Self-organized Critical State Research Articles

Stochastic Oscillation in Self-Organized Critical States of Small Systems: Sensitive Resting State in Neural Systems.

Self-organized critical states (SOCs) and stochastic oscillations (SOs) are simultaneously observed in neural systems, which appears to be theoretically contradictory since SOCs are characterized by scale-free avalanche sizes but oscillations indicate typical scales. Here, we show that SOs can emerge in SOCs of small size systems due to temporal correlation between large avalanches at the finite-size cutoff, resulting from the accumulation-release process in SOCs. In contrast, the critical branching process without accumulation-release dynamics cannot exhibit oscillations. The reconciliation of SOCs and SOs is demonstrated both in the sandpile model and robustly in biologically plausible neuronal networks. The oscillations can be suppressed if external inputs eliminate the prominent slow accumulation process, providing a potential explanation of the widely studied Berger effect or event-related desynchronization in neural response. The features of neural oscillations and suppression are confirmed during task processing in monkey eye-movement experiments. Our results suggest that finite-size, columnar neural circuits may play an important role in generating neural oscillations around the critical states, potentially enabling functional advantages of both SOCs and oscillations for sensitive response to transient stimuli.

Self-organized Criticality Behavior in Bulk Metallic Glasses

Serrated flows are known as repeated yielding of bulk metallic glasses (BMGs) during plastic deformation under different loading conditions, which are associated with the operation of shear banding. According to the statistics of some parameters, the shear avalanches can display a self-organized critical state, suggesting a large ductility of BMGs. The emergence of the self-organized criticality (SOC) behavior in different BMGs is due to the temperature, strain rate, and chemical compositions. The SOC behavior is accompanied with the following phenomena: the interactions occur in the shear bands; the incubation time is longer than the relaxation time; the time interval is lacking of typical time scale; and the spatial or temporal parameters should display a power-law distribution.

Effects of Random Environment on a Self-Organized Critical System: Renormalization Group Analysis of a Continuous Model

We study effects of random fluid motion on a system in a self-organized critical state. The latter is described by the continuous stochastic model, proposed by Hwa and Kardar [{\it Phys. Rev. Lett.} {\bf 62}: 1813 (1989)]. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form $\propto \delta(t-t') / k_{\bot}^{d-1+\xi}$, where $k_{\bot}=|{\bf k}_{\bot}|$ and ${\bf k}_{\bot}$ is the component of the wave vector, perpendicular to a certain preferred direction -- the $d$-dimensional generalization of the ensemble introduced by Avellaneda and Majda [{\it Commun. Math. Phys.} {\bf 131}: 381 (1990)]. Using the field theoretic renormalization group we show that, depending on the relation between the exponent $\xi$ and the spatial dimension $d$, the system reveals different types of large-scale, long-time scaling behaviour, associated with the three possible fixed points of the renormalization group equations. They correspond to ordinary diffusion, to passively advected scalar field (the nonlinearity of the Hwa--Kardar model is irrelevant) and to the "pure" Hwa--Kardar model (the advection is irrelevant). For the special choice $\xi=2(4-d)/3$ both the nonlinearity and the advection are important. The corresponding critical exponents are found exactly for all these cases.

Temporal analysis of acoustic emission from a plunged granular bed.

The statistical property of acoustic emission (AE) events from a plunged granular bed is analyzed by means of actual-time and natural-time analyses. These temporal analysis methods allow us to investigate the details of AE events that follow a power-law distribution. In the actual-time analysis, the calm-time distribution, and the decay of the event-occurrence density after the largest event (i.e., the Omori-Utsu law) are measured. Although the former always shows a power-law form, the latter does not always obey a power law. Markovianity of the event-occurrence process is also verified using a scaling law by assuming that both of them exhibit power laws. We find that the effective shear strain rate is a key parameter to classify the emergence rate of power-law nature and Markovianity in granular AE events. For the natural-time analysis, the existence of self-organized critical states is revealed by calculating the variance of natural time χ(k), where kth natural time of N events is defined as χ(k)=k/N. In addition, the energy difference distribution can be fitted by a q-Gaussian form, which is also consistent with the criticality of the system.

Research on the Characteristic of Automotive Failure Diagnosis Based on Complex Networks

In order to research the mechanism of automotive failure diagnose and to improve, as well as to explore a new perspective to a find automotive failure diagnose quickly. This paper is based on the empirical data to analyze Xian's some 4S shop and its self-organized criticality proposed a new suggestion. In this paper, we analyze in depth the data of automotive failure running status and diagnose index of different period between 2014, based on the theory of automotive failure diagnosed complexity and self-organized criticality, and thus proves the characteristics of power-law under which lies the related scale. The result shows us that, automotive failure diagnose system is a dynamical system that's both extensive and dissipative. In addition, when STATUS is under 20 or less and TPI is above 6, the scale of influenced districts caused by index in automotive diagnose system and the related frequency fits the law-power distribution, and the rising of automotive will reach the state of self-organized criticality, and meets the characteristic of self-organized criticality.

