Biomedical subjects

John C Wierman

Publications and source records attributed to John C Wierman.

4 recordsLinked to original sources

PubMed2005

Improved site percolation threshold universal formula for two-dimensional matching lattices.

A universal formula is proposed for predicting the site percolation threshold of two-dimensional matching lattices. The formula is slightly more accurate for these lattices than the formulas of Galam and Mauger, based on a comparison over a class of 38 lattices, and does not require two universality classes for two-dimensional lattices. The formula is constructed from the Galam-Mauger square root formula for site thresholds, by a modification which makes it consistent with the theoretical relationship between percolation thresholds of matching pairs of lattices. In the framework for evaluation of universal formulas introduced by Wierman and Naor, the formula is currently the best performing universal formula for site thresholds on this class of lattices.

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PubMed2005

Criteria for evaluation of universal formulas for percolation thresholds.

Several universal formulas that predict approximate values for percolation thresholds of all periodic graphs have been proposed in the physics and engineering literature. The existing universal formulas have been found to have substantial errors in their predictions for some lattices. This paper proposes a set of desirable criteria for universal formulas to satisfy, and investigates which criteria are satisfied by two bond threshold formulas and two site threshold formulas most cited in the literature. The analysis is limited to lattices in two dimensions.

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PubMed2002

Percolation threshold is not a decreasing function of the average coordination number.

It is commonly believed that the percolation critical probability is a monotonically decreasing function of the average coordination number for periodic lattice graphs in the same dimension. This paper provides counterexamples-a pair of planar lattices for which the bond percolation critical probabilities and average coordination numbers are in the same order, and a pair for which the site percolation critical probabilities and average coordination numbers are in the same order. These counterexamples confirm the existence of this counterintuitive phenomenon, which was observed in one case in numerical estimates by van der Marck.

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PubMed2002

Accuracy of universal formulas for percolation thresholds based on dimension and coordination number.

Recent mathematical results regarding percolation thresholds are relevant to efforts to find universal formulas for the percolation threshold. This Brief Report uses exact solutions and recent rigorous bounds for site and bond percolation thresholds to demonstrate that any universal formula based on only the dimension and the coordination number must provide estimates differing substantially from the true threshold value for some lattices.

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