Example Of Self-organized Criticality Research Articles

Asymptotics and criticality for a space-dependent branching process

We investigate a non-conservative semigroup determined by a branching process tracing the evolution of particles moving in a domain in . When a particle is killed at the boundary, a new generation of particles with mean number is born at a random point in the domain. Between branching, the particles are driven by a diffusion process with Dirichlet boundary conditions. According to the sign of , we distinguish super/sub-critical regimes and determine the exact exponential rate for the total number of particles , with depending explicitly on . We prove the Yaglom limit , where the quasi-stationary distribution ν is determined by the resolvent of the Dirichlet kernel at the point . The main application is in particle systems, where the normalization of the semigroup by its total mass gives the hydrodynamic limit of the Bak-Sneppen branching diffusions (BSBD). Since ν is the asymptotic profile under equilibrium, and the family of quasi-stationary distributions ν is indexed by , the model provides an explicit example of self-organized criticality.

Self-Organized Criticality of Precipitation in the Rainy Season in East China

Based on daily precipitation data from 1960 to 2017 in the rainy season in east China, to a given percentile threshold of one observation station, the time that precipitation spends below threshold is defined as quiet time τ. The probability density functions τ in different thresholds follow power-law distributions with exponent β of approximately 1.2 in the day, pentad and ten-day period time scales, respectively. The probability density functions τ in different regions follow the same rules, too. Compared with sandpile model, Γ function describing the collapse behavior can effectively scale the quiet time distribution of precipitation events. These results confirm the assumption that for observation station data and low-resolution precipitation data, even in China, affected by complex weather and climate systems, precipitation is still a real world example of self-organized criticality in synoptic. Moreover, exponent β of the probability density function τ, mean quiet time τ¯q and hazard function Hq of quiet times can give sensitive regions of precipitation events in China. Usual intensity precipitation events (UPEs) easily occur and cluster mainly in the middle Yangtze River basin, east of the Sichuan Province and north of the Gansu Province. Extreme intensity precipitation events (EPEs) more easily occur in northern China in the rainy season. UPEs in the Hubei Province and the Hunan Province are more likely to occur in the future. EPEs in the eastern Sichuan Province, the Guizhou Province, the Guangxi Province and Northeast China are more likely to occur.

“There Really Are 50 Eskimo Words For ‘Snow’”: 1177, Big Data, and the Perfect Storm of Collapse

“There Really Are 50 Eskimo Words For ‘Snow’”: 1177, Big Data, and the Perfect Storm of Collapse

Realizable solutions of the Thouless-Anderson-Palmer equations.

We show that the only solutions of the Thouless-Anderson-Palmer (TAP) equations for the Sherrington-Kirkpatrick model of Ising spin glasses which can be found by iteration are those whose free energy lies on the border between replica-symmetric and broken-replica-symmetric states, when the number of spins N is large. Convergence to this same borderline also happens in quenches from a high-temperature initial state to a locally stable state where each spin is parallel to its local field; both are examples of self-organized criticality. At this borderline the band of eigenvalues of the Hessian associated with a solution extends to zero, so the states reached have marginal stability. We have also investigated the factors which determine the free-energy difference between a stationary solution corresponding to a saddle point and its associated minimum, which is the barrier which has to be surmounted to escape from the vicinity of a TAP minimum or pure state.

Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems

In the last decade, several models with network adaptive mechanisms (link deletion-creation, dynamic synapses, dynamic gains) have been proposed as examples of self-organized criticality (SOC) to explain neuronal avalanches. However, all these systems present stochastic oscillations hovering around the critical region that are incompatible with standard SOC. Here we make a linear stability analysis of the mean field fixed points of two self-organized quasi-critical systems: a fully connected network of discrete time stochastic spiking neurons with firing rate adaptation produced by dynamic neuronal gains and an excitable cellular automata with depressing synapses. We find that the fixed point corresponds to a stable focus that loses stability at criticality. We argue that when this focus is close to become indifferent, demographic noise can elicit stochastic oscillations that frequently fall into the absorbing state. This mechanism interrupts the oscillations, producing both power law avalanches and dragon king events, which appear as bands of synchronized firings in raster plots. Our approach differs from standard SOC models in that it predicts the coexistence of these different types of neuronal activity.

