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Persistence in cluster-cluster aggregation.

E K O Hellén1, M J Alava

  • 1Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT, Finland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
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This study explores persistence in diffusion-limited cluster aggregation. Universal persistences decay algebraically for gamma>0, while cluster persistence shows stretched exponential behavior for gamma<0, revealing two key length scales.

Area of Science:

  • Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Diffusion-limited cluster-cluster aggregation (DLCA) is a fundamental model for pattern formation.
  • Understanding the long-term behavior and stability of clusters in aggregation processes is crucial.

Purpose of the Study:

  • To investigate the concept of persistence in one-dimensional DLCA.
  • To analyze how cluster diffusion properties, dependent on size (D(s) ~ s(gamma)), influence persistence.
  • To characterize empty site, filled site, and cluster persistences.

Main Methods:

  • Theoretical analysis of one-dimensional DLCA.
  • Mathematical modeling of cluster diffusion coefficients dependent on cluster size (s).
  • Derivation of persistence probabilities and analysis of their scaling behavior.

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Main Results:

  • Universal persistences (empty site and cluster) exhibit algebraic decay with exponent 2/(2-gamma) for gamma>0.
  • For gamma<0, empty site persistence retains the algebraic decay, while cluster persistence shows stretched exponential behavior.
  • The study identifies two characteristic length scales governing the spatial distribution of persistent regions.

Conclusions:

  • Persistence in DLCA is influenced by cluster size-dependent diffusion.
  • The universality of empty site and cluster persistences is demonstrated, with distinct behaviors for positive and negative gamma exponents.
  • The findings provide insights into the long-term stability and spatial organization of aggregates in diffusion-limited processes.