Cernák Jozef
Institute of Physics, P. J. Šafárik University in Košice, Jesenná 5, 04000 Košice, Slovak Republic.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Dec;82(6 Pt 1):061116. doi: 10.1103/PhysRevE.82.061116. Epub 2010 Dec 9.
The aim of this study is to investigate a wave dynamics and a size scaling of avalanches which were created by the mathematical model [J. Černák, Phys. Rev. E 65, 046141 (2002)]. Numerical simulations were carried out on a two-dimensional lattice L×L in which two constant thresholds E(c)(I) = 4 and E(c)(II) > E(c)(I) were randomly distributed. The density of sites c of the thresholds E(c)(II) and threshold E(c)(II) are parameters of the model. Autocorrelations of avalanche size waves, Hurst exponents, avalanche structures, and avalanche size moments were determined for several densities c and thresholds E(c)(II). The results show correlated avalanche size waves and multifractal scaling of avalanche sizes not only for specific conditions, densities c = 0.0,1.0 and thresholds 8 ≤ E(c)(II) ≤ 32, in which relaxation rules were precisely balanced, but also for more general conditions, densities 0.0 < c < 1.0 and thresholds 8 ≤ E(c)(II) ≤ 32, in which relaxation rules were unbalanced. The results suggest that the hypothesis of a precise relaxation balance could be a specific case of a more general rule.
本研究的目的是研究由数学模型[J. 切尔纳克，《物理评论E》65，046141 (2002)]产生的雪崩的波动动力学和尺寸缩放。在二维晶格L×L上进行了数值模拟，其中两个恒定阈值E(c)(I) = 4和E(c)(II) > E(c)(I)随机分布。阈值E(c)(II)的位点c的密度和阈值E(c)(II)是该模型的参数。针对几种密度c和阈值E(c)(II)，确定了雪崩尺寸波的自相关、赫斯特指数、雪崩结构和雪崩尺寸矩。结果表明，不仅在特定条件下，即密度c = 0.0、1.0且阈值8≤E(c)(II)≤32（其中弛豫规则精确平衡）时，雪崩尺寸波相关且雪崩尺寸具有多重分形缩放，而且在更一般的条件下，即密度0.0 < c < 1.0且阈值8≤E(c)(II)≤32（其中弛豫规则不平衡）时，也是如此。结果表明，精确弛豫平衡的假设可能是更一般规则的一个特殊情况。
