A synthesis method for the reference trajectory of an unmanned aerial vehicle that flies around obstacles of urban buildings in the horizontal and vertical planes is proposed. To solve this problem, for the first time a conformal mapping is constructed for a collection of rectangles that approximate the obstacles on the digital map of a terrain.

The structure of an operator that determines the partial conditions of radiation in the scalar problem of diffraction theory is considered. Nonlocal boundary conditions are determined by a series setting a certain integro-differential operator. The principal part of this operator is presented in the explicit form of a hyper-singular operator and its components with lower-order singularities. The remaining rapidly converging part of the functional series determines an integral operator with a continuous kernel.

We apply the method of mixed finite elements to the junction problem for coaxial and radial waveguides. The problem is reduced to an internal boundary-value problem with nonlocal boundary-value conditions. In the low-frequency range, we compare the results of the finite-element method with the Otto relationship.

The effect of spherical SiO2 nanoparticles of 20 to 80 nm in diameter embedded into the PEDOT: PSS buffer layer of organic solar cells (OSC) based on star-shaped oligomers on their efficiency was studied experimentally in detail. Measurements and analysis of the current-voltage characteristics of the samples, their absorption spectra and study of the morphology of the surface of the buffer layer with embedded nanoparticles were carried out. It is shown an increase in the OSE efficiency for the case of embedded into the PEDOT:PSS layer SiO2 nanoparticles with a diameter of 20 and 50 nm, which slightly depends on the concentration of the nanoparticles in the buffer layer.

The localization problem is considered for eigenfunctions of the Laplace operator in a domain that consists of two rectangles linked by a small hole. The localization of the eigenfunction is proven in a subdomain. The velocity is estimated for the convergence of an eigenvalue of the original problem to a subdomain eigenvalue.

The distribution of special points of dispersion curves for an anisotropic filled waveguide is considered. The existence of special curves is substantiated for some relationship between anisotropy coefficients. These points are connected with complex and backward waves. It is proven that the curve of special points is an ellipse.

The CLAS12 experiment is intended to study the generalized parton distributions in exclusive reactions. The CLAS12 Silicon Vertex Tracker must provide the registration of all reaction products at the expected high luminosity. The results of a GEANT4 simulation of the expected physical rates in the SVT are presented. The frequency of the noise hits of the readout electronics is determined on the basis of the capacitive load generated by the attached sensors. In order to find the fraction of the events that are lost due to delays in the readout electronics, a computer simulation of the logic of the data-driven readout FSSR2 chip is performed. At a signal-to-noise ratio of 8 to 1 the readout electronics are capable of processing the expected rates, provided a registration threshold of 0.4 mip is preset.

We studied the radiation-directivity pattern and the near-field polarization of a spheroidal metallic nanoparticle located over a silicon substrate by interaction with a linearly and circularly polarized field. It is shown that the directivity pattern of the spheroidal particle near the silicon substrate becomes strongly asym- metric and forward scattering is predominant compared with the symmetric diagram of a particle in free space. The change of the near-field polarization of the nanoparticle in presence of the substrate is studied for different wavelengths in the vicinity of the plasmonic resonance. The near-field polarization is described using the generalized Stokes parameters, which allow pictorial visualization of results.

A model for the description of the distribution of magnetization across the thickness of a ferromagnetic

semiconductor film is considered. Applying a constant electric field perpendicular to the film surface

makes it possible to change the Curie temperature. The obtained formulas determine the dependence

that this distribution has on the values of the physical parameters of the film.

In this paper, the problem of electromagnetic wave diffraction by extensive conducting bodies with uniform cross sections and continuous curvature boundaries is studied. Corrugated cylinders are considered as diffusers. A resonant decrease in the radiation visibility of such bodies was discovered.

Observational data regarding anomalously high waves on the sea’s surface (freak or rogue waves) are reviewed. The objectives of the research are identified, and the difficulties encountered are noted. The main physical mechanisms employed in explaining rogue waves are listed, and possible approaches to predicting marine hazards are discussed. Principles for ongoing short-term forecasting of extreme waves (within tens of wave periods or wavelengths) are proposed. Some preliminary results are presented.

A model for describing the distribution of magnetization over the thickness of a film of a ferromagnetic

semiconductor in an external constant electric field perpendicular to the film surface is considered. The

formulas obtained make it possible to determine the dependence of this distribution on the values of the

physical parameters of the film.

We observe the self-assembling of the dipolar hard sphere particles at low temperature by Monte Carlo simulation. We find different types of stable structures of dipolar particles which appear when the isotropic phase of the system becomes unstable. Specifically, we find an interesting case of parallel cylindrical domains. The value of the total dipole moment of each domain is significantly large compared to the average value of the whole system. Models with dipolar interactions may form structures comprised of layers with anti-parallel dipole orientation.