This paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on , including periodic and almost periodic functions. In addition to constructing a bounded strong solution, we determine a time-dependent source coefficient via an integral overdetermination condition ensuring well-posedness. After reducing the inverse problem to a direct one, we first establish existence and uniqueness of solutions to an associated problem on finite time intervals. We then extend these solutions to half-lines and construct a bounded strong solution on the whole real line as a limit of such extensions, and subsequently establish its uniqueness. In particular, periodic and almost periodic data yield periodic and almost periodic solutions.

We apply a Lyapunov function to obtain conditions for the existence and uniqueness of small classical time-periodic solutions to first order quasilinear 1D hyperbolic systems with (nonlinear) nonlocal boundary conditions in a strip. The boundary conditions cover different types of reflections from the boundary as well as integral operators with delays. In the first step we use a Lyapunov approach to derive sufficient conditions for the robust exponential stability of the boundary value problems for a linear(ized) homogeneous problem. Under those conditions and a number of non-resonance conditions, in the second step we prove the existence and uniqueness of smooth time-periodic solutions to the corresponding linear nonhomogeneous problems. In the third step, we prove a perturbation theorem stating that the periodic solutions survive under small perturbations of all coefficients of the hyperbolic system. In the last step, we apply the linear results to construct small and smooth time-periodic solutions to the quasilinear problems.

We investigate global bounded solutions of higher regularity to boundary value problems for a general linear nonautonomous first order 1D hyperbolic system in a strip. We establish the existence of such solutions under the assumption of exponential stability and certain dissipativity (or non-resonant) conditions. Our results demonstrate the existence and uniqueness of $C^1$- and $C^2$-bounded solutions, in particular, periodic and almost periodic solutions. The number of imposed dissipativity conditions is related to the regularity of solutions. This connection arises due to the nonautonomous nature of the hyperbolic system under consideration, in contrast to autonomous settings. In the general case of global bounded smooth solutions we assume exponential stability in $H^1$. In the case of periodic solutions, the weaker assumption of $L^2$-exponential stability proves to be sufficient.

A technique has been developed for determining the linear tension of steps with one-ion and two-ion heights that form growth/evaporation spirals on NaCl(100). This technique is based on the interpretation of experimentally obtained nonlinear dependences of the steady-state distance between spiral’s turns in relation to the inverse undersaturation by numerical simulation performed using the analytical solution of the Barton, Cabrera, and Frank diffusion problem, taking into account the step kinetic coefficient and the back stress effect. The linear tension value of steps with one-ion height is found to be less than half the linear tension value of steps with two-ion height. This suggests that the studied vicinal surfaces are thermodynamically stable. The proposed technique can also be applied to other alkali halide crystals.

The object of this study is the process of directing the bogies of model 18-100 freight cars along a rail track, in particular, along curved sections of the track. The task to be solved was to determine the influence of wheelset arrangement on the level of steering forces in the flange contacts. A calculation diagram and a mathematical model of fitting the bogie into the curved section of the track have been built. The bogie loading scheme by external forces, including lateral rocking forces acting on the car in a curve, has been refined. In this case, the method of pseudo-statics of the mechanical system, which is a system of nonlinear algebraic equations, was applied. The calculation module Given-Find in the Mathcad software package (USA) was used to solve the mathematical model. It was established that the misalignment of wheelsets in the frames of model 18-100 bogies was of an accumulative nature. At the maximum operating angles of misalignment of wheelsets, the lateral steering forces in the flange contacts increase by 40–60 % compared to the rated setting. These angles can be up to 0.015 rad (0.85 degrees). The field of practical application of the results is railroad transportation, in particular, the system of maintenance and repair of freight cars on bogies of the 18-100 model. At the same time, the condition for the practical application of the research results is the expediency of introducing into the maintenance system the technological operation of controlling the deviation of wheelset arrangement in the bogie relative to the rated one. The current study will contribute to the construction of a measuring system for monitoring the deviation of wheelset arrangement in the bogie relative to the rated one. This proves the expediency of introducing into the trolley maintenance system the technological operation of controlling the deviation of wheelsets and designing a device for monitoring this parameter

