Physics Commons^™

Crossover From Contact Propagation To Chemical Propagation In First-Passage Percolation, A. R. Kerstein, Boyd F. Edwards

All Physics Faculty Publications

On lattices whose bonds are assigned time delays from a bimodal distribution with modes at b and a≫b whose relative weights are p and 1-p, the dependence of the first-passage velocity v on p is investigated by means of scaling arguments and computations. As p increases, v exhibits a sharp rise near the percolation threshold due to a crossover from the contact-propagation regime, in which slow-bond crossings are rate limiting, to the chemical-propagation regime, in which the tortuosity of the shortest path through the fast-bond network is rate limiting. Previous analyses of criticality in the limit a/b→∞ are extended by …