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Related Experiment Videos

Diffusion-limited aggregation as a Markovian process: site-sticking conditions.

B Kol1, A Aharony

  • 1Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel Aviv University, 69978 Ramat Aviv, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
Summary

This study solves cylindrical lattice diffusion-limited aggregation for site-sticking using a Markovian matrix method. The fractal dimensionality of the resulting aggregate was extrapolated to approximately 1.68.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Materials Science

Background:

  • Diffusion-limited aggregation (DLA) models pattern formation in various physical and biological systems.
  • Previous Markovian matrix methods were developed for bond-sticking DLA.
  • Site-sticking DLA presents unique challenges due to different growth dynamics.

Purpose of the Study:

  • To adapt and apply a Markovian matrix method for cylindrical lattice DLA under site-sticking conditions.
  • To accurately calculate the probabilities of front configuration changes during growth.
  • To determine the fractal dimensionality of the resulting DLA aggregates.

Main Methods:

  • Utilized a previously developed Markovian matrix method, adapted for site-sticking.
  • Calculated transition probabilities by solving the Laplace equation with proper normalization.

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  • Applied approximations involving a finite number of rows near the aggregate front.

    • Main Results:

    • Successfully implemented the Markovian matrix method for cylindrical site-sticking DLA.
    • The method accurately captures the probabilistic evolution of the aggregate front.
    • Extrapolated fractal dimensionality for the aggregate approaches a value of approximately 1.68.

    Conclusions:

    • The Markovian matrix method is effective for analyzing cylindrical site-sticking DLA.
    • The study provides a quantitative measure of the fractal nature of these aggregates.
    • The findings contribute to understanding pattern formation in DLA models.