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Directed avalanche processes with underlying interface dynamics.

Chun-Chung Chen1, Marcel den Nijs

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
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We developed a directed avalanche model where sandpile surfaces represent fluctuating interfaces. This model, belonging to the Kardar-Parisi-Zhang (KPZ) universality class, reveals unique scaling behaviors and finite-size corrections.

Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Avalanche phenomena are common in nature and exhibit complex dynamics.
  • The Kardar-Parisi-Zhang (KPZ) universality class describes interface growth in many systems.
  • Understanding the relationship between avalanche distributions and interface roughness is crucial.

Purpose of the Study:

  • To introduce and analyze a directed avalanche model based on a slowly unloading sandbox.
  • To investigate the connection between avalanche critical exponents and interface roughness exponents within the KPZ universality class.
  • To examine the impact of avalanche dynamics on KPZ scaling behavior and finite-size corrections.

Main Methods:

  • Development of a directed avalanche model simulating a slowly unloading sandbox.

Related Experiment Videos

  • Interpretation of stable sand surfaces as world sheets of fluctuating interfaces.
  • Formulation of relations between avalanche and interface critical exponents.
  • Numerical analysis using Monte Carlo simulations to study scaling exponents and finite-size effects.

    • Main Results:

    • The interface growth dynamics were found to belong to the KPZ universality class.
    • Numerical values of avalanche exponents closely approximated conventional KPZ values but showed distinct differences.
    • Avalanche-correlated sampling did not alter the scaling exponents of KPZ interfaces.
    • Previous avalanche traces caused significant finite-size corrections to scaling, indicating slow convergence.

    Conclusions:

    • The study establishes a link between avalanche distributions and KPZ interface dynamics.
    • Finite-size corrections in this avalanche model are substantial and intrinsic to the dynamics.
    • The findings offer insights into complex systems exhibiting both avalanche behavior and interface growth.