Signatures Of Self-organized Criticality Research Articles

Rotating self-gravitating Bose-Einstein condensates with a crust: A model for pulsar glitches

We develop a minimal self-gravitating model for pulsar glitches by introducing a solid-crust potential in the three-dimensional Gross-Pitaevskii-Poisson equation, which we have used earlier to study gravitationally bound Bose-Einstein condensates, i.e., bosonic stars. In the absence of the crust potential, we show that, if we rotate such a bosonic star, it is threaded by vortices. We then show, via extensive direct numerical simulations, that the interaction of these vortices with the crust potential yields (a) stick-slip dynamics and (b) dynamical glitches. We demonstrate that, if enough momentum is transferred to the crust from the bosonic star, then the vortices are expelled from the star, and the crust's angular momentum ${J}_{c}$ exhibits features that may be interpreted as glitches. From the time series of ${J}_{c}$, we compute the cumulative probability distribution functions (CPDFs) of event sizes, event durations, and waiting times, which are consistent with the previous work. We show that these CPDFs have signatures of self-organized criticality, which are similar to those seen in observations of pulsar glitches and are consistent with previous work.

Hydrodynamic Stabilization of Self-Organized Criticality in a Driven Rydberg Gas.

Signatures of self-organized criticality (SOC) have recently been observed in an ultracold atomic gas under continuous laser excitation to strongly interacting Rydberg states [S. Helmrich etal., Nature, 577, 481-486 (2020)]. This creates unique possibilities to study this intriguing dynamical phenomenon under controlled experimental conditions. Here we theoretically and experimentally examine the self-organizing dynamics of a driven ultracold gas and identify an unanticipated feedback mechanism originating from the interaction of the system with a thermal reservoir. Transport of particles from the flanks of the cloud toward the center compensates avalanche-induced atom loss. This mechanism sustains an extended critical region in the trap center for timescales much longer than the initial self-organization dynamics. The characteristic flattop density profile provides an additional experimental signature for SOC while simultaneously enabling studies of SOC under almost homogeneous conditions. We present a hydrodynamic description for the reorganization of the atom density, which very accurately describes the experimentally observed features on intermediate and long timescales, and which is applicable to both collisional hydrodynamic and chaotic ballistic regimes.

Scaling Behavior of Quasi-One-Dimensional Vortex Avalanches in Superconducting Films

Scaling behaviour of dynamically driven vortex avalanches in superconducting YBa2Cu3O7−δ films deposited on tilted crystalline substrates has been observed using quantitative magneto-optical imaging. Two films with different tilt angles are characterized by the probability distributions of avalanche size in terms of the number of moving vortices. It is found in both samples that these distributions follow power-laws over up to three decades, and have exponents ranging between 1.0 and 1.4. The distributions also show clear finite-size scaling, when the system size is defined by the depth of the flux penetration front – a signature of self-organized criticality. A scaling relation between the avalanche size exponent and the fractal dimension, previously derived theoretically from conservation of the number of magnetic vortices in the stationary state and shown in numerical simulations, is here shown to be satisfied also experimentally.

Publisher Correction: Signatures of self-organized criticality in an ultracold atomic gas.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Emergence of criticality in different topologies of networks of map-based neurons

KTz model is a three-dimensional map representing the action potential, a recovery and a slow variable, and exhibits the usual excitable cells behaviors (fast and regular spiking, bursting, etc). When we connect KTz’s units in different topologies with a probabilistic two-dimensional Chemical Synapse Map (CSM) we obtain spike avalanches, which is a number of connected neurons spiking one after another. The critical systems show a power law distribution of avalanches, and this is also a signature of Self-Organized Criticality (SOC). In vitro systems have shown neuronal avalanches. Comparisons between LFP recordings in monkeys performing a short term memory task and three subsampled SOC models are available in the literature, as well as in vivo data from rats and a cellular automaton model. These results are promising, and show close connection between critical models and neuronal activity. We simulate KTz neurons connected through CSM on different types of networks (square, scale-free, small world) and our preliminary results show criticality in the square lattice. Random topologies are under check, and they may be of close interest of the medical community, since they can be related to the development of some neural diseases.

