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We have studied the 27-day variations and their harmonics in Galactic cosmic ray (GCR) intensity, solar wind velocity, and interplanetary magnetic field (IMF) components during the recent prolonged solar minimum 23/24. The time evolution of the quasiperiodicity in these parameters connected with the Sun's rotation reveals that the synodic period of these variations is ≈ 26 -27 days and is stable. This means that the changes in the solar wind speed and the IMF are related to the Sun's near-equatorial regions in considering the differential rotation of the Sun. However, the solar wind parameters observed near the Earth's orbit provide only the conditions in the limited local vicinity of the equatorial region in the heliosphere (within ± 7• in latitude). We also demonstrate that the observed period of the GCR intensity connected with the Sun's rotation increased up to ≈ 33 -36 days in 2009. This means that the process that drives the 27-day GCR intensity variations takes place not only in the limited local surroundings of the equatorial region but in the global 3-D space of the heliosphere, covering also higher latitude regions. A relatively long period (≈ 34 days) found for 2009 in the GCR intensity gives possible evidence of the onset of cycle 24 due to active regions at higher latitudes and rotating slowly because of the Sun's differential rotation. We also discuss the effect of differential rotation on the theoretical model of the 27-day GCR intensity variations.

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We study the relationship of the 27-day variation of the galactic cosmic ray intensity with similar changes of the solar wind velocity and the interplanetary magnetic field based on the experimental data for the Bartels rotation period # 2379 of 23 November 2007 -19 December 2007. We develop a three dimensional (3-D) model of the 27-day variation of galactic cosmic ray intensity based on the heliolongitudinally dependent solar wind velocity. A consistent, divergence-free interplanetary magnetic field is derived by solving Maxwell's equations with a heliolongitudinally dependent 27-day variation of the solar wind velocity reproducing in situ observations. We consider two types of 3-D models of the 27-day variation of galactic cosmic ray intensity -(1) with a plane heliospheric neutral sheet, and (2)-with the sector structure of the interplanetary magnetic field. The theoretical calculation shows that the sector structure does not influence significantly on the 27-day variation of galactic cosmic ray intensity as it was shown before based on the experimental data. Also a good agreement is found between the time profiles of the theoretically expected and experimentally obtained first harmonic waves of the 27-day variation of the galactic cosmic ray intensity (correlation coefficient equals 0.98 ± 0.02). The expected 27-day variation of the galactic cosmic ray intensity is inversely correlated with the modulation parameter ζ (correlation coefficient equals -0.91 ± 0.05) which is proportional to the product of the solar wind velocity V and the strength of the interplanetary magnetic field B (ζ~ VB). The high anticorrelation between these quantities indicates that the predictable 27-day variation of the galactic cosmic ray intensity mainly is caused by this basic modulation effect.

Nowadays, when the global and national industry is addicted from various electrical and electronic equipment at a very high level, it is of a special interest to understand the possible origins of the interruptions in the electricity supply. Failures in ground-based electrical and electronic systems, or disturbances of satellites operation caused by influential magnetic storms initiated by the changeable Sun can have a high economic impact on the industry. These strong magnetic storms are triggered by solar-driven disturbances in interplanetary space. Studies of these phenomena have gained a special attention since the incident that had occurred in northern Canada in March 1989. During this event the work of the hydroelectric plant in the region of Quebec was blocked for long, winter hours and many citizens of this region of Canada suffered from a blackout. Analysis performed in the Oak Ridge National Laboratory showed that if that blackout have had taken place in the USA then costs generated only by a not supplied electricity could even reach 6 billion USD. In our paper, we apply time series and statistical analysis tools, i.e. superposed epoch analysis and Wilcoxon Matched Pairs Test, for a large set of data, among them: 4625 failures of electrical grids in southern Poland in 2010, from the total number of 25,616, and 10,656 in the first seven months of 2014, from the total number of 30,155. We investigate only those failures which might be connected with the above described effects. We analyze data of breakdowns with unidentified reasons, as well as failures connected to the aging and electronic devices breakdowns, which occurred during the periods of an increased geomagnetic activity. Based on the data from The Institute of Meteorology and Water Management-National Research Institute we eliminate from the consideration those failures which had meteorological grounds. Our analysis shows the usefulness of these mathematical tools in such a vital for the global and national industry issue, as well, that powerful phenomena of solar origin, somewhat disturbed in 2010 and January-July 2014 the electrical grids productivity in southern Poland.