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Active width at a slanted active boundary in directed percolation.

C C Chen1, H Park, M den Nijs

  • 1Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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The width of active regions in directed percolation processes diverges at the percolation threshold. This divergence is influenced by screening effects from subclusters, as confirmed by numerical data.

Area of Science:

  • Statistical Physics
  • Complex Systems
  • Phase Transitions

Background:

  • Directed percolation describes systems with quenched disorder and absorbing states.
  • Understanding critical phenomena, like the percolation threshold, is crucial in statistical physics.
  • Active moving walls introduce dynamic boundaries in these systems.

Purpose of the Study:

  • To investigate the scaling behavior of the active region width near the percolation threshold.
  • To identify the factors contributing to the divergence of the active region width.
  • To analyze the role of subclusters in the active region dynamics.

Main Methods:

  • Theoretical analysis of the directed percolation process.
  • Derivation of scaling laws for the active region width (W).

Related Experiment Videos

  • Numerical simulations to confirm the theoretical predictions.

    • Main Results:

    • The active region width W diverges at the percolation threshold p(c) as W ~ ε(-ν∥) ln(ε(0)/ε).
    • The critical exponent ν∥ = 1.734 governs the characteristic time to reach a stationary state.
    • A logarithmic factor arises from screening of independent needle-shaped subclusters.

    Conclusions:

    • The study confirms the predicted scaling behavior for the active region width.
    • Screening of subclusters is identified as the cause of the logarithmic correction.
    • The findings provide insights into the critical dynamics of directed percolation with active boundaries.