Self-organized Critical Phenomena Research Articles

Effects of electron-to-ion mass ratio in driving magnetic oscillations of magnetohydrodynamic plasmas and self-organized criticality

Evolutions of nonlinear magnetic fields have been shown to be governed by a set of coupled nonlinear equations of second order in magnetohydrodynamic (MHD) plasmas by Lee and Parks [Geophys. Res. Lett. 19, 637–640 (1992)]. We have considered the same set of coupled nonlinear equations for further analysis in this work by neglecting the presence of external forcing term in it. Different modes of oscillations of magnetic field have been found to exist in special limiting cases of this set of undriven second order coupled nonlinear equations having frequencies that are multiples of lower hybrid frequency. Numerical solutions of these coupled equations have been analysed revealing a quasi-periodic route to chaotic oscillations of the nonlinear magnetic fields as electron-to-ion mass ratio signifying presence of linear coupling effects is increased. Some signatures of the phenomenon of self-organized criticality (SOC) in typical quasi-periodic oscillations of magnetic field have also been noticed using Fourier analysis. The presence of long range correlations has been witnessed in quasi-periodic oscillations whereas both long range correlations and anticorrelations are found in chaotic oscillations using rescaled range analysis. Concluding remarks are provided in addition to various results and discussions.

Noise-induced excitation wave and its size distribution in coupled FitzHugh-Nagumo equationson a square lattice.

There are various research topics such as stochastic resonance, coherent resonance, and neuroavalanche in excitable systems under external noises. We perform numerical simulation of coupled noisy FitzHugh-Nagumo equationson the square lattice. Excitation waves are generated most efficiently at an intermediate noise strength. The cluster size distributions obey a power-law-like distribution at a certain parameter range. However, we consider that this is not a self-organized critical phenomenon, partly because the exponent of the power law is not constant. We have studied the propagation of excitation waves in the coupled noisy FitzHugh-Nagumo equationswith a one-dimensional pacemaker region and found that there is a phase-transition-like phenomenon from the short-range propagation to the whole-system propagation by changing the noise strength T. The power-law distribution is observed most clearly near the phase transition of the propagation of excitation waves in the coupled noisy FitzHugh-Nagumo equationswithout the one-dimensional pacemaker.

Signatures of the Self-organized Criticality Phenomenon in Precursors of Gamma-Ray Bursts

Precursors provide important clues to the nature of gamma-ray burst (GRB) central engines and can be used to contain GRB physical processes. In this Letter, we study the self-organized criticality in precursors of long GRBs in the third Swift/Burst Alert Telescope catalog. We investigate the differential and cumulative size distributions of 100 precursors, including peak flux, duration, rise time, decay time, and quiescent time with the Markov Chain Monte Carlo technique. It is found that all of the distributions can be well described by power-law models and understood within the physical framework of a self-organized criticality system. In addition, we inspect the cumulative distribution functions of the size differences with a q-Gaussian function. The scale-invariance structures of precursors further strengthen our findings. Particularly, similar analyses are made in 127 main bursts. The results show that both precursors and main bursts can be attributed to a self-organized criticality system with the spatial dimension S = 3 and driven by a similar magnetically dominated process.

Evidence for the Self-organized Criticality Phenomenon in the Prompt Phase of Short Gamma-Ray Bursts

The prompt phase of gamma-ray bursts (GRBs) contains essential information regarding their physical nature and central engine, which are as yet unknown. In this paper, we investigate the self-organized criticality phenomenon in GRB prompt phases as done in X-ray flares of GRBs. We obtain the differential and cumulative distributions of 243 short GRB pulses, such as peak flux, FWHM, rise time, decay time, and peak time in the fourth BATSE Time-Tagged Event Catalog with the Markov Chain Monte Carlo technique. It is found that these distributions can be well described by power-law models. In particular, comparisons are made with 182 short GRB pulses in the third Swift GRB Catalog from 2004 December to 2019 July. The results are essentially consistent with the BATSE ones. We notice that there is no obvious power-law index evolution across different energy bands for either BATSE or Swift short GRBs. The joint analysis suggests that the GRB prompt phase can be explained by a fractal-diffusive self-organized criticality system with the spatial dimension S = 3 and the classical diffusion β = 1. Our findings show that GRB prompt phases and X-ray flares possess the very same magnetically dominated stochastic process and mechanism.

