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Effective conductivities of some multi-color, isotropic, regular tessellations

General Physics 2024-02-20 v1

Abstract

Algebraic expressions are found for the effective conductivities of some infinite tessellations composed of conducting square, triangular, or hexagonal tiles. A tessellation is further characterized by the number N of different colors (different tile conductivities) represented. Tiles of a color are distributed randomly, and constitute an areal fraction 1/N of the tessellation. The expressions take account of the percolation threshold associated with the tile type. This generates a series of expressions for the three-color case, that suggests this approach gives lower bounds for the true effective conductivities.

Keywords

Cite

@article{arxiv.2402.10909,
  title  = {Effective conductivities of some multi-color, isotropic, regular tessellations},
  author = {Clinton DeW. Van Siclen},
  journal= {arXiv preprint arXiv:2402.10909},
  year   = {2024}
}

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4 pages