Shapoval Alexander, Shnirman Mikhail
Department of Mathematics and Computer Science of the <a href="https://ror.org/05cq64r17">University of Łódż</a>, Banacha 22, Łódż 90-238, Poland.
<a href="https://ror.org/00s1q1t70">Institute of Earthquake Prediction Theory and Mathematical Geophysics</a> RAS, Profsoyuznaya 84/32, 117997 Moscow, Russia.
Phys Rev E. 2024 Jul;110(1-1):014106. doi: 10.1103/PhysRevE.110.014106.
With the original Bak-Tang-Wisenefeld (BTW) sandpile we uncover the 1/φ noise in the mechanism maintaining self-organized criticality (SOC)-the question raised together with the concept of SOC. The BTW sandpile and the phenomenon of SOC in general are built on the slow time scale at which the system is loaded and the fast time scale at which the stress is transported outward from overloaded locations. Exploring the dynamics of stress in the slow time in the BTW sandpile, we posit that it follows cycles of gradual stress accumulation that end up with an abrupt stress release and the drop of the system to subcritical state. As the system size grows, the intracycle dynamics exhibits the 1/φ-like spectrum that extends boundlessly and corresponds to the stress release within the critical state.
通过原始的巴克 - 唐 - 维森费尔德（BTW）沙堆模型，我们揭示了维持自组织临界性（SOC）机制中的1/φ噪声——这是与SOC概念一同提出的问题。一般而言，BTW沙堆模型和SOC现象建立在系统加载的慢时间尺度以及应力从过载位置向外传输的快时间尺度之上。通过研究BTW沙堆模型中慢时间尺度下的应力动力学，我们假定它遵循逐渐应力积累的循环，最终以应力的突然释放和系统降至亚临界状态而告终。随着系统规模的增大，循环内动力学呈现出无界延伸的1/φ类频谱，这对应于临界状态下的应力释放。
