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Exchange-driven growth.

E Ben-Naim1, P L Krapivsky

  • 1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. ebn@lanl.gov

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
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Particle exchange in cluster growth leads to three outcomes: indefinite growth, finite-time gelation, or instant gelation. Cluster size distributions exhibit self-similarity, with tails depending on the exchange rate

Area of Science:

  • Statistical Physics
  • Materials Science
  • Chemical Engineering

Background:

  • Cluster growth processes are fundamental in various physical and chemical systems.
  • Understanding particle exchange dynamics is crucial for predicting system evolution.

Purpose of the Study:

  • To investigate cluster evolution driven by particle exchange.
  • To identify distinct regimes of growth and gelation based on exchange rates.
  • To analyze the resulting cluster size distributions and their scaling properties.

Main Methods:

  • Theoretical modeling of cluster growth dynamics.
  • Analysis of particle exchange rates and their influence on system evolution.
  • Derivation of cluster size distribution functions and their asymptotic behavior.

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Main Results:

  • Identified three regimes: indefinite growth, finite-time gelation, and instant gelation.
  • Demonstrated self-similar cluster size distributions in growth and finite-time gelation regimes.
  • Characterized the large-size tail of the distribution as exponential or algebraic, depending on the exchange rate homogeneity degree (nu).
  • Showed that gelation time vanishes logarithmically for finite systems in the large system size limit.

Conclusions:

  • The rate of particle exchange dictates the macroscopic behavior of cluster growth systems.
  • The theoretical framework provides insights into phenomena like coarsening in the Ising-Kawasaki model and granular layers.