Journal of Experimental and Theoretical Physics

, Volume 121, Issue 2, pp 229–236 | Cite as

Effective conductivity of the rectangular and hexagonal tessellations in the plane

Order, Disorder, and Phase Transition in Condensed System

Abstract

The effective conductivity of the two-dimensional periodic polygonal tessellations in the plane is determined using the perturbation theory and numerically. A diagram technique in perturbation theory for the effective conductivity of the tesselations in the plane is established using oblique coordinates. Calculations for the three color hexagonal tesselation have been carried out. A numerical method is developed for obtaining effective conductivity with high accuracy both when the perturbation theory is applicable and when the conductivities of the tessellation components are substantially different. For small differences between the conductivities of the components, the approach of the perturbation theory agrees with the numerical results.

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© Pleiades Publishing, Inc. 2015

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsChernogolovka, Moscow oblastRussia
  2. 2.Science Center in ChernogolovkaChernogolovka, Moscow oblastRussia

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