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

TL;DR

This paper extends the universal GM law for percolation thresholds to dynamical systems, proposing a conjecture that replaces the coordination number with the second nearest neighbors, and confirms its validity through a dynamic epidemic model.

Contribution

It introduces a new conjecture that adapts the GM law for dynamical percolation using second nearest neighbors, verified in a mobile epidemic model.

Findings

The GM law applies to dynamical percolation with a modified variable.

The conjecture shows good agreement in a mobile epidemic system.

The approach generalizes percolation threshold predictions to dynamic scenarios.

Abstract

The universal law for percolation thresholds proposed by Galam and Mauger (GM) is found to apply also to dynamical situations. This law depends solely on two variables, the space dimension d and a coordinance numberq. For regular lattices, q reduces to the usual coordination number while for anisotropic lattices it is an effective coordination number. For dynamical percolation we conjecture that the law is still valid if we use the number q_2 of second nearest neighbors instead of q. This conjecture is checked for the dynamic epidemic model which considers the percolation phenomenon in a mobile disordered system. The agreement is good.