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Register a new userRecord statistics of bursts signals the onset of acceleration towards failure
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Forecasting the imminent catastrophic failure has a high importance for a large variety of systems from the collapse of engineering constructions, through the emergence of landslides and earthquakes, to volcanic eruptions. Failure forecast methods predict the lifetime of the system based on the time-to-failure power law of observables describing the final acceleration towards failure. We show that the statistics of records of the event series of breaking bursts, accompanying the failure process, provides a powerful tool to detect the onset of acceleration, as an early warning of the impending catastrophe. We focus on the fracture of heterogeneous materials using a fiber bundle model, which exhibits transitions between perfectly brittle, quasi-brittle, and ductile behaviors as the amount of disorder is increased. Analyzing the lifetime of record size bursts, we demonstrate that the acceleration starts at a characteristic record rank, below which record breaking slows down due to the dominance of disorder in fracturing, while above it stress redistribution gives rise to an enhanced triggering of bursts and acceleration of the dynamics. The emergence of this signal depends on the degree of disorder making both highly brittle fracture of low disorder materials, and ductile fracture of strongly disordered ones, unpredictable.
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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 uni-axial 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. 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. Sub-sequences of bursts 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 bursts 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 crackling bursts. The record statistics of the uncorrelated surrogates agrees very well with the corresponding predictions of independent identically distributed random variables, which confirms that the temporal and spatial correlation of cracking bursts are responsible for the observed unique behaviour.
We study the statistics of avalanches, as a response to an applied force, undergone by a particle hopping on a one dimensional lattice where the pinning forces at each site are independent and identically distributed (I.I.D), each drawn from a continuous $f(x)$. The avalanches in this model correspond to the inter-record intervals in a modified record process of I.I.D variables, defined by a single parameter $c>0$. This parameter characterizes the record formation via the recursive process $R_k > R_{k-1}-c$, where $R_k$ denotes the value of the $k$-th record. We show that for $c>0$, if $f(x)$ decays slower than an exponential for large $x$, the record process is nonstationary as in the standard $c=0$ case. In contrast, if $f(x)$ has a faster than exponential tail, the record process becomes stationary and the avalanche size distribution $pi(n)$ has a decay faster than $1/n^2$ for large $n$. The marginal case where $f(x)$ decays exponentially for large $x$ exhibits a phase transition from a non-stationary phase to a stationary phase as $c$ increases through a critical value $c_{rm crit}$. Focusing on $f(x)=e^{-x}$ (with $xge 0$), we show that $c_{rm crit}=1$ and for $c<1$, the record statistics is non-stationary. However, for $c>1$, the record statistics is stationary with avalanche size distribution $pi(n)sim n^{-1-lambda(c)}$ for large $n$. Consequently, for $c>1$, the mean number of records up to $N$ steps grows algebraically $sim N^{lambda(c)}$ for large $N$. Remarkably, the exponent $lambda(c)$ depends continously on $c$ for $c>1$ and is given by the unique positive root of $c=-ln (1-lambda)/lambda$. We also unveil the presence of nontrivial correlations between avalanches in the stationary phase that resemble earthquake sequences.
We investigate site percolation in a hierarchical scale-free network known as the Dorogovtsev- Goltsev-Mendes network. We use the generating function method to show that the percolation threshold is 1, i.e., the system is not in the percolating phase when the occupation probability is less than 1. The present result is contrasted to bond percolation in the same network of which the percolation threshold is zero. We also show that the percolation threshold of intentional attacks is 1. Our results suggest that this hierarchical scale-free network is very fragile against both random failure and intentional attacks. Such a structural defect is common in many hierarchical network models.
A glacier table consists of a rock supported by a slender column of ice and form naturally on glaciers. We investigate the onset of their formation at a smaller scale in a controlled environment. Depending on the size and thermal conductivity of a cap, it can either form of a table standing on an ice foot, or sink into the ice block. A one-dimension conduction model shows that the differential ice melting is controlled by a competition between two effects: a geometrical amplification, and a heat flux reduction due to the higher temperature of the cap as compared to the ice. Our model captures the transition between the two regimes and identifies a dimensionless number which controls the onset of glacier tables formation.
We investigate the scaling properties of the sources of crackling noise in a fully-dynamic numerical model of sedimentary rocks subject to uniaxial compression. The model is initiated by filling a cylindrical container with randomly-sized spherical particles which are then connected by breakable beams. Loading at a constant strain rate the cohesive elements fail and the resulting stress transfer produces sudden bursts of correlated failures, directly analogous to the sources of acoustic emissions in real experiments. The source size, energy, and duration can all be quantified for an individual event, and the population analyzed for their scaling properties, including the distribution of waiting times between consecutive events. Despite the non-stationary loading, the results are all characterized by power law distributions over a broad range of scales in agreement with experiments. As failure is approached temporal correlation of events emerge accompanied by spatial clustering.
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