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Modeling temporal fluctuations in avalanching systems.

M Rypdal1, K Rypdal

  • 1Department of Mathematics and Statistics, University of Tromsø, Norway.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2008
PubMed
Summary
This summary is machine-generated.

This study models sandpile avalanches using stochastic differential equations (SDEs), revealing how noise and system size affect avalanche behavior and exponents.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Dynamical Systems

Background:

  • Sandpile models are used to study self-organized criticality.
  • Classical mean-field approaches have limitations in capturing avalanche dynamics.

Purpose of the Study:

  • To develop a stochastic differential equation (SDE) model for sandpile toppling activity.
  • To generalize existing mean-field approaches using Itô's SDE framework.
  • To analyze the impact of noise and system size on avalanche exponents.

Main Methods:

  • Formulation of a generalized Itô's SDE with fractional Gaussian noise and a drift term.
  • Computation of avalanche exponents in the continuum limit as a function of the Hurst exponent.
  • Analysis of probability density functions for toppling activity fluctuations.

Main Results:

  • The stochastic model accurately predicts avalanche exponents, aligning with numerical simulations of Bak-Tang-Wiesenfeld and Zhang sandpile models.
  • Sandpiles do not exhibit universal non-Gaussian probability density functions for global activity.
  • Key differences are identified between sandpile toppling activity fluctuations and kinetic energy fluctuations in 2D turbulence.

Conclusions:

  • Stochastic differential equations provide a robust framework for modeling sandpile avalanches.
  • The model elucidates the role of noise and finite system size in governing avalanche dynamics.
  • Sandpile activity fluctuations differ fundamentally from those observed in other complex systems like 2D turbulence.