Self-organized Critical Systems Research Articles

Fragmented perspective of self-organized criticality and disorder in log gravity

We use a statistical model to discuss nonequilibrium fragmentation phenomena taking place in the stochastic dynamics of the log sector in log gravity. From the canonical Gibbs model, a combinatorial analysis reveals an important aspect of the n-particle evolution previously shown to generate a collection of random partitions according to the Ewens distribution realized in a disconnected double Hurwitz number in genus zero. By treating each possible partition as a member of an ensemble of fragmentations, and ensemble averaging over all partitions with the Hurwitz number as a special case of the Gibbs distribution, a resulting distribution of cluster sizes appears to fall as a power of the size of the cluster. Dynamical systems that exhibit a distribution of sizes giving rise to a scale-invariant power-law behavior at a critical point possess an important property called self-organized criticality. As a corollary, the log sector of log gravity is a self-organized critical system at the critical point μl = 1. A similarity between self-organized critical systems, spin glass models and the dynamics of the log sector which exhibits aging behavior reminiscent of glassy systems is pointed out by means of the Pòlya distribution, also known to classify various models of (randomly fragmented) disordered systems, and by presenting the cluster distribution in the log sector of log gravity as a distinguished member of this probability distribution. We bring arguments from a probabilistic perspective to discuss the disorder in log gravity, largely anticipated through the conjectured AdS3/LCFT2 correspondence.

Avalanche dynamics in nonconservative water droplet

The self-organized criticality (SOC) exhibits excellent performance in describing the dynamic features of multi-body systems in nature. It is usually considered that conservative law is a necessary condition for the existence of SOC. However, mass or energy dissipation typically exists in the process from self-organization to a critical state in natural systems such as earthquakes and air pollution, namely, non-conservation. At present, few physical experiments have systematically explored the SOC behavior in a non-conservative system, compared to numerical simulations. This study is the first to design a non-conservative sandpile experiment using water droplets. Based on this experiment, the dynamic evolution process of avalanches in a non-conservative system has been analyzed. The results show that the avalanche size of water droplets follows a power-law distribution, as the water mass decays with time. This phenomenon obeys the rules of scale-free distribution, which is consistent with SOC behavior. Moreover, the waiting time of water droplets avalanche follows a stretched exponential distribution. These results suggest that SOC behavior still exists in non-conservative multi-body systems, which is affected by the decay coefficient. We then explore the mechanism by which the decay coefficient affects the transition of the system to a critical state in the non-conservative sandpile model (NBTW). We find that only when the decay coefficient is small do the inequality measures, Gini coefficient g and Kolkata index k, exhibit nearly universal values, similar to the mechanism of the system transitioning to a critical state in the traditional BTW model. When the decay coefficient is large, the NBTW model shows scaling-limited effects and the scaling exponent of avalanche size increases with the decay coefficient. Furthermore, we use the NBTW model to study how the decay coefficient influences the scaling exponent of avalanche size. We find that the NBTW model can effectively explain the variability of scaling exponents observed in different SOC systems and establish a quantitative relationship between the mass decay coefficient and the avalanche size scaling exponent. This study provides new insight into SOC behavior in non-conservative systems in nature.

Scale-invariant Features of X-Ray Bursts from SGR J1935+2154 Detected by Insight-HXMT

In this work, we restudy the scale-invariant features of X-ray bursts from the soft gamma repeater (SGR) J1935+2154. To compare with previous studies, we choose 75 bursts from a dedicated 33 days-long observation carried out by Insight-HXMT. We investigate the size difference distributions of net counts, duration, and waiting time. It is found that the cumulative difference distributions of net counts and duration follow the q-Gaussian models with approximately steady q-values, confirming that the scale-invariant features exist in X-ray bursts of SGR J1935+2154. Regarding the varying results of waiting time reported by Sang & Lin and Wei et al, we find that the distributions of waiting time can be well described by the q-Gaussian model. Furthermore, the q-values of waiting time remain relatively stable at the 3σ confidence level, corroborating the scale invariance in the X-ray bursts. Additionally, we note that there is no significant q-value evolution across three Insight-HXMT telescopes. These findings statistically affirm that the X-ray bursts from SGR J1935+2154 can be attributed to an fractal-diffusive self-organized criticality system with a plausible Euclidean spatial dimension S = 3, implying that X-ray bursts from SGR J1935+2154 and associated astrophysical phenomena may share a similar magnetically dominated stochastic process.

