Natural time analysis of critical phenomena
Natural time analysis of critical phenomena
复制标题
DOI：
10.1073/pnas.1108138108
复制
发表时间：
2011-06
期刊：
影响因子：
--
通讯作者：
P. Varotsos;N. Sarlis;E. Skordas;S. Uyeda;M. Kamogawa
中科院分区：
文献类型：
--
作者：
P. Varotsos;N. Sarlis;E. Skordas;S. Uyeda;M. Kamogawa
存在一个量，人们可以通过它来识别动力系统接近临界状态的方法，否则很难识别它。这个量是自然时间χ的方差，其中Pk是在第k个事件期间释放的归一化能量，其中自然时间被定义为χk=k/N，并且N代表事件的总数。然后，我们证明了对于各种动力系统，κ1在临界态变得等于0.070。这适用于2D Ising和Bak-Tang-Wiesenfeld沙堆等临界性模型，这是自组织临界性的标准例子。κ1=0.070的条件适用于稻谷堆积、地震电信号和随后的主震前地震活动等临界现象的实验结果。
A quantity exists by which one can identify the approach of a dynamical system to the state of criticality, which is hard to identify otherwise. This quantity is the variance of natural time χ, where and pk is the normalized energy released during the kth event of which the natural time is defined as χk = k/N and N stands for the total number of events. Then we show that κ1 becomes equal to 0.070 at the critical state for a variety of dynamical systems. This holds for criticality models such as 2D Ising and the Bak–Tang–Wiesenfeld sandpile, which is the standard example of self-organized criticality. This condition of κ1 = 0.070 holds for experimental results of critical phenomena such as growth of rice piles, seismic electric signals, and the subsequent seismicity before the associated main shock.