Radial Restricted Solid-on-Solid and Etching Interface Growth Models

Abstract

In this work, an approach to generate radial interfaces is presented. A radial network recursively obtained is used to implement discrete model rules designed originally for the investigation in flat substrates. In order to test the proposed scheme, we have used the restricted solid-on-solid and etching models. The results indicate the KPZ conjecture is fully verified. Besides, a very good agreement between the interface radius fluctuation distribution and the GUE one was observed. The evolution of the radius agrees very well with the generalized conjecture, and the two-point correlation function exhibits a very good agreement with the covariance of Airy${}_2$ process. So, this approach can be used to investigate radial interfaces evolution for others universality classes.

6 pages, 7 figures

References in corpus (14)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Growing interfaces uncover universal fluctuations behind scale invariance
• An exact solution for the KPZ equation with flat initial conditions
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• Universal correlators and distributions as experimental signatures of 2+1 Kardar-Parisi-Zhang growth
• Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections
• 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
• Memory and universality in interface growth
• The height distribution of the KPZ equation with sharp wedge initial condition: numerical evaluations
• Universality and dependence on initial conditions in the class of the nonlinear molecular beam epitaxy equation
• Temperature effect on (2+1) experimental Kardar-Parisi-Zhang growth
• On the origins of scaling corrections in ballistic growth models
• Scaling, cumulant ratios and height distribution of the ballistic deposition in 3+1 and 4+1 dimensions

Cited by in corpus (3)

• Circular Kardar-Parisi-Zhang interfaces evolving out of the plane
• One-point height fluctuations and two-point correlators of $(2+1)$ cylindrical KPZ systems
• Numerical Simulation and the Universality Class of the KPZ Equation for Curved Substrates