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Dynamical real space renormalization group applied to sandpile models.

E V Ivashkevich1, A M Povolotsky, A Vespignani

  • 1Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna 141980, Russia.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

This study introduces a general framework for analyzing self-organized critical sandpile models using a dynamically driven renormalization group. It details the branching nature of sandpile avalanches and their critical behavior.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Dynamical Systems

Background:

  • Self-organized criticality (SOC) describes systems that naturally evolve to a critical state.
  • Sandpile models are canonical examples used to study SOC phenomena.
  • Standard renormalization group methods require adaptation for nonequilibrium dynamical systems.

Purpose of the Study:

  • To formulate a general framework for renormalization group analysis of self-organized critical sandpile models.
  • To describe the boundary and bulk critical behavior of these models.
  • To provide a detailed description of sandpile avalanche branching.

Main Methods:

  • Development of a dynamically driven renormalization group.
  • Incorporation of feedback relations from stationarity conditions.

Related Experiment Videos

  • Application of generating functions from branching processes.

    • Main Results:

    • A general framework for renormalization group analysis of sandpile models is established.
    • The boundary and bulk critical behavior of sandpile models are described.
    • The branching nature of sandpile avalanches is characterized using generating functions.

    Conclusions:

    • The dynamically driven renormalization group provides a suitable method for analyzing critical phenomena in sandpile models.
    • Understanding avalanche branching is key to characterizing the critical behavior of these complex systems.