ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Podlazov A. V. Solution of two-dimensional self-organized critical Manna model. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 6, pp. 69-87. DOI: 10.18500/0869-6632-2013-21-6-69-87

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Language: 
Russian
Heading: 
Autowaves. Self-organization
Article type: 
Article
UDC: 
519.6
DOI: 
10.18500/0869-6632-2013-21-6-69-87

Solution of two-dimensional self-organized critical Manna model

Autors: 
Podlazov Andrej Viktorovich, Keldysh Institute of Applied Mathematics (Russian Academy of Sciences)
Abstract: 

We propose a full solution for Manna model – two-dimensional conservative sandpile model with the rules of grains redistribution isotropic at the average. Indices of the probability distributions of avalanches main characteristics (size, area, perimeter, duration, topplings multiplicity) are determined for this model both from theory and from simulations. The solution bases on the spatiotemporal decomposition of avalanches described in terms of toppling layers and waves. The motion of grains is divided into directed and undirected types. The former is treated as the dynamics of active particles with some physical properties described.

Key words: 
Self-organized criticality
scale invariance
power laws
finite-size scaling
sandpile models
Manna model
layers of toppling
waves of toppling
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Received: 
27.06.2013
Accepted: 
17.12.2013
Published: 
28.02.2014
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