2000/05/31 by М. Г. Степанов, M. G. Stepanov, Leonid Levitov +1 · 3 citations
Materials Science · Mathematics · Physics and Astronomy · #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech #nlin.CD
paper · pdf · doi:10.1103/physreve.63.061102
published as Phys. Rev. E 63, 061102 (2001) · 13 pages, 15 figures
arxiv created 2001/02/23 · openalex publication_date 2001/05/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Conformal mapping models are used to study the competition of noise and anisotropy in Laplacian growth. For this purpose, a family of models is introduced with the noise level and directional anisotropy controlled independently. Fractalization is observed in both anisotropic growth and growth with varying noise. The fractal dimension is determined from the cluster size scaling with cluster area. For isotropic growth d=1.7, at both high and low noise. For anisotropic growth with reduced noise the dimension can be as low as d=1.5 and apparently is not universal. Also, we study the fluctuations of particle areas and observe, in agreement with previous studies, that exceptionally large particles may appear during growth, leading to pathologically irregular clusters. This difficulty is circumvented by using an acceptance window for particle areas.