Universality of non-extensive Tsallis statistics and time series analysis: Theory and applications

Pavlos, G. P.; Karakatsanis, L. P.; Xenakis, M.N.; Pavlos, E.G.; Iliopoulos, A. C.; Sarafopoulos, D. V.

doi:10.1016/j.physa.2013.08.026

Cited by 49 publications

(36 citation statements)

References 69 publications

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“…To calculate q from observational time-series, the algorithm described in Karakatsanis et al (2013) and Pavlos et al (2014) was used. It was applied to time-series of the magnetic field magnitude recorded at various locations (see Figure 2) in both the magnetosphere (THEMIS Ein the bow shock and THEMIS Cin the magnetotail) and the IP medium (Cluster near the bow shock and ACE at L1).…”

Section: Non-extensive Dynamics Of Ip and Magnetospheric Plasmasmentioning

confidence: 99%

The Major Geoeffective Solar Eruptions of 2012 March 7: Comprehensive Sun-to-Earth Analysis

Patsourakos

Georgoulis

Vourlidas

et al. 2016

ApJ

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During the interval 2012 March 7-11 the geospace experienced a barrage of intense space weather phenomena including the second largest geomagnetic storm of solar cycle 24 so far. Significant ultra-low-frequency wave enhancements and relativistic-electron dropouts in the radiation belts, as well as strong energetic-electron injection events in the magnetosphere were observed. These phenomena were ultimately associated with two ultra-fast (>2000 km s −1 ) coronal mass ejections (CMEs), linked to two X-class flares launched on early 2012 March 7. Given that both powerful events originated from solar active region NOAA 11429 and their onsets were separated by less than an hour, the analysis of the two events and the determination of solar causes and geospace effects are rather challenging. Using satellite data from a flotilla of solar, heliospheric and magnetospheric missions a synergistic Sun-to-Earth study of diverse observational solar, interplanetary and magnetospheric data sets was performed. It was found that only the second CME was Earth-directed. Using a novel method, we estimated its near-Sun magnetic field at 13 R e to be in the range [0.01, 0.16] G. Steep radial fall-offs of the near-Sun CME magnetic field are required to match the magnetic fields of the corresponding interplanetary CME (ICME) at 1 AU. Perturbed upstream solar-wind conditions, as resulting from the shock associated with the Earth-directed CME, offer a decent description of its kinematics. The magnetospheric compression caused by the arrival at 1 AU of the shock associated with the ICME was a key factor for radiation-belt dynamics.

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Section: Non-extensive Dynamics Of Ip and Magnetospheric Plasmasmentioning

confidence: 99%

The Major Geoeffective Solar Eruptions of 2012 March 7: Comprehensive Sun-to-Earth Analysis

Patsourakos

Georgoulis

Vourlidas

et al. 2016

ApJ

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“…[57,58]). Nonlinear interactions can create fractal structuring of the phase space and produce global correlations in the entire multiscale system.…”

Section: Introductionmentioning

confidence: 99%

“…According to Milovanov & Zelenyi [59], Tsallis entropy can be rigorously obtained as the solution of a nonlinear functional equation referred to the spatial entropies. The complexity of dynamics is far beyond the simple ergodic complexity and can be described by non-extensive Tsallis statistics based on the extended concept of q-entropy [57]:…”

Section: Introductionmentioning

confidence: 99%

Dynamic properties of small-scale solar wind plasma fluctuations

Рязанцева

Budaev

Zelenyǐ

et al. 2015

Phil. Trans. R. Soc. A.

