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Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three-dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics analogs are vortex rings. An analysis of the shape of the sections of the rings, depending on the angular speed of rotation and the major diameter, is carried out. Successively, spherical electromagnetic vortex rings of Hill's type are taken into consideration. For some interesting peculiar configurations, explicit numerical solutions are exhibited.

In this paper, we present two options of the toroid magnetic spectrometer dedicated to measure the energy and the polar and the azimuthal angles of the scattered from the ion’s nuclear electrons in the future electron-ion collider DERICA at JINR. These options differ by the opposite sign of the magnetic field. In one of the options, the toroid magnetic field bends electrons towards the collision line, while in the option with the inverted field a bent is done outwards from the beam axis. We show that the last case provides much larger useful fraction of a solid angle for detection of the scattered electrons. The momentum resolution of such a spectrometer is estimated.

Actors in the Prisoner’s Dilemma agent-based model presented here decide between cooperation and defection in binary interactions determined by distance and overall gains. The paper thus tries to answer one of the fundamental questions of international politics: how does cooperative behavior perform in an environment governed by power and location? Two kinds of noise and the reward for mutual cooperation oscillating between temptation and punishment payoffs with a variable speed were added similarly like few completely new strategies inspired by foreign policy behavior of states. The initial success of generous reciprocal altruists is no surprise, but the lacking relationship between frequency of interactions and cooperativeness at the level of pairs already suggests some similarity with the system of states. Yet, the most important outcome is victory of the balance of threat strategy in all reruns with a heterogeneous pool of actors, despite the fact that this strategy was one of the least cooperative ones. At the same time, rules pre-selected by their success in the homogeneous and cooperative environment were still able to sustain intensive cooperation among themselves even within the heterogeneous pool of strategies.