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• W2557852221 abstract "This thesis focuses on some mathematical aspects and a few recent applications ofthe polarization tensor (PT). Here, the main concern of the study is to characterizeobjects presented in electrical or electromagnetic fields by only using the PT. This ispossible since the PT contains significant information about the object such as shape,orientation and material properties. Two main applications are considered in the studyand they are electrosensing fish and metal detection. In each application, we present amathematical formulation of the PT and briefly discuss its properties.The PT in the electrosensing fish is actually based on the first order generalizedpolarization tensor (GPT) while the GPT itself generalizes the classical PT called asthe P I�olya-Szeg I�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 isdirectly based on the quadrature method of numerical integration while the secondmethod 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 iswritten 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 ismore 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 isbecause we would like to propose an experiment to test whether electrosensing fish candiscriminate a pair of different objects but with the same first order PT such that thepair could be an ellipsoid and some other object. In addition, the first order PT (orthe P I�olya-Szeg I�o PT) with complex conductivity (or complex permittivity) which issimilar to the PT for Maxwellâ��s equations is also investigated.On the other hand, following recent mathematical foundation of the PT from theeddy current model, we use the new proposed explicit formula to compute the rank2 PT for a few metallic targets relevance in metal detection. We show that the PTfor the targets computed from the explicit formula agree to some degree of accuracywith the PT obtained from metal detectors during experimental works and simulationsconducted by the engineers. This suggests to alternatively use the explicit formulawhich depends only on the geometry and material properties of the target as well asoffering lower computational efforts than performing measurements with metal detectorsto obtain the PT. By using the explicit formula of the rank 2 PT, we also numericallyinvestigate some properties of the rank 2 PT where, the information obtained could beuseful to improve metal detection and also in other potential applications of the eddycurrent. In this case, if the target is magnetic but non-conducting, the rank 2 PT ofthe target can also be computed by using the explicit formula of the first order PT." @default.
• W2557852221 created "2016-12-08" @default.
• W2557852221 creator A5033922514 @default.
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• W2557852221 date "2016-11-16" @default.
• W2557852221 modified "2023-09-24" @default.
• W2557852221 title "Characterization of objects by fitting the polarization tensor" @default.
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