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The paper presents the latest results of the studies of small-scale fluctuations in a turbulent flow of solar wind (SW) using measurements with extremely high temporal resolution (up to 0.03 s) of the bright monitor of SW (BMSW) plasma spectrometer operating on astrophysical SPECTR-R spacecraft at distances up to 350 000 km from the Earth. The spectra of SW ion flux fluctuations in the range of scales between 0.03 and 100 s are systematically analysed. The difference of slopes in low- and high-frequency parts of spectra and the frequency of the break point between these two characteristic slopes was analysed for different conditions in the SW. The statistical properties of the SW ion flux fluctuations were thoroughly analysed on scales less than 10 s. A high level of intermittency is demonstrated. The extended self-similarity of SW ion flux turbulent flow is constantly observed. The approximation of non-Gaussian probability distribution function of ion flux fluctuations by the Tsallis statistics shows the non-extensive character of SW fluctuations. Statistical characteristics of ion flux fluctuations are compared with the predictions of a log-Poisson model. The log-Poisson parametrization of the structure function scaling has shown that well-defined filament-like plasma structures are, as a rule, observed in the turbulent SW flows.

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“…In the following we present recent representative studies (a nonexhaustive list, mostly the ones the author of this paper was involved with), concerning the application of nonlinear time series algorithms, described in previous paragraphs, in various physical systems, such as seismogenesis, plastic deformation of materials, space plasmas, brain dynamics, economy and DNA (see also [59]). …”

Section: Applications Of Nonlinear Time Series Analysis In Various Comentioning

confidence: 99%

Complex Systems: Phenomenology, Modeling, Analysis

Iliopoulos¹

2016

Int J Appl Exp Math

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In this paper a short overview on complex systems and their basic features, as well as the models and mathematical tools developed for their analysis, is given. This review is formed according to the related experience, activity and scientific interests of the author, namely focused on mainly in nonlinear time series analysis and statistics and their applications on different physical systems. In particular, rough outlines are given concerning the phenomenology of complex systems, e.g. far from equilibrium thermodynamics and Tsallis statistics, power law scaling, multi-fractality, low dimensional chaos, SOC, strange kinetics and anomalous diffusion and turbulent intermittency. In addition, a non-complete list of models, based on equations or agent based, is briefly described such as Kuramoto -Sivashinsky equation, cubic complex Ginzburg-Landau Equation, reaction-diffusion Equation, fractional equations, cellular automata, complex networks and artificial neural networks. A more extended review is provided concerning the nonlinear time series analysis complex systems, describing tools like mutual information, flatness coefficient, structure functions, Tsallis q-triplet, correlation dimension and Lyapunov exponents in the reconstructed phase space, which can provide valuable information for the complex system's dynamics. Finally, applications of nonlinear time series analysis on various physical systems, such as earthquakes, Earth's magnetosphere, solar plasma and solar wind, plastic deformation of materials, epilepsy, economical indices and DNA structure, are provided. Mini ReviewOpen Access Complex SystemsIn general, even though there is no precise definition of complex systems, a complex system can be thought of as a collection of nonlinearly interacting elements summing up as a whole which is characterized by novel large scale effects. These effects arise as emergent properties related with nonlinear-complex behavior, which is the most distinguishing feature of complex systems [1]. A nonexhaustive list of complex systems contains among others (in fact most systems can be considered as complex systems): geophysical processes (earthquakes), biophysics (brain dynamics, DNA), space plasmas (solar wind, solar flares, Earth's magnetosphere), plastic deformation of materials, economy (stock indices), socio-technical systems and many others. The aforementioned complex systems, even though they are completely different in many aspects (e.g. different elements), share common characteristics such as:1. They consist of a large number of interacting elements. This fact allows the description of these systems in two different hierarchical levels, namely microscopic and macroscopic. 2. Their subsystems and their interactions are nonlinear. 3. They exhibit emergent behavior, namely a self-organizing collective behavior, which is not predictable from the knowledge of the element's behavior. 4. These systems are open, namely they interact with their environment. This allows these systems to be driven to metastable state...

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Universality of non-extensive Tsallis statistics and time series analysis: Theory and applications

Cited by 49 publications

References 69 publications

The Major Geoeffective Solar Eruptions of 2012 March 7: Comprehensive Sun-to-Earth Analysis

The Major Geoeffective Solar Eruptions of 2012 March 7: Comprehensive Sun-to-Earth Analysis

Dynamic properties of small-scale solar wind plasma fluctuations

Complex Systems: Phenomenology, Modeling, Analysis

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