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Tuning is an essential requirement for the search of dark matter axions employing haloscopes since its mass is not known yet to the scientific community. At the present day, most haloscope tuning systems are based on mechanical devices which can lead to failures due to the complexity of the environment in which they are used. However, the electronic tuning making use of ferroelectric materials can provide a path that is less vulnerable to mechanical failures and thus complements and expands current tuning systems. In this work, we present and design a novel technique for using the ferroelectric Potassium Tantalate ( $KTaO_{3}$ or KTO) material as a tuning element in haloscopes based on coupled microwave cavities. In this line, the structures used in the Relic Axion Detector Exploratory Setup (RADES) group are based on several cavities that are connected by metallic irises, which act as interresonator coupling elements. In this article, we also show how to use these $KTaO_{3}$ films as interresonator couplings between cavities, instead of inductive or capacitive metallic windows used in the past. These two techniques represent a crucial upgrade over the current systems employed in the dark matter axions community, achieving a tuning range of 2.23% which represents a major improvement as compared to previous works ( $< 0.1\%$ ) for the same class of tuning systems. The theoretical and simulated results shown in this work demonstrate the interest of the novel techniques proposed for the incorporation of this kind of ferroelectric media in multicavity resonant haloscopes in the search for dark matter axions.

The paper considers the thermally stressed state of fuel rods when their geometric shape changes. The temperature fields for the sphere and the ellipsoid are determined. It is shown that, while maintaining volumetric heat release, maximum stresses occur in fuel rods of circular cross-section. Similar results were obtained when changing the geometric shape of a spherical fuel element: all other things being equal, maximum thermal stresses occur in spherical fuel elements.

In accordance with the local climatic conditions and folk traditions in the Republic of Bashkortostan, dairy horse breeding occupies a leading position. Mare's milk is a unique raw material for the production of a wide variety of highly nutritious, complete and easily digestible food products. Scientists recommend mare's milk as a medicinal and dietary product. The paper presents a yogurt recipe developed on the basis of a composition using mare's milk. The composition received patent No 2677219 (Composition…, 2019). It is known that mare's milk fat is rich in polyunsaturated fatty acids, which are of particular physiological importance for the human body. There is a need to ration and ensure a constant intake of polyunsaturated fatty acids of the ?-3 family with food. The purpose of this work is to study the fatty acid composition of yoghurt. To obtain a fermented milk product, milk from Bashkir mares was used as raw material. The production and research of prototypes of yoghurt were carried out on the basis of the Faculty of Food Technologies of the Bashkir State Agrarian University. The determination of the fatty acid composition of the yoghurt sample took place in the accredited testing laboratory centre "Federal Research Centre for Nutrition and Biotechnology" (Moscow). The use of mare's milk allows one to change the fatty acid composition of the finished fermented milk product. Analysis of the fatty acid composition of the sample has showed that it has a high content of oleic, ?-linolenic, ?-linolenic and arachidonic acids.

Friction forces affect the strength of the fuel assembly at all stages of its life cycle. The work is devoted to the issues of reducing friction and wear of fuel elements of a nuclear reactor. It presents methods and results of pre-reactor experimental studies of static and dynamic processes involving friction forces. Because of the conducted research, it was found that the transformation of the movable joints of the guide channels and spacing gratings into fixed ones by means of spot welding in “rigid” fuel assemblies, together with other measures, solved the problem of curvature of the fuel assemblies. It is also shown that during the assembly of fuel assemblies, the friction force can be reduced using ultrasound.

The problem of thermoelectricity is considered. The problem of stability of an ellipsoidal shell of rotation is considered. The analysis of the described method is carried out. Mathematical analysis is used in the work. Based on mathematical modeling, it was shown that the level of thermal stresses arising during the transition from a circular cross-section to an elliptical one decreases.

This paper provides a solution to the heat transfer problem for a hollow elliptical cylinder under boundary conditions of the first and third kind. In this paper, a solution is given for the distribution of the temperature field in a field with an elliptical cross section under boundary conditions of the third kind. The solution is obtained by considering equidistant surfaces.

The paper proposes a theoretical justification of the test method for thermal strength, similar to the method of radiation heating. The use of the induction heating method itself provides for the ability to control the heating temperature with good accuracy, which makes it possible to heat the part evenly and quickly to the desired temperature due to overheating of the product, and also with the chosen method it is possible to completely eliminate the appearance of smoke, oil pollution and strong odours. In this case, external heating of samples of electrically conductive materials is carried out by high-frequency currents, which significantly expands the possibilities of obtaining preliminary experimental results and simplifies the experimental technique.

