Incorporating variability into an approximation formula for bond percolation thresholds of planar periodic lattices.
Approximation formulas to predict values for bond percolation thresholds of periodic graphs make use of certain features of lattice graphs such as dimension and average degree. We show that a relationship exists between the average and second-moment of the degree of a graph and the average degree of its line graph. Using this relationship together with the well-known bond-to-site transformation between the bond percolation model on a graph and the site percolation model on its line graph, we create a new approximation formula that improves the accuracy of bond percolation threshold predictions.
Wierman
John C
JC
Department of Applied Mathematics and Statistics, 302 Whitehead Hall, Johns Hopkins University, Baltimore, Maryland 21218, USA.
Naor
Dora Passen
DP
Smalletz
Jonathan
J