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Energy constrained sandpile models

Alessandro Chessa·Enzo Marinari·Alessandro Vespignani
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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.

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Alessandro Chessa, Enzo Marinari, Alessandro Vespignani. 1997-12-11. Energy constrained sandpile models. https://doi.org/10.1103/physrevlett.80.4217

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