Two theoretical problem from the International Physics Olympiad (IPhO) are presented. First of them was assigned at the 42th IPhO in 2012 in Thailand. The motivation for the problem was to describe the motion of three satelites forming together the Laser Interferometry Space Antenna (LISA), the device designed to detect gravitational waves. The second presented problem (from 45th IPhO in 2014 in Kazakhstan) concerns the simplest models of gas discharges. and Jan Kříž, Filip Studnička, Ľubomír Konrád, Bohumil Vybíral.
We demonstrate that both in the global scale and in the scale of large and complex active regions the high flare activity is dosely related to the changes in the whole background magnetic field distribution. We found that the disturbances of the normal course of MALs during the years 1965 -1980 correlated with the maxima of flare activity and the mode of MALs distribution with the mean level of solar flare numbers. We showed that the development of activity during the last two ^submaxima of the 21st cycle of solar activity, especially the formation of the white-light flare region of April 1984, were parts of global processes in the solar atmosphere. They
were accompanied by a complete reorganization of the MALs patterns, background field sector structure and restructuralization of coronal holes. In both cases, in the global and in the local scales, we could follow the geophysical consequences of the entire reconstruction of global solar field amplified by the direct influence of many large flares.
The time evolutlon of the metalliclty wlthln the Galaxy has been analysed on the base of published data for star clusters. The resulting age-metalliclty relation seems to split into two independent paths, passing the same age range over 10^10 years. The lower relationship resembles that for the Magellanic Clouds. Such a picture of the chemical evolutlon of the galactic matter is consistent wlth the observed division of the considered sample of open clusters into two groups differing in metallicity and spatial distribution, similarly to the division found for globular clusters. The metal-poor open clusters resemble metal-rich globulars. This can suggest that our galaxy has evolved from spherical metal-poor configuration represented in the considered sample of star clusters by metal-poor globulars, through a thick dlsk phase wlth the middle metallicity up to thin metal-rich disk wlth its representative
metal-rich open clusters. The transition between each of the above phases was more or less abrupt in its characteristic chemical and spatial properties.