We discuss intermittent time series consisting of discrete bursts or avalanches separated by waiting or silent times. The short time correlations can be understood to follow from the properties of individual avalanches, while longer time correlations often present in such signals reflect correlations between triggerings of different avalanches. As one possible source of the latter kind of correlations in experimental time series, we consider the effect of a finite detection threshold, due to e.g. experimental noise that needs to be removed. To this end, we study a simple toy model of an avalanche, a random walk returning to the origin or a Brownian bridge, in the presence and absence of superimposed delta-correlated noise. We discuss the properties after thresholding of artificial timeseries obtained by mixing toy avalanches and waiting times from a Poisson process. Most of the resulting scalings for individual avalanches and the composite timeseries can be understood via random walk theory, except for the waiting time distributions when strong additional noise is added. Then, to compare with a more complicated case we study the Manna sandpile model of self-organized criticality, where some further complications appear.
Avalanches are often defined as signals higher than some detection level in bursty systems. The choice of the detection threshold affects the number of avalanches, but it can also affect their temporal correlations. We simulated the depinning of a long-range elastic interface and applied different thresholds including a zero one on the data to see how the sizes and durations of events change and how this affects temporal avalanche clustering. Higher thresholds result in steeper size and duration distributions and cause the avalanches to cluster temporally. Using methods from seismology, the fr…
Avalanche Size and Interevent Time Statistics in Amorphous System
Eindhoven University of Technology（埃因霍温理工大学）；North University of China（中北大学）；University of Tor Vergata（托尔维加塔大学）；INFN（意大利国家核物理研究所）；Utrecht University（乌得勒支大学）
We study the avalanche statistics observed in a minimal random growth model. The growth is governed by a reproduction rate obeying a probability distribution with finite mean a and variance va. These two control parameters determine if the avalanche size tends to a stationary distribution, (Finite Scale statistics with finite mean and variance or Power-Law tailed statistics with exponent in (1, 3]), or instead to a non-stationary regime with Log-Normal statistics. Numerical results and their statistical analysis are presented for a uniformly distributed growth rate, which are corroborated and …
Disordered elastic interfaces display avalanche dynamics at the depinning transition. For short-range interactions, avalanches correspond to compact reorganizations of the interface well described by the depinning theory. For long-range elasticity, an avalanche is a collection of spatially disconnected clusters. In this paper we determine the scaling properties of the clusters and relate them to the roughness exponent of the interface. The key observation of our analysis is the identification of a Bienaym{é}-Galton-Watson process describing the statistics of the cluster number. Our work has a …
