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Unusual features of coarsening when detachment rates decrease with cluster mass.

F D A Aarão Reis1, R B Stinchcombe

  • 1Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340 Niterói RJ, Brazil. reis@if.uff.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
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This study investigates particle diffusion models where detachment rates decrease with cluster size. We found typical cluster size scales with logarithmic corrections, and small clusters can dominate system behavior.

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Studying particle diffusion, attachment, and detachment is crucial for understanding material formation and evolution.
  • Previous models often assume size-independent detachment rates, limiting their applicability to systems with complex interactions.

Purpose of the Study:

  • To investigate conserved one-dimensional models of particle diffusion with size-dependent detachment rates.
  • To analyze the scaling behavior of cluster size and density under these conditions.
  • To understand the impact of decreasing detachment rates on cluster coarsening dynamics.

Main Methods:

  • Heuristic scaling arguments based on random walk properties.
  • Master equation analysis using an independent interval approximation.

Related Experiment Videos

  • Numerical simulations to validate theoretical predictions.

    • Main Results:

    • Typical cluster size scales as (t/ln t)^z, with z=1/(k+2), where detachment rate gamma(m) ~ m^(-k).
    • Logarithmic corrections arise from asymmetric particle flux between clusters due to unbalanced detachment.
    • Small clusters (mass of order unity) can be statistically dominant for k<1, exhibiting densities of order t^(-mz(1)).
    • Cluster size distributions show a power-law decay for small masses and a skewed peak in the scaling region.

    Conclusions:

    • The model captures unusual cluster size distributions and scaling behavior driven by size-dependent detachment rates.
    • The findings are relevant for systems with strong attractive interactions and suggest potential for even faster rate decays in physical systems.
    • Theoretical predictions are robustly confirmed by simulation results.