Self-organized Criticality Model for Ocean Internal Waves

In this paper, we present a simple spring-block model for ocean internal waves based on the self-organized criticality （SOC）. The oscillations of the water blocks in the model display power-law behavior with an exponent of -2 in the frequency domain, which is similar to the current and sea water temperature spectra in the actual ocean and the universal Garrett and Munk deep ocean internal wave model [Geophysical Fluid Dynamics 2 （1972） 225; J. Geophys. Res. 80 （1975） 291]. The influence of the ratio of the driving force to the spring coefficient to SOC behaviors in the model is also discussed.

Self-Organized Criticality Analysis of Earthquake Model Based on Heterogeneous Networks

The original Olami-Feder-Christensen （OFC） model, which displays a robust power-law behavior, is a quasistatic two-dimensional version of the Burridge-Knopoff spring-block model of earthquakes. In this paper, we introduce a modified OFC model based on heterogeneous network, improving the redistribution rule of the original model. It can be seen as a generalization of the originM OFC model We numerically investigate the influence of the parameters θandβ, which respectively control the intensity of the evolutive mechanism of the topological growth and the inner selection dynamics in our networks, and find that there are two distinct phases in the parameter space （θ,β）. Meanwhile, we study the influence of the control parameter a either. Increasing a, the earthquake behavior of the model transfers from local to global.

A Modified Earthquake Model of Self-Organized Criticality on Small World Networks

A modified Olami Feder-Christensen model of self-organized criticality on a square lattice with the properties of small world networks has been studied.We find that our model displays power-law behavior and the exponent τ of the model depends on φ,the density of long-range connections in our network.

Self-Organized Criticality Theory Model of Thermal Sandpile

A self-organized criticality model of a thermal sandpile is formulated for the first time to simulate the dynamic process with interaction between avalanche events on the fast time scale and diffusive transports on the slow time scale. The main characteristics of the model are that both particle and energy avalanches of sand grains are considered simultaneously. Properties of intermittent transport and improved confinement are analyzed in detail. The results imply that the intermittent phenomenon such as blobs in the low confinement mode as well as edge localized modes in the high confinement mode observed in tokamak experiments are not only determined by the edge plasma physics, but also affected by the core plasma dynamics.

Effects of Vertex Activity and Self-organized Criticality Behavior on a Weighted Evolving Network

Effects of vertex activity have been analyzed on a weighted evolving network.The network is characterized by the probability distribution of vertex strength,each edge weight and evolution of the strength of vertices with different vertex activities.The model exhibits self-organized criticality behavior.The probability distribution of avalanche size for different network sizes is also shown.In addition,there is a power law relation between the size and the duration of an avalanche and the average of avalanche size has been studied for different vertex activities.

Self-organized Criticality in an Earthquake Model on Random Network

A simplified Olami-Feder-Christensen model on a random network has been studied. We propose a new toppling rule -- when there is an unstable site toppling, the energy of the site is redistributed to its nearest neighbors randomly not averagely. The simulation results indicate that the model displays self-organized criticality when the system is conservative, and the avalanche size probability distribution of the system obeys finite size scaling. When the system is nonconservative, the model does not display scaling behavior. Simulation results of our model with different nearest neighbors q is also compared, which indicates that the spatial topology does not alter the critical behavior of the system.

Landslide and Basin Self-organized Criticality in the Lushan Hot Spring Area

Defining a basin under a critical state （or a self-organized criticality） that has the potential to initiate landslides, debris flows, and subsequent sediment disasters, is a key issue for disaster prevention. The Lushan Hot Spring area in Nantou County, Taiwan, suffered serious sediment disasters after typhoons Sinlaku and Jangmi in aoo8, and following Typhoon Morakot in 2009. The basin＇s internal slope instability after the typhoons brought rain was examined using the landslide frequency-area distribution. The critical state indices attributed to landslide frequency-area distribution are discussed and the marginally unstable characteristics of the study area indicated. The landslides were interpreted from Spot 5 images before and after disastrous events. The results of the analysis show that the power-law landslide frequency-area curves in the basin for different rainfall-induced events tend to coincide with a single line. The temporal trend of the rainfall- induced landslide frequency-area distribution shows 1If noise and scale invariance. A trend exists for landslide frequency-area distribution in log-log space for larger landslides controlled by the historical maximum accumulated rainfall brought by typhoons. The unstable state of the basin, including landslides, breached dams, and debris flows, are parts of the basin＇s self-organizing processes. The critical state of landslide frequency-area distribution could be estimated by a critical exponent of 1.0. The distribution could be used for future estimation of the potential landslide magnitude for disaster mitigation and to identify the current state of a basin for management.

Self-organized Criticality in an Integrate-and-Fire Neuron Model Based on Modified Aging Networks

Based on an integrate-and-fire mechanism, we investigate self-organized criticality of a simple neuron model on a modified BA scale-free network with aging nodes. In our model, we find that the distribution of avalanche size follows power-law behavior. The critical exponent τ depends on the aging exponent α. The structures of the network with aging of nodes change with an increase of α. The different topological structures lead to different behaviors in models of integrate-and-fire neurons.

Self-organized Criticality in Hierarchical Brain Network

It is shown that the cortical brain network of the macaque displays a hierarchically clustered organizationand the neuron network shows small-world properties.Now the two factors will be considered in our model and thedynamical behavior of the model will be studied.We study the characters of the model and find that the distribution ofavalanche size of the model follows power-law behavior.

Self-Organized Criticality in a Simple Neuron Model Based on Scale-Free Networks

A simple model for a set of interacting idealized neurons in scale-free networks is introduced. The basic elements of the model are endowed with the main features of a neuron function. We find that our model displays powerlaw behavior of avalanche sizes and generates long-range temporal correlation. More importantly, we find different dynamical behavior for nodes with different connectivity in the scale-free networks.

