Isotropic Conductivity of Two-Dimensional Three-Component Symmetric Composites

Abstract

The effective dc-conductivity problem of isotropic, two-dimensional (2D), three-component, symmetric, regular composites is considered. A simple cubic equation with one free parameter for ${\sigma }_e({\sigma }_1,{\sigma }_2,{\sigma }_3)$ is suggested whose solutions automatically have all the exactly known properties of that function. Numerical calculations on four different symmetric, isotropic, 2D, three-component, regular structures show a non-universal behavior of ${\sigma }_e({\sigma }_1,{\sigma }_2,{\sigma }_3)$ with an essential dependence on micro-structural details, in contrast with the analogous two-component problem. The applicability of the cubic equation to these structures is discussed. An extension of that equation to the description of other types of 2D three-component structures is suggested, including the case of random structures. Pacs: 72.15.Eb, 72.80.Tm, 61.50.Ah

8 pages (two columns), 8 figures. J. Phys. A - submitted

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