Fluctuation and relaxation properties of pulled fronts: A scenario for nonstandard Kardar-Parisi-Zhang scaling

We argue that while fluctuating fronts propagating into an unstable state should be in the standard Kardar-Parisi-Zhang (KPZ) universality class when they are pushed, they should not when they are pulled: The lit velocity relaxation of deterministic pulled fronts makes it unlikely that the KPZ equation is their proper effective long-wavelength low-frequency theory. Simulations in 2D confirm the proposed scenario, and yield exponents beta approximate to 0.29 +/- 0.01, zeta approximate to 0.40 +/- 0.02 for fluctuating pulled fronts, instead of the (1 + 1)D KPZ values beta = 1/3, zeta = 1/2. Our value of beta is consistent with an earlier result of Riordan et al., and with a recent conjecture that the exponents are the (2 + 1)D KPZ values.