Energy constrained sandpile models

Abstract

We study two driven dynamical systems with conserved energy. The two automata contain the basic dynamical rules of the Bak, Tang and Wiesenfeld sandpile model. In addition a global constraint on the energy contained in the lattice is imposed. In the limit of an infinitely slow driving of the system, the conserved energy $E$ becomes the only parameter governing the dynamical behavior of the system. Both models show scale free behavior at a critical value $E_c$ of the fixed energy. The scaling with respect to the relevant scaling field points out that the developing of critical correlations is in a different universality class than self-organized critical sandpiles. Despite this difference, the activity (avalanche) probability distributions appear to coincide with the one of the standard self-organized critical sandpile.

4 pages including 3 figures

References in corpus (4)

• Universality in Sandpile Models
• Order Parameter and Scaling Fields in Self-Organized Criticality
• Numerical Determination of the Avalanche Exponents of the Bak-Tang-Wiesenfeld Model
• Large scale simulations of the Zhang sandpile model

Cited by in corpus (14)

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• Critical behavior of a one-dimensional fixed-energy stochastic sandpile
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• Sandpiles with height restrictions
• The Oslo model, hyperuniformity, and the quenched Edwards-Wilkinson model
• Short period attractors and non-ergodic behavior in the deterministic fixed energy sandpile model
• N-Site approximations and CAM analysis for a stochastic sandpile
• Self-organized Criticality and Absorbing States: Lessons from the Ising Model
• Critical Behavior of Sandpile Models with Sticky Grains
• Steady State and Relaxation Spectrum of the Oslo Rice-pile
• Probability distribution of residence-times of grains in sandpile models
• Abrupt transition in a sandpile model
• Conserved sandpile with a variable height restriction