Bhaumik Himangsu, Santra S B
Department of Physics, Indian Institute of Technology Guwahati, Guwahati-781039, Assam, India.
Phys Rev E. 2016 Dec;94(6-1):062138. doi: 10.1103/PhysRevE.94.062138. Epub 2016 Dec 27.
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 s_{c}. Stochastic scaling is found to occur for s<s_{c} and the mean-field scaling is found to occur for s>s_{c}. 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.
构建了一个耗散随机沙堆模型，并在具有不同捷径密度ϕ的一维和二维小世界网络上进行研究，其中ϕ = 0表示规则晶格，ϕ = 1表示随机网络。分析了维度、网络拓扑结构和特定耗散模式（体或边界）对非耗散和耗散雪崩以及所有雪崩的稳态临界特性的影响。尽管所有雪崩和非耗散雪崩的分布在ϕ = 0时显示随机标度，在ϕ = 1时显示平均场标度，但耗散雪崩在一维和二维的ϕ = 0和1时都显示出非平凡的临界特性。在小世界区域（2^{-12}≤ϕ≤0.1）中，发现不同类型雪崩的大小分布在交叉倒塌大小s_{c}周围表现出不止一种具有不同标度指数的幂律标度。发现对于s < s_{c}发生随机标度，对于s > s_{c}发生平均场标度。由于在单个概率分布中发现不同的标度形式共存，因此发展了小世界网络上的共存标度理论并进行了数值验证。
