Diffusion-limited deposition with dipolar interactions: fractal dimension and multifractal structure

TL;DR

This study uses computer simulations to analyze the structure of dipole-based diffusion-limited deposits, revealing constant fractal dimension and multifractal growth probability distributions that vary with dipolar strength.

Contribution

It demonstrates that the fractal dimension remains unchanged with dipolar strength and characterizes the multifractal nature of growth probabilities in dipolar deposits.

Findings

Fractal dimension remains constant during deposition.

Growth probability distribution exhibits multifractal scaling.

Increasing dipolar strength decreases local growth exponents and information dimension.

Abstract

Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation function at a given height, the mean height of the upper surface for a given number of deposited particles and the interfacial width at a given height. Evidences are given that the fractal dimension of the deposits remains constant as the deposition proceeds, independently of the dipolar strength. These same deposits are used to obtain the growth probability measure through Monte Carlo techniques. It is found that the distribution of growth probabilities obeys multifractal scaling, i.e. it can be analyzed in terms of its $f(\alpha)$ multifractal spectrum. For low dipolar strengths, the $f(\alpha)$ spectrum is similar to that of diffusion-limited aggregation. Our results suggest that for increasing dipolar strength both the minimal local growth exponent $\alpha_{min}$ and the information dimension $D_1$ decrease, while the fractal dimension remains the same.