Self-organized criticality in proteins: Hydropathic roughening profiles of G-protein-coupled receptors

Proteins appear to be the most dramatic natural example of self-organized criticality (SOC), a concept that explains many otherwise apparently unlikely phenomena. Protein conformational functionality is often dominated by long-range hydrophobic or hydrophilic interactions which both drive protein compaction and mediate protein-protein interactions. Superfamily transmembrane G-protein-coupled receptors (GPCRs) are the largest family of proteins in the human genome; their amino acid sequences form the largest database for protein-membrane interactions. While there are now structural data on the heptad transmembrane structures of representatives of several heptad families, here we show how fresh insights into global and some local chemical trends in GPCR properties can be obtained accurately from sequences alone, especially by algebraically separating the extracellular and cytoplasmic loops from transmembrane segments. The global mediation of long-range water-protein interactions occurs in conjunction with modulation of these interactions by roughened interfaces. Hydropathic roughening profiles are defined here solely in terms of amino acid sequences, and knowledge of protein coordinates is not required. Roughening profiles both for GPCR and some simpler protein families display accurate and transparent connections to protein functionality, and identify natural length scales for protein functionality.

A new model for seismicity parameterization and predictive aspects of its application to the Sakhalin region

Seismicity is generally treated as an example of self-organized criticality. One alternative to this treatment may possibly be furnished by a model of seismicity that is thought of as a set of episodes of avalanching relaxation that occur randomly on a set of metastable subsystems. This model is defined by the parameter r, which specifies the hierarchical divisibility of the block structure of the medium, and by the parameter p, which specifies the probability for the incipient relaxation of a metastable state to continue. These two parameters together define the modeled value of the slope of the recurrence curve, or b-value, thus determining the mode of seismicity occurrence. This model is used to describe the seismicity in southern Sakhalin Island. In this modeling, the coefficient of hierarchical divisibility r in the block structure of the medium was assumed to be stationary and the disequilibrium parameter p was assumed to describe time-dependent variations of seismicity. We calculated models for the spatial variability of r and the time variability of p. We found abnormal growth in p during the Gornozavodsk earthquake (2006, Mw = 5.6) and the Nevel’sk earthquake (2007, Mw = 6.2). At present, we report values of p that are high (and increasing over time) in the wide area of the Poyasok isthmus. The results derived here are compared with other ideas on seismicity and with the experience that was previously gained in the area of earthquake prediction.

Wenchuan aftershocks as an example of self-organized criticality

Analysis of the magnitude and temporal distributions, described by the Gutenberg–Richter and Omori laws respectively, in the sequence of aftershocks of the Wenchuan Ms8.0 earthquake occurred on Longmenshan tectonic zone of Sichuan Province in China, has been performed. The power exponent b=0.71±0.13 and p=2.08±0.29 in the form of the Gutenberg–Richter and Omori laws respectively. Dose there exist a simple mechanism which can explain these statistical relations of Wenchuan aftershocks together? In order to provide a possible explanation for these observed distributions, we develop a new self-organized criticality (SOC) model by introducing stress decay coefficient and anisotropic diffusion factors into Olami–Feder–Christensen model of earthquakes. The self-organized criticality properties of the model are discussed. The model displays a robust power law behavior in certain stress decay coefficient region. The model can give a good prediction of the Gutenberg–Richter and Omori laws in Wenchuan aftershock together. The high correspondence of the simulated results to observations shows that Wenchuan aftershock is an example of a SOC process. It is SOC of Wenchuan aftershock process that makes it is impossible to give a fairly accurate forecast of large aftershocks.

Natural time analysis of critical phenomena

A quantity exists by which one can identify the approach of a dynamical system to the state of criticality, which is hard to identify otherwise. This quantity is the variance κ(1)(≡<χ(2)> - <χ>(2)) of natural time χ, where <f(χ)> = Σp(k)f(χ(k)) and p(k) is the normalized energy released during the kth event of which the natural time is defined as χ(k) = k/N and N stands for the total number of events. Then we show that κ(1) becomes equal to 0.070 at the critical state for a variety of dynamical systems. This holds for criticality models such as 2D Ising and the Bak-Tang-Wiesenfeld sandpile, which is the standard example of self-organized criticality. This condition of κ(1) = 0.070 holds for experimental results of critical phenomena such as growth of rice piles, seismic electric signals, and the subsequent seismicity before the associated main shock.

