Kardar-Parisi-Zhang Interfaces with Inward Growth

Abstract

We study the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) interfaces growing inward from ring-shaped initial conditions, experimentally and numerically, using growth of a turbulent state in liquid-crystal electroconvection and an off-lattice Eden model, respectively. To realize the ring initial condition experimentally, we introduce a holography-based technique that allows us to design the initial condition arbitrarily. Then, we find that fluctuation properties of ingrowing circular interfaces are distinct from those for the curved or circular KPZ subclass and, instead, are characterized by the flat subclass. More precisely, we find an asymptotic approach to the Tracy-Widom distribution for the Gaussian orthogonal ensemble and the ${\text{Airy}}_1$ spatial correlation, as long as time is much shorter than the characteristic time determined by the initial curvature. Near this characteristic time, deviation from the flat KPZ subclass is found, which can be explained in terms of the correlation length and the circumference. Our results indicate that the sign of the initial curvature has a crucial role in determining the universal distribution and correlation functions of the KPZ class.

6 pages, 4 figures

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• Geometry dependence in linear interface growth
• When fast and slow interfaces grow together: connection to the half-space problem of the Kardar-Parisi-Zhang class
• Kardar-Parisi-Zhang growth on one-dimensional decreasing substrates
• Direct Evidence for Universal Statistics of Stationary Kardar-Parisi-Zhang Interfaces
• Kardar-Parisi-Zhang Interfaces with Curved Initial Shapes and Variational Formula
• Circular Kardar-Parisi-Zhang interfaces evolving out of the plane
• Transition between chaotic and stochastic universality classes of kinetic roughening
• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Stochastic growth in time dependent environments
• Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation
• KPZ fluctuations in finite volume
• Surface growth on treelike lattices and the upper critical dimension of the KPZ class
• Initial perturbation matters: implications of geometry-dependent universal Kardar-Parisi-Zhang statistics for spatiotemporal chaos
• The role of the non-linearity in controlling the surface roughness in the one-dimensional Kardar--Parisi--Zhang growth process
• The Two Scaling Regimes of the Thermodynamic Uncertainty Relation for the KPZ-Equation
• Height distributions in interface growth: The role of the averaging process