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Bulk transport properties and exponent inequalities for random resistor and flow networks. (English) Zbl 0617.60099
Authors’ abstract: The properties of random resistor and flow networks are studied as a function of the density, p, of bonds which permit transport. It is shown that percolation is sufficient for bulk transport, in the sense that the conductivity and flow capacity are bounded away from zero whenever p exceeds an appropriately defined percolation threshold.
Relations between the transport coefficients and quantities in ordinary percolation are also derived. Assuming critical scaling, these relations imply upper and lower bounds on the conductivity and flow exponents in terms of percolation exponents. The conductivity exponent upper bound so derived saturates in mean field theory.
Reviewer: G.Grimmett

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C70 Transport processes in time-dependent statistical mechanics
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
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