Scaling and self-organized criticality in proteins: Lysozymec

Proteins appear to be the most dramatic natural example of self-organized criticality (SOC), a concept that explains many otherwise apparently unlikely phenomena. Protein functionality is often dominated by long-range hydro(phobic/philic) interactions, which both drive protein compaction and mediate protein-protein interactions. In contrast to previous reductionist short-range hydrophobicity scales, the holistic Moret-Zebende hydrophobicity scale [Phys. Rev. E 75, 011920 (2007)] represents a hydroanalytic tool that bioinformatically quantifies SOC in a way fully compatible with evolution. Hydroprofiling identifies chemical trends in the activities and substrate binding abilities of model enzymes and antibiotic animal lysozymes c , as well as defensins, which have been the subject of tens of thousands of experimental studies. The analysis is simple and easily performed and immediately yields insights not obtainable by traditional methods based on short-range real-space interactions, as described either by classical force fields used in molecular-dynamics simulations, or hydrophobicity scales based on transference energies from water to organic solvents or solvent-accessible areas.

Scaling and self-organized criticality in proteins II

The complexity of proteins is substantially simplified by regarding them as archetypical examples of self-organized criticality (SOC). To test this idea and to elaborate it, this article applies the Moret-Zebende (MZ) SOC hydrophobicity scale to transport repeat proteins of the HEAT superfamily, importin beta, and transportin, as well as the export protein Cse1p, and their ubiquitous cargo manager Ran. The difference between the MZ scale and conventional hydrophobicity scales reflects long-range conformational forces that are central to protein functionality. These compete with long-range Coulomb forces associated with cationic and anionic side chains in a revealing way.

Scaling and self-organized criticality in proteins I.

The complexity of proteins is substantially simplified by regarding them as archetypical examples of self-organized criticality (SOC). To test this idea and elaborate on it, this article applies the Moret-Zebende SOC hydrophobicity scale to the large-scale scaffold repeat protein of the HEAT superfamily, PR65/A. Hydrophobic plasticity is defined and used to identify docking platforms and hinges from repeat sequences alone. The difference between the MZ scale and conventional hydrophobicity scales reflects long-range conformational forces that are central to protein functionality.

Stairway to Self-Organized Criticality: SOC on a Slope using Relative Critical Heights

A computational model of loose snow avalanches was studied as an example of Self-Organized Criticality (SOC). The distribution of the magnitudes of avalanches was measured for a stair-stepped system with various critical relative differences and system slopes. Depending on the configuration, the model showed either power law behaviors or a Gaussian distribution. For configurations that displayed power laws, the slope of the power law was dependent on the configuration of the system.

Interannual variability of Mars global dust storms: an example of self-organized criticality?

Previous simulations of martian global dust storms with a simple low-order model showed the desired interannual variability of storms if one of the model parameters—the threshold wind speed for starting saltation and lifting dust from the surface—was finely tuned. In this paper we show that the fine-tuning of this parameter could be the result of negative feedback in which processes associated with global dust storms raise the threshold and small-scale processes like dust devils, which are active in years between the storms, lower the threshold.

A heavenly example of scale-free networks and self-organized criticality

The sun provides an explosive, heavenly example of self-organized criticality. Sudden bursts of intense radiation emanate from rapid rearrangements of the magnetic field network in the corona. Avalanches are triggered by loops of flux that reconnect or snap into lower-energy configurations when they are overly stressed. Our recent analysis of observational data reveal that the loops (links) and footpoints (nodes), where they attach on the photosphere, embody a scale-free network. The statistics of the avalanches and of the network structure are unified through a simple dynamical model where the avalanches and network co-generate each other into a complex, critical state. This particular example points toward a general dynamical mechanism for self-generation of complex networks.

A heavenly example of scale-free networks and self-organized criticality

The sun provides an explosive, heavenly example of self-organized criticality. Sudden bursts of intense radiation emanate from rapid rearrangements of the magnetic field network in the corona. Avalanches are triggered by loops of flux that reconnect or snap into lower-energy configurations when they are overly stressed. Our recent analysis of observational data reveal that the loops (links) and footpoints (nodes), where they attach on the photosphere, embody a scale-free network. The statistics of the avalanches and of the network structure are unified through a simple dynamical model where the avalanches and network co-generate each other into a complex, critical state. This particular example points toward a general dynamical mechanism for self-generation of complex networks.