Self-organized Criticality in a Modified Evolution Model on Generalized Barabasi-Albert Scale-Free Networks

A modified evolution model of self-organized criticality on generalized Barabasi-Albert （GBA）.scale-free networks is investigated. In our model, we find that spatial and temporal correlations exhibit critical behaviors. More importantly, these critical behaviors change with the parameter b, which weights the distance in comparison with the degree in the GBA network evolution.

Self-organized Criticality and Synchronization in a Pulse-coupled Integrate-and-Fire Neuron Model Based on Small World Networks＊

A lattice model for a set of pulse-coupled integrate-and-fire neurons with small world structure is introduced.We find that our model displays the power-law behavior accompanied with the large-scale synchronized activities among the units. And the different connectivity topologies lead to different behaviors in models of integrate-and-fire neurons.

Effects of Aging and Self-organized Criticality in a Pulse-Coupled Integrate-and-Fire Neuron Model Based on Small World Networks

Effects of aging and self-organized criticality in a pulse-coupled integrate-and-fire neuron model based on small world networks have been studied. We give the degree distribution of aging network, average shortest path length, the diameter of our network, and the clustering coefficient, and find that our neuron model displays the power-law behavior, and with the number of added links increasing, the effects of aging become smaller and smaller. This shows that if the brain works at the self-organized criticality state, it can relieve some effects caused by aging.

The Research of Transmission Network Planning Based on System’s Self-organized Criticality

This paper presents a new line importance degree evaluation index for the propagation of cascading failures, which is used to quantify transmission lines for cascade spread. And propose an improved capital matching model, according to the results of the evaluation, to enhanced robustness of the power system. The simulation results proved that in the case of the same system, the new model can inhibit cascade spread, reduce the probability of large-scale blackouts.

On Origin of Power-Law Distributions in Self-Organized Criticality from Random Walk Treatment

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. We assume that the variation of the number of active sites has three possibilities in each update： to increase by 1 with probability f1, to decrease by 1 with probability f2, or remain unchanged with probability 1 - f1 - f2. This mimics the dynamics in the system. Power-law distributions of the lifetime are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions.

Evidence for self-organized criticality in unscheduled downtime data of equipment

How to reduce downtime and improve availability of the complex equipment is very important. Although the unscheduled downtime（USDT） issues of the equipment are very complex, the self-organized criticality（SOC） is the right theory to study complex systems evolution and opens up a new window to the investigation of disasters, such as the sudden failure of the equipment. Firstly,SOC theory and its validation method are introduced. Then an SOC validation method for USDT of the equipment is proposed based on the above theory. Case study is done on bottleneck equipment in a factory and corresponding data pre-process work is done. The rescaled-range（R/S） analysis method is used to calculate the Hurst exponent of USDT time-series data in order to determine the long-range correlation of USDT data on time scale;at the same time the spatial power-law characteristic of USDT time series data is studied. The result shows that the characteristics of SOC are revealed in USDT data of the equipment according to the criterion of SOC. In addition, based on the characteristics of SOC,the overall framework of the prediction method for major sudden failure of the equipment is proposed based on SOC.

Self-organized criticality of liquefaction in saturated granules

Utilizing the dissipative structure theory, the evolutionary process of vibrating liquefaction in saturated granules was analyzed. When the irreversible force increases to some degree, the system will be in a state far from equilibrium, and the new structure probably occurs. According to synergetics, the equation of liquefaction evolution was deduced, and the evolutionary process was analyzed by dynamics. The evolutionary process of vibrating liquefaction is a process in which the period doubling accesses to chaos, and the fluctuation is the original driving force of system evolution. The liquefaction process was also analyzed by fractal geometry. The steady process of vibrating liquefaction obeys the scaling form, and shows self-organized criticality in the course of vibration. With the increment of the recurrence number, the stress of saturated granules will decrease rapidly or lose completely, and the strain will increase rapidly, so that the granules can not sustain load and the "avalanche" phenomenon takes place.

Neuronal avalanches:Sandpiles of self-organized criticality or critical dynamics of brain waves?

Analytical expressions for scaling of brain wave spectra derived from the general nonlinear wave Hamiltonian form show excellent agreement with experimental“neuronal avalanche”data.The theory of the weakly evanescent nonlinear brain wave dynamics[Phys.Rev.Research 2,023061(2020);J.Cognitive Neurosci.32,2178(2020)]reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states,from oscillatory wave-like modes,to neuronal avalanches,to incoherent spiking,showing that the neuronal avalanches are just the manifestation of the different nonlinear side of wave processes abundant in cortical tissue.In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order nonlinear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws.To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.

POWER LAW DISTRIBUTION AND SELF-ORGANIZED CRITICALITY OF DISPERSED PARTICLES

Research on particulate characteristics has been an important frontier in physics and chemistry during the past decades. It has however been mostly focused on granular materials with short-range interactions. In this work, it was found that the power law of particle size distribution applied to the long-range interacting system of floating dust in air, from which we deduced that self-organized criticality might hold for floating dust just as granular materials with short-range interactions. This feature may reveal underlying kinetic mechanisms, important in dispersed particle systems. In industry, power law of size distribution of dispersed particles can be used to investigate the change of dust size, and the power law parameter could be taken as an important index for dust separation.

Effect of Correlations on the Exponents for the Power-Law Distributions in Self-Organized Criticality

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is mapped to a first-return random-walk process in a one-dimensional lattice. In order to understand the reason of variant exponents for the power-law distributions in different self-organized critical systems, we introduce the correlations among evolution steps. Power-law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. It is found that the longer the correlation length, the smaller values of the exponents for the power-law distributions.