The Abelian Sandpile Model is a cellular automaton whose discrete dynamics reaches an out-of-equilibrium steady state resem- bling avalanches in piles of sand. The fundamental moves defining the dynamics are encoded by the toppling rules. The transition monoid corresponding to this dynamics in the set of stable configurations is abelian, a property which seems at the basis of our understanding of the model. By including also antitoppling rules, we introduce and in- vestigate a larger monoid, which is not abelian anymore. We prove a number of algebraic properties of this monoid, and describe their prac- tical implications on the emerging structures of the model.

Multiple and inverse topplings in the Abelian Sandpile Model / S. Caracciolo, G. Paoletti, A. Sportiello. - In: THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS. - ISSN 1951-6355. - 212:1(2012), pp. 23-44.

Multiple and inverse topplings in the Abelian Sandpile Model

S. Caracciolo
Primo
;
A. Sportiello
Ultimo
2012

Abstract

The Abelian Sandpile Model is a cellular automaton whose discrete dynamics reaches an out-of-equilibrium steady state resem- bling avalanches in piles of sand. The fundamental moves defining the dynamics are encoded by the toppling rules. The transition monoid corresponding to this dynamics in the set of stable configurations is abelian, a property which seems at the basis of our understanding of the model. By including also antitoppling rules, we introduce and in- vestigate a larger monoid, which is not abelian anymore. We prove a number of algebraic properties of this monoid, and describe their prac- tical implications on the emerging structures of the model.
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
2012
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/205369
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