Correlation between the geometrical characteristics and dielectric polarizability of polyhedra
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Correlation between the geometrical characteristics and dielectric polarizability of polyhedraAbstract
This article analyzes polarizability characteristics of the five regular polyhedra (tetrahedron, cube, octahedron, dodecahedron, and icosahedron) and sphere. In particular, the variation of the polarizabilities (polarizability is the amplitude of the static dipole moment caused by an incident electric field of unit amplitude) is correlated with various geometrical parameters of these Platonic solids: specific surface, number of edges, vertices, and faces, and the volumes of inscribed and circumscribed spheres. It is found that the polarizabilities of perfect electric conductor (PEC) and perfect electric insulator (PEI) objects are most strongly correlated with two different parameters: the radius ratio of circum- and inscribed spheres (PEC case) and the normalized radius of the inscribed sphere (PEI case).
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References
J.D. Jackson, Classical Electrodynamics, Third
Edition, John Wiley, New York, 1999.
A. Sihvola, Electromagnetic Mixing Formulas and
Applications, IEE Publishing, Electromagnetic
Wave Series 47, London, 1999.
A. Sihvola, P. Yl ̈a-Oijala, S. J ̈arvenp ̈a ̈a, J. Avelin:
Polarizabilities of Platonic solids. To appear in
IEEE Transactions on Antennas and Propagation,
M. Schiffer and G. Szeg ̈o: Virtual mass and polar-
ization, Transactions of the American Mathemati-
cal Society, Vol. 67, pp. 130-205, 1949.
J. Van Bladel: Electromagnetic Fields, New York,
Hemisphere Publishing Corporation, 1985. Re-
vised edition.
R. F. Harrington: Field Computation by Moment
Methods, Macmillan, New York, 1968.
D. R. Wilton, S. M. Rao, A. W. Glisson, D. H.
Schaubert, O. M. Al-Bundak and C. M. Butler: Po-
tential integrals for uniform and linear source dis-
tributions on polygonal and polyhedral domains.
IEEE Transactions on Antennas and Propagation,
Vol. 32, pp. 276-281, March 1984.
R. D. Graglia, On the numerical integration of
the linear shape functions times the 3-D Green’s
function or its gradient on a plane triangle: IEEE
Transactions on Antennas and Propagation, Vol.
, pp. 1448-1455, October 1993
S. J ̈arvenp ̈a ̈a, M. Taskinen and P. Yl ̈a-Oijala, Sin-
gularity extraction technique for integral equation
methods with higher order basis functions on plane
triangles and tetrahedra: International Journal for
Numerical Methods in Engineering, Vol. 58, pp.
-1165, 2003.
J. Avelin, R. Sharma, I. H ̈anninen, and A. H.
Sihvola: Polarizability analysis of cubical and
square-shaped dielectric scatterers: IEEE Transac-
tions on Antennas and Propagation, Vol. 49, No. 3,
pp. 451-457, March 2001.
Y. Saad and M. H. Schultz: GMRES: a general-
ized minimal residual algorithm for solving non-
symmetric linear systems, SIAM Journal of Sci-
entific and Statistical Computing, Vol. 7, pp. 856-
, 1986.
M. S. H ̈am ̈al ̈ainen and J. Sarvas: Realistic con-
ductivity geometry model of the human head for
interpretation of neuromagnetic data, IEEE Trans-
actions on Biomedical Engineering, Vol. 36, No.
, February 1989.
L. R ̊ade and B. Westergren: Mathematics Hand-
book for science and engineering, Studentlitter-
atur, Lund, 1995.
