Attacks and infections in percolation processes

Abstract

We discuss attacks and infections at propagating fronts of percolation processes based on the extended general epidemic process. The scaling behavior of the number of the attacked and infected sites in the long time limit at the ordinary and tricritical percolation transitions is governed by specific composite operators of the field-theoretic representation of this process. We calculate corresponding critical exponents for tricritical percolation in mean-field theory and for ordinary percolation to 1-loop order. Our results agree well with the available numerical data.

Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media

“…any contacts between infected and susceptible sites, or infections, i.e. such contacts that lead actually to an infection of the immune site [40,41]. Let us define m f and m b as the number of forward and backward attacks/infections, and [19], the other points are from simulations and have error bars much smaller than the symbols.…”

“…It was shown in [40] that these should in general satisfy power laws with new critical exponents, and it is shown…”

“…any contacts between infected and susceptible sites, or infections, i.e. such contacts that lead actually to an infection of the immune site [40,41]. Let us define m f and m b as the number of forward and backward attacks/infections, and It was shown in [40] that these should in general satisfy power laws with new critical exponents, and it is shown in [41] that a(t) = b(t) ∼ t −0.5189 (1) for OP.…”