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 $\beta \approx 0.29\pm 0.01$, $\zeta \approx 0.40\pm 0.02$ for fluctuating pulled fronts, instead of the KPZ values $\beta =1/3$, $\zeta =1/2$. Our value of $\beta$ is consistent with an earlier result of Riordan {\em et al.}

Replaced with revised version

References in corpus (3)

• Shift in the velocity of a front due to a cut-off
• Subdiffusive fluctuations of "pulled" fronts with multiplicative noise
• Breakdown of the standard Perturbation Theory and Moving Boundary Approximation for "Pulled" Fronts

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