Today, the use of solar panels is becoming widely used. At the same time, accumulators act as accumulators of the generated solar energy. The article suggests using an ionistor as a storage option. Unlike a battery, the ionistor is most effectively charged not with a constant voltage, but with a current, and with the maximum, i.e. with everything that is only able to give the source. For an energy source, a discharged ionistor is a short-circuited load. Just solar cells can operate at zero resistance, which means they are able to charge the ionistor from scratch. The analysis of the problem of using this method is carried out. The article provides connection diagrams, as well as formulas for calculating charging characteristics.

The work is devoted to the process of heat exchange in fuel rods of different cross-sections. It considers a stationary process without internal heat sources under boundary conditions of the first kind. The nature of the change in the temperature field during the transition from a cylindrical to an elliptical section is shown. A formula was also obtained for finding the temperature in a fuel element formed by elliptical surfaces of co-focal ellipses

In this paper, the problem of heat transfer is solved for a hollow elliptical cylinder, taking into account the asymmetry of heat transfer on surfaces. In this case, the boundary conditions are boundary conditions of the first and third kind. In this paper, a solution is given for the distribution of the temperature field in a field with an elliptical cross-section under boundary conditions of the third kind. The solution is obtained by considering equidistant surfaces.

The work is devoted to the heat exchange of a nuclear reactor. Attention was paid to the mathematical modeling of the temperature field of the fuel element and the thin gas layer. It is assumed that the thermal contact between the solid–interlayer system is ideal. Methods of differentiation, integration and approximate methods were used for numerical modeling. The dependence of the thermal conductivity of uranium oxide on temperature was also taken into account. Based on the obtained expression, the linear heat transfer coefficient and linear thermal resistance were also found.

In this article, the question of finding the temperature field of a heating element made in the form of a cylinder enclosed in a shell of cylindrical shape is considered. It is assumed that the thermal contact between the solid–coating systems is ideal. In this case, heat exchange occurs under boundary conditions of the third and fourth kind. In this paper, based on the methods of differentiation and integration, a solution was obtained to the problem of the distribution of the temperature field in both bodies. The resulting solution has an analytical form containing quadratic and logarithmic functions.

The article is devoted to the thermal calculation of a flat plate solar collector. In this case, the boundary conditions are boundary conditions of the third kind. The solution is found in the transition to an elliptical coordinate system. The author has obtained an analytical solution for the distribution of the temperature field of a collector with an elliptical cross-section at zero ambient temperature with partial adiabatic isolation in the form of a functional series using hypergeometric functions.

The article is devoted to the issues of nuclear energy. It considers a simplified dynamic model simulating the main processes occurring in a nuclear power plant. The basis of the proposed model is a model of heat release in the reactor, simulating the relative neutron power and temperature of the coolant in the hot thread of the circulation circuit. The position of the absorbing assemblies, which determines the reactivity introduced by them, is formed in an operational control model that simulates bringing the assemblies into a pre-start state, displacement of the control assembly under the influence of a power regulator, as well as under the action of protections of various levels. The purge/recharge model describes the dynamics of the concentration of boron absorber during water exchange between the deaerator and the circulation circuit. Models of thermal deaeration, pressure compensation and heat exchange in the circuit simulate the pressure and temperature of the coolant.

Currently, many residential buildings and businesses use solar water heating systems. This is an economical and reliable type of hot water supply. Heating water for domestic purposes or heating using solar energy is a natural and simple method of saving energy and preserving fossil fuel reserves. The use of renewable energy sources is relevant for all countries of the world. The article deals with the issue of improving the energy efficiency of the solar heat supply system of buildings based on vacuum collectors with natural circulation of the coolant.

The article is devoted to the determination of thermal stresses in a flat plate solar collector and the calculation of its optimal size. The solution is found when moving to an elliptical coordinate system. The obtained result is useful because by varying the geometric shape of the cross-section, it is possible to reduce the level of thermal stresses that occur, and, consequently, to increase the reliability and durability of the solar collector design.

Fuel elements (fuel rods) and spacer grids are the main elements of the fuel assembly of a nuclear reactor. Friction forces affect the strength of the fuel assembly at all stages of its life cycle. The paper presents methods and results of pre-reactor experimental studies of static and dynamic processes involving friction forces. These include the assembly of the fuel assembly at the manufacturer’s factory, hydrodynamic vibration of fuel rods and fretting corrosion in the “fuel cell” nodes of the spacing grid, movement of the control and protection system controls in the guide channels of the fuel assembly, transverse bending of the fuel assembly, loading and unloading of the fuel assembly into the reactor, the growth of fuel rods under irradiation and thermomechanical interaction tvelov.

