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

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          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.

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          Author and article information

          Journal
          12 January 2024
          Article
          2402.10909
          a282cac0-2af3-49b9-8e52-71f2ec2de6c0

          http://creativecommons.org/licenses/by/4.0/

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          Custom metadata
          4 pages
          physics.gen-ph

          General physics
          General physics

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