Enhanced plasticity of a Fe-based bulk amorphous alloy by thin Ni coating

A thin Ni coating well adhering on a Fe81Mo1P7.5C5.5B2Si3 bulk amorphous alloy (BAA) has been successfully prepared by electroless plating. It has been found that the plastic strain of the BAA is significantly increased to 8% (28 times enhanced) by the thin Ni coating. It shows that the coating with nanograin could promote the nucleation of shear bands, constrain the propagation of them and change the flow serration into a self-organized critical state, which drastically increase the plasticity of the BAA.

The Self-Organized Critical Behavior in Pd-based Bulk Metallic Glass

Bulk metallic glasses (BMGs) deform irreversibly through shear banding manifested as serrated-flow behavior during compressive tests. The strain-rate-dependent plasticity under uniaxial compression at the strain rates of 2 × 10−2, 2 × 10−3, and 2 × 10−4·s−1 in a Pd-based BMG is investigated. The serrated flow behavior is not observed in the stress-strain curve at the strain rate of 2 × 10−2·s−1. However, the medial state occurs at the strain rates of 2 × 10−3·s−1, and eventually the self-organized critical (SOC) behavior appears at the strain rate of 2 × 10−4·s−1. The distribution of the elastic energy density shows a power-law distribution with the power-law exponent of −2.76, suggesting that the SOC behavior appears. In addition, the cumulative probability is well approximated by a power-law distribution function with the power-law exponent of 0.22 at the strain rate of 2 × 10−4·s−1. The values of the goodness of fit are 0.95 and 0.99 at the strain rates of 2 × 10−3 and 2 × 10−4·s−1, respectively. The transition of the dynamic serrated flows of BMGs is from non-serrated flow to an intermediate state and finally to the SOC state with decreasing the strain rates.

Self-organized braiding in solar coronal loops

AbstractIn this paper, we investigate the evolution of braided solar coronal loops. We assume that coronal loops consist of several internal strands which twist and braid about each other. Reconnection between the strands leads to small flares and heating of the loop to x-ray temperatures. Using a method of generating and releasing braid structure similar to a forest fire model, we show that the reconnected field lines evolve to a self-organised critical state. In this state, the frequency distributions of coherent braid sequences as well as flare energies follow power law distributions. We demonstrate how the presence of net helicity in the loop alters the distribution laws.

Acoustic emission during quench training of superconducting accelerator magnets

Acoustic emission (AE) sensing is a viable tool for superconducting magnet diagnostics. Using in-house developed cryogenic amplified piezoelectric sensors, we conducted AE studies during quench training of the US LARP’s high-field quadrupole HQ02 and the LBNL’s high-field dipole HD3. For both magnets, AE bursts were observed, with spike amplitude and frequency increasing toward the quench current during current up-ramps. In the HQ02, the AE onset upon current ramping is distinct and exhibits a clear memory of the previously-reached quench current (Kaiser effect). On the other hand, in the HD3 magnet the AE amplitude begins to increase well before the previously-reached quench current (felicity effect), suggesting an ongoing progressive mechanical motion in the coils. A clear difference in the AE signature exists between the untrained and trained mechanical states in HD3. Time intervals between the AE signals detected at the opposite ends of HD3 coils were processed using a combination of narrow-band pass filtering; threshold crossing and correlation algorithms, and the spatial distributions of AE sources and the mechanical energy release were calculated. Both distributions appear to be consistent with the quench location distribution. Energy statistics of the AE spikes exhibits a power-law scaling typical for the self-organized critical state.

From Migmatites to Plutons: Power Law Relationships in the Evolution of Magmatic Bodies

