Goh K-I, Lee D-S, Kahng B, Kim D
School of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea.
Phys Rev Lett. 2003 Oct 3;91(14):148701. doi: 10.1103/PhysRevLett.91.148701. Epub 2003 Oct 1.
We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on scale-free (SF) networks, where the threshold height of each node is distributed heterogeneously, given as its own degree. We find that the avalanche size distribution follows a power law with an exponent tau. Applying the theory of the multiplicative branching process, we obtain the exponent tau and the dynamic exponent z as a function of the degree exponent gamma of SF networks as tau=gamma divided by (gamma-1) and z=(gamma-1) divided by (gamma-2) in the range 2<gamma<3 and the mean-field values tau=1.5 and z=2.0 for gamma>3, with a logarithmic correction at gamma=3. The analytic solution supports our numerical simulation results. We also consider the case of a uniform threshold, finding that the two exponents reduce to the mean-field ones.
我们研究了无标度（SF）网络上Bak-Tang-Wiesenfeld沙堆模型的雪崩动力学，其中每个节点的阈值高度呈非均匀分布，由其自身的度给出。我们发现雪崩规模分布遵循幂律，指数为τ。应用乘法分支过程理论，我们得到指数τ和动力学指数z作为SF网络度指数γ的函数，在2<γ<3范围内，τ = γ / (γ - 1)且z = (γ - 1) / (γ - 2)，对于γ>3，τ = 1.5且z = 2.0为平均场值，在γ = 3处有对数修正。解析解支持了我们的数值模拟结果。我们还考虑了均匀阈值的情况，发现这两个指数简化为平均场指数。
