Self-organized Critical State Research Articles

Dynamical complexity in microscale disk-wind systems

Powerful winds at accretion-disk scales have been observed in the past 20 years in many active galactic nuclei (AGN). These are the so-called ultrafast outflows (UFOs). Outflows are intimately related to mass accretion through the conservation of angular momentum, and they are therefore a key ingredient of most accretion disk models around black holes (BHs). At the same time, nuclear winds and outflows can provide the feedback that regulates the joint BH and galaxy growth. We reconsidered UFO observations in the framework of disk-wind scenarios, both magnetohydrodynamic disk winds and radiatively driven winds. We studied the statistical properties of observed UFOs from the literature and derived the distribution functions of the ratio $ of the mass-outflow and -inflow rates and the ratio $ of the mass-outflow and the Eddington accretion rates. We studied the links between $ and $ and the Eddington ratio $ L_ bol L_ Edd $. We derived the typical wind-activity history in our sources by assuming that it can be statistically described by population functions. We find that the distribution functions of $ and $ can be described as power laws above some thresholds, suggesting that there may be many wind subevents for each major wind event in each AGN activity cycle, which is a fractal behavior. We then introduced a simple cellular automaton to investigate how the dynamical properties of an idealized disk-wind system change following the introduction of simple feedback rules. We find that without feedback, the system is overcritical. Conversely, when feedback is present, regardless of whether it is magnetic or radiation driven, the system can be driven toward a self-organized critical state. Our results corroborate the hypothesis that AGN feedback is a necessary key ingredient in disk-wind systems, and following this, in shaping the coevolution of galaxies and supermassive BHs.

The role of intervention mechanisms on a self-organized system: dynamics of a sandpile with site reinforcement

We revisit the sandpile model and examine the effect of introducing site-dependent thresholds that increase over time based on the generated avalanche size. This is inspired by the simplest means of introducing stability into a self-organized system: the locations of collapse are repaired and reinforced. Statistically, for the case of finite driving times, we observe that the site-dependent reinforcements decrease the occurrence of very large avalanches, leading to an effective global stabilization. Interestingly, however, long simulation runs indicate that the system will persist in a state of self-organized criticality (SOC), recovering the power-law distributions with a different exponent as the original sandpile. These results suggest that tipping the heavy-tailed power-laws into more equitable and normal statistics may require unrealistic scales of intervention for real-world systems, and that, in the long run, SOC mechanisms still emerge. This may help explain the robustness of power-law statistics for many complex systems.

Do Successful Researchers Reach the Self-Organized Critical Point?

The index of success of the researchers is now mostly measured using the Hirsch index (h). Our recent precise demonstration, that statistically h∼Nc∼Np, where Np and Nc denote, respectively, the total number of publications and total citations for the researcher, suggests that average number of citations per paper (Nc/Np), and hence h, are statistical numbers (Dunbar numbers) depending on the community or network to which the researcher belongs. We show here, extending our earlier observations, that the indications of success are not reflected by the total citations Nc, rather by the inequalities among citations from publications to publications. Specifically, we show that for highly successful authors, the yearly variations in the Gini index (g, giving the average inequality of citations for the publications) and the Kolkata index (k, giving the fraction of total citations received by the top (1−k) fraction of publications; k=0.80 corresponds to Pareto’s 80/20 law) approach each other to g=k≃0.82, signaling a precursor for the arrival of (or departure from) the self-organized critical (SOC) state of his/her publication statistics. Analyzing the citation statistics (from Google Scholar) of thirty successful scientists throughout their recorded publication history, we find that the g and k for the highly successful among them (mostly Nobel laureates, highest rank Stanford cite-scorers, and a few others) reach and hover just above (and then) below that g=k≃0.82 mark, while for others they remain below that mark. We also find that all the lower (than the SOC mark 0.82) values of k and g fit a linear relationship, k=1/2+cg, with c=0.39, as suggested by an approximate Landau-type expansion of the Lorenz function, and this also indicates k=g≃0.82 for the (extrapolated) SOC precursor mark.

