Expansion and contraction of avalanches in the two-dimensional Abelian sandpile

Abstract

We present a detailed analysis of large scale simulations of avalanches in the two-dimensional 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., Phys. Rev. Lett. 76, 2093 (1996)] is confirmed. We also give more elaborate argumentation for the exact values of the exponents characterizing the statistics of waves.