First and second order non-equilibrium phase transition and evidence for non-extensive Tsallis statistics in Earth’s magnetosphere

Pavlos, G. P.; Iliopoulos, A. C.; Tsoutsouras, V. G.; Sarafopoulos, D. V.; Sfiris, Dimitris S.; Karakatsanis, L. P.; Pavlos, E.G.

doi:10.1016/j.physa.2011.03.005

Cited by 41 publications

(23 citation statements)

References 46 publications

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“…In many situations the distributions have a "suprathermal" power-law tail at high energies, which has been well modeled by the so called κ-distribution 16 . It has been reported recently that the plasma system far away from equilibrium may be often with power-law distributions in many physical situations 17,18 , which can be studied in the framework of nonextensive statistics 19 , initiated by Tsallis in 1988 as a generalization of BG statistics 0 . The power-law distributions in the nonequilibrium systems with long-range interactions have been studied by the diverse recent and previous statistical theories made for the power-law q-distributions 19,[21][22][23][24][25] .…”

Section: Introductionmentioning

confidence: 99%

Dust charging processes in the nonequilibrium dusty plasma with nonextensive power-law distribution

Gong

2012

Physics of Plasmas

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The dust charging processes in the collections of electrons and ions in the nonequilibrium dusty plasma with power-law distributions are investigated on the basic of a new q-distribution function theory in nonextensive statistics. Electrons and ions obey the power-law distributions and are with q-parameters different from each other. We derive the generalized formulae for the dust charging currents in which the nonextensive effects play roles. Further we investigate the dust charging processes taking place in the homogeneous dusty plasma where only the particle velocities are power-law distributions and in the dust cloud plasma where the particle velocities and densities are both power-law distributions. By numerical analyses, we show that the nonextensive power-law distributions of electrons and ions have significant effects on the dust charging processes in the nonequilibrium dusty plasma.

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Section: Introductionmentioning

confidence: 99%

Dust charging processes in the nonequilibrium dusty plasma with nonextensive power-law distribution

Gong

2012

Physics of Plasmas

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“…The source code is accessible from http://www.bitools.ir/projects.html and is used to predict Kp (Kennziffer planetarisch), AE (Auroral electrojet) and Ds storm time index which are used to characterize the geomagnetic activity of the earth's magnetosphere [27][28][29][30][31]. These time series have chaotic behavior [36][37][38] with low dimensional chaos [39][40] and many researchers used them as case study to assess the new methods [41][42]. A 78912 hourly samples data set from 2000 to 2008 has been used for online prediction.…”

Section: Exprimental Resultsmentioning

confidence: 99%

Emotional Brain-Inspired Adaptive Fuzzy Decayed Learning for online prediction problems

Lotfi

Akbarzadeh-T

2013

2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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In this paper, we propose a Fuzzy Adaptive BrainInspired Emotional Decayed Learning named Fuzzy ADBEL. Fuzzy ADBEL is a computational model that models the forgetting process and inhibitory mechanism of the emotional brain. In the model, the fuzzy decay rate simulates the forgetting process, and the stimulus and learning weights are considered as fuzzy variables trained by fuzzy learning rules. The final output of the model is evaluated by a fuzzy decision making layer that simulates the inhibitory mechanism. The proposed Fuzzy ADBEL is utilized to predict the Kp, AE and Dst indices showing opposite behaviors and characterizing the chaotic activity of the earth's magnetosphere. Experimental results show that fuzzy approaches including Fuzzy ADBEL and ANFIS (Adaptive NeuroFuzzy Inference System) reaches steady state faster than non-fuzzy approaches, ADBEL and MLP (Multilayer Perceptron). Hence, we hope the proposed model can be used in real time chaotic time series prediction.

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“…The RNG mechanism, more than a simple mathematical description of the self similar and multiscale character of the system at its far from equilibrium critical states, includes the non local self organization physical mechanism creating long range correlations. From this point of view the q  entropy of Tsallis statistical theory is closely related to the far from equilibrium RNG physical mechanism of creation of long range correlations and non Gaussian statistical dynamics at the metaequilibrium stationary states of the system [8,57,60]. From this point of view the fractal Fokker -Planck equation (5.1) must be the self organizing reduction of infinite dimensional dynamics to a low dimensional chaotic dynamics or correlated SOC dynamics at the macroscopic fixed points of the metaequilibrium states.…”

Section: Discussion and Theoretical Interpretation Of Data Analysis Rmentioning

confidence: 99%

Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma, Part one: Sunspot dynamics

Pavlos

Karakatsanis

Xenakis

2012

Physica A: Statistical Mechanics and its Applications

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In this study, the nonlinear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis [5,7,8]. The triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the SVD components of the sunspot index timeseries. Also the multifractal scaling exponent spectrum q  ( ) f a , the generalized Renyi dimension spectrum ( ) D q and the spectrum ( ) J p of the structure function exponents were estimated experimentally and theoretically by using the q  entropy principle included in Tsallis non extensive statistical theory, following Arimitsu and Arimitsu [67,69]. Our analysis showed clearly the following: a) a phase transition process in the solar dynamics from high dimensional non Gaussian SOC state to a low dimensional non Gaussian chaotic state, b) strong intermittent solar turbulence and anomalous (multifractal) diffusion solar process, which is strengthened as the solar dynamics makes phase transition to low dimensional chaos in accordance to Ruzmakin, Zeleny and Milovanov studies [19,20,21] c) faithful agreement of Tsallis non equilibrium statistical theory with the experimental estimations of i) non-Gaussian probability distribution function ( ) P x , ii) multifractal scaling exponent spectrum ( ) f a and generalized Renyi dimension spectrum q D , iii) exponent spectrum ( ) J p of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics.

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First and second order non-equilibrium phase transition and evidence for non-extensive Tsallis statistics in Earth’s magnetosphere

Cited by 41 publications

References 46 publications

Dust charging processes in the nonequilibrium dusty plasma with nonextensive power-law distribution

Dust charging processes in the nonequilibrium dusty plasma with nonextensive power-law distribution

Emotional Brain-Inspired Adaptive Fuzzy Decayed Learning for online prediction problems

Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma, Part one: Sunspot dynamics

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