Describing rotations of the spheroids based on the first order polarization tensor

Taufiq Khairi Ahmad Khairuddin, Nurhazirah Mohd Yunos

Abstract


Polarization Tensor (PT) can be used to describe conducting objects presented in electric or electromagnetic fields. In this paper, we investigate specifically the first order PT when the conducting object is a spheroid. First of all, we evaluate the first order PT for a prolate and an oblate spheroid. After that, by using these first order PT and a specific matrix transformation, we numerically present some transformation of the first order PT representing the first order PT after the spheroids are being rotated. Moreover, it is found that the first order PT for the spheroid before it is being rotated and after it is being rotated actually have the same determinant.


Keywords


Conductivity; Rotation Matrix; Determinant

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References


Ammari, H. and Kang, H. Polarization and Moment Tensors; with Applications to inverse Problems and Effective Medium Theory. New York: Springer. 2007.

Milton, G. Theory of Composites. Cambridge University Press, USA. 2002.

Ahmad Khairuddin, T.K. and Lionheart, W.R.B. Characterization of objects by electrosensing fish based on the first order polarization tensor. Bioinspiration and Biomimetics. 2016. 11(5): 1-8.

Ahmad Khairuddin, T.K. and Lionheart, W.R.B. Polarization Tensor: Between Biology and Engineering. Malaysian Journal of Mathematical Sciences. 2016. 10(S): 179–191.

Khairuddin, T.K.A. and Lionheart W.R.B. Does electro-sensing fish use the first order polarization tensor for object characterization? Object discrimination test. Sains Malaysiana. 2014. 43(11): 1775–1779.

Ledger, P.D. and Lionheart, W. R. B. Understanding the Magnetic Polarizability Tensor. IEEE Transactions on Magnetic. 2016. 52(5): 6201216.

Khairuddin, T.K.A., Ledger, P.D. and Lionheart W.R.B. Investigating the Polarization Tensor to Describe and Identify Metallic Objects. Proc. of the World Congress on Engineering. 2015. I: 122–127.

Ahmad Khairuddin, T. K. and Lionheart, W. R. B. Some Properties of the First Order Polarization Tensor for 3-D Domains. MATEMATIKA UTM. 2013. 29(1): 1-18.

Ahmad Khairuddin, T. K. Characterization of Objects by Fitting the Polarization Tensor. The University of Manchaster: Ph.D. Thesis. 2016.

Osborn, J. Demagnetizaing Factors of the General Ellipsoid. Physical review. 1945. 67(11-12): 351-357.

Stoner, E. C. The Demagnetizing Factors for Ellipsoids. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1945. 36(263): 803-821.

Khairuddin, T. K. A. and Lionheart, W. R. B. Fitting ellipsoids to objects by the first order polarization tensor. Malaya Journal of Matematik, 2013. 4(1): 44-53.

Ahmad Khairuddin, T. K., Mohamad Yunos, N., Aziz, Z. A., Ahmad, T. and Lionheart, W. R. B. Classification of materials for conducting spheroids based on the first order polarization tensor. ICoAIMS. 2017. 890(1). 1-7.


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