Linking Flickering to Waves and Whole-Cell Oscillations in a Mitochondrial Network Model

It has been shown that transient single mitochondrial depolarizations, known as flickers, tend to occur randomly in space and time. On the other hand, many studies have shown that mitochondrial depolarization waves and whole-cell oscillations occur under oxidative stress. How single mitochondrial flickering events and whole-cell oscillations are mechanistically linked remains unclear. In this study, we developed a Markov model of the inner membrane anion channel in which reactive-oxidative-species (ROS)-induced opening of the inner membrane anion channel causes transient mitochondrial depolarizations in a single mitochondrion that occur in a nonperiodic manner, simulating flickering. We then coupled the individual mitochondria into a network, in which flickers occur randomly and sparsely when a small number of mitochondria are in the state of high superoxide production. As the number of mitochondria in the high-superoxide-production state increases, short-lived or abortive waves due to ROS-induced ROS release coexist with flickers. When the number of mitochondria in the high-superoxide-production state reaches a critical number, recurring propagating waves are observed. The origins of the waves occur randomly in space and are self-organized as a consequence of random flickering and local synchronization. We show that at this critical state, the depolarization clusters exhibit a power-law distribution, a signature of self-organized criticality. In addition, the whole-cell mitochondrial membrane potential changes from exhibiting small random fluctuations to more periodic oscillations as the superoxide production rate increases. These simulation results may provide mechanistic insight into the transition from random mitochondrial flickering to the waves and whole-cell oscillations observed in many experimental studies.

Long-range correlation and nonlinearity in geochemical time series of gas discharges from Mt. Etna, and changes with 2001 and 2002–2003 eruptions

Abstract. In this paper, spectral and detrended fluctuation analyses, as well as time reversibility and magnitude-sign decomposition, have been applied to the 10-year time-series data resulting from geochemical monitoring of gas emissions on the flanks of Mt. Etna, and gases from a CO2 exploitation well located tens of kilometers from the volcano. The analysis of the time series which showed main effects of fractionation between gases due to selective dissolution in aquifers (e.g., the CO2 concentration series), revealed the occurrence of random fluctuations in time, typical of systems where several processes combine linearly. In contrast, the series of He isotopic composition exhibited power-law behavior of the second-order fluctuation statistics, with values of the scaling exponent close to 0.9. When related to the spectral exponent, this value indicates that the isotopic series closely resemble fractal flicker-noise signals having persistent long-range correlations. The isotopic signals also displayed asymmetry under time reversal and long-range correlation of the associated magnitude series, therefore it was statistically proved the presence of nonlinearity. Both long-range correlation and nonlinearity in time series have been generally considered as distinctive features of dynamic systems where numerous processes interact by feedback mechanisms, in accordance with the paradigm of self-organized criticality (SOC). Thus, it is here proposed that the system that generated the isotope series worked under conditions of SOC. Since the fluctuations of the isotope series have been related to magma degassing, the previous results place constraints on the dynamics of such process, and suggest that nonequilibrium conditions must be dominant. It remains unclear whether the signature of SOC is directly due to volatile degassing from magma, or if it derives from the interaction between melt and the stress field, which certainly influences magma decompression. The strength of scaling appears to increase after 2002 (α values from 0.8 up to 1.2), focusing on transition of the Etnean system from typical SOC toward conditions of lower criticality. By comparing this transition with those of geophysical observables, it can be suggested that the drop in the rate of magma supply, subsequent to the paroxysms of 2001 and 2002–2003, was the main cause of the scaling change.

Brain dynamics across levels of organization

After initially presenting evidence that the electrical activity recorded from the brain surface can reflect metastable state transitions of neuronal configurations at the mesoscopic level, I will suggest that their patterns may correspond to the distinctive spatio-temporal activity in the dynamic core (DC) and the global neuronal workspace (GNW), respectively, in the models of the Edelman group on the one hand, and of Dehaene–Changeux, on the other. In both cases, the recursively reentrant activity flow in intra-cortical and cortical–subcortical neuron loops plays an essential and distinct role. Reasons will be given for viewing the temporal characteristics of this activity flow as signature of self-organized criticality (SOC), notably in reference to the dynamics of neuronal avalanches. This point of view enables the use of statistical physics approaches for exploring phase transitions, scaling and universality properties of DC and GNW, with relevance to the macroscopic electrical activity in EEG and EMG.

A Signature of Self-Organized Criticality in the HT-6M Edge Plasma Turbulence

Power spectra of electron density and floating potential fluctuations inthe velocity shear layer of the HT-6M edge region have been measured andanalysed. All the spectra have three distinct frequency regions with thespectral decay indices typical of self-organized criticality systems(0, -1 and -4) when Doppler shift effects induced by the plasmaE×Bflow velocity have been taken into account. These results are consistentwith the predictions of the self-organizedcriticality models, which maybe an indication of edge plasma turbulence in the HT-6M tokamak evolvinginto a critical state independent of local plasma parameters.