New insights into spatio-temporal dynamics of irradiation defects rafting

The self-organization of irradiation defects has continuously attracted numerous experimental and theoretical attentions, due to its influence on the service performance of irradiated materials. This work developed the discrete dislocation dynamics method by considering the thermal fluctuations, in order to statistically clarify the contribution of elastic interactions and thermal fluctuations to the temporal and spatial dynamics of raft formation. On temporal scales, this work for the first time demonstrates the existence of power-law scaling of raft formation time, and its insensitivity to the thermal fluctuations, and loop size distribution. The power-law exponent is consistent with many other self-organized critical phenomena, such as earthquakes, sandpile sliding, and dislocation avalanches, etc. On spatial scales, the deviation between the normal direction of the raft habit plane and the Burgers vector of the irradiation-induced interstitial loops was carefully analyzed, which agrees well with the experimental results.

Optimal reinforcement learning near the edge of a synchronization transition.

Recent experimental and theoretical studies have indicated that the putative criticality of cortical dynamics may correspond to a synchronization phase transition. The critical dynamics near such a critical point needs further investigation specifically when compared to the critical behavior near the standard absorbing state phase transition. Since the phenomena of learning and self-organized criticality (SOC) at the edge of synchronization transition can emerge jointly in spiking neural networks due to the presence of spike-timing dependent plasticity (STDP), it is tempting to ask the following: what is the relationship between synchronization and learning in neural networks? Further, does learning benefit from SOC at the edge of synchronization transition? In this paper, we intend to address these important issues. Accordingly, we construct a biologically inspired model of a cognitive system which learns to perform stimulus-response tasks. We train this system using a reinforcement learning rule implemented through dopamine-modulated STDP. We find that the system exhibits a continuous transition from synchronous to asynchronous neural oscillations upon increasing the average axonal time delay. We characterize the learning performance of the system and observe that it is optimized near the synchronization transition. We also study neuronal avalanches in the system and provide evidence that optimized learning is achieved in a slightly supercritical state.

Investigation on the serrated flow behavior of bulk metallic glasses based on machine learning

This study proposed a long short-term memory (LSTM) model for predicting the serrated flow behaviors of bulk metallic glasses (BMGs) under nanoindentation. A series of load-controlled nanoindentation tests were conducted on a Pd40Cu30Ni10P20 BMG. The LSTM model was introduced to establish a neural network for predicting the serrated flow at different loading rates, and was verified by the comparisons of experimental data with predictive results. Further investigation based on the predictive serrated flows under different loading rates showed that the serrations exhibit a significant self-organized critical (SOC) phenomenon at different loading rates. The SOC phenomena of the serrations under a lower loading rate were more obvious than that under a higher loading rate.

Slope movement classification and new insights into failure prediction based on landslide deformation evolution

This study aims to investigate the features of landslide evolution from the perspectives of statistics and nonlinear systems. First, to understand the complex processes of landslide evolution intuitively, a new landslide classification based on deformation patterns is presented. Then, frequency-size statistics of velocity events are performed in five historical landslides, including four failure cases and one non-failure case. The results show that velocity events follow power-law distributions within a certain size range. The power-law behaviors are usually associated with a ubiquitous phenomenon of self-organized criticality (SOC). A statistical test indicates that some outliers with extreme sizes significantly exceed power-law extrapolation. One possible explanation is that they are “dragon-kings” (DKs), possessing different formation mechanisms from their peers in power laws. Herein, the role of SOC and DKs in landslide evolution is analyzed in detail. The two theories provide new ways to understand the underlying mechanisms of landslide evolution. Meanwhile, power-law distributions and DKs provide new insights to predict landslide deformation.

Avalanches in an extended Schelling model: An explanation of urban gentrification

In this work we characterize sudden increases in the land price of certain urban areas, a phenomenon causing gentrification, via an extended Schelling model. An initial price rise forces some of the disadvantaged inhabitants out of the area, creating vacancies which other groups find economically attractive. Intolerance issues forces further displacements, possibly giving rise to an avalanche. We consider how gradual changes in the economic environment affect the urban architecture through such avalanche processes, when agents may enter or leave the city freely. The avalanches are characterized by power-law histograms, as it is usually the case in self-organized critical phenomena.

Fractal-like frontier structure of avalanches in a sandpile model

The self-organized criticality (SOC) phenomena for dynamical systems with spatial degrees of freedom is commonly observed in application to different aspects of natural sciences. In our study we also consider our sandpile model as such a system. Since the first mention in 1987, a sandpile model, which is a common example of spatiotemporal evolution, became widely applied for avalanche-like processes. With a simple computer simulation we show that an avalanche as a result of natural system evolution has a fractal border structure, and approves SOC phenomena of a sandpile model. We also demonstrate Gutenberg-Richter dependence for avalanche process in a sandpile model.

