Experimental evidence on the development of scale invariance in the internal structure of self-affine aggregates

TL;DR

This paper investigates the development of scale invariance in the internal structure of self-affine aggregates by analyzing frozen structures in electrochemically formed silver patterns, revealing universality class behavior.

Contribution

It introduces a novel statistical approach analyzing frozen structures to characterize growing patterns and identify their universality class.

Findings

Frozen structures exhibit scale invariance in size distribution.

Measured exponents align with Kardar-Parisi-Zhang predictions.

Analysis applies to electrochemical silver branched patterns.

Abstract

It is shown that an alternative approach for the characterization of growing branched patterns consists of the statistical analysis of frozen structures, which cannot be modified by further growth, that arise due to competitive processes among neighbor growing structures. Scaling relationships applied to these structures provide a method to evaluate relevant exponents and to characterize growing systems into universality classes. The analysis is applied to quasi-two-dimensional electrochemically formed silver branched patterns showing that the size distribution of frozen structures exhibits scale invariance. The measured exponents, within the error bars, remind us those predicted by the Kardar-Parisi-Zhang equation.