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Association of evaluation methods of the effective permittivity of heterogeneous media on the basis of a generalized singular approximation. (Russian, English) Zbl 1299.41023

Dokl. Akad. Nauk, Ross. Akad. Nauk 452, No. 1, 27-31 (2013); translation in Dokl. Phys. 58, No. 9, 379-383 (2013).
Summary: Various methods for evaluation of the effective permittivity of heterogeneous media, namely, the effective medium approximation (Bruggeman approximation), the Maxwell-Garnett approximation, Wiener’s bounds, and the Hashin-Shtrikman variational bounds (for effective static characteristics) are combined on the basis of a generalized singular approximation.

MSC:

41A20 Approximation by rational functions
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References:

[1] T. D. Shermergor, Elasticity Theory of Microinhomogeneous Media (Nauka, Moscow, 1977) [in Russian].
[2] T. D. Shermergor, A. N. Nikitin, K. Val’ter, V. Foitus, T. I. Ivankina, and V. B. Yakovlev, Izv. Akad. Nauk SSSR, Fiz. Zemli, No. 12, 84 (1991).
[3] V. I. Kolesnikov, V. V. Bardushkin, V. B. Yakovlev, A. P. Sychev, and I. V. Kolesnikov, Mechanics of Polycrystals and Composites (Stressed-Strained State and Destruction) (RGUPS, Rostov-on-Don, 2012) [in Russian].
[4] C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
[5] J. C. Maxwell, Treatise on Electricity and Magnetism (Clarendon, Oxford, 1873), Vol. 1. · JFM 05.0556.01
[6] Rayleigh, J. W S., No article title, Philos. Mag., 34, 481 (1892)
[7] Garnett, J. C M., No article title, Phil. Trans. Roy. Soc., 203, 385 (1904) · JFM 35.0844.04 · doi:10.1098/rsta.1904.0024
[8] Wiener, O., No article title, Abh.-Sachs. Geselsch., 32, 509 (1912)
[9] Stroud, D., No article title, Phys. Rev. B, 12, 3368 (1975) · doi:10.1103/PhysRevB.12.3368
[10] Hashin, Z.; Shtrikman, S., No article title, J. Appl. Phys., 33, 3125 (1962) · Zbl 0111.41401 · doi:10.1063/1.1728579
[11] Fokin, A. G., No article title, Zh. Tekh. Fiz., 41, 1073 (1971)
[12] Odelevskii, V. I., No article title, Zh. Tekh. Fiz., 21, 667 (1951)
[13] I. V. Lavrov, Ekolog. Vestn. Nauch. Tsentrov Chernomor. Ekon. Sotrudn. (ChES), No. 1, 52 (2009).
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