Fundamental equation for the dynamics of complex fracture

基于基本方程的标度性，研究了复杂断裂过程的动力学。由断裂核的随机大小效应产生的标度已被统计导出，它描述了自然地震活动的时空分布和长时间尾行为。考虑Lagevin方程，建立了从复杂系统的集合描述复合系统的随机标度。它预测了复杂系统的超慢动力学和慢动力学。

The dynamics of complex fracture process has been studied based on the scaling nature of the fundamental equation. The scaling resulting from the random size effect of fracture nuclei has been statistically derived and it describes the temporal/spacial distribution and long time-tail behavior of the natural earthquake activity. Stochastic scaling to describe the compound system from the aggregate of complex systems has been formulated considering the Lagevin equation. It predicts the super-slow dynamics as well as slow dynamics of complex system.