Growth rate distribution of NH_4Cl dendrite and its scaling structure

Abstract

Scaling structure of the growth rate distribution on the interface of a dendritic pattern is investigated. The distribution is evaluated for an $\mathrm{N}{\mathrm{H}}_4\mathrm{Cl}$ 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.

5 pages, 6 figures

References in corpus (3)

• Multifractal Structure of the Harmonic Measure of Diffusion Limited Aggregates
• Scaling exponent of the maximum growth probability in diffusion-limited aggregation
• Dendritic side-branching with anisotropic viscous fingering

Cited by in corpus (1)

• Multifractal Distribution of Dendrite on One-dimensional Support