Dissipative stochastic sandpile model on small-world networks: Properties of nondissipative and dissipative avalanches
Abstract
A dissipative stochastic sandpile model is constructed and studied on small-world networks in one and two dimensions with different shortcut densities ϕ , where ϕ =0 represents regular lattice and ϕ =1 represents random network. The effect of dimension, network topology, and specific dissipation mode (bulk or boundary) on the the steady-state critical properties of nondissipative and dissipative avalanches along with all avalanches are analyzed. Though the distributions of all avalanches and nondissipative avalanches display stochastic scaling at ϕ =0 and mean-field scaling at ϕ =1 , the dissipative avalanches display nontrivial critical properties at ϕ =0 and 1 in both one and two dimensions. In the small-world regime (2-12≤ϕ ≤0.1 ) , the size distributions of different types of avalanches are found to exhibit more than one power-law scaling with different scaling exponents around a crossover toppling size sc. Stochastic scaling is found to occur for s <sc and the mean-field scaling is found to occur for s >sc . As different scaling forms are found to coexist in a single probability distribution, a coexistence scaling theory on small world network is developed and numerically verified.
- Publication:
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Physical Review E
- Pub Date:
- December 2016
- DOI:
- 10.1103/PhysRevE.94.062138
- arXiv:
- arXiv:1612.06662
- Bibcode:
- 2016PhRvE..94f2138B
- Keywords:
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- Condensed Matter - Statistical Mechanics
- E-Print:
- 8 pages, 7 figures, accepted for publication in Physical Review E