The study of the interaction of a nanoporous material with a non-wetting liquid is of interest not only from the point of fundamental science view in terms of liquid distribution in nanochannels, but also as an application of such systems to absorb the energy of impact, explosion and vibrations. It is for these applications that it is especially important to know the mechanism of liquid distribution in nanoporous materials and to make estimates of the time characteristics of the system response to high-speed pulse effects. The purpose of this work was to study the effect of the rate of pressure change in the system on the process of filling the pores of a nanoporous material with a non-wetting liquid. A series of intrusion – extrusion experiments was carried out in the nanoporous material (hydrophobized nanoporous silica gel Fluka 100 C₈ (60759-50G) by Sigma-Aldrich) – non-wetting liquid (deionized distilled water) system at internal volume change rates of 0.24 ÷ 11.78 10^‒2 cc/s at a temperature of 20 °C. Based on experimental data, a method for determining the filling rate of a nanoporous material with a non-wetting liquid has been developed. The developed technique will be further used to study the filling of nanoporous materials with non-wetting liquids.

The modes of the water outflow from a vertical cylindrical vessel through a Tesla valve connected in direct or reverse directions were experimentally studied. The kinematics of the water level decrease in the vessel was recorded. It was found that the time of the vessel emptying through a Tesla valve considerably exceeds the time of the vessel emptying through an ordinary tube of a smaller cross-section (both for direct and reverse switching on of the valve). Emptying of the valve at the direct switching on is twice faster than at the reverse one. The velocity of the water column level decreases with time linearly. The obtained data prove that the valve has diodicity, and that the liquid outflow from the vessel through the Tesla valve follow to some analog of the Torricelli's law kinematically with different effective slowing factors.

In this paper, we propose a new method for constructing an irregular grid for the numerical solution of problems containing a one-dimensional convection-diffusion equation, which is often encountered in various fields of computational mathematics, physics, and chemistry. Traditional approaches either use regular grids with a large number of nodes or adaptive grids that require rebuilding at each solution step, which can be computationally expensive. Our method is based on transforming a non-uniform grid into a uniform one using a local deformation function determined based on a monotonicity criterion. This allows us to obtain a monotonic solution on a grid with a significantly smaller number of nodes, thereby increasing the efficiency of the difference scheme. We consider both stationary and non-stationary convection-diffusion equations, describing the corresponding grid construction algorithms for divergent and non-divergent forms of recording convective terms. Examples of applying the method to various problems are given, demonstrating its advantages over existing approaches on regular grids. The presented approach combines the advantages of irregular grids to improve the solution efficiency and the use of a monotonicity criterion to ensure the stability of the scheme, expanding the capabilities of numerical methods for differential equations.

The article clarifies the numerical model and the results of calculations of equilibrium plasma configurations in the magnetic trap «Belt» from the class of Galatea traps proposed by A.I. Morozov. The confining magnetic field is created by current-carrying conductors immersed in the plasma but not in contact with it. In a series of previous works, the geometry and basic regularities of configurations in the toroidal trap «Belt» straightened into a cylinder with two conductors parallel to its axis were researched. The two-dimensional plasmostatic model of the configuration is based on the numerical solution of the boundary value problem with the known Grad-Shafranov equation for the magnetic flux function in the cross-section of the cylinder. It contained an essential simplifying assumption, that makes it possible to deal with a single-connected domain of the problem solution: conductors were not excluded from the domain, and currents in them were represented by additional summands in equation. In the proposed work this simplification is absent, and the problem is posed in a multiply connected domain of out of conductors of square cross section. The role of the electric current in the formation and maintenance of the equilibrium magnetoplasma configuration is played by a boundary condition containing the circulation of the magnetic field along the boundary of each conductor. In a series of calculations with different values of dimensionless parameters of the problem in the multiply connected domain, it was found that the main properties of the configuration and the regularities of their dependence on the parameters qualitatively coincide with those obtained earlier in the single-connected domain. This indicates the legitimacy of the previous version of the model and at the same time clarifies its result. The dependence of the geometry and quantitative characteristics of configurations on the dimensionless parameters of the problem has been clarified

We consider the nonlinear inverse problem of determining the $x$-dependent lower coefficient in a uniformly parabolic equation with many spatial variables. The coefficients of the equation can depend on both the time and spatial variables and are assumed to be bounded, but generally speaking, discontinuous. However (in contrast to the papers of other authors), there are no restrictions on the signs of the lower coefficients of the equation and its right-hand side. As an additional condition, we put the condition of the final (at the final moment of time) observation. The solution of the inverse problem is understood in a generalized sense and is sought in Sobolev classes. We establish two types of sufficient conditions under which a generalized solution of the inverse problem exists and is unique. We also give the example of the inverse problem for which the results proved in the work are valid. It is noted that the solution of the specified problem exists and is unique either if the time interval on which the problem is considered is sufficiently large (and the domain of spatial variables is fixed) or if the domain of spatial variables is sufficiently small (and the time period is fixed).

Schrödinger equations with cubic and more complex nonlinearities containing the desired function with a delayed argument are considered. The physical considerations that can lead to the appearance of a delay in such nonlinear equations and models are expressed. One-dimensional reductions are described that lead the studied partial differential equations with delay to simpler ordinary differential equations or ordinary differential equations with delay. Exact solutions of the nonlinear Schrödinger equation of general form with delay, which are expressed in quadratures, are found. Special attention is paid to three equations with cubic nonlinearity, which allow simple solutions in elementary functions, as well as more complex exact solutions with generalized separation of variables. In addition to nonlinear Schrödinger equations with constant delay, some more complex equations with variable delay of general form are also studied. The results obtained can be useful for testing mathematical models described by the nonlinear Schrödinger equation with delay.

Nuclear energy plays an important role in ensuring the safety of many countries in the world.When designing and operating complex technological objects (CTO) such as nuclear power plants (NPP), it is critical to take into account their characteristics to ensure safe operation.The relevance of the research topic lies in the need to develop a methodology that can speed up the process of identifying target information contained in scientific publications for nuclear industry enterprises.The lack of scientific papers describing the use of language models for analyzing and extracting characteristics from complex technological objects emphasizes the need for research.In this paper, a NPP is chosen as an example of such an object.To conduct a series of experiments to identify the technical characteristics of the CTO, a list of parameters of the nuclear power plant profile (35 parameters) was compiled and a data set on nuclear power plants was formed (60 scientific publications containing information about the Ling Ao NPP).A program was developed that allows processing the data contained in scientific publications by loading articles into a language model, writing queries and receiving responses for subsequent compilation of a profile of a complex technological object.The results of the work showed that the proposed technique allows programmatic processing of scientific publications to compile a profile of a NPP.

The article considers the application of various machine vision algorithms for automation of functional testing of LCD displays of pressure sensors. Neural networks and classical algorithms, as well as the algorithm developed by the author, are analyzed. The purpose of the study is to find an algorithm that can be used in the development of an automatic display testing system. The algorithm should be highly accurate and minimize the number of false negative results in order to avoid missing defective products. It should also be able to detect backlight defects, lack of segment glow, unexpected segment glow, spots and mechanical damage on the display. The article describes the stages of algorithm development, including image preprocessing, binarization, analysis and defect search. The presented results of testing the algorithm on a test sample confirm its high accuracy and completeness. In the course of the work, it was found that no standard algorithm is suitable for the functional testing of display modules, while the algorithm developed by the author fully meets all the requirements. The developed algorithm is used to create an automatic LCD display testing system, currently used in the production of pressure sensors.