Magma is generated by partial melting from micrometre-scale droplets at the source and may accumulate to form >100 km-scale plutons. Magma accumulation thus spans well over ten orders of magnitude in scale. Here we provide measurements of migmatitic leucosomes and granitic veins in drill cores from the Estonian Proterozoic basement and outcrops at Masku in SW Finland and Montemor-o-Novo, central Portugal. Despite the differences in size and number of measured leucosomes and magmatic veins, differences in host rock types and metamorphic grades, the cumulative width distribution of the studied magmatic leucosomes/veins follows a power law with exponents usually between 0.7 and 1.8. Published maps of the SE Australian Lachlan Fold Belt were used to investigate the distribution of granitoid pluton sizes. The granites occupy ca. 22 % of the 2.6 × 105 km2 area. The cumulative pluton area distributions show good power law distributions with exponents between 0.6 and 0.8 depending on pluton area group. Using the self-affine nature of pluton shapes, it is possible to estimate the total volume of magma that was expelled from the source in the 2.6 × 105 km2 map area, giving an estimated 0.8 km3 of magma per km2. It has been suggested in the literature that magma batches in the source merge to form ever-bigger batches in a self-organized way. This leads to a power law for the cumulative distribution of magma volumes, with an exponent m V between 1 for inefficient melt extraction, and 2/3 for maximum accumulation efficiency as most of the volume resides in the largest batches that can escape from the source. If m V ≥ 1, the mass of the magma is dominated by small batches; in case m = 2/3, about 50 % of all magma in the system is placed in a single largest batch. Our observations support the model that the crust develops a self-organized critical state during magma generation. In this state, magma batches accumulate in a non-continuous, step-wise manner to form ever-larger accumulations. There is no characteristic length or time scale in the partial melting process or its products. Smallest melt segregations and >km-scale plotuns form the end members of a continuous chain of mergers of magma batches.

Study on Blackout Model for Power Grid Growth Process

In this paper a blackout AC power flow model considering the probability of line stoppage in the process of power grid growth is given,and the self-organized critical state in the process of power grid growth is studied with the power grid upgrade rate is equal、greater or less than the load growth rate.Simulation results show that power grid upgrading rate must meet the system's load growth, or the probability of failure will be greatly increased with the grid exceed the critical state while the load growth faster than the grid upgrading in the long process of building the power grid. The model and simulation results presented in this paper provide a theoretical basis for the planning and construction of the power grid.

SPATIOTEMPORAL ORGANIZATION OF ENERGY RELEASE EVENTS IN THE QUIET SOLAR CORONA

Using data from STEREO and SOHO spacecraft, we show that temporal organization of energy release events in the quiet solar corona is close to random, in contrast to the clustered behavior of flaring times in solar active regions. The locations of the quiet-Sun events follow the meso- and supergranulation pattern of the underling photosphere. Together with earlier reports of the scale-free event size statistics, our findings suggest that quiet solar regions responsible for bulk coronal heating operate in a driven self-organized critical state, possibly involving long-range Alfv\'{e}nic interactions.

Self-organized criticality in a spherically closed cellular automaton: Modeling soft gamma repeater bursts driven by magnetic reconnection

A new cellular automaton (CA) model is presented for the self-organized criticality (SOC) in recurrent bursts of soft gamma repeaters (SGRs), which are interpreted as avalanches of reconnection in the magnetosphere of neutron stars. The nodes of a regular dodecahedron and a truncated icosahedron are adopted as spherically closed grids enclosing a neutron star. It is found that the system enters the SOC state if there are sites where the expectation value of the added perturbation is nonzero. The energy distributions of SOC avalanches in CA simulations are described by a power law with a cutoff, which is consistent with the observations of SGR 1806-20 and SGR 1900+14. The power-law index is not universal and depends on the amplitude of the perturbation. This result shows that the SOC of SGRs can be illustrated not only by the crust quake model but also by the magnetic reconnection model.

Fractal evolution of MHz electromagnetic signals prior to earthquakes: results collected in Greece during 2009

This paper addressed a fractal evolution of 11 one-month lasting MHz electromagnetic disturbances, recorded in Greece prior to nine significant earthquakes of 2009. Time-space wavelet-based power spectral techniques were employed in the analysis. All investigated signals evolved naturally to epochs of fractal organization in space and time. Continuous organization was detected in seven signals. Significant number of successive () power-law -values were observed lying between 1.5 and 3.0 or above. The majority of fractal segments exhibited anti-persistent () or persistent () behaviour. Switching between persistency and anti-persistency was also found. Locality and sensitivity were traced. Findings were considered indicative of self-organized critical states of the last stages of preparation of the investigated earthquakes. Results implied fractional Brownian modelling. Explanations were proposed in view of the asperity model. Persistent–anti-persistent MHz anomalies were due to self-organized micro-cracking of the heterogeneous medium of the earth's crust which may have led the system's evolution towards global failure. The precursory value of the signals was discussed.

Serrated creep and spatio-temporal structures of macrolocalized plastic deformation

The dynamics and morphology of macrolocalized deformation bands have been investigated using a complex of high-speed in situ methods under the conditions of serrated creep of flat samples of the aluminum-magnesium alloy 5456 with different aspect ratios. It has been found that, at the front of a macroscopic plastic deformation jump, a complex structure of propagating deformation bands, which are considered as macrolocalized deformation “quanta,” is spontaneously formed in the material. It has been shown that, with an increase in the sample length, the deformation behavior of the alloy tends to the state of self-organized criticality.

