Conductivity of continuum percolating systems
We study the conductivity of a class of disordered continuum systems represented by the Swiss-cheese model, where the conducting medium is the space between randomly placed spherical holes, near the percolation threshold. This model can be mapped onto a bond percolation model where the conductance s...
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| Published in | Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 64; no. 5 Pt 2; p. 056105 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
United States
01.11.2001
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| Online Access | Get more information |
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| Summary: | We study the conductivity of a class of disordered continuum systems represented by the Swiss-cheese model, where the conducting medium is the space between randomly placed spherical holes, near the percolation threshold. This model can be mapped onto a bond percolation model where the conductance sigma of randomly occupied bonds is drawn from a probability distribution of the form sigma(-a). Employing the methods of renormalized field theory we show to arbitrary order in epsilon expansion that the critical conductivity exponent of the Swiss-cheese model is given by t(SC)(a) = (d-2)nu + max[phi,(1-a)(-1)], where d is the spatial dimension and nu and phi denote the critical exponents for the percolation correlation length and resistance, respectively. Our result confirms a conjecture that is based on the "nodes, links, and blobs" picture of percolation clusters. |
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| ISSN: | 1539-3755 |
| DOI: | 10.1103/PhysRevE.64.056105 |