In this paper, the question of finding the temperature field of a rectangular thermoelectric element under boundary conditions of the third kind with an adibatically-isolated side is considered. Based on the Fourier method, the distribution of the temperature field of the thermoelectric element is obtained. The solution itself is obtained in the form of a series containing trigonometric and exponential functions. The reliability of the obtained result is confirmed by the fact that one of the special cases leads the problem to a problem with boundary conditions of the first kind, when the surface temperature is constant. The presented analysis of the main characteristics of thermoelectric converters makes it possible to determine the criteria for selecting materials and temperature conditions in order to increase the efficiency of such converters.

The article deals with the distribution of the temperature field in an elliptical body without internal heat sources. In this case, the boundary conditions are boundary conditions of the third kind. The solution is found when moving to an elliptic coordinate system. The author has obtained an analytical solution for the distribution of the temperature field in a body with an elliptical cross section of infinite length at a given ambient temperature with partial adiabatic isolation in the form of a functional series using hypergeometric functions.

The work is devoted to the issues of stationary heat transfer. The article presents a solution for the distribution of the temperature field in a rectangular plate. At the same time, the law of change of thermal conductivity along one of the coordinates is known. Heat exchange at the two opposite ends of the plate occurs under boundary conditions of the third kind, there is no heat exchange at the other two. The solution is found by decomposition into a functional series. As a result, an analytical expression of the plate temperature distribution is obtained in the form of a Fourier series containing modified zero-order Bessel functions.

The use of CAD in various industries in a competitive environment becomes profitable for both the designer and the customer. The subject of the study is a system of computer-aided design of systems for comfortable living on the territory of a country house, private apartment or office work. The considered system makes it possible to increase the economic efficiency of the heating system as a whole.

The work is devoted to earthquake forecasting. The physics of an earthquake, despite the fact that this problem has been facing humanity for more than 100 years, it still remains unclear. What is the reason and why this is a very important problem, which is being solved by a huge number of universities, institutes and companies around the world. The physical model of a tectonic earthquake is presented in the form of a plate connection loaded with a shear force, in which the non-displacement is provided by friction forces. In calculating the contact interaction, the pliability of the plates and the tangential pliability of the contact layer are taken into account. A system of equations has been obtained, the solution of which makes it possible to specify to some extent the location, strength and time of the earthquake occurrence.

It is well known that gravitational quantities are in many ways similar to electromagnetic quantities. The masses that create a gravitational field are similar in this to electric charges. A gravitational static field, like an electrostatic field, is characterized by potential and intensity. Vortex and rotational movements of masses are often and quite justifiably compared with a magnetic field. According to existing concepts, there are four types of different fundamental physical interactions: strong, weak, electromagnetic and gravitational. Strong and weak interactions are manifested inside atomic nuclei and between elementary particles, electromagnetic – between charges, and gravitational acts between massive bodies, becoming the main one in the case of astronomical objects. The article presents a comparison of mechanical and gravitational quantities from the condition of their similarity to electromagnetic quantities. Visual systemically possible patterns involving field gravitational quantities similar to electromagnetic ones are given.

The article deals with heat transfer through a rod with a small cross-section. The rod is assumed to be so thin that the temperature at all points of its cross-section can be considered the same. When finding a solution, the power series decomposition method is used. Formulas were derived not only for finding the temperature field, taking into account the correction for heat loss through the lateral surface of the rod, but also for determining the coefficient of external heat transfer and the coefficient of thermal conductivity from known values of temperatures and heat flows at its ends.

The main purpose of the work is mathematical modelling of heat exchange of steam-water flow in a geothermal pipe of a vertical well. Within the framework of the hydraulic approximation, a numerical study of the steady isothermal motion of a thermodynamically equilibrium steam-water mixture in a vertical well has been carried out, taking into account heat losses into the surrounding rocks. In this task, the process of coolant movement along the borehole and its thermal interaction with its wall is considered. Because of the implementation of the described model, the values of specific heat losses in the rock mass for various initial conditions for wells were obtained.

The work is devoted to improving the reliability of nuclear power plants. During operation, the fuel elements of nuclear reactors operate at sufficiently high temperatures. The heterogeneity of the temperature field leads to the appearance of so-called thermal stresses. The main objective of this work is mathematical modeling of temperature stresses of fuel elements of cylindrical and elliptical cross-sections reactors. Based on mathematical modeling, it was shown that the level of thermal stresses arising during the transition from a circular cross-section to an elliptical one decreases.

