The one-dimensional Kardar-Parisi-Zhang and Kuramoto-Sivashinsky universality class: limit distributions

Abstract

Tracy-Widom and Baik-Rains distributions appear as universal limit distributions for height fluctuations in the one-dimensional Kardar-Parisi-Zhang (KPZ) \textit{stochastic} partial differential equation (PDE). We obtain the same universal distributions in the spatiotemporally chaotic, nonequilibrium, but statistically steady state (NESS) of the one-dimensional Kuramoto-Sivashinsky (KS) \textit{deterministic} PDE, by carrying out extensive pseudospectral direct numerical simulations to obtain the spatiotemporal evolution of the KS height profile $h(x,t)$ for different initial conditions. We establish, therefore, that the statistical properties of the 1D KS PDE in this state are in the 1D KPZ universality class.

References in corpus (26)

• Level-Spacing Distributions and the Airy Kernel
• Shape Fluctuations and Random Matrices
• The multifractal nature of turbulent energy dissipation
• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• The one-dimensional KPZ equation: an exact solution and its universality
• Growing interfaces uncover universal fluctuations behind scale invariance
• On the Numerical Evaluation of Fredholm Determinants
• Exact scaling functions for one-dimensional stationary KPZ growth
• A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
• An exact solution for the KPZ equation with flat initial conditions
• The one-dimensional KPZ equation and its universality class
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• Top eigenvalue of a random matrix: large deviations and third order phase transition
• Exact solution for the stationary Kardar-Parisi-Zhang equation
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Intermittency exponents and energy spectrum of the Burgers and KPZ equations with correlated noise
• Crossover from Growing to Stationary Interfaces in the Kardar-Parisi-Zhang Class
• A pseudo-spectral method for the Kardar-Parisi-Zhang equation
• Universal aspects of curved, flat & stationary-state Kardar-Parisi-Zhang statistics
• Turbulence and Multiscaling in the Randomly Forced Navier Stokes Equation
• Limit processes for TASEP with shocks and rarefaction fans
• Anomalous scaling and universality in hydrodynamic systems with power-law forcing
• Hydrodynamics of the Kuramoto-Sivashinsky Equation in Two Dimensions
• Some connections between the Classical Calogero-Moser model and the Log Gas
• A pseudo-spectral approach to inverse problems in interface dynamics
• Competing Universalities in Kardar-Parisi-Zhang (KPZ) Growth Models

Cited by in corpus (12)

• Transition between chaotic and stochastic universality classes of kinetic roughening
• KPZ fluctuations in finite volume
• Scaling regimes of the one-dimensional phase turbulence in the deterministic complex Ginzburg-Landau equation
• Kardar-Parisi-Zhang growth on square domains that enlarge nonlinearly in time
• Out-of-time-ordered correlator in the one-dimensional Kuramoto-Sivashinsky and Kardar-Parisi-Zhang equations
• Phase diagram and universal scaling regimes of two-dimensional exciton-polariton Bose-Einstein condensates
• Initial perturbation matters: implications of geometry-dependent universal Kardar-Parisi-Zhang statistics for spatiotemporal chaos
• GPU Methodologies for Numerical Partial Differential Equations
• One-point height fluctuations and two-point correlators of $(2+1)$ cylindrical KPZ systems
• The non-perturbative sides of the Kardar-Parisi-Zhang equation
• Mechanism underlying dynamic scaling properties observed in the contour of spreading epithelial monolayer
• The Galerkin-truncated Burgers equation: Crossover from inviscid-thermalised to Kardar-Parisi-Zhang scaling