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Frish, U. and Parisi, G. (1985) On the Singularity Structure of Fully Developed Turbulence. In: Ghil, M., Benzi, R. and Parisi, G., Eds., Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, North-Holland, New York, 84-88.

has been cited by the following article:

  • TITLE: Relationship between the Sunspot Number and Solar Polar Field by Wavelet-Based Multifractal Analysis

    AUTHORS: Fumio Maruyama

    KEYWORDS: Sunspot Number, Solar Polar Field, Wavelet, Multifractal

    JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.5, May 17, 2019

    ABSTRACT: There is increasing interest in finding the relation between the sunspot number (SSN) and solar polar field. In general, fractal properties may be observed in the time series of the dynamics of complex systems, such as solar activity and climate. This study investigated the relations between the SSN and solar polar field by performing a multifractal analysis. To investigate the change in multifractality, we applied a wavelet transform to time series. When the SSN was maximum and minimum, the SSN showed monofractality or weak multifractality. The solar polar field showed weak multifractality when that was maximum and minimum. When the SSN became maximum, the fractality of the SSN changed from multifractality to monofractality. The multifractality of SSN became large before two years of SSN maximum, then that of the solar polar field became large and changed largely. It was found that the change in SSN triggered the change in the solar polar field. Hence, the SSN and solar polar field were closely correlated from the view point of fractals. When the maximum solar polar field before the maximum SSN was larger, the maximum SSN of the next cycle was larger. The formation of the magnetic field of the sunspots was correlated with the solar polar field.