Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen, Hungary.
School of Geosciences, University of Edinburgh, EH9 3FE Edinburgh, United Kingdom.
Phys Rev E. 2016 Mar;93(3):033006. doi: 10.1103/PhysRevE.93.033006. Epub 2016 Mar 31.
An accurate understanding of the interplay between random and deterministic processes in generating extreme events is of critical importance in many fields, from forecasting extreme meteorological events to the catastrophic failure of materials and in the Earth. Here we investigate the statistics of record-breaking events in the time series of crackling noise generated by local rupture events during the compressive failure of porous materials. The events are generated by computer simulations of the uniaxial compression of cylindrical samples in a discrete element model of sedimentary rocks that closely resemble those of real experiments. The number of records grows initially as a decelerating power law of the number of events, followed by an acceleration immediately prior to failure. The distribution of the size and lifetime of records are power laws with relatively low exponents. We demonstrate the existence of a characteristic record rank k(*), which separates the two regimes of the time evolution. Up to this rank deceleration occurs due to the effect of random disorder. Record breaking then accelerates towards macroscopic failure, when physical interactions leading to spatial and temporal correlations dominate the location and timing of local ruptures. The size distribution of records of different ranks has a universal form independent of the record rank. Subsequences of events that occur between consecutive records are characterized by a power-law size distribution, with an exponent which decreases as failure is approached. High-rank records are preceded by smaller events of increasing size and waiting time between consecutive events and they are followed by a relaxation process. As a reference, surrogate time series are generated by reshuffling the event times. The record statistics of the uncorrelated surrogates agrees very well with the corresponding predictions of independent identically distributed random variables, which confirms that temporal and spatial correlation in the crackling noise is responsible for the observed unique behavior. In principle the results could be used to improve forecasting of catastrophic failure events, if they can be observed reliably in real time.
准确理解随机过程和确定性过程在产生极端事件中的相互作用，在许多领域都至关重要，从预测极端气象事件到材料和地球的灾难性破坏。在这里，我们研究了在多孔材料压缩破坏过程中局部破裂事件产生的噼啪噪声时间序列中破纪录事件的统计特性。这些事件是通过沉积岩离散元模型中单轴压缩圆柱形样品的计算机模拟产生的，与实际实验非常相似。记录的数量最初随事件数量的减速幂律增长，然后在失效前立即加速。记录的大小和寿命分布是幂律分布，具有相对较低的指数。我们证明了存在特征记录秩 k(*), 它将时间演化的两个区域分开。在这个等级之前，减速是由于随机无序的影响。然后，记录突破会加速到宏观失效，此时导致空间和时间相关的物理相互作用主导了局部破裂的位置和时间。不同秩记录的大小分布具有与记录秩无关的通用形式。连续记录之间发生的事件序列具有幂律大小分布，随着接近失效，指数减小。高秩记录之前是连续事件之间的较小事件和等待时间增加，之后是松弛过程。作为参考，通过重新排列事件时间生成替代时间序列。无关联的替代时间序列的记录统计与独立同分布随机变量的相应预测非常吻合，这证实了噼啪噪声中的时间和空间相关性是导致观察到的独特行为的原因。如果可以在实时可靠地观察到这些结果，则原则上可以将其用于改进灾难性破坏事件的预测。
