A new conjecture extends the GM law for percolation thresholds to dynamical situations

摘要

The universal law for percolation thresholds proposed by Galam and Mauger(GM) is found to apply also to dynamical situations. This law depends solely ontwo variables, the space dimension d and a coordinance numberq. For regularlattices, q reduces to the usual coordination number while for anisotropiclattices it is an effective coordination number. For dynamical percolation weconjecture that the law is still valid if we use the number q_2 of secondnearest neighbors instead of q. This conjecture is checked for the dynamicepidemic model which considers the percolation phenomenon in a mobiledisordered system. The agreement is good.