Self-organized criticality in multi-pulse gamma-ray bursts

The variability in multi-pulse gamma-ray bursts (GRBs) may help to reveal the mechanism of underlying processes from the central engine. To investigate whether the self-organized criticality (SOC) phenomena exist in the prompt phase of GRBs, we statistically study the properties of GRBs with more than 3 pulses in each burst by fitting the distributions of several observed physical variables with a Markov Chain Monte Carlo approach, including the isotropic energy Eiso, the duration time T, and the peak count rate P of each pulse. Our sample consists of 454 pulses in 93 GRBs observed by the CGRO/BATSE satellite. The best-fitting values and uncertainties for these power-law indices of the differential frequency distributions are: $$\alpha_E^d=1.54\pm0.09, \alpha_T^d=1.82\pm_{0.15}^{+0.14}\;and\;\alpha_P^d=2.09_{-019}^{+0.18}$$ , while the power-law indices in the cumulative frequency distributions are: $$\alpha_E^c=1.44_{-0.10}^{+0.08}, \alpha_T^c=1.75_-{0.13}^{+0.141}\;and\;\alpha_P^c=1.99_{-019}^{+0.16}$$ . We find that these distributions are roughly consistent with the physical framework of a Fractal-Diffusive, Self-Organized Criticality (FD-SOC) system with the spatial dimension S = 3 and the classical diffusion I²=1. Our results support that the jet responsible for the GRBs should be magnetically dominated and magnetic instabilities (e.g., kink model, or tearing-model instability) lead the GRB emission region into the SOC state.

Scaling in the Local Strain-Rate Field during Jerky Flow in an Al-3%Mg Alloy

Jerky flow in alloys, or the Portevin-Le Chatelier effect, presents an outstanding example of self-organization phenomena in plasticity. Recent acoustic emission investigations revealed that its microscopic dynamics is governed by scale invariance manifested as power-law statistics of intermittent events. As the macroscopic stress serrations show both scale invariance and characteristic scales, the micro-macro transition is an intricate question requiring an assessment of intermediate behaviors. The first attempt of such an investigation is undertaken in the present paper by virtue of a one-dimensional (1D) local extensometry technique and statistical analysis of time series. The data obtained complete the missing link and bear evidence to a coexistence of characteristic large events and power laws for smaller events. The scale separation is interpreted in terms of the phenomena of self-organized criticality and synchronization in complex systems. Furthermore, it is found that both the stress serrations and local strain-rate bursts agree with the so-called fluctuation scaling related to general mathematical laws and unifying various specific mechanisms proposed to explain scale invariance in diverse systems. Prospects of further investigations including the duality manifested by a wavy spatial organization of the local bursts of plastic deformation are discussed.

Ordered Avalanches on the Bethe Lattice

We discuss deterministic sequences of avalanches on a directed Bethe lattice. The approach is motivated by the phenomenon of self-organized criticality. Grains are added only at one node of the network. When the number of grains at any node exceeds a threshold b, each of k out-neighbors gets one grain. The probability of an avalanche of size s is proportional to . When the avalanche mass is conserved (), we get . For an application of the model to social phenomena, the conservation condition can be released. Then, the exponent is found to depend on the model parameters; . The distribution of the time duration of avalanches is exponential. Multifractal analysis of the avalanche sequences reveals their strongly non-uniform fractal organization. Maximal value of the singularity strength in the bifractal spectrum is found to be .

Scaling properties of rainfall records in some Mexican zones

Since the 1990 decade, it has been suggested that atmospheric processes associated with rainfall could be a self-organized critical (SOC) phenomenon similar, for example, to seismicity. In this sense, the rain events taken as the output of the complex atmospheric system (sun’s radiation, water evaporation, clouds, etc.) are analogous to earthquakes, as the output of a relaxation process of the earth crust. A clue on this possible SOC behavior of rain phenomenon has been the ubiquitous presence of power laws in rain statistics. In the present article, we report the scaling properties of rain precipitation data taken from meteorological stations located at six zones of Mexico. Our results are consistent with those that assert that rainfall is a SOC phenomenon. We also analyze the Hurst exponent, which is appropriate to measure long-term memory of time series.

Applying a cellular automaton model to describing the anomalous relaxation of the metastable states in the disordered porous media

We propose a numerical model of outflow of the nonwetting liquid from previously completely filled nanoporous media based on cellular automata theory. It was shown that the relaxation of this system has an avalanche-like behaviour, which is inherent to phenomenon of self-organized criticality (SOC). Avalanche size and energy distributions were obtained. It was found that spectra have a typical for SOC theory power-law dependence N(s) ∼ s-β with β = 2.73, and N(E) ∼ E-βen with βen = 2.25.

