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

Abstract

We have studied front dynamics for the discrete A + A ↔ A reactiondiffusion 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 onedimensional 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. arXiv:1910.06211v1 [cond-mat.stat-mech]

Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation

“…Notably, the universality class thus uncovered for Eq. ( 2) has been reported earlier for discrete growth models related with isotropic percolation [40][41][42]. Furthermore, we obtain it here for yet another paradigmatic continuous system related with the stochastic Korteweg-de Vries (KdV) equation with timedependent noise.…”

“…Summarizing, we have elucidated a well-defined universality class for the tensionless KPZ equation for one-dimensional interfaces that encompasses additional discrete and continuum models. The former include at least systems related to invasion percolation [40][41][42], while the latter include models related with the KdV equation, Eq. ( 5), with time-dependent noise.…”

Spreading fronts of wetting liquid droplets: microscopic simulations and universal fluctuations

“…in Ref. [42]. In view of the fact that the kinetic roughening of our kMC fronts is intrinsically anomalous (while it is standard FV type for the KPZ equation [17]) and with non-KPZ exponents, the agreement of our numerical PDF with the TW distribution for |χ| 2.5 is unexpected.…”

Spreading fronts of wetting liquid droplets: Microscopic simulations and universal fluctuations

“…In practice, Eq. ( 11) allows one to compute the correlation length at a given time t [42]. Indeed, we can define a correlation length ξ a (t ) by means of…”

“…The uncertainties of the fluctuations and the correlation functions have been calculated following the jackknife procedure [43,44]; see also Appendix B of Ref. [42] for more details.…”