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Related Experiment Videos

Roughness of sandpile surfaces.

J G Oliveira1, J F F Mendes, G Tripathy

  • 1Departamento de Física, Universidade de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2004
PubMed
Summary

Surface roughness in self-organized criticality (SOC) models shows ambiguous scaling exponents due to nonlinear steady states. Non-SOC models lack this ambiguity, though they may exhibit intermediate crossovers that differ from true asymptotic behavior.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Dynamical Systems

Background:

  • Self-organized criticality (SOC) describes complex systems that naturally evolve to a critical state.
  • Surface roughness is a key property for characterizing the behavior of many physical systems, including sandpiles.
  • Understanding scaling exponents is crucial for distinguishing between critical and non-critical system behaviors.

Purpose of the Study:

  • To investigate and compare the surface roughness scaling exponents in one-dimensional self-organized criticality (SOC) models and their noncritical variants.
  • To resolve the ambiguity in surface roughness definitions for SOC systems.
  • To differentiate true asymptotic behavior from intermediate crossovers in non-SOC models.

Main Methods:

  • Analytical approximations were employed to study the scaling properties.

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  • Extensive numerical simulations were conducted to validate theoretical findings.
  • Comparison of surface roughness definitions in SOC and non-SOC models.

    • Main Results:

    • Two distinct definitions of surface roughness yield different asymptotic scaling exponents for SOC systems.
    • This ambiguity in SOC systems arises from the unique scaling properties of their nonlinear steady-state surfaces.
    • Non-SOC models do not exhibit this definitional ambiguity, but may show intermediate crossovers.

    Conclusions:

    • The ambiguity in surface roughness scaling for SOC models is attributed to nonlinear steady-state properties.
    • Careful distinction between asymptotic behavior and intermediate crossovers is necessary, particularly for non-SOC models.
    • The findings clarify the characterization of surface roughness in critical and non-critical complex systems.