Angular gaps in radial diffusion-limited aggregation: two fractal dimensions and nontransient deviations from linear...

Area of Science:

• Physics
• Materials Science
• Complex Systems

Background:

• Diffusion-limited aggregation (DLA) is a fundamental model for pattern formation.
• Off-lattice DLA allows for more realistic growth simulations compared to lattice-based models.
• Understanding the geometry of DLA clusters, particularly angular distributions, is crucial for characterizing their properties.

Purpose of the Study:

• To investigate the distribution of angular gaps between branches in off-lattice radial diffusion-limited aggregation.
• To determine how this distribution scales with cluster size (M).
• To identify the asymptotic fractal dimension and effective dimensions governing the growth patterns.

Main Methods:

• Simulations of off-lattice radial diffusion-limited aggregation were performed.
• Angular gaps between neighboring branches were systematically measured.
• The distribution of these gaps was analyzed as a function of cluster size (M) and rescaled.

Main Results:

• The distribution of angular gaps approaches a size-independent limit upon suitable rescaling.
• A power-law distribution corresponding to the asymptotic fractal dimension D = 1.71 is observed only for very small gaps in extremely large clusters (M > 10^6).
• Intermediate angular gaps, dominating the distribution for smaller clusters (M < 10^6), exhibit an effective dimension around 1.67, persisting even as M approaches infinity.

Conclusions:

• The fractal dimension of off-lattice radial DLA is not uniformly expressed across all angular gap sizes.
• Effective dimensions govern the behavior of dominant gap sizes in realistically sized clusters.
• The largest angular gap converges to a finite limit very slowly, with a correction term dependent on cluster size.