The Modified Form of the Gutenberg-Richter Law ‎in ‎Solar ‎Flare ‎Complex ‎Network‎ : ‎Approach of Genetic Algorithm on the Thresholded Power-Law Behavior

Document Type : Research Paper

Author

Department of Physics, Technical and Vocational University (TVU), Tehran, Iran.

Abstract

The hybrid model approach is adopted to construct the solar flare complex network. The modified form of Gutenberg-Richter law is obtained as the frequency-magnitude distribution of the empirical data. The frequency-magnitude distributions of positive-definite data are sometimes observed to follow a power-law over several orders of size. There are reasons to the deviation of the frequency-magnitude distribution from an ideal power distribution. Among many alternative forms of the power-law function, we found that the threshold power-law is well fitted with solar empirical data at small values. A statistical method based on optimization of the ‎$‎‎chi‎‎^{2}‎$-test by application of the genetic algorithm have been developed.‎
Here, the analytical details of a method based on genetic algorithm is presented to calculate the parameters of the frequency-Magnitud‎‏e distribution of the empirical data sets. This method estimates the best parameters of the threshold power-law function as the frequency-magnitude distribution of the empirical data, as well.

Keywords

References

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Iranian Journal of Astronomy and Astrophysics
Volume 7, Issue 1
April 2020
Pages 47-56

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