A Comparative Analysis of Scale-invariant Phenomena in Repeating Fast Radio Bursts and Glitching Pulsars

The recent discoveries of a remarkable glitch/antiglitch accompanied by fast radio burst (FRB)-like bursts from the Galactic magnetar SGR J1935+2154 have revealed the physical connection between the two. In this work, we study the statistical properties of radio bursts from the hyperactive repeating source FRB 20201124A and of glitches from the pulsar PSR B1737–30. For FRB 20201124A, we confirm that the probability density functions of fluctuations of energy, peak flux, duration, and waiting time well follow the Tsallis q-Gaussian distribution. The derived q values from q-Gaussian distribution keep approximately steady for different temporal interval scales, which indicates that there is a common scale-invariant structure in repeating FRBs. Similar scale-invariant properties can be found in PSR B1737–30's glitches, implying an underlying association between the origins of repeating FRBs and pulsar glitches. These statistical features can be well understood within the same physical framework of self-organized criticality systems.

Finding the Particularity of the Active Episode of SGR J1935+2154 during Which FRB 20200428 Occurred: Implication from Statistics of Fermi/GBM X-Ray Bursts

By using the Fermi/Gamma-ray Burst Monitor data of the X-ray bursts (XRBs) of SGR J1935+2154, we investigate the temporal clustering of the bursts and the cumulative distribution of the waiting time and fluence/flux. It is found that the bursts occurring in the episode hosting FRB 20200428 have obviously shorter waiting times than those in the other episodes. The general statistical properties of the XRBs further indicate they could belong to a self-organized critical system (e.g., starquakes), making them very similar to the earthquake phenomena. Then, according to a unified scaling law between the waiting time and energy of the earthquakes as well as their aftershocks, we implement an analogy analysis on the XRBs and find that the fast radio burst (FRB) episode owns more dependent burst events than the other episodes. It is indicated that the FRB emission could be produced by the interaction between different burst events, which could correspond to a collision between different seismic/Alfvén waves or different explosion outflows. Such a situation could appear when the magnetar enters into a global intensive activity period.

Phase transitions of civil unrest across countries and time

Phase transitions, characterized by abrupt shifts between macroscopic patterns of organization, are ubiquitous in complex systems. Despite considerable research in the physical and natural sciences, the empirical study of this phenomenon in societal systems is relatively underdeveloped. The goal of this study is to explore whether the dynamics of collective civil unrest can be plausibly characterized as a sequence of recurrent phase shifts, with each phase having measurable and identifiable latent characteristics. Building on previous efforts to characterize civil unrest as a self-organized critical system, we introduce a macro-level statistical model of civil unrest and evaluate its plausibility using a comprehensive dataset of civil unrest events in 170 countries from 1946 to 2017. Our findings demonstrate that the macro-level phase model effectively captures the characteristics of civil unrest data from diverse countries globally and that universal mechanisms may underlie certain aspects of the dynamics of civil unrest. We also introduce a scale to quantify a country’s long-term unrest per unit of time and show that civil unrest events tend to cluster geographically, with the magnitude of civil unrest concentrated in specific regions. Our approach has the potential to identify and measure phase transitions in various collective human phenomena beyond civil unrest, contributing to a better understanding of complex social systems.

Prediction of depinning transitions in interface models using Gini and Kolkata indices.

The intermittent dynamics of driven interfaces through disordered media and its subsequent depinning for large enough driving force is a common feature for a myriad of diverse systems, starting from mode-I fracture, vortex lines in superconductors, and magnetic domain walls to invading fluid in a porous medium, to name a few. In this work, we outline a framework that can give a precursory signal of the imminent depinning transition by monitoring the variations in sizes or the inequality of the intermittent responses of a system that are seen prior to the depinning point. In particular, we use measures traditionally used to quantify economic inequality, i.e., the Gini index and the Kolkata index, for the case of the unequal responses of precritical systems. The crossing point of these two indices serves as a precursor to imminent depinning. Given a scale-free size distribution of the responses, we calculate the expressions for these indices, evaluate their crossing points, and give a recipe for forecasting depinning transitions. We apply this method to the Edwards-Wilkinson, Kardar-Parisi-Zhang, and fiber bundle model interface with variable interaction strengths and quenched disorder. The results are applicable for any interface dynamics undergoing a depinning transition. The results also explain previously observed near-universal values of Gini and Kolkata indices in self-organized critical systems.

Distributions of Energy, Luminosity, Duration, and Waiting Times of Gamma-Ray Burst Pulses with Known Redshift Detected by Fermi/GBM

Discovered more than 50 years ago, gamma-ray burst (GRB) prompt emission remains the most puzzling aspect of GRB physics. Its complex and irregular nature should reveal how newborn GRB engines release their energy. In this respect, the possibility that GRB engines could operate as self-organized critical (SOC) systems has been put forward. Here, we present the energy, luminosity, waiting time, and duration distributions of individual pulses of GRBs with known redshift detected by the Fermi Gamma-ray Burst Monitor. This is the first study of this kind in which selection effects are accounted for. The compatibility of our results with the framework of SOC theory is discussed. We found evidence for an intrinsic break in the power-law models that describe the energy and the luminosity distributions.

