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Anisotropic diffusion-limited aggregation.

M N Popescu1, H G E Hentschel, F Family

  • 1Max-Planck-Institut für Metallforschung, Heisenbergstrasse 3, D-70569 Stuttgart, Germany. popescu@mf.mpg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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Anisotropic perturbations in diffusion-limited aggregation (DLA) were studied using conformal mappings. Increasing anisotropy transforms DLA clusters into needle-like structures, reducing their fractal dimension.

Area of Science:

  • Complex Systems
  • Statistical Physics
  • Fractal Geometry

Background:

  • Diffusion-Limited Aggregation (DLA) is a fundamental model for pattern formation.
  • Anisotropic growth can lead to complex, finger-like structures.

Purpose of the Study:

  • To investigate the impact of anisotropic perturbations on DLA in two dimensions.
  • To characterize the transition from isotropic DLA to anisotropic, multi-fingered growth.

Main Methods:

  • Utilized stochastic conformal mappings to model growth probability.
  • Mapped preferred growth directions to a distribution on a unit circle.
  • Introduced anisotropy strength parameter kappa based on angular width sigma.

Main Results:

Related Experiment Videos

  • Demonstrated a continuous transition from DLA to m needle-like fingers with increasing anisotropy (kappa).
  • Observed a decrease in the effective fractal dimension D(m,kappa) with increasing kappa, from ~1.71 for DLA to a lower bound of 3/2.
  • Scaling arguments predicted the fractal dimension's dependence on kappa for large values, aligning with numerical results.

Conclusions:

  • Anisotropy significantly alters DLA cluster morphology and fractal dimension.
  • The parameter space (m,kappa) provides a framework for studying anisotropic growth transitions.