The work is devoted to the process of heat exchange of a nuclear reactor. Attention was paid to improving the reliability of the fuel rods of the nuclear reactor. At the same time, two cases of the cross section of the rod shell were considered: cylindrical and elliptical. Based on the application of the differentiation method, it was shown that the level of thermal stresses arising during the transition from a circular cross-section to an elliptical one decreases. Which confirms the choice of the section of the reduced elements in the form of an ellipse. The optimal size of the section itself was also obtained. The obtained result is useful because by varying the geometric shape of the cross-section, it is possible to reduce the level of thermal stresses that occur, and, consequently, to increase the reliability and durability of nuclear rocket engine designs.

The article discusses the main structural schemes of three types of uninterruptible power supply sources: backup; interactive; double conversion. The main functions of which are: performing the function of a backup or emergency power source; performing the function of protective devices, improving the quality of the power supply voltage. The features of operation, advantages and disadvantages of three groups of uninterruptible power supplies are also disclosed. New approaches in the structural and circuit design of uninterruptible power supplies based, including on the use of renewable energy sources are disclosed. Based on the analysis, one of the variants of the block diagram of an uninterruptible power supply with a double conversion of the system is presented and explanations and principles of its operation, as well as advantages and disadvantages are given.

The work is devoted to the issues of non-stationary heat transfer. The article presents a solution for the distribution of the temperature field in an infinite rectangular plate with an adiabatically isolated side. As a result, an analytical expression of the plate temperature distribution is obtained in the form of a series containing trigonometric and exponential functions. The paper also considered special cases when the internal thermal resistance of thermal conductivity is greater and when the external resistance of heat output is less. Special cases were interpreted physically. One of the special cases leads the problem to a problem with boundary conditions of the first kind, when the surface temperature is constant, which indicates the reliability of the results obtained.

The article is devoted to such a natural phenomenon as ball lightning. The relevance of the work is due to the fact that the phenomenon itself is widespread, but in itself has not been sufficiently studied. In it, the ball lightning is considered as a plasma ball. The main purpose of the work is mathematical modeling of the lightning temperature field taking into account radiation heat transfer. Based on the obtained result, an analysis of the behavior of the temperature field was carried out.

The work is devoted to mathematical modeling of the plasma temperature field. To do this, it was represented as a conducting sphere under boundary conditions of the third kind. The simulation of the thermal process is based on the numerical integration of the heat equation. This takes into account the change in the thermal conductivity of the plasma and convective heat transfer. Also, based on the obtained result, an analysis of the behavior of the temperature field was carried out.

The article is devoted to mathematical modelling of the plasma temperature field taking into account the temperature dependence of thermal conductivity. The channel model was taken as a basis. Neglecting a very small fraction of the energy received by the ions during their acceleration in the longitudinal field, it can be assumed that all the energy taken by the arc discharge from an external source in the arc column passes directly to the plasma electrons. To find the temperature field by the integration method, the equation of thermal conductivity was solved. At the same time, the arc column is considered as a cylindrical continuous conductive rod in which all the supplied electrical energy is diverted due to thermal conductivity to the cooled walls of the discharge tube. The arc itself is represented by two regions: conductive and non-conductive. Based on mathematical modelling, the law of temperature field change in the arc cross-section was obtained. A formula was also derived to determine the effective radius of an electrically conductive channel.

The existing experimental methods do not allow us to accurately determine the limiting temperature stresses that cause the destruction of brittle bodies. In this work, a method of testing for thermal resistance is proposed and investigated, which is similar to the method of radiation heating. However, in this case, external heating of samples of electrically conductive materials is carried out by high-frequency currents, which significantly expands the possibilities of obtaining representative experimental results and simplifies the technique of the experiment itself.

The work is devoted to the heat exchange of a nuclear reactor. Attention was paid to the mathematical modeling of the temperature field of the fuel element and the thin gas layer. It is assumed that the thermal contact between the solid–interlayer system is ideal. Methods of differentiation, integration and approximate methods were used for numerical modeling. The dependence of the thermal conductivity of plutonium dioxide on temperature was also taken into account.

The work is devoted to the heat exchange of a nuclear reactor. Attention was paid to the mathematical modeling of the temperature field of a heat-generating element of circular cross-section and surrounding it with a thin gas layer. It is assumed that the thermal contact between the solid–interlayer system is ideal. Differentiation and integration methods were used for numerical modeling.