2016/12/20 by Himangsu Bhaumik, S. B. Santra · 6 citations
Computer Science · Mathematics · Physics and Astronomy · #Abelian sandpile model #Criticality #Dissipation #Dissipative system #Geometry #Mathematical physics #Mathematics #Physics #Power law #Quantum mechanics #Scaling #Scaling law #Self-organized criticality #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topological and Geometric Data Analysis #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.94.062138
published in Physical review. E 94(6), 062138 (American Physical Society) · 8 pages, 7 figures, accepted for publication in Physical Review E
arxiv created 2016/12/20 · openalex publication_date 2016/12/27 · arxiv updated 2022/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.