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Register a new userRupture cascades in a discrete element model of a porous sedimentary rock
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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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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 present a statistical model which is able to capture some interesting features exhibited in the Brazilian test. The model is based on breakable elements which break when the force experienced by the elements exceed their own load capacity. In this model when an element breaks, the capacity of the neighboring elements are decreased by a certain amount assuming weakening effect around the defected zone. We numerically investigate the stress-strain behavior, the strength of the system, how it scales with the system size and also its fluctuation for both uniformly and weibull distributed breaking threshold of the elements in the system. We find that the strength of the system approaches its asymptotic value $sigma_c=1/6$ and $sigma_c=5/18$ for uniformly and Weibull distributed breaking threshold of the elements respectively. We have also shown the damage profile right at the point when the stress-strain curve reaches at its maximum and then it is compared with our experimental observations.
Tipping elements in the climate system are large-scale subregions of the Earth that might possess threshold behavior under global warming with large potential impacts on human societies. Here, we study a subset of five tipping elements and their interactions in a conceptual and easily extendable framework: the Greenland and West Antarctic Ice Sheets, the Atlantic Meridional Overturning Circulation (AMOC), the El-Nino Southern Oscillation (ENSO) and the Amazon rainforest. In this nonlinear and multistable system, we perform a basin stability analysis to detect its stable states and their associated Earth system resilience. Using this approach, we perform a system-wide and comprehensive robustness analysis with more than 3.5 billion ensemble members. Further, we investigate dynamic regimes where some of the states lose stability and oscillations appear using a newly developed basin bifurcation analysis methodology. Our results reveal that the state of four or five tipped elements has the largest basin volume for large levels of global warming beyond 4 {deg}C above pre-industrial climate conditions. For lower levels of warming, states including disintegrated ice sheets on West Antarctica and Greenland have higher basin volume than other state configurations. Therefore in our model, we find that the large ice sheets are of particular importance for Earth system resilience. We also detect the emergence of limit cycles for 0.6% of all ensemble members at rare parameter combinations. Such limit cycle oscillations mainly occur between the Greenland Ice Sheet and AMOC (86%), due to their negative feedback coupling. These limit cycles point to possibly dangerous internal modes of variability in the climate system that could have played a role in paleoclimatic dynamics such as those unfolding during the Pleistocene ice age cycles.
Many real-world networks are embedded into a space or spacetime. The embedding space(time) constrains the properties of these real-world networks. We use the scale-dependent spectral dimension as a tool to probe whether real-world networks encode information on the dimensionality of the embedding space. We find that spacetime networks which are inspired by quantum gravity and based on a hybrid signature, following the Minkowski metric at small spatial distance and the Euclidean metric at large spatial distance, provide a template relevant for real-world networks of small-world type, including a representation of the internets architecture and biological neural networks.
Experiments on particles motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading to continuous-time random walks) can easily be distinguished from the rest by testing their non-ergodicity, the latter two cases are harder to distinguish. We propose a statistical test for distinguishing between these two based on the space-filling properties of trajectories, and prove its feasibility and specificity using synthetic data. We moreover present a flow-chart for making a decision on a type of subdiffusion for a broader class of models.
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