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Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part two: Solar Flares dynamics

机译:Tsallis非广泛统计,间歇性湍流,sOC和混乱   在太阳能等离子体中。第二部分:太阳耀斑动力学

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摘要

In the second part of this study and similarly with part one, the nonlinearanalysis of the solar flares index is embedded in the non-extensive statisticaltheory of Tsallis [1]. The triplet of Tsallis, as well as the correlationdimension and the Lyapunov exponent spectrum were estimated for the SVDcomponents of the solar flares timeseries. Also the multifractal scalingexponent spectrum, the generalized Renyi dimension spectrum and the spectrum ofthe structure function exponents were estimated experimentally andtheoretically by using the entropy principle included in Tsallis non extensivestatistical theory, following Arimitsu and Arimitsu [2]. Our analysis showedclearly the following: a) a phase transition process in the solar flaredynamics from high dimensional non Gaussian SOC state to a low dimensional alsonon Gaussian chaotic state, b) strong intermittent solar corona turbulence andanomalous (multifractal) diffusion solar corona process, which is strengthenedas the solar corona dynamics makes phase transition to low dimensional chaos:c) faithful agreement of Tsallis non equilibrium statistical theory with theexperimental estimations of i) non-Gaussian probability distribution function,ii) multifractal scaling exponent spectrum and generalized Renyi dimensionspectrum, iii) exponent spectrum of the structure functions estimated for thesunspot index and its underlying non equilibrium solar dynamics. e) The solarflare dynamical profile is revealed similar to the dynamical profile of thesolar convection zone as far as the phase transition process from SOC to chaosstate. However the solar low corona (solar flare) dynamical characteristics canbe clearly discriminated from the dynamical characteristics of the solarconvection zone.
机译:在本研究的第二部分中,与第一部分类似,太阳耀斑指数的非线性分析被嵌入到Tsallis的非广义统计理论中[1]。针对太阳耀斑时间序列的SVD分量,估计了Tsallis的三元组以及相关维数和Lyapunov指数谱。遵循Arimitsu和Arimitsu [2],利用Tsallis非广义统计理论中包含的熵原理,从理论和实验上估算了多重分形标度指数谱,广义Renyi维数谱和结构函数指数谱。我们的分析清楚地表明以下内容:a)太阳耀斑动力学中的一个相变过程,从高维非高斯SOC态到低维索非非高斯混沌态,b)强间歇性太阳电晕湍流和异常(多重分形)扩散太阳电晕过程,这是由于太阳电晕动力学使相变转变为低维混沌而得到加强:c)Tsallis非平衡统计理论与i)非高斯概率分布函数,ii)多重分形标度指数谱和广义Renyi维谱的实验估计的忠实协议,iii)指数太阳黑子指数及其潜在的非平衡太阳动力学估计的结构函数的光谱。 e)在从SOC到混沌的相变过程中,太阳耀斑的动力学剖面与太阳能对流区的动力学剖面相似。但是,可以将太阳低电晕(太阳耀斑)的动力特性与太阳对流区的动力特性清楚地区分开。

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