Statistics of interfacial fluctuations of radially growing clusters

TL;DR

This paper investigates the statistical properties of radially growing interfaces using stochastic growth equations, revealing how fast growth and dilution influence correlation, roughening, and universality in surface dynamics.

Contribution

It introduces a formalism for analyzing fluctuating radially growing interfaces and identifies the role of dilution in restoring universality and affecting surface roughness.

Findings

Dilution erases initial condition memory and attenuates instabilities.

Fast growth leads to rapid roughening and scale-dependent fractality.

Radial Eden model likely belongs to a dilution-free universality class.

Abstract

The dynamics of fluctuating radially growing interfaces is approached using the formalism of stochastic growth equations on growing domains. This framework reveals a number of dynamic features arising during surface growth. For fast growth, dilution, which spatially reorders the incoming matter, is responsible for the transmission of correlations. Its effects include the erasing of memory with respect to the initial condition, a partial attenuation of geometrically originated instabilities, and the restoring of universality in some special cases in which the critical exponents depend on the parameters of the equation of motion. In this sense, dilution rends the dynamics more similar to the usual one of planar systems. This fast growth regime is also characterized by the spatial decorrelation of the interface, which in the case of radially growing interfaces naturally originates rapid roughening and scale dependent fractality, and suggests the advent of a self-similar fractal dimension. The center of mass fluctuations of growing clusters are also studied, and our analysis suggests the possible non-applicability of usual scalings to the long range surface fluctuations of the radial Eden model. In fact, our study points to the fact that this model belongs to a dilution-free universality class.