Abstract
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 preferred directions for growth to a distribution on the unit circle, which is a periodic function with peaks in such that the angular width of the peak defines the “strength” of anisotropy along any of the chosen directions. The two parameters map out a parameter space of perturbations that allows a continuous transition from DLA (for small enough ) to needlelike fingers as . We show that at fixed the effective fractal dimension of the clusters obtained from mass-radius scaling decreases with increasing from to a value bounded from below by . Scaling arguments suggest a specific form for the dependence of the fractal dimension on for large which compares favorably with numerical results.
- Received 20 July 2003
DOI:https://doi.org/10.1103/PhysRevE.69.061403
©2004 American Physical Society