Doklady Rossijskoj akademii nauk. Fizika, tehničeskie nauki

The symmetries of the classical Heisenberg model are examined. It is shown that such symmetries are groups of conformal transformations and rotations. The invariance of vortex structures with respect to a group of rotations is studied. The application of the found transformations of the group of field rotations to the already known solutions of the Heisenberg model (such as instantons, vortex “targets” and “spirals”) generates other structures, which are also solutions of this model, with the properties being determined by the original structures.

The results of statistical processing of measurements of auroral kilometric radiation detected on the WIND satellite near the libration point L1 are presented. It is shown that the frequency of auroral kilometric radiation registration varies in antiphase with variations in solar activity. It is hypothesized that such a change in the detection frequency of auroral kilometer radio emissions is related to the characteristics of radio wave propagation in the inhomogeneous plasma of the solar wind.

It is well known that shock waves in sandy environments are absorbed, i.e. as they pass through the bulk medium, their amplitude decreases. In shock tubes, as a rule, the results of the impact of shock wave pulses on an object are studied, leading to a change in the shape and amplitude of the pulse that characterizes the medium. In a shock tube equipped with a section of bulk media, the wave is repeatedly reflected from the surfaces of the porous medium under study and the upper end of the tube. The amplitude and shape of the reflected wave differs insignificantly from the main pulse. At the same time, the amplitude of the re-reflected wave propagating in the sand immediately after exposure (13 ms) to the main pulse increases more than three times compared to the amplitude of the main pulse at this depth. Compared to its value at the sand surface, the amplitude in the sand thickness becomes almost twice as high. The maximum amplification of the amplitude of a reflected wave in a bulk medium increases with increasing layer through which the pulse passes to a certain depth, and then begins to decrease.

A scheme of a quasistatic experiment in a linear viscoelastic isotropic cylindrical layer is presented, where there is a state in which shear creep and shear relaxation are realized simultaneously in two orthogonal directions to each other. The external surface of the layer is stationary, and by setting tangential displacements and shear stresses on its inner surface in a certain way and measuring the remaining components on the same surface, it is possible to experimentally confirm the integral relations of reciprocity of the shear creep and shear relaxation functions.