Statistics of circular interface fluctuations in an off-lattice Eden model

Abstract

Scale-invariant fluctuations of growing interfaces are studied for circular clusters of an off-lattice variant of the Eden model, which belongs to the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class. Statistical properties of the height (radius) fluctuations are numerically determined and compared with the recent theoretical developments as well as the author's experimental result on growing interfaces in turbulent liquid crystal [K. A. Takeuchi and M. Sano, arXiv:1203.2530]. We focus in particular on analytically unsolved properties such as the temporal correlation function and the persistence probability in space and time. Good agreement with the experiment is found in characteristic quantities for them, which implies that the geometry-dependent universality of the KPZ class holds here as well, but otherwise a few dissimilarities are also found. Finite-time corrections in the cumulants of the distribution are also studied and shown to decay as $t^{-2/3}$ for the mean, in contrast to $t^{-1/3}$ reported for all the previously known cases.

15 pages, 10 figures; reference updated (v2,v3); minor changes in text (v3)

References in corpus (5)

• 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
• Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
• Slow decorrelations in KPZ growth

Cited by in corpus (5)

• Growing interfaces uncover universal fluctuations behind scale invariance
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections
• Eden clusters in three-dimensions and the Kardar-Parisi-Zhang universality class
• Height distributions in competitive one-dimensional Kardar-Parisi-Zhang systems