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Diffusion-limited aggregation with power-law pinning.

H G E Hentschel1, M N Popescu, F Family

  • 1Department of Physics, Emory University, Atlanta, Georgia 30322, USA. phshgeh@physics.emory.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2004
PubMed
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This study explores Laplacian growth patterns using stochastic conformal mapping. Results show distinct fractal dimensions based on growth thresholds, revealing a pinning transition at gamma=1/2.

Area of Science:

  • Complex Systems
  • Statistical Physics
  • Fractal Geometry

Background:

  • Laplacian growth models fractal patterns in various physical phenomena.
  • Diffusion Limited Aggregation (DLA) is a key model with a specific universality class.
  • Understanding growth dynamics and pattern formation is crucial in complex systems.

Purpose of the Study:

  • Investigate Laplacian growth with power-law decaying thresholds.
  • Analyze how varying growth thresholds affect pattern universality and fractal dimension.
  • Identify critical transitions in growth behavior, such as pinning transitions.

Main Methods:

  • Employ stochastic conformal mapping techniques.
  • Utilize multifractal analysis to characterize growth patterns.

Related Experiment Videos

  • Study the impact of a power-law decaying threshold, R(-gamma)(N), on cluster growth.

    • Main Results:

    • For gamma > 1, growth patterns align with Diffusion Limited Aggregation (DLA) universality.
    • For gamma < 1, patterns exhibit a lower fractal dimension (D(gamma)) due to enhanced tip growth.
    • A pinning transition is identified at gamma = 1/2, deviating from DLA multifractal spectrum predictions.

    Conclusions:

    • The study establishes analytic expressions for fractal dimension D(gamma) near DLA universality breakdown and the pinning transition.
    • The findings reveal a transition to one-dimensional line-like growth at the pinning transition.
    • Laplacian growth dynamics are sensitive to threshold parameters, leading to diverse fractal behaviors.