2003/07/20 by Mihail N. Popescu, M. N. Popescu, H. G. E. Hentschel +2
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.69.061403
6 pages, 4 figures, submitted to Phys. Rev. E
arxiv created 2003/07/20 · openalex publication_date 2004/06/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 [\ensuremath-\ensuremathπ,\ensuremathπ) such that the angular width \ensuremathσ of the peak defines the ``strength'' of anisotropy \ensuremath\varkappa=\ensuremathσ^\ensuremath-1 along any of the m chosen directions. The two parameters (m,\ensuremath\varkappa) map out a parameter space of perturbations that allows a continuous transition from DLA (for small enough \ensuremath\varkappa) to m needlelike fingers as \ensuremath\varkappa\ensuremath→\ensuremath∞. We show that at fixed m the effective fractal dimension of the clusters D(m,\ensuremath\varkappa) obtained from mass-radius scaling decreases with increasing \ensuremath\varkappa from DDLA\ensuremath≃1.71 to a value bounded from below by Dmin=(3)/(2). Scaling arguments suggest a specific form for the dependence of the fractal dimension D(m,\ensuremath\varkappa) on \ensuremath\varkappa for large \ensuremath\varkappa which compares favorably with numerical results.