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Stochastic self-similarity and self-affinity in the data on the solar activity phenomena is discussed in this paper. The following results are given and discussed. Firstly, the area–perimeter method was applied to obtain the fractal dimension values of solar spot umbras and of equal-intensity field lines in solar active regions (ARs). The fractal dimension value D 0=1.35±0.03 has been obtained for sunspot umbras. Field lines of equal intensity have different values of fractal dimensions for north and south polarities. Secondly, it is shown that the fractal dimension extracted from correlation between the magnetic flux and its cross-sectional area (i.e. a photosphere) is temporally invariant for an AR, but the fractal dimensions can be considerably different for various ARs. Thirdly, the multifractal nature of ARs magnetic fields was confirmed by a study of the scaling properties of their Renyi entropy. Fourthly, the R/S analysis was used for the Wolf series with purpose of estimating the long-time ‘memory...

In the paper the results of investigations on ten solar active regions are presented. The main results are as follows: firstly, the total down-flow velocity exceeds the up-flow velocity by about two orders of magnitude in all the active regions; secondly, no correlation was found between the mean integral velocity flux and the mean integral magnetic flux for all the active regions; thirdly, it was found that, besides a direct correlation between the total sunspot area and the total magnetic flux in active regions, occasionally there is an inverse correlation between these parameters, and the inverse correlation times often corresponded to the structural and topological rebuilding of magnetic flux in the active regions; fourthly, a good correlation was found between some parameters of integral fluxes (magnetic and velocity) and X-ray flux variations.

In this paper, several integral parameters of solar active regions are defined. The values of these parameters can be calculated from observational data. It is shown that only five of them are inde...

A new method of long-term solar activity forecasting based on one-step extrapolation of the Walsh presentation of the Wolf numbers is used to predict the 23rd and 24th solar cycles.

On the basis of observational data, we estimated the fractal dimension of the solar spot umbras is made. The estimation is obtained using the method of “cross-section area - outline length” and it is equal to 1.35 f 0.03. This value of the fractal dimension corresponds to turbulent structures of the “elastic sceletons” type. 1 METHOD There exist different methods for the evaluation of fractal dimensions of natural structures. One of them is an analysis of such ratios as surface-to-volume or crosssection area-to-outline length. This method has wide applications in various cases: for the study of laboratory turbulence, in the analysis of fractal structures of the storm clouds with strong convective fluxes, in the numerical simulation of clusters of correlated magnetic moments in the king model, and others (Proc. Sympos., 1986).

“Tamm could not believe his ears, since this problem belongs to a rather special branch of higher mathematics.” (G. Gamow “My World Line”). The Statistically-thermodynamic mechanism of self-organiz...

The well-known problem of the correlations between eruptive processes in the chromosphere and corona and peculiarities of the magnetic field structure in solar active regions (ARs) on the photospheric level are discussed in this paper. We study the time variations in the first four moments of distribution (over the field) of four integral parameters of the magnetic field of an AR. We used Huairou (PR China) and Solar Orbit Heliospheric Observatory, Michelson–Doppler Interferometer (SOHO/MDI) measurements of longitudinal magnetic fields for ten ARs. We study the following integral parameters of an AR: total magnetic flux F a, tilting angle A n, complexity parameter H u and relative total magnetic flux imbalance O v. The distributions of these parameters show essential differences between quiet and flare productive ARs. One can observe specific differences in the distributions before and during flares. The four first distribution moments take into account these differences and so they can be good quantitati...