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Local rigidity in sandpile models.

S Ciliberti1, G Caldarelli, V Loreto

  • 1INFM UdR Roma1 and La Sapienza University, Physics Department, P.le A. Moro 5, 00185 Rome, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
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Local rigidity in sandpile systems is defined and analyzed. Researchers found that finite rigidity values approach infinity at large scales, distinguishing sandpile-like from diffusive systems.

Area of Science:

  • Complex systems
  • Statistical physics
  • Dynamical systems

Background:

  • Sandpile models are used to study self-organized criticality.
  • Local rigidity is a key parameter in understanding system behavior.
  • Distinguishing sandpile-like from diffusive systems is an ongoing challenge.

Purpose of the Study:

  • To investigate the role and behavior of local rigidity in sandpile systems.
  • To define local rigidity as the ratio of critical energy to external perturbation amplitude.
  • To determine if local rigidity can differentiate between sandpile-like and diffusive systems.

Main Methods:

  • Utilizing the dynamically driven renormalization group framework for analytical calculations.
  • Defining and analyzing local rigidity within a generalized sandpile model.

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  • Conducting numerical simulations to validate analytical findings.

    • Main Results:

    • Any finite local rigidity value in generalized sandpile models renormalizes to infinity at the fixed point (large scales).
    • The fixed-point value of rigidity provides a clear distinction between sandpile-like and diffusive systems.
    • Analytical results are supported by numerical simulations.

    Conclusions:

    • Local rigidity plays a crucial role in characterizing sandpile systems.
    • The concept of local rigidity, especially its infinite fixed-point value, offers a robust method for system classification.
    • This work clarifies the fundamental differences between sandpile-like and diffusive behaviors.