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Generic sandpile models have directed percolation exponents.

P K Mohanty1, Deepak Dhar

  • 1Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, India.

Physical Review Letters
|September 13, 2002
PubMed
Summary
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This study explores sticky sandpile models with stochastic rules, revealing avalanche exponents match critical directed percolation clusters. Undirected models show exponents corresponding to directed percolation in a higher dimension.

Area of Science:

  • Complex systems
  • Statistical physics
  • Self-organized criticality

Background:

  • Sandpile models are crucial for understanding self-organized criticality.
  • Stochasticity and dissipation are key factors influencing system dynamics.
  • Previous models often assume ideal grain behavior.

Purpose of the Study:

  • To investigate the impact of 'sticky' grains and dissipation on sandpile model dynamics.
  • To determine the avalanche exponents in these modified sandpile systems.
  • To compare the behavior of directed and undirected sandpile models.

Main Methods:

  • Simulating sandpile models with stochastic toppling rules.
  • Incorporating a non-zero probability of no toppling due to grain stickiness.

Related Experiment Videos

  • Introducing dissipation via particle loss during toppling.
  • Analyzing avalanche size and duration distributions.

    • Main Results:

    • For models with a preferred direction, avalanche exponents align with critical directed percolation clusters.
    • For undirected models, avalanche exponents correspond to directed percolation clusters in one higher dimension.
    • The introduction of stickiness and dissipation alters the critical behavior.

    Conclusions:

    • Sticky grains and dissipation significantly modify sandpile model behavior.
    • The observed avalanche exponents provide insights into universality classes.
    • Results highlight the importance of grain properties and energy dissipation in complex systems.