Surface fluctuations in a slowly driven granular system

We report an experiment on a granular packing: a box filled with glass beads is tilted very slowly up to the maximum angle of stability where a big avalanche is produced. During the build-up period many rearrangements occur on the free surface of the packing. Digital imaging was used to study these rearrangements. The probability distribution of sizes for the observed mass fluctuations follow a power-law behavior, which is the signature of self-organized criticality. However, this description breaks down in the limit of big rearrangements where inertia effects are not negligible.

Critical fluctuation in daily incidence of acute myocardial infarction

Continuous periodogram power spectral analysis of daily incidence of acute myocardial infarction (AMI) reported at a hospital for cardiology in Pune, India for the two-year period June 1992–May 1994 show that the power spectra follow the universal and unique inverse power law form of the statistical normal distribution. The same time inverse power law form for power spectra of space-time fluctuations are also ubiquitous to dynamical systems in nature and have been identified as signatures of self-organized criticality. The unique quantification for self-organized criticality presented in this paper is shown to be intrinsic to quantumlike mechanics governing fractal space-time fluctuation patterns in dynamical systems and suggest a possibly fruitful relation and analogy between different subject such as chaos, diffusion and quantum physics. The results found which mimic those obtained in quantum physics by El Naschie using the concept of Cantorian space ε (∞) suggest that, that tools developed in some of these areas may be used advantageously in the medical field as pioneered by A.T. Winfree [Int. J. Bifurcation and Chaos 7 (3) (1997) 487–526] and A.V. Holden [Chaos, Solitons and Fractals 5 (3/4) (1995) 691–704; Int. J. Bifurcation and Chaos 7 (9) (1997) 2075–2104].

IDENTIFICATION OF SELF-ORGANIZED CRITICALITY IN ATMOSPHERIC LOW FREQUENCY VARIABILITY

Atmospheric flows exhibit long-range spatiotemporal correlations manifested as self-similar fractal geometry to the global cloud cover pattern concomitant with inverse power law form fB. Such non-local connections are ubiquitous to dynamical systems in nature and are identified as signatures of self-organized criticality. Standard models in meteorological theory cannot explain satisfactorily the observed self-organized criticality in atmospheric flows. A recently developed cell dynamical model for atmospheric flows predicts the observed self-organized criticality as a direct consequence of quantumlike mechanics governing flow dynamics. The model predictions are in agreement with continuous periodogram power spectral analyses of two-day mean TOGA temperature time-series. The application of model concepts for prediction of atmospheric low frequency variability is discussed.

Superstrings, Cantorian-fractal Spacetime and Quantum-like Chaos in Atmospheric Flows

Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with the inverse power law form for spectra of temporal fluctuations. Such non-local connections are ubiquitous to dynamical systems in nature and are identified as signatures of self-organized criticality. A recently developed cell dynamical system model for atmospheric flows predicts the observed self-organized criticality as a natural consequence of quantum-like mechanics governing flow dynamics. The model is based on the concept that spatial integration of enclosed small scale fluctuations results in the formation of large eddy circulations. The model predicts the following: (a) The flow structure consists of an overall logarithmic spiral trajectory with the quasiperiodic Penrose tiling pattern for the internal structure. (b) Conventional power spectrum analysis will resolve such spiral trajectories as a continuum of eddies with progressive increase in phase. (c) Increments in phase are concomitant with increases in period length and also represent the variance, a characteristic of quantum systems identified as Berrys phase. (d) The universal algorithm for self-organized criticality is expressed in terms of the universal Feigenbaum constants, a and d, as 2 a 2= πd, where the fractional volume intermittency of occurrence πd contributes to the total variance 2 a 2 of fractal structures. (e) The Feigenbaum constants are expressed as functions of the golden mean. ( f) The quantum mechanical constants fine structure constant and ratio of proton mass to electron mass, which are pure numbers and are obtained by experimental observations only, are now derived in terms of the Feigenbaum constant, a. (g) Atmospheric flow structure follows Keplers third law of planetary motion. Therefore, Newtons inverse square law for gravitation also applies to eddy masses. The centripetal acceleration representing the inertial masses (of eddies) are equivalent to gravitational masses. The fractal-Cantorian structure of spacetime can also be visualized as a nested continuum of vortex (eddy) circulations, whose inertial masses obey Newtons inverse square law of gravitation. The model concept resembles a superstring model for subatomic dynamics which incorporates gravitational forces.

