Nonuniversality and the role of tails in reaction-subdiffusion fronts

Recently there has been a certain controversy about the scaling properties of reaction-subdiffusion fronts. Some works seem to suggest that these fronts should move with constant speed, as do classical reaction-diffusion fronts, while other authors have predicted propagation failure, i.e., that the front speed tends asymptotically to zero. In the present work we confirm by Monte Carlo experiments that the two situations can actually occur depending on the way the reaction process is implemented. Also, we present a general analytical model that includes these two different behaviors as particular cases. From our analysis, we reach two main conclusions. First, the differences found in the scaling properties show the lack of universality of reaction-subdiffusion fronts. Second, we prove that, contrary to the widespread belief, the tail of the waiting time distributions is not always decisive to determine the speed of these fronts, but sometimes it plays just a marginal role in the front dynamics. © 2009 The American Physical Society.