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

TL;DR

This study investigates the scale-invariant fluctuations of circular interfaces in an off-lattice Eden model within the KPZ universality class, revealing both universal behaviors and unique finite-time correction properties through numerical analysis.

Contribution

It provides the first detailed numerical analysis of temporal correlations and persistence in off-lattice Eden model interfaces, confirming universality and identifying novel finite-time correction decay rates.

Findings

Good agreement with experimental results on turbulent liquid crystals.

Finite-time corrections in cumulants decay as t^{-2/3}, differing from previous cases.

Universal scaling behaviors are confirmed despite some dissimilarities.

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.