Expansion and Contraction of Avalanches in 2D Abelian Sandpile

Abstract

We present a detailed analysis of large scale simulations of avalanches in the 2D Abelian sandpile model. We compare statistical properties of two different decompositions of avalanches into clusters of topplings and waves of topplings. Auxiliary critical exponents are introduced and the existence of the exponent governing the contraction of avalanches claimed in our previous work [Priezzhev et al, PRL 76,2093 (1996)] is confirmed. We also give more elaborated argumentation for the exact values of the exponents characterizing the statistics of waves.

7 pages, 4 figures

References in corpus (2)

• Numerical Determination of the Avalanche Exponents of the Bak-Tang-Wiesenfeld Model
• Avalanches and Waves in the Abelian Sandpile Model

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• Quenched noise and over-active sites in sandpile dynamics
• From waves to avalanches: two different mechanisms of sandpile dynamics
• Avalanche frontiers in dissipative abelian sandpile model as off-critical SLE(2)
• Abelian Sandpile Model on the Honeycomb Lattice
• Bak-Tang-Wiesenfeld Model in the Finite Range Random Link Lattice
• Some Properties of Sandpile Models as Prototype of Self-Organized Critical Systems
• Sandpile probabilities on triangular and hexagonal lattices
• Natural Measures on Polyominoes Induced by the Abelian Sandpile Model