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Bethe lattice representation for sandpiles.

O Sotolongo-Costa1, A Vazquez, J C Antoranz

  • 1Departamento de Física Teórica, Faculdad de Física, Universidad de La Habana, Havana 10400, Cuba.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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Sandpile avalanches are modeled using percolation on a Bethe lattice, offering a better match to experimental data than cellular automata. This approach reconciles discrepancies and explains critical behavior through percolation properties.

Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Sandpile avalanches exhibit complex dynamics.
  • Previous models, like cellular automata, have limitations in accurately reproducing experimental avalanche characteristics.

Purpose of the Study:

  • To develop a more accurate model for sandpile avalanches.
  • To reconcile discrepancies in experimental findings across different studies.
  • To elucidate the critical behavior of sandpile avalanches.

Main Methods:

  • Modeling sandpile avalanches as a percolation process on a Bethe lattice.
  • Incorporating a feedback mechanism into the percolation model.
  • Analyzing the frequency spectrum and probability distribution of simulated avalanches.

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Main Results:

  • The Bethe lattice percolation model with feedback closely matches experimental frequency spectra and probability distributions.
  • This model successfully reconciles apparent discrepancies between different experimental studies.
  • The critical behavior of sandpile avalanches is effectively described by the critical properties of percolation.

Conclusions:

  • Percolation on a Bethe lattice with feedback provides a superior framework for understanding sandpile avalanches.
  • The model offers a unified explanation for experimental observations.
  • Critical phenomena in sandpiles are intrinsically linked to percolation theory.