Gyrokinetic analysis of turbulent transport by electromagnetic turbulence in finite β plasmas with weak magnetic shear on HL-2A

Turbulent transport and zonal flow (ZF) dynamics in the mixed kinetic ballooning mode (KBM) and ion temperature gradient (ITG) mode dominated turbulence states are analyzed by gyrokinetic simulations based on the experimental observations of KBMs in the HL-2A Internal Transport Barrier (ITB) plasmas with weak magnetic shear configuration. Results have shown that KBMs and ITGs are the main candidates for turbulent transport and the inclusion of fast ions (FIs) can destabilize both instabilities, which is resulted by the decrease of ballooning parameter αMHD hence reduced Shafranov shift stabilization due to the negative FI density gradient, making them more unstable according to the ŝ-αMHD diagram. In addition, the ITGs are suppressed by both dilution and finite-β stabilization effects caused by FIs. Nonlinear simulations excluding the effects of FIs indicate that the transport is minimum at as the turbulence predominated by ITGs is strongly suppressed by the nonlinear electromagnetic (EM) stabilization and enhancement of ZFs. However, the transport is further increased with β e although the ZFs become stronger due to the transition from ITG to KBM dominated turbulence state. The presence of FIs can modify the relation between ZF shearing rate and β e. The transport level is insensitive to β e when but increases significantly because of the KBM destabilization. Meanwhile, the ZF amplitude reaches maximum at whereas it suffers an erosion at higher values, implying that the plasma might be a self-organized critical state owning to the interactions among ZFs, KBMs and FI effects hence setting the plasma β around β exp. The results have also provided a possible explanation that the destabilization of EM turbulence is responsible for the ion heat transport stiffness under weak magnetic shear configurations in the off-axis neutral beam injection heated ITB plasmas on HL-2A.

Relationship between structural heterogeneity and serrated flow in nanoscale phase separated Zr-Cu-Fe-Al bulk metallic glasses

In this work, the relationship between structural heterogeneity and serrated flow in nanoscale phase separated Zr-Cu-Fe-Al bulk metallic glasses with different plasticity was investigated. The results showed that liquid-liquid phase separation would occur during rapid cooling of Zr59(Cu1-xFex)33Al8 (x = 0.4 and 0.5) alloys, resulting in the microstructure formation of amorphous FeZr-rich nanoparticles embedded in the amorphous CuZr-rich matrix. The compression test and statistical analysis indicated that serration dynamics transforms from a chaotic state with a characteristic length scale of stress drop to a self-organized critical (SOC) state with the increase of the atomic ratio of Cu to Fe. This transformation is ascribed to the increase of the number of nucleation sites for shear transformation zones with the increase of structural heterogeneity, which is conducive to the formation of multiple shear bands. This work will be helpful to understand the relationship between the microstructure and deformation behavior.

Ductile Ni-based bulk metallic glasses at room temperature

In this work, a series of new Ni76-xCoxNb4P16B4 (x = 5, 10, 15, in at.%) bulk metallic glasses (BMGs) with the maximum diameter in the range of 1.2–1.6 mm were prepared by combining fluxing and J-quenching technology. The effects of Co content on glass forming ability (GFA), thermal stability, mechanical properties, serrated-flow behaviors and corrosion performance of the present Ni-based BMGs were systematically investigated. The ranges of Tg and ΔTx are 664–668 K and 21–31 K, respectively. Uniaxial compressive tests revealed that the present Ni-based BMGs have the compressive plastic strain (εp), yield strength (δy), and fracture strength (δf) that range from 16% to 27%, 2.1–2.6 GPa, and 2.2–3.6 GPa, respectively. The unprecedented mechanical properties originate from more icosahedral-like clusters (ILCs) and crystal-like clusters (CLCs) in the present Ni-based BMGs. It is found that the serrated-flow behaviors of the present Ni-based BMGs transition self-organized critical state (SOCs) into chaotic state (Cs) as plasticity decreases. The stick-slip dynamics were used to calculate the average shear-band velocity (ASBV), which shows an increasing trend as the Co content rises from 5 at.% to 15 at.%. Electrochemical measurements in 3.5 wt.% NaCl solution showed that the Ni71Co5Nb4P16B4 BMG has a self-corrosion current density of 3.30 × 10−8 A/cm2 and significantly stronger corrosion resistance than austenite 316L and 304L stainless steel. The present Ni-based BMGs have excellent comprehensive performance, which has great potential for industrial applications.

