Anisotropic diffusion-limited aggregation

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 69; no. 6 Pt 1; p. 061403
• Main Authors: Popescu, M N, Hentschel, H G E, Family, F
• Format: Journal Article
• Language: English
• Published: United States 01-06-2004
• ISSN: 1539-3755; 1550-2376
• DOI: 10.1103/PhysRevE.69.061403

Using stochastic conformal mappings, we study the effects of anisotropic perturbations on diffusion-limited aggregation (DLA) in two dimensions. The harmonic measure of the growth probability for DLA can be conformally mapped onto a constant measure on a unit circle. Here we map m preferred directions for growth to a distribution on the unit circle, which is a periodic function with m peaks in [-pi,pi) such that the angular width sigma of the peak defines the "strength" of anisotropy kappa= sigma(-1) along any of the m chosen directions. The two parameters (m,kappa) map out a parameter space of perturbations that allows a continuous transition from DLA (for small enough kappa ) to m needlelike fingers as kappa--> infinity. We show that at fixed m the effective fractal dimension of the clusters D(m,kappa) obtained from mass-radius scaling decreases with increasing kappa from D(DLA) approximately 1.71 to a value bounded from below by D(min) = 3 / 2. Scaling arguments suggest a specific form for the dependence of the fractal dimension D(m,kappa) on kappa for large kappa which compares favorably with numerical results.