Finite-size electrical resistivity and resistance in fractals

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Abstract
It is shown that, from an ansatz recently proposed by Dekeyser et al (1987) for anomalous diffusion and electrical resistance in fractals, one can derive predictions for the relation between intensive (resistivity) and extensive (resistance) quantities in these structures, which differ from the usually assumed forms. Numerical predictions for the ratio of finite-size resistance to resistivity in percolation clusters in space dimensions 2<or=d<or=6 are made, which are amenable to testing via, e.g., Monte Carlo simulations.