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

In the second part of this study and similarly with part one, the nonlinear analysis of the solar flares index is embedded in the non-extensive statistical theory of Tsallis [1]. The triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the SVD components of the solar flares timeseries. Also the multifractal scaling exponent spectrum, the generalized Renyi dimension spectrum and the spectrum of the structure function exponents were estimated experimentally and theoretically by using the entropy principle included in Tsallis non extensive statistical theory, following Arimitsu and Arimitsu [2]. Our analysis showed clearly the following: a) a phase transition process in the solar flare dynamics from high dimensional non Gaussian SOC state to a low dimensional also non Gaussian chaotic state, b) strong intermittent solar corona turbulence and anomalous (multifractal) diffusion solar corona process, which is strengthened as the solar corona dynamics makes phase transition to low dimensional chaos: c) faithful agreement of Tsallis non equilibrium statistical theory with the experimental estimations of i) non-Gaussian probability distribution function, ii) multifractal scaling exponent spectrum and generalized Renyi dimension spectrum, iii) exponent spectrum of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics. e) The solar flare dynamical profile is revealed similar to the dynamical profile of the solar convection zone as far as the phase transition process from SOC to chaos state. However the solar low corona (solar flare) dynamical characteristics can be clearly discriminated from the dynamical characteristics of the solar convection zone.Comment: 21 pages, 11 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:1201.649

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

In this study, the nonlinear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis. 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, the generalized Renyi dimension spectrum and the spectrum of the structure function exponents were estimated experimentally and theoretically by using the entropy principle included in Tsallis non extensive statistical theory, following Arimitsu and Arimitsu. 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 Ruzmaikin, Zeleny and Milovanov studies c) faithful agreement of Tsallis non equilibrium statistical theory with the experimental estimations of i) non-Gaussian probability distribution function, ii) multifractal scaling exponent spectrum and generalized Renyi dimension spectrum, iii) exponent spectrum of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics.Comment: 40 pages, 11 figure

Estimating the Fractal Dimension, K_2-entropy, and the Predictability of the Atmosphere

The series of mean daily temperature of air recorded over a period of 215 years is used for analysing the dimensionality and the predictability of the atmospheric system. The total number of data points of the series is 78527. Other 37 versions of the original series are generated, including ``seasonally adjusted'' data, a smoothed series, series without annual course, etc. Modified methods of Grassberger and Procaccia are applied. A procedure for selection of the ``meaningful'' scaling region is proposed. Several scaling regions are revealed in the ln C(r) versus ln r diagram. The first one in the range of larger ln r has a gradual slope and the second one in the range of intermediate ln r has a fast slope. Other two regions are settled in the range of small ln r. The results lead us to claim that the series arises from the activity of at least two subsystems. The first subsystem is low-dimensional (d_f=1.6) and it possesses the potential predictability of several weeks. We suggest that this subsystem is connected with seasonal variability of weather. The second subsystem is high-dimensional (d_f>17) and its error-doubling time is about 4-7 days. It is found that the predictability differs in dependence on season. The predictability time for summer, winter and the entire year (T_2 approx. 4.7 days) is longer than for transition-seasons (T_2 approx. 4.0 days for spring, T_2 approx. 3.6 days for autumn). The role of random noise and the number of data points are discussed. It is shown that a 15-year-long daily temperature series is not sufficient for reliable estimations based on Grassberger and Procaccia algorithms.Comment: 27 pages (LaTex version 2.09) and 15 figures as .ps files, e-mail: [email protected]

On the torus automorphisms: Analytic solution, computability and quantization

The exact solution of the classical torus automorphism, which partial case is Arnold Cat map is obtained and compared with the numerical solution. The torus, considered as the classical phase space admits the quantization in terms of the Weyl pair. The remarkable fact is that quantum map, as the evolution with respect to the discrete time, preserves the Weyl commutation relation. We have obtained also the operator solution of this quantum torus automorphism. © 2001 Elsevier Science Ltd.SCOPUS: cp.jinfo:eu-repo/semantics/publishe

Embedding the torus automorphisms to Hamiltonian flows

Two Hamiltonian flows, one resulting from the embedding of the torus automorphisms into R2 and the other restricted on the torus were studied. Some remarks on the geodesic flow on the Lobachevski plane, integrability, embeddability and quantization are presented.SCOPUS: cp.jinfo:eu-repo/semantics/publishe

Quasi-periodic emissions (15- 80 min ) from the poles of Jupiter as a principal source of the large-scale high-latitude magnetopause boundary layer of energetic particle

In this study, we concentrate on the examination of the quasi-periodic behavior of 0.5-1.6 MeV (∼40-400 keV) protons (electrons) and of relativistic (> 16 MeV) electrons, observed at Jupiter by two different experiments onboard Ulysses, the HI-SCALE and COSPIN, respectively, within the large-scale south duskside magnetopause boundary layer (MPBL) of energetic particles, from ∼20:00 UT, day 41, to 12:00 UT, day 43. During those times, the observations confirm the transition of Ulysses to an important magnetospheric region with particle intensities comparable to the magnetodisk levels. A careful analysis of high time-resolution intensity, anisotropy and spectral measurements suggests the following: (1) The quasi-periodic ∼40 min (QP-40) energetic electron (> ∼40 keV) and proton (> ∼0.5 MeV) emissions from the south pole were a characteristic phenomenon in the south duskside MPBL; an almost continuous QP 40-min variation has been confirmed in energetic electron observations. (2) When the QP-40 modulation was not evident in energetic particle intensities, it was still detectable in spectral and anisotropy observations. (3) The QP-40 emission is a principal, but not the only periodic, energetic electron and proton emission; other periodicities (∼15, ∼20, ∼30, ∼50, ∼60, ∼80 min) were also significant in energetic particle spectral and anisotropy observations. We infer that QP-40 emissions along with other periodic emissions (∼15, ∼20, ∼30, ∼50, ∼60, ∼80 min) were the principal source of the large-scale high-latitude MPBL of energetic particles during Ulysses outbound pass of Jupiter. © 2003 Elsevier Ltd. All rights reserved