Effective conductivity tensor of ordered and disordered composite media: Exact relations and numerical simulations

Yakov M. Strelniker, David J. Bergman, Shlomo Havlin, Emma Mogilko, Leonid Burlachkov, Yehuda Schlesinger

Research output: Contribution to journalConference articlepeer-review

9 Scopus citations

Abstract

Generic three-dimensional (3D) exact relations were found recently (Phys. Rev. B (2002) 184416) between macroscopic or bulk effective moduli of composite systems with related microstructures which are, in general, different. As an example of possible application of these relations, a new numerical approach is proposed for simulations of composite systems with oblate inclusions: The initially anisotropic shape of the inclusions can be transformed to spherical, but the local conductivity tensor σ̂2 of the host in the initial system should be replaced by the corresponding transformed value μ̂2. We simulate large 3D networks of circuit elements in this new μ-system using relaxation, network-reduction, and other methods. The effective value of the conductivity, σ̂e, of the initial σ-system, can be found from the effective value μ̂ e of the transformed μ-system, using our exact relations. We propose to apply this approach for simulations of the phase transition in the high-Tc superconducting granular ceramics.

Original languageEnglish
Pages (from-to)291-294
Number of pages4
JournalPhysica A: Statistical Mechanics and its Applications
Volume330
Issue number1-2
DOIs
StatePublished - 1 Dec 2003
EventRandomes and Complexity - Eilat, Israel
Duration: 5 Jan 20039 Jan 2003

Bibliographical note

Funding Information:
This research was supported in part by grants from the Israel Science Foundation, US-Israel Binational Science Foundation, and the KAMEA Fellowship program of the Ministry of Absorption of the State of Israel.

Keywords

  • Composite media
  • Disordered systems
  • Percolation

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