Cantorian Fractal Spacetime and Information in Neural Network of the Human Brain

The neural networks of the human brain act as very efficient parallel processing computers co-ordinating memory related responses to a multitude of input signals from sensory organs. Information storage, update and appropriate retrieval are controlled at the molecular level by the neuronal cytoskeleton which serves as the internal communication network within neurons. Information flow in the highly ordered parallel networks of the filamentous protein polymers which make up the cytoskeleton may be compared to atmospheric flows which exhibit long-range spatiotemporal correlations, i.e. long-term memory. Such long-range spatiotemporal correlations are ubiquitous to real world dynamical systems and is recently identified as signature of self-organized criticality or chaos. The signatures of self-organized criticality i.e. long-range temporal correlations have recently been identified in the electrical activity of the brain. The physics of self-organized criticality or chaos is not yet identified. A recently developed non-deterministic cell dynamical system model for atmospheric flows predicts the observed long-range spatiotemporal correlations as intrinsic to quantum-like mechanics governing flow dynamics. The model visualises large scale circulations to form as the result of spatial integration of enclosed small scale perturbations with intrinsic two-way ordered energy flow between the scales. Such a concept maybe applied for the collection and integration of a multitude of signals at the cytoskeletal level and manifested in activation of neurons in the macroscale. The cytoskeleton networks inside neurons may be the elementary units of a unified dynamic memory circulation network with intrinsic global response to local stimuli. A cell dynamical system model for human memory circulation network analogous to atmospheric circulations network is presented in this paper. The model like the analysis of Koruga et al. make use of certain connections to the concept of Cantorian-Fractal spacetime.

Signatures of a universal spectrum for atmospheric interannual variability in some disparate climatic regimes

Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for power spectra of temporal fluctuations on all space-tie scales ranging from turbulence (centimetersseconds) to climate (kilometers-years). Long-range spatiotemporal correlations are ubiquitous to dynamical systems in nature and are identified as signatures ofself-organized criticality. Standard models in meteorological theory cannot explain satisfactorily the observed self-organized criticality in atmospheric flows. Mathematical models for simulation and prediction of atmospheric flows are nonlinear and do not possess analytical solutions. Finite precision computer realizations of nonlinear models give unrealistic solutions because ofdeterministic chaos, a direct consequence of round-off error growth in iterative numerical computations. Recent studies show that roundoff error doubles on an average for each iteration of iterative computations. Round-off error propagates to the main stream computation and gives unrealistic solutions in numerical weather prediction (NWP) and climate models which incorporate thousands of iterative computations in long-term numerical integration schemes. An alternative non-deterministic cell dynamical system model for atmospheric flows described in this paper predicts the observed self-organized criticality as intrinsic to quantumlike mechanics governing flow dynamics. The model provides universal quantification for self-organized criticality in terms of the statistical normal distribution. Model predictions are in agreement with a majority of observed spectra of time series of several standard climatological data sets representative of disparate climatic regimes. Universal spectrum for natural climate variability rules out linear trends. Man-made greenhouse gas related atmospheric warming will result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference to possible prediction of climate change.

SIGNATURES OF A UNIVERSAL SPECTRUM FOR ATMOSPHERIC INTERANNUAL VARIABILITY IN COADS SURFACE PRESSURE TIME SERIES

Annual and seasonal mean global surface pressure time series for the 25 years 1964–1988 obtained from the Comprehensive Ocean Atmosphere Data Set (COADS) were subjected to quasi-continuous periodogram spectral analysis. Periodogram estimates are summarized in the following: (i) the atmospheric interannual variability exhibits a broadband (eddy continuum) structure; (ii) the spectra follow the universal inverse power-law form of the statistical normal distribution; (ii) periodicities up to 5 years contribute to as much as 50 per cent of the total variance; (v) the high- and low-frequency El Niño–Southern Oscillation (ENSO) cycles of respective periodicities 3–4 years and 4–8 years and interdecadal oscillations are present in all the data sets. The inverse power-law form for power spectra is ubiquitous to real-world dynamical systems and is identified as a signature of self-organized criticality or deterministic chaos. The above results are consistent with a recently developed cell dynamical system model for atmospheric flows, which predicts self-organized criticali ty as intrinsic to quantum-like mechanics governing atmospheric flow dynamics. Identification of self-organized criticality in annual and seasonal mean surface pressure fluctuations and its unique quantification implies predictability of the total pattern of fluctuations. A universal spectrum for interannual variability rules out linear trends in atmospheric surface pressure patterns.

