 Output 7180781 application/pdf Version of Record true 2018-12-13T00:00:00.0000000 true eng
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
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
author_id_fullname_str_mv 068dd31af167bcda33878951b2a01e97_***_Paul, Ledger
author Paul, Ledger
format Journal article
container_title Mathematical Methods in the Applied Sciences
publishDate 2018
institution Swansea University
issn 0170-4214
1099-1476
doi_str_mv 10.1002/mma.5387
college_str College of Engineering
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hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
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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 2018-01-01T13:08:34Z
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score 10.873003