Ledger, P and Lionheart, WRB (2022) Properties of Generalised Magnetic Polarizability Tensors. Mathematical Methods in the Applied Sciences. ISSN 0170-4214

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We present new alternative complete asymptotic expansions for the time harmonic low–frequency magnetic field perturbation caused by the presence of a conducting permeable object as its size tends to zero for the eddy current approximation of the Maxwell system. Our new alternative formulations enable a natural extension of the well known rank 2 magnetic polarizability tensor (MPT) object characterisation to higher order tensor descriptions by introducing generalised MPTs (GMPTs) using multi-indices. In particular, we identify the magnetostatic contribution, provide new results on the symmetries of GMPTs, derive explicit formulae for the real and imaginary parts of GMPT coefficients and also describe the spectral behaviour of GMPT coefficients. We also introduce the concept of harmonic GMPTs (HGMPTs) that have fewer coefficients than other GMPT descriptions of the same order. We describe the scaling, translation and rotational properties of HGMPTs and describe an approach for obtaining those HGMPT coefficients that are invariant under the action of a symmetry group. Such an approach is one candidate for selecting features in object classification for hidden object identification using HGMPTs.

Item Type: Article
Additional Information: This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.© 2022 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd.
Uncontrolled Keywords: asymptotic analysis; eddy current; inverse problems; magnetic polarizability tensor; metal detection; spectral problems
Subjects: Q Science > Q Science (General)
T Technology > T Technology (General)
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 22 Nov 2022 10:01
Last Modified: 23 Feb 2023 09:52
URI: https://eprints.keele.ac.uk/id/eprint/11731

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