Testing universality in critical exponents: The case of rainfall.

One of the key clues to consider rainfall as a self-organized critical phenomenon is the existence of power-law distributions for rain-event sizes. We have studied the problem of universality in the exponents of these distributions by means of a suitable statistic whose distribution is inferred by several variations of a permutational test. In contrast to more common approaches, our procedure does not suffer from the difficulties of multiple testing and does not require the precise knowledge of the uncertainties associated to the power-law exponents. When applied to seven sites monitored by the Atmospheric Radiation Measurement Program the tests lead to the rejection of the universality hypothesis, despite the fact that the exponents are rather close to each other. We discuss the reasons of the rejection.

Statistical analysis of Nomao customer votes for spots of France

We investigate the statistical properties of votes of customers for spots of France collected by the startup company NOMAO. The frequencies of votes per spot and per customer are characterized by a power law distributions which remain stable on a time scale of a decade when the number of votes is varied by almost two orders of magnitude. Using the computer science methods we explore the spectrum and the eigenvalues of a matrix containing user ratings to geolocalized items. Eigenvalues nicely map to large towns and regions but show certain level of instability as we modify the interpretation of the underlying matrix. We evaluate imputation strategies that provide improved prediction performance by reaching geographically smooth eigenvectors. We point on possible links between distribution of votes and the phenomenon of self-organized criticality.

Extremal dynamics in random replicator ecosystems

The seminal numerical experiment by Bak and Sneppen (BS) is repeated, along with computations with replicator models, including a greater amount of features. Both types of models do self-organize, and do obey power-law scaling for the size distribution of activity cycles. However species extinction within the replicator models interferes with the BS self-organized critical (SOC) activity. Speciation–extinction dynamics ruins any stationary state which might contain a steady size distribution of activity cycles. The BS-type activity appears as a dissimilar phenomenon in comparison to speciation–extinction dynamics in the replicator system. No criticality is found from the speciation–extinction dynamics. Neither are speciations and extinctions in real biological macroevolution known to contain any diverging distributions, or self-organization towards any critical state. Consequently, biological macroevolution probably is not a self-organized critical phenomenon.

Size-distribution of scoria cones within the Eğrikuyu Monogenetic Field (Central Anatolia, Turkey)

Eğrikuyu Monogenetic Field (EMF) is one of the five clusters of monogenetic volcanoes in Quaternary Central Anatolian Volcanic Province (CAVP). EMF consists mainly of scoria cones and a few maars (e.g. Kutören, Obruk). Previous studies on monogenetic volcanoes of CAVP mainly focused on petrologic evolution of scoria cones rather than the statistical analyses of their morphological parameters.Using the database compiled by Arcasoy (2001) for the morphometric parameters of the scoria cones in the EMF, we present the power-law behavior of their size distribution with respect to basal diameters (Wco) of 77-scoria cones from the whole database. Both empirical (maximum likelihood estimation, MLE) and graphical (log–log plot) methods are used for the estimation of scaling parameter “b-value” of power-law for the scoria cones which have basal diameter greater than or equal to 0.36km. However, graphical method gives the precise result with the b-value of 2.78±0.08 for 77-scoria cones over the width range 0.1–1.23km. Herein, b-value indicates the relative number of the small scoria cones with respect to large ones for a given area.The power-law behavior of the size distribution of scoria cones in the EMF suggests that their occurrence is self-organized critical phenomena similar to earthquakes. Since the size-distribution of scoria cones provides information about their eruptive magnitude and occurrence mechanism, our results can be directly applied to future risk assessment of the CAVP.

Effect of equal channel angular pressing on the Portevin–Le Chatelier effect in an Al3Mg alloy

Plastic deformation of alloys is often accompanied with discontinuous flow known as the Portevin–Le Chatelier (PLC) instability. Recent studies of mechanical behavior of alloys subjected to severe plastic deformation (SPD) revealed different forms this phenomenon can take as a result of grain refinement. In the present work, it is reported that SPD may effectively suppress the macroscopic stress serrations characteristic of the PLC effect. At the same time, small-scale stress fluctuations can still be resolved on the deformation curves. To investigate their nature, stress vs time curves for an Al3Mg alloy processed by equal channel angular pressing (ECAP) are compared with those obtained for the initial coarse-grained (CG) material, using statistical and multifractal approaches to multi-scale analysis of time series. An interpretation of the results in terms of the concurrency of phenomena of self-organized criticality and synchronization in the dislocation system is proposed.