SIGNATURES OF A UNIVERSAL SPECTRUM FOR ATMOSPHERIC INTERANNUAL VARIABILITY IN COADS SURFACE PRESSURE TIME SERIES

Annual and seasonal mean global surface pressure time series for the 25 years 1964-1988 obtained from the Comprehensive Ocean Atmosphere Data Set (COADS) were subjected to quasi-continuous periodogram spectral analysis. Periodograrn estimates are summarized in the following: (i) the atmospheric interannual variability exhibits a broadband (eddy continuum) structure; (ii) the spectra follow the universal inverse power-law form of the statistical normal distribution; (ii) periodicities up to 5 years contribute to as much as 50 per cent of the total variance; (v) the highand low-frequency El Niii-Southern Oscillation (ENSO) cycles of respective periodicities 3-4 years and 4-8 years and interdecadal oscillations are present in all the data sets. The inverse power-law form for power spectra is ubiquitous to real-world dynamical systems and is identified as a signature of self-organized criticality or deterministic chaos. The above results are consistent with a recently developed cell dynamical system model for abnospheric flows, which predicts self-organized criticality as intrinsic to quantum-like mechanics governing abnospheric flow dynamics. Identification of selforganized criticality in annual and seasonal mean surface pressure fluctuations and its unique quantification implies predictability of the total pattern of fluctuations. A universal spectnun for interannual variability rules out linear trends in atmospheric surface pressure patterns.

Scaling behavior of a directed sandpile automata with random defects.

In a recent paper [B. Tadi\ifmmode \acute{c}\else \'{c}\fi{}, U. Nowak, K. D. Usadel, R. Ramaswamy, and S. Padlewski, Phys. Rev. A 45, 8536 (1992)], the directed two-dimensional sandpile is modified to include a concentration p of randomly placed holes. For p>0, they observe a characteristic cutoff size for the duration (and mass) of avalanches. This breaks the formal power-law behavior that is a signature of self-organized criticality. The scaling of these characteristic sizes with the concentration of defects is observed empirically to follow a power law, and the exponents are numerically determined. In this Brief Report, it is shown that a previously described mean-field approximation can account for the observed exponents.

Structuration of the lithosphere in plate tectonics as a self‐organized critical phenomenon

The concept of self‐organized criticality (SOC) has recently been suggested to be relevant for understanding the processes underlying earthquakes. In this work, we attempt to clarify the basic physical and geological mechanisms responsible for the self‐organization of the crust within a continental plate. Toward this goal, a field theory is proposed which is not deduced from constitutive or microscopic theological and mechanical laws but rather from symmetry and conservation laws, in a way similar to Landau theory of second‐order critical phase transitions. In order to construct the theory, one has first to identify the relevant field or order parameter, which we propose to be the coarse‐grained fluctuating strain tensor. We then discuss the existence of a global conservation law. It stems from two facts: (1) a continental plate, which is in mechanical equilibrium and which is faulted over its whole surface, corresponds to a state of the crust nearly obeying the rupture criterion almost everywhere, a condition intimately related to the observation of active faults almost everywhere within plates. We thus argue that stress fields obeying the rupture criterion almost everywhere are attracting states of the plate dynamics. (2) The different components (dilation/compression, shear, and rotation) of the plate deformation must be kinematically compatible with each other. Both conditions (1) and (2) can be casted under the form of a diffusion‐like conservation equation. Using this equation and the symmetries imposed by the tensorial character of the order parameter, we propose a generalized tensorial nonlinear diffusion equation controlling the spatiotemporal evolution of the strain tensor. The nonlinear part of the equation is devised to take into account the threshold nature of rupture in the upper crust. From the diffusion‐luce structure of the governing equation, we deduce that the dynamical mechanical equilibrium of the crust is characterized by long‐range and long‐time correlations in the strain fluctuations. These long‐range correlations are the signature of SOC and are intimately related to the existence of a global conservation equation. In other words, this means that local fluctuations are relaxed via a generalized diffusion process progressively invading adjacent domains. The spatiotemporal correlation functions of the strain tensor define a set of critical exponents: the dynamic exponent z governs the spatial diffusion with time of the strain fluctuations; the field exponent describes the renormalization of strain with changes of scales; the spatial anisotropy exponents control the spatial anisotropy of the strain diffusion. A solution of the generalized tensorial nonlinear diffusion equation would involve the determination of these exponents. We have not succeeded in this goal for the full problem but present a scalar analogy which has been examined recently and solved exactly (Hwa and Kardar, 1989). Finally, we discuss the relation between our field theory and earthquakes and especially the connection between the critical exponents introduced in our approach and the b value entering the Richter‐Gutemberg law, linking the number of earthquakes to their magnitude. The connection relies on the idea that the average energy released in an earthquake gives the order of magnitude of typical fluctuations of the elastic energy in the crust.