Spectral and dynamic analysis of plastic instabilities during serrated creep of the aluminum-magnesium alloy

The force response to the development of a macroscopic plastic deformation jump under the conditions of serrated creep of the aluminummagnesium alloy 5456 has been studied using spectral and dynamic analysis methods. The flicker-noise structure of the force response indicating the self-organized criticality state has been revealed. It has been found that a short-term state of plastic instability flatter spontaneously appears during the development of the macroscopic deformation step.

Self-organized cooperative criticality in coupled complex systems

We show that the coupled complex systems can evolve into a new kind of self-organized critical state where each subsystem is not critical; however, they cooperate to be critical. This criticality is different from the classical sandpile criticality where the single system itself evolves into a critical state. We also find that the outflows can be accumulated in the coupled systems. This will lead to the emergence of spatiotemporal intermittency in the critical state.

Spike avalanches in vivo suggest a driven, slightly subcritical brain state.

In self-organized critical (SOC) systems avalanche size distributions follow power-laws. Power-laws have also been observed for neural activity, and so it has been proposed that SOC underlies brain organization as well. Surprisingly, for spiking activity in vivo, evidence for SOC is still lacking. Therefore, we analyzed highly parallel spike recordings from awake rats and monkeys, anesthetized cats, and also local field potentials from humans. We compared these to spiking activity from two established critical models: the Bak-Tang-Wiesenfeld model, and a stochastic branching model. We found fundamental differences between the neural and the model activity. These differences could be overcome for both models through a combination of three modifications: (1) subsampling, (2) increasing the input to the model (this way eliminating the separation of time scales, which is fundamental to SOC and its avalanche definition), and (3) making the model slightly sub-critical. The match between the neural activity and the modified models held not only for the classical avalanche size distributions and estimated branching parameters, but also for two novel measures (mean avalanche size, and frequency of single spikes), and for the dependence of all these measures on the temporal bin size. Our results suggest that neural activity in vivo shows a mélange of avalanches, and not temporally separated ones, and that their global activity propagation can be approximated by the principle that one spike on average triggers a little less than one spike in the next step. This implies that neural activity does not reflect a SOC state but a slightly sub-critical regime without a separation of time scales. Potential advantages of this regime may be faster information processing, and a safety margin from super-criticality, which has been linked to epilepsy.

Can human-like Bots control collective mood: agent-based simulations of online chats

Using an agent-based modeling approach, in this paper, we study self-organized dynamics of interacting agents in the presence of chat Bots. Different Bots with tunable ‘human-like’ attributes, which exchange emotional messages with agents, are considered, and the collective emotional behavior of agents is quantitatively analyzed. In particular, using detrended fractal analysis we determine persistent fluctuations and temporal correlations in time series of agent activity and statistics of avalanches carrying emotional messages of agents when Bots favoring positive/negative affects are active. We determine the impact of Bots and identify parameters that can modulate that impact. Our analysis suggests that, by these measures, the emotional Bots induce collective emotion among interacting agents by suitably altering the fractal characteristics of the underlying stochastic process. Positive emotion Bots are slightly more effective than negative emotion Bots. Moreover, Bots which periodically alternate between positive and negative emotion can enhance fluctuations in the system, leading to avalanches of agent messages that are reminiscent of self-organized critical states.

Temperature dependent dynamics transition of intermittent plastic flow in a metallic glass. II. Dynamics analysis

By reducing the testing temperatures down to the temperature well below the glassy transition temperature, the serrated flow behaviour during plastic deformation of a Zr-based metallic glass was experimentally investigated and the results were presented in Part I of the present paper. It shows that the yield strength, the plastic deformation ability, the density of shear bands of the metallic glass increase with decreasing temperature. In order to understand the mechanisms for the changes of the mechanical behaviour at low temperatures, in Part II of this study, the stress-time sequence in the plastic strain regime is characterized by a comprehensive dynamical and statistical analysis. The stress-time sequence is found to exhibit a chaotic state at high temperatures (>203 K), whereas a self-organized critical state is obtained at low temperatures (≤203 K) due to the freezing effect. The reasons for the transition between these two distinct spatio-temporal dynamical states are elucidated by investigating the effect of temperature on the deformation units (shear transformation zones) and the elastic interactions between neighbouring shear bands. The results demonstrate that the low temperatures results in an enhancement of the interactions between the elastic strain fields initiated by neighbouring shear bands, which is primarily responsible for the enhanced plasticity of the metallic glass and a dynamics transition.