Conductance distributions in random resistor networks. Self-averaging and disorder lengths |
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Authors: | Rafael F Angulo Ernesto Medina |
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Institution: | (1) Coordinación de Investigación Básica, INTEVEP S.A., 1070A Caracas, Venezuela |
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Abstract: | The self-averaging properties of the conductanceg are explored in random resistor networks (RRN) with a broad distribution of bond strengthsP(g)g
–1. The RRN problem is cast in terms of simple combinations of random variables on hierarchical lattices. Distributions of equivalent conductances are estimated numerically on hierarchical lattices as a function of sizeL and the distribution tail strength parameter . For networks above the percolation threshold, convergence to a Gaussian basin is always the case, except in the limit 0. Adisorder length D is identified, beyond which the system is effectively homogeneous. This length scale diverges as Dµ–v ( is the regular percolation correlation length exponent) when the microscopic distribution of conductors is exponentially wide (0). This implies that exactly the same critical behavior can be induced by geometrical disorder and by strong bond disorder with the bond occupation probabilityp. We find that only lattices at the percolation threshold have renormalized probability distributions in aLevy-like basin. At the percolation threshold the disorder length diverges at a critical tail strength µc as µ––z withz3.2±0.1, a new exponent.Critical path analysis is used in a generalized form to give the macroscopic conductance in the case of lattices abovep
c. |
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Keywords: | Resistor networks hierarchical lattices disorder probability distributions |
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