Skip to main content
SpringerLink
Log in

Reciprocity relations for the effective electrical conductivity of randomly inhomogeneous media in the fractal regime

  • Solids
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

An exact relation for the realization-averaged effective conductivities in the fractal region is found for two-dimensional randomly inhomogeneous media. It has the form {σ e (τ,L)~× {1/σ e (−τ,L)~−1=σ 2e (τ=0, L≫ξ), where ξ is the correlation length (the self-averaging scale), L is the size of the system, τ=(p-p c )/p c , and p c is the percolation threshold. For L≫ ξ, the system is self-averaged, and the relation transforms into the Dykhne reciprocity relation, A. M. Dykhne, Zh. Éksp. Teor. Fiz. 59, 110 (1970) [Sov. Phys. JETP 32, 63 (1971)] σ e (τ)σ e (−τ])=σ 2e (τ=0)= σ 1 σ 2. A similar relation is obtained for media with an exponentially broad distribution of local conductivities, as well as for individual realizations of some deterministic structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Google Scholar 

  2. D. Stauffer and A. Aharony, Introduction to Percolation Theory, Taylor and Francis, London-Washington, DC (1992).

    Google Scholar 

  3. J. Feder, Fractals, Plenum Press, New York (1988) [Russ. transl., Mir, Moscow (1991)].

    Google Scholar 

  4. J. Helsing and G. Grimvall, Phys. Rev. B 41, 11 364 (1990).

  5. T. Ohtsuki and T. Keyes, J. Phys. A: Math. Gen. 17, L559 (1984).

    ADS  MathSciNet  Google Scholar 

  6. B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors, Springer-Verlag, Berlin (1984).

    Google Scholar 

  7. Yu. A. Dreizin and A. M. Dykhne, Zh. Éksp. Teor. Fiz. 84, 1756 (1983) [Sov. Phys. JETP 57, 1024 (1983)].

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  10. J. P. Straley, J. Phys. D 14, 2101 (1981).

    Article  ADS  Google Scholar 

  11. V. Halpern, J. Phys. C: Solid State Phys. 16, L217 (1983).

    Article  ADS  Google Scholar 

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

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ukrainian National Technical University (Kiev Polytechnical Institute), 252056, Kiev, Ukraine

    A. A. Snarskii & K. V. Slipchenko

  2. Nauka-Service, 103473, Moscow, Russia

    I. V. Bezsudnov

Authors
  1. A. A. Snarskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. V. Slipchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. V. Bezsudnov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Zh. Éksp. Teor. Fiz. 113, 1484–1490 (April 1998)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Snarskii, A.A., Slipchenko, K.V. & Bezsudnov, I.V. Reciprocity relations for the effective electrical conductivity of randomly inhomogeneous media in the fractal regime. J. Exp. Theor. Phys. 86, 811–814 (1998). https://doi.org/10.1134/1.558543

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.558543

Keywords

Search

Navigation