Aim. We consider the simplest model of point motion in a non-inertial coordinate system, which explains the formation of vortices in the atmosphere.

Procedure and methods. The given model is analytically solved, and the results and average parameters of real cyclones and anticyclones are assessed.

Results. It follows from the obtained solution that the trajectory has the form of a spiral, whose twisting direction depends on the directions of the Coriolis force and the speed of the point, which is associated with the location of the region of the phenomenon formation relative to the Earth hemispheres (northern, clockwise; and southern, counterclockwise). The dependence of the solution on the formulation of boundary and initial conditions is considered. It is shown that in the mathematical formulation of problems of this kind, difficulties arise with the introduction of boundary and initial conditions associated with a singularity at the zero point. The proposed model and dimensional considerations make it possible to estimate the average sizes of cyclones and anticyclones.

Research implications. The theoretical significance lies in the analytical substantiation of the connection between the motion of a point in a non-inertial frame of reference and the occurrence of vortices in the atmosphere.

Aim. An attempt is made to find how the combination of the mass of an atom of hydrogen and helium (taking into account its isotopes) and its polarizability affect the movement of a Frenkel‒Kontorova soliton.

Methodology. Use is made of the relations (previously obtained by the authors) to relate the characteristics of the atom with the characteristics of the lattice through which the soliton moves.

Results. A strong relationship is found between the mass of an atom and its polarizability, which determines the soliton structure.

Research implications. It is shown that the possibility of moving a soliton is determined by both the mass of the atom and its polarisability; for example, due to polarizability, a helium atom will not move.

Aim. We select corrective corrections in the form of additional variables in the equations of motion to analyze the problem of dark matter.

Methodology. The research is based on the introduction of higher-order derivatives in the form of non-local variables to describe the gravitational interaction at intergalactic distances. Works are analyzed that correlate the formula of gravitational interaction at galactic distances from acceleration and its higher derivatives with respect to time.

Results. The selected theoretical formula yields good agreement between theory and the experimental results, and makes it possible to explain previously unexplained effects leading to the concept of dark matter. This becomes possible by introducing additional variables in the form of higher-order derivatives.

Research implications. We have obtained new results that allow the behavior of galaxies to be calculated using the correction formula for the gravitational interaction at intergalactic distances. Theoretical calculations coincide with the experimental data.

Aim. We evaluate the uncertainties of modern nuclear data libraries and perform a comparative analysis of the induced activity of the blanket of a thermonuclear neutron source containing uranium-238 and thorium-232 nuclides.

Methodology. The obtained data on the activity of unstable nuclides formed in the blanket of a thermonuclear reactor are analyzed.

Results. The results of the studies show that the residual activity of the discharged blanket with U-238 is approximately two-to-three times greater than the activity of Th-232 normalized by one formed fissile nuclide. To make the activity of the unloaded uranium blanket similar to that of the Th-232-based blanket, a slightly longer exposure time is required.

Research implications. The obtained results can be used to optimize the blanket of a thermonuclear neutron source.

Aim. We construct algorithms that allow calculating the interaction of a heterogeneous flow with nanostructured surfaces of solids made of various materials, as well as wetting processes and movement of particles on the surface in an air flow.

Methodology. Use is made of methods of molecular modeling and known physical laws; studies performed by other authors are analyzed.

Results. A method is developed for calculating the interaction of a flow with a solid body, whose coating has a relief and a different degree of hydrophobicity. Parametric studies are performed using the molecular dynamics method.

Research implications. The results can be used to study the possibilities of controlling the state of the boundary layer and the initiation of turbulence at the molecular level.

Aim. Formulae for temperature and concentration fields around two evaporating identical aerosol drops in the electromagnetic radiation field are generalized to the case of two drops with arbitrary radii.

Methodology. Coefficients in expansions of temperature and concentration fields by spherical functions are considered as coordinates of vectors of an infinite-dimensional linear normalized space, which are found from boundary conditions by means of linear operators.

Results. Generalized formulae for temperature and concentration fields around two drops with arbitrary radii are obtained. Calculations are carried out using these formulae and graphs of temperature and concentration field profiles for two unequal drops for different distances between drop centers are given.

Research implications. The obtained theoretical formulae for temperature and concentration fields around two drops with arbitrary radii allow one to make simple algorithms for practical calculations.