English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Realistic applications in metal detection involve multiple inhomogeneousconducting permeable objects and the aim of this paper is to characterise suchobjects by polarizability tensors. We show that, for the eddy current model,the leading order terms for the perturbation in the magnetic field, due to thepresence of $N$ small conducting permeable homogeneous inclusions, comprises ofa sum of $N$ terms with each containing a complex symmetric rank 2polarizability tensor. Each tensor contains information about the shape andmaterial properties of one of the objects and is independent of its position.The asymptotic expansion we obtain extends a previously known result for asingle isolated object and applies in situations where the object sizes aresmall and the objects are sufficiently well separated. We also obtain a secondexpansion that describes the perturbed magnetic field for inhomogeneous andclosely spaced objects, which again characterises the objects by a complexsymmetric rank 2 tensor. The tensor's coefficients can be computed by solving avector valued transmission problem and we include numerical examples toillustrate the agreement between the asymptotic formula describing theperturbed fields and the numerical prediction. We also include algorithms forthe localisation and identification of multiple inhomogeneous objects.

Characterisation of Multiple Conducting Permeable Objects in Metal Detection by Polarizability Tensors