Critical Drift in a Neuro-Inspired Adaptive Network.

It has been postulated that the brain operates in a self-organized critical state that brings multiple benefits, such as optimal sensitivity to input. Thus far, self-organized criticality has typically been depicted as a one-dimensional process, where one parameter is tuned to a critical value. However, the number of adjustable parameters in the brain is vast, and hence critical states can be expected to occupy a high-dimensional manifold inside a high-dimensional parameter space. Here, we show that adaptation rules inspired by homeostatic plasticity drive a neuro-inspired network to drift on a critical manifold, where the system is poised between inactivity and persistent activity. During the drift, global network parameters continue to change while the system remains at criticality.

Sandpile Universality in Social Inequality: Gini and Kolkata Measures.

Social inequalities are ubiquitous and evolve towards a universal limit. Herein, we extensively review the values of inequality measures, namely the Gini (g) index and the Kolkata (k) index, two standard measures of inequality used in the analysis of various social sectors through data analysis. The Kolkata index, denoted as k, indicates the proportion of the 'wealth' owned by (1-k) fraction of the 'people'. Our findings suggest that both the Gini index and the Kolkata index tend to converge to similar values (around g=k≈0.87, starting from the point of perfect equality, where g=0 and k=0.5) as competition increases in different social institutions, such as markets, movies, elections, universities, prize winning, battle fields, sports (Olympics), etc., under conditions of unrestricted competition (no social welfare or support mechanism). In this review, we present the concept of a generalized form of Pareto's 80/20 law (k=0.80), where the coincidence of inequality indices is observed. The observation of this coincidence is consistent with the precursor values of the g and k indices for the self-organized critical (SOC) state in self-tuned physical systems such as sand piles. These results provide quantitative support for the view that interacting socioeconomic systems can be understood within the framework of SOC, which has been hypothesized for many years. These findings suggest that the SOC model can be extended to capture the dynamics of complex socioeconomic systems and help us better understand their behavior.

Response of cross-correlations between high PM2.5 and O3 with increasing time scales to the COVID-19: different trends in BTH and PRD

The air pollution in China currently is characterized by high fine particulate matter (PM2.5) and ozone (O3) concentrations. Compared with single high pollution events, such double high pollution (DHP) events (both PM2.5 and O3 are above the National Ambient Air Quality Standards (NAAQS)) pose a greater threat to public health and environment. In 2020, the outbreak of COVID-19 provided a special time window to further understand the cross-correlation between PM2.5 and O3. Based on this background, a novel detrended cross-correlation analysis (DCCA) based on maximum time series of variable time scales (VM-DCCA) method is established in this paper to compare the cross-correlation between high PM2.5 and O3 in Beijing-Tianjin-Heibei (BTH) and Pearl River Delta (PRD). At first, the results show that PM2.5 decreased while O3 increased in most cities due to the effect of COVID-19, and the increase in O3 is more significant in PRD than in BTH. Secondly, through DCCA, the results show that the PM2.5-O3 DCCA exponents α decrease by an average of 4.40% and 2.35% in BTH and PRD respectively during COVID-19 period compared with non-COVID-19 period. Further, through VM-DCCA, the results show that the PM2.5-O3 VM-DCCA exponents [Formula: see text] in PRD weaken rapidly with the increase of time scales, with decline range of about 23.53% and 22.90% during the non-COVID-19 period and COVID-19 period respectively at 28-h time scale. BTH is completely different. Without significant tendency, its [Formula: see text] is always higher than that in PRD at different time scales. Finally, we explain the above results with the self-organized criticality (SOC) theory. The impact of meteorological conditions and atmospheric oxidation capacity (AOC) variation during the COVID-19 period on SOC state are further discussed. The results show that the characteristics of cross-correlation between high PM2.5 and O3 are the manifestation of the SOC theory of atmospheric system. Relevant conclusions are important for the establishment of regionally targeted PM2.5-O3 DHP coordinated control strategies.