The self-organized criticality behaviours of two new parameters in SGR J1935+2154

ABSTRACT The minimum variation time-scale (MVT) and spectral lag of hundreds of X-ray bursts (XRBs) from soft gamma-ray repeater (SGR) J1935+2154 were analysed in detail for the first time in our recent work, which are important probes for studying the physical mechanism and radiation region. In this work, we investigate their differential and cumulative distributions carefully and find that they follow power-law models. Besides, the distributions of fluctuations in both parameters follow the Tsallis q-Gaussian distributions and the q values are consistent for different scale intervals. Therefore, these results indicate that both parameters are scale-invariant, which provides new parameters for the study of self-organized criticality systems. Interestingly, we find that the q values for MVT and spectral lag are similar with duration and fluence, respectively.

Universal Complexity Science and Theory of Everything: Challenges and Prospects

This article argues that complexity scientists have been searching for a universal complexity in the form of a “theory of everything” since some important theoretical breakthroughs such as Bertalanffy’s general systems theory, Wiener’s cybernetics, chaos theory, synergetics, self-organization, self-organized criticality and complex adaptive systems, which brought the study of complex systems into mainstream science. In this respect, much attention has been paid to the importance of a “reductionist complexity science” or a “reductionist theory of everything”. Alternatively, many scholars strongly argue for a holistic or emergentist “theory of everything”. The unifying characteristic of both attempts to account for complexity is an insistence on one robust explanatory framework to describe almost all natural and socio-technical phenomena. Nevertheless, researchers need to understand the conceptual historical background of “complexity science” in order to understand these longstanding efforts to develop a single all-inclusive theory. In this theoretical overview, I address this underappreciated problem and argue that both accounts of the “theory of everything” seem problematic, as they do not seem to be able to capture the whole of reality. This realization could mean that the idea of a single omnipotent theory falls flat. However, the prospects for a “holistic theory of everything” are much better than a “reductionist theory of everything”. Nonetheless, various forms of contemporary systems thinking and conceptual tools could make the path to the “theory of everything” much more accessible. These new advances in thinking about complexity, such as “Bohr’s complementarity”, Morin’s Complex thinking, and Cabrera’s DSRP theory, might allow the theorists to abandon the EITHER/OR logical operators and start thinking about BOTH/AND operators to seek reconciliation between reductionism and holism, which might lead them to a new “theory of everything”.

Criticality Analysis: Bio-Inspired Nonlinear Data Representation.

The representation of arbitrary data in a biological system is one of the most elusive elements of biological information processing. The often logarithmic nature of information in amplitude and frequency presented to biosystems prevents simple encapsulation of the information contained in the input. Criticality Analysis (CA) is a bio-inspired method of information representation within a controlled Self-Organised Critical system that allows scale-free representation. This is based on the concept of a reservoir of dynamic behaviour in which self-similar data will create dynamic nonlinear representations. This unique projection of data preserves the similarity of data within a multidimensional neighbourhood. The input can be reduced dimensionally to a projection output that retains the features of the overall data, yet has a much simpler dynamic response. The method depends only on the Rate Control of Chaos applied to the underlying controlled models, which allows the encoding of arbitrary data and promises optimal encoding of data given biologically relevant networks of oscillators. The CA method allows for a biologically relevant encoding mechanism of arbitrary input to biosystems, creating a suitable model for information processing in varying complexity of organisms and scale-free data representation for machine learning.

Dragon kings in self-organized criticality systems

Dragon kings in self-organized criticality systems

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.

Renormalization group analysis of a self-organized critical system: intrinsic anisotropy vs random environment

Abstract We study a self-organized critical system coupled to an isotropic random fluid environment. The former is described by a strongly anisotropic continuous (coarse-grained) model introduced by Hwa and Kardar (1989 Phys. Rev. Lett. 62 1813; 1992 Phys. Rev. A 45 7002); the latter is described by the stirred Navier–Stokes equation due to Forster et al (1977 Phys. Rev. A 16 732). The full problem of two coupled stochastic equations is represented as a field-theoretic model, which is shown to be multiplicatively renormalizable. The corresponding renormalization group (RG) equations possess a semi-infinite curve of fixed points in the four-dimensional space of the model parameters. The whole curve is infrared attractive for realistic values of parameters; its endpoint corresponds to the purely isotropic regime where the original Hwa–Kardar nonlinearity becomes irrelevant. There, one is left with a simple advection of a passive scalar field by the external environment. The main critical dimensions are calculated to leading (one-loop) order (first terms in the ϵ = 4 − d expansion); some of them are exact in all orders. These dimensions remain the same along that curve, which makes it reasonable to interpret it as a single universality class. However, the correction exponents do vary along the curve. It is therefore not clear whether the curve survives in all orders of the RG expansion or shrinks to a single point when the higher-order corrections are taken into account.

