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

Pavlos, G. P.; Karakatsanis, L. P.; Xenakis, M.N.

doi:10.1016/j.physa.2012.07.066

Cited by 27 publications

(32 citation statements)

References 110 publications

(204 reference statements)

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“…For our sunspot area data, we have calculated λ 1 ≈ 0.063 bits month -1 , which implies a very short horizon of 15.9 months (or 1.33 years) 9 . There have been many previous attempts to calculate the Lyapunov exponents (Ostriakov & Usoskin 1990;Mundt et al 1991;Pavlos et al 1992;Zhang 1995Zhang , 1996Zhang 1998;Consolini et al 2006;Baranovski et al 2008;Greenkorn 2009;Consolini et al 2009;Crosson & Binder 2009;Werner 2012;Pavlos et al 2012;Shapoval et al 2013;Zachilas & Gkana 2015). Most values for the first or maximal Lyapunov exponent are around 0.01 − 0.03 bits month -1 , which corresponds to 3 to 8 years.…”

Section: Effectiveness Of the Prediction Per Cyclementioning

confidence: 99%

Spatial-temporal forecasting the sunspot diagram

Covas¹

2017

A&A

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Aims. We attempt to forecast the Sun's sunspot butterfly diagram in both space (i.e. in latitude) and time, instead of the usual onedimensional time series forecasts prevalent in the scientific literature. Methods. We use a prediction method based on the non-linear embedding of data series in high dimensions. We use this method to forecast both in latitude (space) and in time, using a full spatial-temporal series of the sunspot diagram from 1874 to 2015.Results. The analysis of the results shows that it is indeed possible to reconstruct the overall shape and amplitude of the spatialtemporal pattern of sunspots, but that the method in its current form does not have real predictive power. We also apply a metric called structural similarity to compare the forecasted and the observed butterfly cycles, showing that this metric can be a useful addition to the usual root mean square error metric when analysing the efficiency of different prediction methods. Conclusions. We conclude that it is in principle possible to reconstruct the full sunspot butterfly diagram for at least one cycle using this approach and that this method and others should be explored since just looking at metrics such as sunspot count number or sunspot total area coverage is too reductive given the spatial-temporal dynamical complexity of the sunspot butterfly diagram. However, more data and/or an improved approach is probably necessary to have true predictive power.

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Section: Effectiveness Of the Prediction Per Cyclementioning

confidence: 99%

Spatial-temporal forecasting the sunspot diagram

Covas¹

2017

A&A

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“…Tsallis statistics is now widely applied e.g. to solar and space plasmas such as the heliosphere magnetic field and the solar wind [28][29][30] .…”

Section: Introductionmentioning

confidence: 99%

A fractional Fokker-Planck model for anomalous diffusion

2014

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In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution.The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.

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“…Typical relaxation of observable O t −1/τ q rel Ω(t) = e −t/τ q rel q rel A plethora of q-triplets have been found in solar plasma [89,90,125,126,127], the ozone layer [128], logistic map (see [41,42,43,48,49,50,51,54,55,56,57,58]), El Niño/Southern Oscillation [129], geological faults [130], finance [131,132], DNA sequence [133], and elsewhere [134,135].…”

Section: Q-tripletsmentioning

confidence: 99%

Generalization of the possible algebraic basis of q-triplets

Tsallis

2017

Eur. Phys. J. Spec. Top.

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The so called q-triplets were conjectured in 2004 [Tsallis, Physica A 340, 1 (2004)] and then found in nature in 2005 [Burlaga and Vinas, Physica A 356, 375 (2005)]. A relevant further step was achieved in 2005 [Tsallis, Gell-Mann and Sato, PNAS 102, 15377 (2005)] when the possibility was advanced that they could reflect an entire infinite algebra based on combinations of the self-dual relations q → 2 − q (additive duality) and q → 1/q (multiplicative duality). The entire algebra collapses into the single fixed point q = 1, corresponding to the Boltzmann-Gibbs entropy and statistical mechanics. For q 1, an infinite set of indices q appears, corresponding in principle to an infinite number of physical properties of a given complex system describable in terms of the so called q-statistics. The basic idea that is put forward is that, for a given universality class of systems, a small number (typically one or two) of independent q indices exist, the infinite others being obtained from these few ones by simply using the relations of the algebra. The q-triplets appear to constitute a few central elements of the algebra. During the last decade, an impressive amount of q-triplets have been exhibited in analytical, computational, experimental and observational results in natural, artificial and social systems. Some of them do satisfy the available algebra constructed solely with the additive and multiplicative dualities, but some others seem to violate it. In the present work we generalize those two dualities with the hope that a wider set of systems can be handled within. The basis of the generalization is given by the selfdual relation q → q a (q) ≡ (a+2)−aq a−(a−2)q (a ∈ R). We verify that q a (1) = 1, and that q 2 (q) = 2 − q and q 0 (q) = 1/q. To physically motivate this generalization, we briefly review illustrative applications of q-statistics, in order to exhibit possible candidates where the present generalized algebras could be useful.

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

Cited by 27 publications

References 110 publications

Spatial-temporal forecasting the sunspot diagram

Spatial-temporal forecasting the sunspot diagram

A fractional Fokker-Planck model for anomalous diffusion

Generalization of the possible algebraic basis of q-triplets

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