Aim. The purpose of the paper is to find exact solutions of a mixed boundary value problem for a system of Moisil–Teodorescu equations in an infinite layer.

Methodology. The paper considers mixed boundary value problems for the Moisil–Teodorescu system of equations in a layer and for the Cauchy–Riemann system in a strip. These problems are reduced to mixed Dirichlet–Neumann boundary value problems for the Laplace equation in a layer and in a strip, respectively, whose explicit solutions were previously obtained by the authors using the Fourier transform of generalized functions of slow growth.

Results. Exact solutions of mixed boundary value problems for the Moisil–Teodorescu system and for the Cauchy–Riemann system are obtained, which are written as convolutions of rapidly decreasing, infinitely differentiable functions (kernels) with boundary functions that are considered to be generalized functions of slow growth. If the boundary functions are ordinary functions of slow growth, then the solutions are written using integral formulas, which can be considered analogous to the Keldysh–Sedov formulas. In particular, if the boundary functions are polynomials, then the solutions are also polynomials.

Research implications. Exact solutions of mixed boundary value problems for the Moisil–Teodorescu system and for the Cauchy–Riemann system are obtained.

Aim. The purpose is an experimental study of a complex system that combines a honeycomb structure that is normal-conjugated with a compositional structure and has imperfections.

Methodology. The influence of the defectiveness of the honeycomb structure on acoustic emission in the ‘“honeycomb matrix – composite’ system, when a changing temperature field acts as an external disturbance, is considered. Acoustic emission methods are used. Instead of loading the sample with external forces, a temperature field is used. Temperature field gradients generate mechanical stresses in the sample, exciting acoustic fields in the sample. Acoustic signals and sample temperature are recorded.

Results. Time dependences of the amplitudes of acoustic signals are obtained by heating samples with and without defects. It is also found that the sample size affects the acoustic emission.

Research implications. The amplitude characteristics of acoustic emission signals make it possible to control complex systems at different temperatures and detect defects without using mechanical loading of products. The developed methods of acoustic emission in temperature fields are applicable to the analysis and control of complex engineering structures.

Aim. The purpose is to study the kinetics of Bose-condensed atoms in a three-well trap.

Methodology. Temporal evolution of the population of atoms in the wells of a three-well trap is investigated theoretically.

Results. Oscillatory modes of atomic evolution and the manifestation of quantum self-capture of the system are demonstrated.

Research implications. The tunneling kinetics of Bose-condensed atoms in a three-well trap is determined by the parameters of the trap.

Aim. For a body of revolution with a power-law generatrix, we investigate the Galkin effect – a change in the sign of the lifting force with a change in the angle of attack in high-speed flat flows.

Methodology. A method for calculating aerodynamic forces and moments based on the hypothesis of locality is used. Using this method, aerodynamic forces and moments are calculated by numerical integration over body triangulation, taking into account shading effects.

Results. The critical elongation of a power-law body of revolution is calculated as a function of the degree of generatrix in a wide range of Reynolds numbers and for various temperature factors.

Research implications. The obtained results are of great importance for the creation of aircrafts in the aerospace industry.

Aim. The purpose of the paper is to prove that the principle of least action follows from the principle of stability.

Methodology. The paper proposes a formulation of the principle of stability of physical systems, which makes it possible to replace the principle of least action, since from the principle of stability follows the principle of least action.

Results. Two theorems are proved to achieve these goals.

Research implications. The work clarifies the origin of one of the basic physical laws, the principle of least action, and allows a different formulation of stability.

Aim. The paper formulates and solves the problem of obtaining analytical formulae for calculating the evaporation time of small and large droplets of spherical shape.

Methodology. The paper relies on analytical methods of mathematical physics in solving the problem of non-stationary evaporation of droplets. Use is also made of numerical composite methods to construct a general formula for all regimes of evaporation of droplets.

Results. A unified analytical expression linking the lifetimes of both small and large spherical water droplets is obtained. The mentioned cases of large and small droplets correspond to different asymptotics. Separate formulae for calculating the evaporation time of small and large spherical aerosol droplets are found. As a result of the numerical analysis of these formulae in the non-stationary process of evaporation of water droplets, a simpler formula acceptable for calculating the lifetime of both small and large spherical water droplets is derived. Formula-built graphs of the dependence of the lifetime of the drop on its initial radius at different values of the ambient temperature are compared with those obtained by other authors.

Research implications. The paper is of great interest both for the theory of non-stationary evaporation of droplets, and for the use of the obtained results in numerous practical applications.