Repeating Fast Radio Bursts Reveal Memory from Minutes to an Hour

Fast radio bursts (FRBs) are brief, luminous pulses with unknown physical origin. The repetition pattern of FRBs contains essential information about their physical nature and emission mechanisms. Using the two largest samples of FRB 20121102 and FRB 20201124A, we report that the sources of the two FRBs reveal memory over a large range of timescales, from a few minutes to about an hour. The memory is detected from the coherent growths in burst-rate structures and the Hurst exponent. The waiting time distribution displays an approximate power-law tail, which is consistent with a Poisson model with a time-varying rate. From cellular automaton simulations, we find that these characteristics can be well understood within the physical framework of a self-organized criticality system driven in a correlation way, such as random walk functions. These properties indicate that the triggers of bursts are correlated, preferring the crustal failure mechanism of neutron stars.

Anomalous Self-Organization in Active Piles.

Inspired by recent observations on active self-organized critical (SOC) systems, we designed an active pile (or ant pile) model with two ingredients: beyond-threshold toppling and under-threshold active motions. By including the latter component, we were able to replace the typical power-law distribution for geometric observables with a stretched exponential fat-tailed distribution, where the exponent and decay rate are dependent on the activity's strength (ζ). This observation helped us to uncover a hidden connection between active SOC systems and α-stable Levy systems. We demonstrate that one can partially sweep α-stable Levy distributions by changing ζ. The system undergoes a crossover towards Bak-Tang-Weisenfeld (BTW) sandpiles with a power-law behavior (SOC fixed point) below a crossover point ζ<ζ*≈0.1.

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.

The universality of power law slopes in the solar photosphere and transition region observed with HMI and IRIS

We compare the size distributions of self-organized criticality (SOC) systems in the solar photosphere and the transition region, using magnetogram data from Helioseismic and Magnetic Imager (HMI) and Interface Region Imaging Spectrograph (IRIS) data. For each dataset we fit a combination of a Gaussian and a power law size distribution function, which yields information on four different physical processes: (i) Gaussian random noise in IRIS data; (ii) spicular events in the plages of the transition region (described by power law size distribution in IRIS data); (iii) salt-and-pepper small-scale magnetic structures (described by the random noise in HMI magnetograms); and (iv) magnetic reconnection processes in flares and nanoflares (described by power law size distributions in HMI data). We find a high correlation (CCC = 0.90) between IRIS and HMI data. Datasets with magnetic flux balance are generally found to match the SOC-predicted power law slope αF = 1.80 (for mean fluxes F), but exceptions occur due to arbitrary choices of the HMI field-of-view. The matching cases confirm the universality of SOC-inferred flux size distributions, and agree with the results of Parnell et al. (ApJ, 2009, 698, 75–82), αF = 1.85 ± 0.14.

Computing sandpile configurations using integer linear programming

Sandpile group or Abelian sandpile model was the first example of a self-organized critical system studied by Bak, Tang and Wiesenfeld. It is well known that these recurrent configurations can be characterized as the optimal solution of certain non-linear optimization problems. We show that recurrent configurations of the Abelian sandpile model of a graph correspond to optimal solutions of some integer linear programs. More precisely, we present two new integer linear programming models, one that computes recurrent configurations and other one that computes the order of the configuration. As an application, we calculate the identity configuration for the cone of a regular graph and the cycle with n+1 vertices using the Weak Duality Theorem in linear programming.

Power-law Distribution and Scale-invariant Structure from the First CHIME/FRB Fast Radio Burst Catalog

We study the statistical property of fast radio bursts (FRBs) based on a selected sample of 190 one-off FRBs in the first CHIME/FRB catalog. Three power law models are used in the analysis, and we find the cumulative distribution functions of energy can be well fitted by bent power law and thresholded power law models. The distribution functions of fluctuations of energy well follow the Tsallis q-Gaussian distribution. The q values in the Tsallis q-Gaussian distribution are constant with small fluctuations for different temporal scale intervals, indicating a scale-invariant structure of the bursts. The earthquakes and soft gamma repeaters show similar properties, which are consistent with the predictions of self-organized criticality systems.