Metaphorical language change is Self-Organized Criticality

Abstract One way to resolve the actuation problem of metaphorical language change is to provide a statistical profile of metaphorical constructions and generative rules with antecedent conditions. Based on arguments from the view of language as complex systems and the dynamic view of metaphor, this paper argues that metaphorical language change qualifies as a Self-Organized Criticality state and the linguistic expressions of a metaphor can be profiled as a fractal with spatio-temporal correlations. Synchronously, these metaphorical expressions self-organize into a self-similar, scale-invariant fractal that follows a power-law distribution; temporally, long range interdependence constrains the self-organization process by the way of transformation rules that are intrinsic of a language system. This argument is verified in the paper with statistical analyses of twelve randomly selected Chinese verb metaphors in a large-scale diachronic corpus.

Shear transformation zones and serrated flow dynamics of metallic glasses revealed by nanoindentation

The relationship between shear transformation zones (STZs) and serrated flow dynamics of Co-, Fe-, Zr-, La- and Al-based metallic glasses (MGs) with different plasticity were analyzed by nanoindentation. The serrated flow dynamic behaviors were analyzed using statistical analysis of shear stress drops, Δτ. The STZ size was estimated via the nanoindentation creep method based on the cooperative shear model. Examination of two distinct types of serrated flow dynamics were performed. For MGs (e.g., Al- or Zr-based) where STZs could be easily activated or at low loading rates, shear stress exhibited a decreasing trend and followed a power-law distribution, which was an indicator of a self-organized critical (SOC) state in the dynamics. In contrast, a Gaussian law distribution was found for STZs in hard MGs (e.g., La-, Co-, and Fe-based) or at high loading rate. In the case of Gaussian distribution case, serrated flow dynamics were in a chaotic state, which indicated that STZ aggregation reduced the stresses required for plastic deformation.

Avalanches of magnetic flux rope in the state of self-organized criticality

ABSTRACT The self-organized criticality (SOC) is a universal theory to explain the ubiquitous power-law size distributions of astrophysical instabilities such as solar eruptions. One way to understand the dynamical processes of an SOC system is through cellular automaton (CA) simulations. Here, we develop a three-dimensional solar CA model that assumes a twisted magnetic flux rope (MFR), in which the avalanche takes place when a local magnetic vector potential exceeds a Gaussian distributed instability criterion, triggered by a global and space-dependent energy driving mechanism. To avoid non-physical released energies, an energy screening mechanism is applied to calculate the avalanche energies of each time-step. Our results show that the statistics of the CA simulated flaring events are comparable to the frequency distributions of observed solar flares originating from an individual active region. Due to the fact of the universality of MFRs, the CA model can be applied to many other astrophysical SOC systems.

Application of the Theory of Self-organized Criticality to the Analysis of the Liberal Agenda in the Press of 1815-1825.

The subject of the research in this paper is the liberal agenda in the Russian press of the pre-Decabrist period. The object of the study is the newspapers published during this period. The novelty of the work lies in the fact that the proposed study searches for pink noise in the data that were obtained from the press of the first quarter of the XIX century. The paper shows that the public consciousness of this period was in a state of self-organized criticality. Previously, the state of self-organized criticality could be found only in systems that arose at the end of the XIX century or later. The difficulty of the problem considered in this paper is that there are almost no mass sources for such an early historical period, and very few of the available ones lend themselves to formalization. The novelty of the conducted research lies in the application of the scientific tool of the theory of self-organized criticality to data having origins in the first quarter of the XIX century. The main conclusion made by the authors of the article is that the public consciousness in the pre-Decabrist period was in a state of self-organized criticality. For the analysis, statistics of publications in newspapers and magazines were collected, which served as a reflection of the liberal agenda relevant to the period of the genesis of the Decembrists. The paper shows that the sequence of publications on liberal information issues in the Russian press in the period 1815-1825 contains pink noise. Fourier analysis was used to determine it in the dynamic series.

