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Topological estimation of percolation thresholds
 J. Stat. Mech. Theory Exp
, 2008
"... Abstract. Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount importance. For two dimensional lattice graphs, we use th ..."
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Abstract. Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount importance. For two dimensional lattice graphs, we use
Topology invariance in Percolation Thresholds
, 1998
"... An universal invariant for site and bond percolation thresholds ( pcs and pcb respectively) is proposed. The invariant writes {pcs} 1 1 as a {pcb} b = δ/d where as, ab and δ are positive constants, and d the space dimension. It is independent of the coordination number, thus exhibiting a topology in ..."
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An universal invariant for site and bond percolation thresholds ( pcs and pcb respectively) is proposed. The invariant writes {pcs} 1 1 as a {pcb} b = δ/d where as, ab and δ are positive constants, and d the space dimension. It is independent of the coordination number, thus exhibiting a topology
Universal formulas for percolation thresholds
 Phys. Rev. E
, 1996
"... A power law is postulated for both site and bond percolation thresholds. The formula writes pc = p0[(d − 1)(q − 1)] −a d b, where d is the space dimension and q the coordination number. All thresholds up to d → ∞ are found to belong to only three universality classes. For first two classes b = 0 fo ..."
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Cited by 6 (0 self)
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A power law is postulated for both site and bond percolation thresholds. The formula writes pc = p0[(d − 1)(q − 1)] −a d b, where d is the space dimension and q the coordination number. All thresholds up to d → ∞ are found to belong to only three universality classes. For first two classes b = 0
Comment on ‘Topology invariance in percolation thresholds ’ ∗
, 1998
"... In a recent article, Galam and Mauger proposed an invariant for site and bond percolation thresholds, based on known values for twenty lattices (Eur. Phys. J. B 1 (1998) 255–258). Here we give a larger list of values for more than forty lattices in two to six dimensions. The list contains examples o ..."
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In a recent article, Galam and Mauger proposed an invariant for site and bond percolation thresholds, based on known values for twenty lattices (Eur. Phys. J. B 1 (1998) 255–258). Here we give a larger list of values for more than forty lattices in two to six dimensions. The list contains examples
Tailoring Percolation Threshold by altering Glass Transition Temperature
"... ABSTRACT: Hypothetically, two substances of different Tg’s with all other properties held relatively constant will have two separate percolation thresholds. Lowering the Tg of an emulsion should theoretically reduce the percolation threshold of the polymer composite. In experiment, this theory holds ..."
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ABSTRACT: Hypothetically, two substances of different Tg’s with all other properties held relatively constant will have two separate percolation thresholds. Lowering the Tg of an emulsion should theoretically reduce the percolation threshold of the polymer composite. In experiment, this theory
Efficient Measurement of the Percolation Threshold for Fully Penetrable Discs
, 2000
"... We study the percolation threshold for fully penetrable discs by measuring the average location of the frontier for a statistically inhomogeneous distribution of fully penetrable discs. We use two different algorithms to efficiently simulate the frontier, including the continuum analogue of an algor ..."
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We study the percolation threshold for fully penetrable discs by measuring the average location of the frontier for a statistically inhomogeneous distribution of fully penetrable discs. We use two different algorithms to efficiently simulate the frontier, including the continuum analogue
Desirable Properties of Universal Formulas for Percolation Thresholds
"... Percolation models are in¯nite random graph models which exhibit phase transition behavior at critical values called percolation thresholds. Several socalled "universal formulas " that predict approximate values for percolation thresholds of all periodic graphs have been proposed in the ..."
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Percolation models are in¯nite random graph models which exhibit phase transition behavior at critical values called percolation thresholds. Several socalled "universal formulas " that predict approximate values for percolation thresholds of all periodic graphs have been proposed
Conductivity and diffusion near the percolation threshold
, 1989
"... Abstract. We consider the scaling properties of the conductivity for nonzero frequencies. We analyse the relevance of various models to descriptions of actual experimental situations. We discuss more particularly the equivalence between conduction and diffusion. In this case, we find a regime where ..."
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Abstract. We consider the scaling properties of the conductivity for nonzero frequencies. We analyse the relevance of various models to descriptions of actual experimental situations. We discuss more particularly the equivalence between conduction and diffusion. In this case, we find a regime where the conductivity is proportional to the size L of the sample, corresponding to an anomalous skin effect. This L dependence leads to a frequencydependent conductivity different from the result of Gefen, Aharony and Alexander. We finally introduce a model consisting of a twodimensional random resistor system lying on a threedimensional substrate made of capacitors. This might be relevant to describe a system of conducting particles deposited on a thin insulating substrate such as considered recently by Laibowitz and Gefen. 1.
Results 1  10
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26,246