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Avalanches and waves in the Abelian sandpile model

Journal Article · · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
 [1];  [2]
  1. Department of Physics, University of Houston, Houston, Texas 77204-5506 (United States)
  2. Center for Nonlinear Studies, MS-B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

We numerically study avalanches in the two-dimensional Abelian sandpile model in terms of a sequence of waves of toppling events. Priezzhev {ital et al.} [Phys. Rev. Lett. {bold 76}, 2093 (1996)] have recently proposed exact results for the critical exponents in this model based on the existence of a proposed scaling relation for the difference in sizes of subsequent waves, {Delta}s=s{sub k}{minus}s{sub k+1}, where the size of the previous wave s{sub k} was considered to be almost always an upper bound for the size of the next wave s{sub k+1}. Here we show that the significant contribution to {Delta}s comes from waves that violate the bound; the average {l_angle}{Delta}s(s{sub k}){r_angle} is actually negative and diverges with the system size, contradicting the proposed solution. {copyright} {ital 1997} {ital The American Physical Society}

OSTI ID:
632561
Journal Information:
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 4 Vol. 56; ISSN 1063-651X; ISSN PLEEE8
Country of Publication:
United States
Language:
English

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