Abstract
Long square-lattice and cubic-lattice samples consisting of many layers are simulated. Within each layer, the concentration of permeable bonds is constant whereas each layer has a different concentration chosen randomly from the interval between the percolation threshold and unit concentration. The conductivity of the random resistor network corresponding to this percolation model is calculated, both parallel and perpendicular to the layers, in both two and three dimensions. For the conductivity parallel to the layers, an effective medium calculation comes within 10% of the true conductivity. For the conductivity perpendicular to the layers, percolation theory is necessary.
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Abbreviations
- G :
-
Total Conductivity in units of the conductivity of one bond
- L :
-
Length of sample in units of the length of one bond
- n :
-
Width of sample in units of the length of one bond
- N :
-
Number of layers
- p :
-
Probability that a bond conduct
- p c :
-
Percolation threshold
- R :
-
Resistivity in units of the resistivity of one bond
- t :
-
Percolation conductivity exponent
- v :
-
Percolation correlation length exponent
- ξ :
-
Correlation length in units of the length of one bond
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Hansen, A., Hinrichsen, E.L. & Stauffer, D. Percolation in layered media — A conductivity approach. Transp Porous Med 11, 45–52 (1993). https://doi.org/10.1007/BF00614634
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DOI: https://doi.org/10.1007/BF00614634