The object of research is the process of dynamic balancing of rotors on a balancing machine in the process of restoring electric machines. The work is aimed at improving the quality of balancing rotors in the process of major repairs of traction electric motors for electric trains. The problem addressed was the quality of balancing the rotors of electric machines on stationary balancing machines. According to the conventional balancing technology, the rotor to be balanced is mounted on the supports of the balancing machine with support surfaces that usually have mechanical defects. These defects cannot be eliminated by machining due to the peculiarities of rotor repair technology. Theoretical and experimental studies of the effect of damage to the rotor support surfaces on the balancing parameters have been carried out. It has been proven that the properties of the bearing surfaces of the rotor during its balancing on a balancing machine significantly affect the results of determining the imbalance. At the same time, the difference in the mass values of balancing loads can reach 25 %. This is because damage to the bearing surfaces of the rotor generates false signals unrelated to the imbalance. In order to increase the accuracy of determining the mass of balancing loads during rotor balancing, it is proposed to improve the technological process of balancing. The improvement involves the inclusion of a frequency filter in the signal conversion chain of acceleration sensors. The filter is designed to separate signals with a frequency greater than the rotational frequency of the rotor. A condition for the practical application of the research results is the expediency of introducing a frequency filter of signals of acceleration sensors with a threshold frequency of filtering signals that exceeds the rotational frequency of the rotor into the schematic diagram of the balancing machine.

The object of the study is the process of monitoring the technical condition of electrical insulation of traction electric machines in order to determine the need for their maintenance or repair. Diagnostics of electric machines is an important aspect of supporting the operation of electric drives. Failure of the windings is one of the main reasons for failure of electric motors. Therefore, the task of developing operational methods for diagnosing the insulation of windings of traction electric motors is urgent. A study of the negative impact of operating conditions on the technical condition of electrical insulation of motors was carried out. The analysis of the existing methods of diagnosis of insulation systems of electric machines was carried out. Special attention was paid to the selection of predictive parameters of the insulation state. A mathematical model was developed to study the frequency characteristics of the stator insulation system of the traction electric motor model AD914. Refined dependences of the effect of changes in the insulation parameters of the motor stator winding on its frequency characteristics were obtained. It was concluded that the method of monitoring the insulation state of electric motor windings based on the assessment of electrical resistance relative to the stator core and amplitude-frequency characteristics is the most effective. The field of practical application of the obtained results is the system for monitoring the condition of electrical insulation of traction electric machines to determine the schedule of their maintenance and repair. The conducted research is a scientific justification for the choice of methods and devices for diagnosing the insulation state of electric motors of railway traction rolling stock.

Clear air turbulence (CAT) is a significant type of atmospheric turbulence that poses risks to aviation. Unlike other forms of turbulence, it occurs without substantial cloudiness, often under clear skies or with minimal cloud cover at the observation site. CAT can arise under various meteorological conditions, such as high atmospheric pressure, sunny weather, or in the presence of mountain ranges. Forecasting CAT is crucial for aviation safety, although its prediction is challenging due to its variability, sharp localization in the air flow, and variability in size and duration. Indirect signs can help predict CAT zones; however, direct observation is difficult, making it essential to develop forecasting methods and conduct research to ensure flight safety.

A method for finding analytical solutions to the Cabrera and Levine differential equation is proposed for the case of the spiral formation on a screw dislocation when there is no difference between the growth and evaporation of a crystal. The method is based on finding asymptotic solutions for small spiral angles, exact solutions in the interval of dimensionless spiral radii equal and exceeding unity, and asymptotic solutions for large radii. Then, the method of matching the obtained solutions and their derivatives by dimensionless radius is used for two radius values determined from the problem conditions. In the particular case, for angular velocity omega 1 = 0.33, the exact solution is the result of matching the asymptotic solution of the original equation for small spiral angles, the exact solution in the interval of dimensionless spiral radii equal and exceeding unity, and the asymptotic solution for large radii. For large spiral radii, the asymptotic solution is the general one of the second kind Abel equation. Analysis of the obtained solution showed that the spiral pitch is not constant and equal to 19, but monotonically decreases with increasing spiral radius.

