Directed Abelian sandpile with multiple downward neighbors
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Accepted version
Published version
Author(s)
Dhar, D
Pruessner, G
Expert, P
Christensen, K
Zachariou, N
Type
Journal Article
Abstract
We study the directed Abelian sandpile model on a square lattice, with K downward neighbors
per site, K > 2. The K = 3 case is solved exactly, which extends the earlier known solution for
the K = 2 case. For K > 2, the avalanche clusters can have holes and side-branches and are thus
qualitatively different from the K = 2 case where avalanche clusters are compact. However, we find
that the critical exponents for K > 2 are identical with those for the K = 2 case, and the large
scale structure of the avalanches for K > 2 tends to the K = 2 case.
per site, K > 2. The K = 3 case is solved exactly, which extends the earlier known solution for
the K = 2 case. For K > 2, the avalanche clusters can have holes and side-branches and are thus
qualitatively different from the K = 2 case where avalanche clusters are compact. However, we find
that the critical exponents for K > 2 are identical with those for the K = 2 case, and the large
scale structure of the avalanches for K > 2 tends to the K = 2 case.
Date Issued
2016-04-08
Date Acceptance
2016-02-10
Citation
Physical Review E, 2016, 042107
ISSN
1539-3755
Publisher
American Physical Society
Journal / Book Title
Physical Review E
Volume
042107
Copyright Statement
© 2016 American Physical Society. This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
License URL
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
EP/P504953/1
Subjects
Fluids & Plasmas
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published
Article Number
042107