Growth rate distribution of NH_4Cl dendrite and its scaling structure

TL;DR

This study analyzes the growth rate distribution of NH4Cl dendrites, revealing multifractal properties and the limited impact of surface tension in large growth regions, with implications for understanding dendritic pattern formation.

Contribution

It provides a numerical analysis of the growth rate distribution of NH4Cl dendrites, highlighting multifractality and the applicability of theoretical conjectures.

Findings

Distribution exhibits multifractality

Surface tension effect is negligible in large growth regions

Fractal dimension and singularity exponents differ from diffusion-limited aggregation patterns

Abstract

Scaling structure of the growth rate distribution on the interface of a dendritic pattern is investigated. The distribution is evaluated for an ${\rm NH_4Cl}$ quasi-two-dimensional crystal by numerically solving the Laplace equation with the boundary condition taking account of the surface tension effect. It is found that the distribution has multifractality and the surface tension effect is almost ineffective in the unscreened large growth region. The values of the minimum singular exponent and the fractal dimension are smaller than those for the diffusion-limited aggregation pattern. The Makarov's theorem, the information dimension equals one, and the Turkevich-Scher conjecture between the fractal dimension and the minimum singularity exponent hold.