Near universal values of social inequality indices in self-organized critical models

We have studied few social inequality measures associated with the sub-critical dynamical features (measured in terms of the avalanche size distributions) of four self-organized critical models while the corresponding systems approach their respective stationary critical states. It has been observed that these inequality measures (specifically the Gini and Kolkata indices) exhibit nearly universal values though the models studied here are widely different, namely the Bak–Tang–Wiesenfeld sandpile, the Manna sandpile and the quenched Edwards–Wilkinson interface, and the fiber bundle interface. These observations suggest that the self-organized critical systems have broad similarity in terms of these inequality measures. A comparison with similar earlier observations in the data of socio-economic systems with unrestricted competitions suggest the emergent inequality as a result of the possible proximity to the self-organized critical states.

Mechanical and tribological behaviors of metallic glass/graphene film with a laminated structure

Metallic glass (MG) film often suffer from high friction and wear, which considerably limit their lifespan in sliding contact service. In this study, graphene (GR) is chosen as an interfacial material to develop a MG/GR multilayer with enhanced mechanical and tribological properties. We report on the fabrication of this multilayer by repeated deposition of Cu50Zr50 MG alternating with transfer of GR. Upon deformation, it is found that the incorporation of GR can lead to extensive shear bands and shear band/interface interactions, which are confirmed by the transition of deformation mode from a chaotic to a self-organized critical state. In comparison with the monolithic MG film, the coefficient of friction and wear rate of the multilayer are decreased by ∼ 35% and 65% respectively, which is attributed to the enhanced mechanical properties and lubricating effect induced by the GR layer. The current work not only broadens our understanding of the positive role of GR in improving the frictional behavior of MG, but opens a new path for designing of novel MG films with a combination of exceptional mechanical and tribological properties.

Early Warning Signals for Critical Transitions in Sandpile Cellular Automata

The sandpile cellular automata, despite the simplicity of their basic rules, are adequate mathematical models of real-world systems, primarily open nonlinear systems capable to self-organize into the critical state. Such systems surround us everywhere. Starting from processes at microscopic distances in the human brain and ending with large-scale water flows in the oceans. The detection of critical transitions precursors in sandpile cellular automata will allow progress significantly in the search for effective early warning signals for critical transitions in complex real systems. The presented paper is devoted to the detection and investigation of such signals based on multifractal analysis of the time series of falls of the cellular automaton cells. We examined cellular automata in square lattice and random graphs using standard and facilitated rules. It has been established that log wavelet leaders cumulant are effective early warning measures of the critical transitions. Common features and differences in the behavior of the log cumulants when cellular automata transit into the self-organized critical state and the self-organized bistability state are also established.

Self-organization of salt marsh patches on mudflats: Field evidence using the UAV technique

The salt marsh system on the tidal flat is one of the most productively ecological wetlands with high biological productivity and blue carbon sequestration levels. The evolution of salt marshes-bare flats boundaries and the shapes of salt marsh margins are of scientific and engineering prospects due to the capability on indicating the morphodynamic patterns of tidal flats. Previous studies are almost qualitative, so far, quantitative analysis on this issue is scarce. To improve our understandings on the spatio-temporal characteristics of salt marsh margins and the mechanism underpinning, we extracted datasets on Spartina alterniflora using orthoimages derived from the quarterly-surveyed UAV photographs and satellite imagery. Results show that the patch-size distribution corresponded to the power law, indicating the marsh patches are in the state of self-organized criticality and the system is scale-independent. It was observed that the external dynamic conditions (i.e., the sediment erosion and accretion on the tidal flat) imposed negative impacts on the self-organization process. In particular, when the short-term morphological changes were negligible, R2 of the power-law relationship notably increased to nearly 1, indicating the salt marsh patches tended to adhere to a high-order self-organization structure in this process.

Aperiodic and Periodic Components of Ongoing Oscillatory Brain Dynamics Link Distinct Functional Aspects of Cognition across Adult Lifespan.