The object of this paper is the process of detecting an aerial object by a radar with active and passive reception channels. The main hypothesis of the study assumed that the introduction of an additional channel of passive reception would increase the conditional probability of correct detection at a fixed value of the conditional probability of false alarms. When detecting an aerial object, it was considered that the signals from aerial object represent a reflected signal after being emitted by the active radar channel elemitted own radio signals. A radar with active and passive reception channels assumes the presence of two channels. The active location channel provides reception of signals reflected from an aerial object, their processing and detection according to the Neumann-Pearson criterion. The passive location channel functions according to the principle of panoramic spectral analysis based on windowed Fourier transforms. The information combining device is intended for the compatible combining of information from active and passive channels of radar reception. At the output of the passive location channel, an output signal is formed, and the coordinates of the aerial object are measured. To ensure the functioning of the radar with active and passive reception channels, it is necessary to ensure the time synchronization of the reception channels. The quality of detection of aerial objects by radar with active and passive signal reception channels was evaluated. The quality indicator defines the conditional probability of correct detection. The dependences of the conditional probability of correct detection are given for a radar with only an active reception channel and a radar with active and passive reception channels. It was established that the introduction of an additional channel of passive reception to the radar increases the conditional probability of correct detection by an average of (20–40) %, depending on the signal-to-noise ratio.

The ways of updating the rolling stock of open-pit railways have been considered and the main methods of using the energy storage on the locomotive for open-pit railways have been determined. A mathematical model has been developed, which includes a model of train movement along the railway section and during maneuvering and a model of energy processes in the traction system with onboard energy storage. Simulations were performed in a cycle that included movement from the crushing plant to the transshipment point with empty dump trucks, maneuvering during loading, movement from the crushing plant to the transshipment point with loaded dump trucks, and maneuvering during unloading. The simulation took into account the limitation of power consumption at the level of 4000 kW. The parameters of the energy storage device were determined, for which Toshiba SCiB 20Ah-HP cells were selected. The power of the energy storage is 3600 kW, and the energy capacity is 414 kWh. The use of modules for the formation of an energy storage device is proposed. It was determined that the energy consumption per work cycle with the selected energy exchange algorithm taking into account electrodynamic braking is about 200 kWh, and the charge reduction per drive cycle is 36%. The service life of the energy storage with the selected cells is estimated at 8 years.

The characteristics of the input energy converter of an electric locomotive with an induction traction electric drive were studied. The efficiency of the 4QS converter has been increased and the level of current harmonic distortions in the power supply system has been reduced. The research resulted in proposals for improving the control algorithm of the input energy converter to improve the traction-energy indicators of the electric drive and reduce the emission of high-frequency harmonics into the contact network. The results were obtained on the basis of simulation modeling of the "traction transformer – 4QS-converter" system on the example of the alternating current electric locomotive DS3 (Dnipro-Simens-3). Modeling of the operation of the 4QS-converter of the electric locomotive was performed for the case of the maximum load of the drive under a traction mode. Two versions of the input converter control algorithm were studied and compared: the basic version of the DS3 electric locomotive and the modified version proposed by us. It was found that in the case of the basic variant of the converter control algorithm, conditions are created at certain time intervals when the capacitor of the constant voltage link on the secondary winding of the traction transformer is discharged under a traction mode. The consequence of this is a decrease in the efficiency factor of the converter and a deterioration of the harmonic distortion factor of the rectified voltage. In the modified algorithm, the discharge time of the capacitor of the constant voltage link on the secondary winding of the traction transformer is significantly reduced and the efficiency of the 4QS converter is increased

Nano-mechanisms of solid-phase bonding of tungsten and tantalum, which are implemented in the manufacture of a neutron source target for the research nuclear facility (RNF) of NSC KIPT, are considered. This facility is a new type of nuclear reactor, in the core of which the intensity of the nuclear fission reaction of the uranium isotope 235U is controlled by an electron accelerator. An installation for joining metals in the solid phase is described, its parameters are given, as well as the parameters of the joined metals. An electron-probe X-ray spectral analysis of the interface between the samples was carried out. The physical foundations of the nano-mechanism of bonding in the solid phase of tungsten and tantalum at the dynamic and isostatic stages at hot vacuum pressing are formulated. Experimental data on the relative temperature convergence of rolls at the dynamic and isostatic stages of hot vacuum pressing have been obtained.

