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Sandpiles with height restrictions.

Ronald Dickman1, Tânia Tomé, Mário J de Oliveira

  • 1Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Caixa Postal 702, 30161-970 Belo Horizonte, MG, Brazil. dickman@fisica.ufmg.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
Summary

This study explores restricted height sandpile models, finding a continuous phase transition to an absorbing state. Critical exponents match unrestricted models, simplifying sandpile dynamics research.

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Area of Science:

  • Statistical physics
  • Complex systems
  • Computational modeling

Background:

  • Sandpile models are used to study self-organized criticality.
  • Previous models had unbounded site heights, complicating analysis.
  • Height restrictions offer a simplified yet relevant system.

Purpose of the Study:

  • Investigate stochastic sandpile models with a maximum height of two.
  • Analyze the impact of height restriction on system dynamics and phase transitions.
  • Compare critical exponents with unrestricted sandpile models.

Main Methods:

  • Developed and simulated one and two-dimensional sandpile models with height restrictions.
  • Employed cluster approximations for theoretical analysis.
  • Conducted extensive simulations to observe system behavior.

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Main Results:

  • The fixed-energy system exhibits a continuous phase transition to an absorbing state.
  • A critical particle density, zeta(c), was identified for this transition.
  • Critical exponents were found to be consistent with the unrestricted Manna sandpile.

Conclusions:

  • Height-restricted sandpile models offer a simplified framework for studying self-organized criticality.
  • The observed phase transition and critical exponents suggest universality.
  • These findings contribute to understanding complex systems with bounded states.