Signal transmission in the brain propagates via distinct oscillatory frequency bands but the aperiodic component, 1/f activity, almost always co-exists which most of the previous studies have not sufficiently taken into consideration. We used a recently proposed parameterization model that delimits the oscillatory and aperiodic components of neural dynamics on lifespan aging data collected from human participants using magnetoencephalography (MEG). Since healthy aging underlines an enormous change in local tissue properties, any systematic relationship of 1/f activity would highlight their impact on the self-organized critical functional states. Furthermore, we have used patterns of correlation between aperiodic background and metrics of behavior to understand the domain general effects of 1/f activity. We suggest that age-associated global change in 1/f baseline alters the functional critical states of the brain affecting the global information processing impacting critically all aspects of cognition, e.g., metacognitive awareness, speed of retrieval of memory, cognitive load, and accuracy of recall through adult lifespan. This alteration in 1/f crucially impacts the oscillatory features peak frequency (PF) and band power ratio, which relates to more local processing and selective functional aspects of cognitive processing during the visual short-term memory (VSTM) task. In summary, this study leveraging on big lifespan data for the first time tracks the cross-sectional lifespan-associated periodic and aperiodic dynamical changes in the resting state to demonstrate how normative patterns of 1/f activity, PF, and band ratio (BR) measures provide distinct functional insights about the cognitive decline through adult lifespan.

Quasistatic kinetic avalanches and self-organized criticality in deviatorically loaded granular media.

The behavior of granular media under quasistatic loading has recently been shown to attain a stable evolution state corresponding to a manifold in the space of micromechanical variables. This state is characterized by sudden transitions between metastable jammed states, involving the partial micromechanical rearrangement of the granular medium. Using numerical simulations of two-dimensional granular media under quasistatic biaxial compression, we show that the dynamics in the stable evolution state is characterized by scale-free avalanches well before the macromechanical stationary flow regime traditionally linked to a self-organized critical state. This, together with the nonuniqueness and the nonmonotony of macroscopic deformation curves, suggests that the statistical avalanche properties and the susceptibilities of the system cannot be reduced to a function of the macromechanical state. The associated scaling exponents are nonuniversal and depend on the interactions between particles. For stiffer particles (or samples at low confining pressure) we find distributions of avalanche properties compatible with the predictions of mean-field theory. The scaling exponents decrease below the mean-field values for softer interactions between particles. These lower exponents are consistent with observations for amorphous solids at their critical point. We specifically discuss the relationship between microscopic and macroscopic variables, including the relation between the external stress drop and the internal potential energy released during kinetic avalanches.

On the similarity of shear deformation of a granular massif and a fragmented medium in the seismically active area

In recent research, the dynamics of the medium located in the seismic region at the boundary of tectonic plates is considered as the behavior of a complex open system that is in a state of self-organized criticality. Such an approach results from the very laws of earthquake generation and the complex structure of these areas. The network of faults and cracks makes seismic zones significantly heterogeneous and fragmented. Therefore, discrete models are increasingly used to model the dynamics of these media. The basis for comparing the model and the full-scale object serves the statistical regularities of their dynamic deformation. Relying on this concept, in the paper it is modeled the shear dynamics of a granular massif composed of identical cubic granules and is compared system’s statistical characteristics with the similar characteristics obtained for the earthquake generation zone. Shear deformation is carried out by means of the box consisting of two parts — movable and immovable ones. The movable part possesses the cover which receives kinetic energy from the granular massif in the process of shear deformation. For numerical simulations of the shear dynamics, the discrete element method is applied. The numerical calculations result in the distribution of cover’s kinetic energy jumps simulating the perturbations transmitted from the granular system to an external medium. It turned out that the distribution for these perturbations is the power dependence with an exponent that is inherent in earthquakes (Gutenberg-Richter law). Before and after large perturbations it is observed the swarms of smaller perturbations which are the analogues of foreshocks and aftershocks. The distributions of element’s velocity fluctuations and the correlation of velocity fluctuations are calculated as well. It is revealed the similarity of distributions for velocity fluctuations in the model massif and in the seismically active region of California, which includes the San Andreas fault. Moreover, the similarity of corresponding correlation functions is shown. They both are the functions of the stretched exponent. The obtained result indicates that shear processes in granular massifs and natural seismic processes in the San Andreas Fault are statistically similar.