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Effective electrical characteristics of a two-dimensional three-component doubly-periodic system with circular inclusions

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Abstract

The problem of the electric conductivity of a two-dimensional three-component system containing periodically arranged conducting circular inclusions of two types has been solved. A consistent method for the calculation of the conductivity and other effective electrical characteristics of this model is proposed, which is applicable in the case of arbitrary component concentrations. A complex potential outside the inclusions is expressed in terms of the Weierstrass zeta function and its derivatives. Undetermined coefficients entering into the general expression for the potential are determined from an infinite system of algebraic equations. In the case of a small concentration of inclusions, this system yields a virial expansion for the conductivity. A numerical analysis of this system of equations provides for the principal possibility of investigating various effective characteristics of the model (including the Hall coefficient and thermo emf) within the entire range of the problem parameters.

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References

  1. A. L. Efros and B. I. Shklovskii, Phys. Status Solidi B 76, 475 (1976).

    Google Scholar 

  2. J. P. Straley, J. Phys. C 9, 783 (1976).

    Article  ADS  Google Scholar 

  3. J. B. Keller, J. Math. Phys. 5, 548 (1964).

    Article  MATH  Google Scholar 

  4. A. M. Dykhne, Zh. Éksp. Teor. Fiz. 59, 110 (1970) [Sov. Phys. JETP 32, 63 (1971)].

    Google Scholar 

  5. B. Ya. Balagurov, Zh. Éksp. Teor. Fiz. 81, 665 (1981) [Sov. Phys. JETP 54, 355 (1981)].

    Google Scholar 

  6. Yu. P. Emets, Electrical Properties of Composites with Regular Structure (Naukova Dumka, Kiev, 1986).

    Google Scholar 

  7. B. Ya. Balagurov, Zh. Éksp. Teor. Fiz. 79, 1561 (1980) [Sov. Phys. JETP 52, 787 (1980)].

    ADS  Google Scholar 

  8. B. Ya. Balagurov and V. A. Kashin, Zh. Éksp. Teor. Fiz. 117, 978 (2000) [JETP 90, 850 (2000)].

    Google Scholar 

  9. A. M. Dykhne, Zh. Éksp. Teor. Fiz. 59, 641 (1970) [Sov. Phys. JETP 32, 348 (1971)].

    Google Scholar 

  10. B. Ya. Balagurov, Zh. Éksp. Teor. Fiz. 85, 568 (1983) [Sov. Phys. JETP 58, 331 (1983)].

    MathSciNet  Google Scholar 

  11. B. Ya. Balagurov, Fiz. Tverd. Tela (Leningrad) 28, 2068 (1986) [Sov. Phys. Solid State 28, 1156 (1986)].

    Google Scholar 

  12. B. I. Shklovskii, Zh. Éksp. Teor. Fiz. 72, 288 (1977) [Sov. Phys. JETP 45, 152 (1977)].

    Google Scholar 

  13. D. J. Bergman and D. Stround, Phys. Rev. B 32, 6097 (1985).

    Article  ADS  Google Scholar 

  14. B. Ya. Balagurov, Zh. Éksp. Teor. Fiz. 93, 1888 (1987) [Sov. Phys. JETP 66, 1079 (1987)].

    Google Scholar 

  15. B. Ya. Balagurov, Fiz. Tekh. Poluprovodn. (Leningrad) 21, 1978 (1987) [Sov. Phys. Semicond. 21, 1198 (1987)].

    Google Scholar 

  16. B. Ya. Balagurov, Fiz. Tverd. Tela (Leningrad) 30, 3501 (1988) [Sov. Phys. Solid State 30, 2013 (1988)].

    Google Scholar 

  17. Yu. P. Emets, Zh. Éksp. Teor. Fiz. 114, 1121 (1998) [JETP 87, 612 (1998)].

    Google Scholar 

  18. Lord Rayleigh, Philos. Mag. 34, 481 (1892).

    MATH  Google Scholar 

  19. Heigher Transcendental Functions (Bateman Manuscript Project), Ed. by A. Erdelyi (McGraw-Hill, New York, 1955; Nauka, Moscow, 1967), Vol. 3.

    Google Scholar 

  20. Handbook of Mathematical Functions, Ed. by M. Abramowitz and I. A. Stegun (Dover, New York, 1971; Nauka, Moscow, 1979).

    Google Scholar 

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Authors and Affiliations

  1. Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, Moscow, 117997, Russia

    B. Ya. Balagurov

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  1. B. Ya. Balagurov
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Translated from Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 119, No. 1, 2001, pp. 142–153.

Original Russian Text Copyright © 2001 by Balagurov.

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Balagurov, B.Y. Effective electrical characteristics of a two-dimensional three-component doubly-periodic system with circular inclusions. J. Exp. Theor. Phys. 92, 123–134 (2001). https://doi.org/10.1134/1.1348468

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  • DOI: https://doi.org/10.1134/1.1348468

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