Fluctuation and relaxation properties of pulled fronts: a possible scenario for non-Kardar-Parisi-Zhang behavior

Abstract

We argue that while fluctuating fronts propagating into an unstable state should be in the standard KPZ universality class when they are {\em pushed}, they should not when they are {\em pulled}: The universal $1/t$ velocity relaxation of deterministic pulled fronts makes it unlikely that the KPZ equation is the appropriate effective long-wavelength low-frequency theory in this regime. Simulations in 2$D$ confirm the proposed scenario, and yield exponents $β\approx 0.29\pm 0.01$, $ζ\approx 0.40\pm 0.02$ for fluctuating pulled fronts, instead of the KPZ values $β=1/3$, $ζ= 1/2$. Our value of $β$ is consistent with an earlier result of Riordan {\em et al.}