Nonequilibrium phase transitions in epidemics and sandpiles

Nonequilibrium phase transitions between an active and an absorbing state are found in models of populations, epidemics, autocatalysis, and chemical reactions on a surface. While absorbing-state phase transitions fall generically in the directed-percolation universality class, this does not preclude other universality classes, associated with a symmetry or conservation law. An interesting issue concerns the dynamic critical behavior of models with an infinite number of absorbing configurations or a long memory. Sandpile models, the principal example of self-organized criticality (SOC), also exhibit absorbing-state phase transitions, with SOC corresponding to a particular mode of forcing the system toward its critical point.

Implications of a Statistical Physics Approach for Earthquake Hazard Assessment and Forecasting

—There is accumulating evidence that distributed seismicity is a problem in statistical physics. Seismicity is taken to be a type example of self-organized criticality. This association has important implications regarding earthquake hazard assessment and forecasting. A characteristic of a thermodynamic system is that it exhibits a background noise that is self-organized. In the case of a dilute gas, this self-organization is the Maxwell–Boltzmann distribution of molecular velocities. In seismicity, it is the Gutenberg–Richter frequency-magnitude scaling; this scaling is fractal. Observations favor the hypothesis that smaller earthquakes in moderate-sized regions occur at rates that are only weakly dependent on time. Thus, the rate of occurrence of smaller earthquakes can be extrapolated to assess the hazard of larger earthquakes in a region. We obtain the rate of occurrence of earthquakes with m > 4 in 1°× 1° areas from the NEIC catalog. Using only this data we produce global maps of the seismic hazard. Observations also favor the hypothesis that the stress level at which an earthquake occurs is a second-order critical point. As a critical point is approached, correlations extend over increasingly larger distances. In terms of seismicity, the approach to a critical point is associated with an increase in the rate of occurrence of intermediate-sized earthquakes prior to a large earthquake. This precursory activation has been shown to exhibit power-law scaling and to occur over a region about ten times larger than the rupture length of the large earthquake. Analyses of the spinoidal behavior associated with second-order critical points predict the power-law increase in seismic activity prior to a characteristic earthquake. This precursory activation provides the basis for intermediate-range earthquake forecasting.

Self-organized criticality in a computer network model

We study the collective behavior of computer network nodes by using a cellular automaton model. The results show that when the load of network is constant, the throughputs and buffer contents of nodes are power-law distributed in both space and time. Also the feature of 1/f noise appears in the power spectrum of the change of the number of nodes that bear a fixed part of the system load. It can be seen as yet another example of self-organized criticality. Power-law decay in the distribution of buffer contents implies that heavy network congestion occurs with small probability. The temporal power-law distribution for throughput might be a reasonable explanation for the observed self-similarity in computer network traffic.

Applications of statistical mechanics to natural hazards and landforms

The concept of self-organized criticality was introduced to explain the behavior of the cellular-automata sandpile model. A variety of multiple slider-block and forest-fire models have been introduced which are also said to exhibit self-organized critical behavior. It has been argued that earthquakes, landslides, forest-fires, and extinctions are examples of self-organized criticality in nature. The basic forest-fire model is particularly interesting in terms of its relation to the critical-point behavior of the site-percolation model. In the basic forest-fire model trees are randomly planted on a grid of points, periodically sparks are randomly dropped on the grid and if a spark drops on a tree that tree and the adjacent trees burn in a model fire. In the forest-fire model there is an inverse cascade of trees from small clusters to large clusters, trees are lost primarily from model fires that destroy the largest clusters. This quasi-steady-state cascade gives a power-law frequency–area distribution for both clusters of trees and smaller fires. The site-percolation model is equivalent to the forest-fire model without fires. In this case there is a transient cascade of trees from small to large clusters and a power-law distribution is found only at a critical density of trees. The earth's topography is an example of both statistically self-similar and self-affine fractals. Landforms are also associated with drainage networks, which are statistical fractal trees. A universal feature of drainage networks and other growth networks is side branching. Deterministic space-filling networks with side-branching symmetries are illustrated. It is shown that naturally occurring drainage networks have symmetries similar to diffusion-limited aggregation clusters.