Kardar-Parisi-Zhang universality class for the critical dynamics of reaction-diffusion fronts

Abstract

We have studied front dynamics for the discrete $A+A\leftrightarrow A$ reaction-diffusion system, which in the continuum is described by the (stochastic) Fisher-Kolmogorov-Petrovsky-Piscunov equation. We have revisited this discrete model in two space dimensions by means of extensive numerical simulations and an improved analysis of the time evolution of the interface separating the stable and unstable phases. In particular, we have measured the full set of critical exponents which characterize the spatio-temporal fluctuations of such front for different lattice sizes, focusing mainly in the front width and correlation length. These exponents are in very good agreement with those computed in [E. Moro, Phys. Rev. Lett. 87, 238303 (2001)] and correspond to those of the Kardar-Parisi-Zhang (KPZ) universality class for one-dimensional interfaces. Furthermore, we have studied the one-point statistics and the covariance of rescaled front fluctuations, which had remained thus far unexplored in the literature and allows for a further stringent test of KPZ universality.

19 pages and 9 figures

References in corpus (6)

• Genetic drift at expanding frontiers promotes gene segregation
• Growing interfaces uncover universal fluctuations behind scale invariance
• The noisy edge of traveling waves
• Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension
• Statistics of circular interface fluctuations in an off-lattice Eden model
• Random geometry and the Kardar-Parisi-Zhang universality class

Cited by in corpus (11)

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• Kardar-Parisi-Zhang fluctuations in the synchronization dynamics of limit-cycle oscillators
• Surface growth on treelike lattices and the upper critical dimension of the KPZ class
• Large-scale kinetic roughening behavior of coffee-ring fronts
• Microscopic fluctuations in the spreading fronts of circular wetting liquid droplets
• Universal interface fluctuations in the contact process
• Numerical Integration of the KPZ and Related Equations on Networks: The Case of the Cayley Tree
• Effects of lattice dilution on the non-equilibrium phase transition in the stochastic Susceptible-Infectious-Recovered model
• Exponents and front fluctuations in the quenched Kardar-Parisi-Zhang universality class of one- and two- dimensional interfaces