The paper proposes a method of controlled heating of a cylindrical plasma using the features of the Exceptional point. It is shown that the coupled system of plasma and dielectric waveguides is capable of generating exceptional points where their dispersion curves cross. By controlling the connection (distance) between the waveguides, it is possible to control the distribution of the electromagnetic field, both in the plasma and in the dielectric waveguides around the exceptional point. It is also shown that in the presence of dissipative losses in the plasma, the degree of heating of the plasma waveguide can be controlled by tuning the distribution and intensity of the exciting electromagnetic field in the coupled waveguide system, which gives a potential advantage among other methods of plasma heating. The results obtained in the work can be considered as an example of a new method of controlled plasma heating, which can be used to overcome the existing problems of controlled thermonuclear fusion.

To intensify heat transfer processes in nuclear power, it is proposed to use natural convection in horizontal heat exchange tubes. In the article, the problem of convection of a viscous, incompressible fluid in a horizontal cylinder heated from below is analyzed analytically. The proposed analytical method is based upon the use of basic functions that satisfy the initial equation but do not satisfy the boundary conditions. The problem with boundary conditions with a sufficient degree of accuracy is solved by dividing the area of the square described around the cylinder into a large number of smaller element cells. This separation has made it possible to obtain analytical expressions of critical Rayleigh numbers for different positions of current lines in a horizontal cylinder with a viscous, incompressible fluid.

The aim of the work is to develop a model of a hybrid reactive power compensator with adaptation of the control system to the parameters of the voltage supply. The task was achieved by applying the control algorithm for the operation of the control system of the active part of the reactive power compensator, which is based on the regression analysis method. The traction drive of the AC electric locomotive VL-80K, which is operated on the railways of the Ukraine, was chosen as the object of study. The simulation of the traction drive operation was carried out for a traction drive with and without a reactive power compensator, for cases where the process of changing the voltage in the catenary was a stationary deterministic process and for the case when this process was a nonstationary non-deterministic process. The most important result is the development of a block diagram of the control system for the active part of the reactive power compensator based on the implementation of the Levinson-Durbin linear prediction algorithm. The significance of the results obtained lies in the possibility of the proposed control scheme for the active part of the compensator to adapt the operation of the compensator to the voltage parameters of the catenary, that is, to the actual operating conditions of the electric locomotive.

An approach to simulation modeling of traction electric drives of electric locomotives with collector engines is proposed which based on taking into account the nonlinear nature of the magnetic characteristic in electric motors, the inductances of the armature and the excitation winding of the electric motor, the nonlinearity of the volt-amperage characteristics of the rectifier unit and the features of the operation of the stage control system of the electric drive.

A physical model is formulated for the motion of liquid inclusions in a crystal in the field of forces caused by the presence of radiation point defects. The model is based on a statistical approach to the processes of induced transitions of structural elements of a crystalline matrix at the interfacial boundary with its solution. From the energy principle, an analytical dependence of the velocity of a spherical azimuthally symmetric inclusion on its size is obtained, considering the threshold nature of the motion. It is shown that the theoretical dependence correlates well with experimental results obtained for inclusions of aqueous saturated solution in potassium chloride crystals irradiated by high-energy electrons. The proposed model of the radiation-induced motion of a liquid inclusion is dynamic and allows us to interpret the nature of inclusion velocity changes in the crystal over time to determine the characteristic energy parameters of point defects.

The paper considers alternative methods for protecting metal surfaces from corrosion-erosion destruction (CED), based on galvanization or on the use of an oxide film. Their advantages and disadvantages are noted. For the manufacture of CED-resistant tungsten targets, which are used in the subcritical assembly created at the NSC KIPT, it is proposed to use the method of vacuum rolling of W and Ti. A layer of Ti serves as a protective coating. To describe the process of combining these metals, a model description is proposed, which is based on the use of the Rayleigh-Taylor dissipative instability theory (DRTI). An estimate of the values of the parameters of a binary metal system subjected to DRTI is given. The obtained characteristic bonding time of dissimilar metals corresponds to that observed in experiments.