Relation between Effective Conductivity and Susceptibility of Two -- Component Rhombic Checkerboard

Details Relation between Effective Conductivity and Susceptibility of Two -- Component Rhombic Checkerboard Relation between Effective Conductivity and Susceptibility of Two -- Component Rhombic Checkerboard

2002-06-23

arxiv.org/abs/cond-mat/0206434v2

Physics

Condensed Matter

Materials Science

11 pages, 2 figures

Scientific paper

10.1088/0305-4470/36/19/311

The heterogeneity of composite leads to the extra charge concentration at the boundaries of different phases that results essentially nonzero effective electric susceptability. The relation between tensors of effective electric susceptability $\hat\chi_{ef}$ and effective conductivity $\hat\sigma_{ef}$ of the infinite two--dimensional two--component regular composite with rhombic cells structure has been established. The degrees of electric field singularity at corner points of cells are found by constructing the integral equation for the effective conductivity problem. The limits of weak and strong contrast of partial conductivities $\sigma_1,\sigma_2$ are considered. The results are valid for thin films and cylindrical samples.

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