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Morphological transition between diffusion-limited and ballistic aggregation growth patterns.

S C Ferreira1, S G Alves, A Faissal Brito

  • 1Departamento de Física, Universidade Federal Viçosa, 36571-000 Viçosa, Minas Gerais, Brazil. silviojr@ufv.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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This study explores the transition between diffusion-limited aggregation (DLA) and ballistic aggregation (BA) models using biased random walks. Findings reveal universal scaling exponents governing fractal patterns and density, independent of the bias parameter.

Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Aggregation phenomena are modeled by diffusion-limited aggregation (DLA) and ballistic aggregation (BA).
  • Understanding the transition between these models is crucial for complex system dynamics.

Purpose of the Study:

  • To investigate the transition between DLA and BA models using biased random walks.
  • To analyze fractal properties and scaling behavior of growing patterns.

Main Methods:

  • Simulated particle trajectories using biased random walks with a bias parameter (lambda).
  • Developed an efficient algorithm for simulating large clusters.
  • Evaluated mean particle density within a radial region.

Main Results:

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  • Patterns exhibit fractal behavior on small scales and homogeneity on large scales for lambda != 0.
  • Identified universal exponent gamma=0.46 for density decay, independent of lambda.
  • Determined scaling exponents beta=0.26, nu=0.61, and alpha=0.97 for asymptotic density, crossover length, and mass.

Conclusions:

  • Established scaling relations between exponents: beta=nu*gamma and beta=2*nu-alpha.
  • The study provides a unified framework for understanding aggregation models.
  • Results offer insights into the transition dynamics of fractal growth processes.