06 May 2015

Multifractals Explaining Physical Mechanism on the Sun

The famous sunspots on the surface of the Earth's star result from the dynamics of strong magnetic fields, and their numbers are an important indicator of the state of activity on the Sun. At the Institute of Nuclear Physics of the Polish Academy of Sciences in Kraków, Poland, researchers have been conducting multifractal analysis into the changes in the numbers of sunspots. The resulting graphs were surprisingly asymmetrical in shape, suggesting that sunspots may be involved in hitherto unknown physical processes. Mathematical analysis of multifractals provides invaluable information on the dynamic phenomena, as they occur to varying degrees of complexity. The results are useful in a number of ways, but most importantly, they can allow us to discard the influence of current, longstanding trends. Researchers have shown for the first time that certain overlooked features of the graphs of multifractals, known as singularity spectra of the time series, have in fact a close relationship with the nature of the analyzed phenomena.

 
The graphs generated by the analysis of multifractals reveal a certain asymmetry, and we've turned our attention towards that. Until now, the asymmetry was treated as a by product of the computational method. We have proven that the asymmetry might carry valuable information about the nature of the analyzed processes. Using this approach, looking at some of the graphs, for example those regarding the number of sunspots on the face of the Sun, we come to some very interesting conclusions. Tests carried out using multifractals disclose the properties encoded in the data relating to the relationships on different scales. The basic graphic tools here are known as multifractal spectra or spectra of singularity. If the data take the structure of a simple fractal, the multifractal graphs are reduced to a point. If the structure of a multifractal is homogenous, then the graph takes the ideal symmetrical form, that of a neat hill -- an inverted parabola. The thing is, with many graphs we've seen on the actual data, there is no ideal symmetry. As a rule, the left side is dominant.

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