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Related Experiment Videos

Exact phase diagram for an asymmetric avalanche process.

V B Priezzhev1, E V Ivashkevich, A M Povolotsky

  • 1Bogoliubov Laboratory of Theoretical Physics, J. I. N. R., Dubna 141980, Russia.

Physical Review Letters
|August 11, 2001
PubMed
Summary

This study analyzes particle flow in an asymmetric avalanche process, revealing a transition from intermittent to continuous flow as particle density increases. The average velocity diverges at a critical density, with the exponent depending on toppling rules.

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Area of Science:

  • Statistical physics
  • Complex systems
  • Non-equilibrium dynamics

Background:

  • Avalanche processes are fundamental in various complex systems, from sandpiles to neural networks.
  • Understanding the dynamics of particle flow, especially in asymmetric systems, is crucial for modeling emergent behaviors.
  • Previous studies often relied on simulations; exact analytical solutions are less common for such systems.

Purpose of the Study:

  • To derive exact results for an asymmetric avalanche process on a ring.
  • To investigate the transition in particle flow behavior as a function of particle density and toppling probabilities.
  • To determine the critical exponent governing the divergence of average velocity.

Main Methods:

  • Utilizing the Bethe ansatz method for exact solutions.

Related Experiment Videos

  • Employing an iterative procedure based on detailed balance.
  • Deriving the average velocity (v) as a function of toppling probabilities and particle density (rho).

    • Main Results:

    • A transition from intermittent to continuous particle flow is observed as rho increases.
    • The average velocity (v) diverges at a critical particle density (rho(c)) with exponent alpha.
    • The exact phase diagram of the transition is determined.
    • The critical exponent alpha is found to be dependent on the specific toppling rules.

    Conclusions:

    • The study provides an exact analytical solution for an asymmetric avalanche process on a ring.
    • The findings elucidate the critical behavior and phase transitions in non-equilibrium systems.
    • The dependence of the critical exponent on toppling rules highlights the sensitivity of system dynamics to local interactions.