# Characterization of Objects by Fitting the Polarization Tensor

Ahmad Khairuddin, Taufiq Khairi bin (2016) Characterization of Objects by Fitting the Polarization Tensor. Doctoral thesis, The University of Manchester. PDF final_thesis_1.pdf Download (5MB)

## Abstract

This thesis focuses on some mathematical aspects and a few recent applications of the polarization tensor (PT). Here, the main concern of the study is to characterize objects presented in electrical or electromagnetic fields by only using the PT. This is possible since the PT contains significant information about the object such as shape, orientation and material properties. Two main applications are considered in the study and they are electrosensing fish and metal detection. In each application, we present a mathematical formulation of the PT and briefly discuss its properties. The PT in the electrosensing fish is actually based on the first order generalized polarization tensor (GPT) while the GPT itself generalizes the classical PT called as the P Ì�olya-Szeg Ì�o PT. In order to investigate the role of the PT in electrosensing fish, we propose two numerical methods to compute the first order PT. The first method is directly based on the quadrature method of numerical integration while the second method is an adaptation of some terminologies of the boundary element method (BEM). A code to use the first method is developed in Matlab while a script in Python is written as an interface for using the new developed code for BEM called as BEM++. When comparing the two methods, our numerical results show that the first order PT is more accurate with faster convergence when computed by BEM++. During this study, we also give a strategy to determine an ellipsoid from a given first order PT. This is because we would like to propose an experiment to test whether electrosensing fish can discriminate a pair of different objects but with the same first order PT such that the pair could be an ellipsoid and some other object. In addition, the first order PT (or the P Ì�olya-Szeg Ì�o PT) with complex conductivity (or complex permittivity) which is similar to the PT for Maxwellâ��s equations is also investigated. On the other hand, following recent mathematical foundation of the PT from the eddy current model, we use the new proposed explicit formula to compute the rank 2 PT for a few metallic targets relevance in metal detection. We show that the PT for the targets computed from the explicit formula agree to some degree of accuracy with the PT obtained from metal detectors during experimental works and simulations conducted by the engineers. This suggests to alternatively use the explicit formula which depends only on the geometry and material properties of the target as well as offering lower computational efforts than performing measurements with metal detectors to obtain the PT. By using the explicit formula of the rank 2 PT, we also numerically investigate some properties of the rank 2 PT where, the information obtained could be useful to improve metal detection and also in other potential applications of the eddy current. In this case, if the target is magnetic but non-conducting, the rank 2 PT of the target can also be computed by using the explicit formula of the first order PT.

Item Type: Thesis (Doctoral) polarization tensor, weakly electric fish, metal detection, inverse problem MSC 2010, the AMS's Mathematics Subject Classification > 31 Potential theoryMSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equationsMSC 2010, the AMS's Mathematics Subject Classification > 45 Integral equationsPACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 41 Electromagnetism; electron and ion optics Prof WRB Lionheart 29 Nov 2016 20 Oct 2017 14:13 http://eprints.maths.manchester.ac.uk/id/eprint/2514 View Item