Department of Theoretical Physics, Doctoral School of Physics, Faculty of Science and Technology, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary.
Chaos. 2022 Jun;32(6):063121. doi: 10.1063/5.0089634.
We investigate how the interplay of the topology of the network of load transmitting connections and the amount of disorder of the strength of the connected elements determines the temporal evolution of failure cascades driven by the redistribution of load following local failure events. We use the fiber bundle model of materials' breakdown assigning fibers to the sites of a square lattice, which is then randomly rewired using the Watts-Strogatz technique. Gradually increasing the rewiring probability, we demonstrate that the bundle undergoes a transition from the localized to the mean field universality class of breakdown phenomena. Computer simulations revealed that both the size and the duration of failure cascades are power law distributed on all network topologies with a crossover between two regimes of different exponents. The temporal evolution of cascades is described by a parabolic profile with a right handed asymmetry, which implies that cascades start slowly, then accelerate, and eventually stop suddenly. The degree of asymmetry proved to be characteristic of the network topology gradually decreasing with increasing rewiring probability. Reducing the variance of fibers' strength, the exponents of the size and the duration distribution of cascades increase in the localized regime of the failure process, while the localized to mean field transition becomes more abrupt. The consistency of the results is supported by a scaling analysis relating the characteristic exponents of the statistics and dynamics of cascades.
我们研究了负载传输连接网络的拓扑结构和连接元素强度的无序程度之间的相互作用如何决定由局部故障事件后负载重新分配驱动的故障级联的时间演化。我们使用材料故障的纤维束模型，将纤维分配到正方形晶格的位置，然后使用 Watts-Strogatz 技术随机重新布线。逐渐增加重新布线的概率，我们证明束经历了从局部到故障现象的平均场普遍性类的转变。计算机模拟表明，在所有网络拓扑上，故障级联的大小和持续时间都呈幂律分布，在两个不同指数的区域之间存在交叉。级联的时间演化由具有右偏不对称性的抛物线轮廓描述，这意味着级联开始缓慢，然后加速，最终突然停止。不对称程度被证明是网络拓扑的特征，随着重新布线概率的增加而逐渐减小。减小纤维强度的方差，级联大小和持续时间分布的指数在故障过程的局部区域中增加，而局部到平均场的转变变得更加突然。统计和级联动力学的特征指数之间的标度分析支持了结果的一致性。
