Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma, Part one: Sunspot dynamics
In this study, the non-linear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis (1988, 2004, 2009) [7,9,10]. The q-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 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 (2001, 2000) [76,77]. 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 a phase transition to low dimensional chaos in accordance to Ruzmaikin, Zeleny and Milovanov’s studies (Zelenyi and Milovanov (1991) ); Milovanov and Zelenyi (1993) ; Ruzmakin et al. (1996) ) (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 Dq, (iii) exponent spectrum J(p) of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 391 (2012)
Issue (Month): 24 ()
|Contact details of provider:|| Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N. & Sarafopoulos, D. & Pavlos, E.G., 2012. "Tsallis statistics and magnetospheric self-organization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3069-3080.
- Arimitsu, Toshihico & Arimitsu, Naoko, 2001. "Analysis of turbulence by statistics based on generalized entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 177-194.
- Lenzi, E.K. & Mendes, R.S. & da Silva, L.R., 2000. "Statistical mechanics based on Renyi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 337-345.
- Kaniadakis, G. & Lavagno, A. & Lissia, M. & Quarati, P., 1998. "Anomalous diffusion modifies solar neutrino fluxes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 359-373.
- McCauley, Joseph L., 1997. "Nonintegrability, chaos, and complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(3), pages 387-404.
- Pavlos, G.P. & Iliopoulos, A.C. & Tsoutsouras, V.G. & Sarafopoulos, D.V. & Sfiris, D.S. & Karakatsanis, L.P. & Pavlos, E.G., 2011. "First and second order non-equilibrium phase transition and evidence for non-extensive Tsallis statistics in Earth’s magnetosphere," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(15), pages 2819-2839.
- Ferri, G.L. & Reynoso Savio, M.F. & Plastino, A., 2010. "Tsallis’ q-triplet and the ozone layer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1829-1833.
When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:391:y:2012:i:24:p:6287-6319. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.