SOLUTION OF TWO-DIMENSIONAL SELF-ORGANIZED CRITICAL MANNA MODEL
Cite this article as:
Podlazov А. V. SOLUTION OF TWO-DIMENSIONAL SELF-ORGANIZED CRITICAL MANNA MODEL. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 6, pp. 69-87. DOI: https://doi.org/10.18500/0869-6632-2013-21-6-69-87
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.
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BibTeX
author = {А. V Podlazov},
title = {SOLUTION OF TWO-DIMENSIONAL SELF-ORGANIZED CRITICAL MANNA MODEL},
year = {2013},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {21},number = {6},
url = {https://old-andjournal.sgu.ru/en/articles/solution-of-two-dimensional-self-organized-critical-manna-model},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2013-21-6-69-87},pages = {69--87},issn = {0869-6632},
keywords = {Self-organized criticality,scale invariance,power laws,finite-size scaling,sandpile models,Manna model,layers of toppling,waves of toppling.},
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. }}