Introduction. The paper is devoted to the study on the three-dimensional model of transport and suspension sedimentation in the coastal area due to changes in the bottom relief. The model considers the following processes: advective transfer caused by the aquatic medium motion, micro-turbulent diffusion, and gravity sedimentation of suspended particles, as well as the bottom geometry variation caused by the particle settling or bottom sediment rising. The work objective was to conduct an analytical study of the correctness of the initial-boundary value problem corresponding to the constructed model.

Materials and Methods. The change in the bottom relief aids in solution to the initial-boundary value problem for a parabolic equation with the lowest derivatives in a domain whose geometry depends on the desired function of the solution, which in general leads to a nonlinear formulation of the problem. The model is linearized on the time grid due to the “freezing” of the bottom relief within a single step in time and the subsequent recalculation of the bottom surface function on the basis of the changed function of the suspension concentration, as well as a possible change in the velocity vector of the aquatic medium.

Research Results. For the linearized problem, a quadratic functional is constructed, and the uniqueness of the solution to the corresponding initial boundary value problem is proved within the limits of an unspecified time step. On the basis of the quadratic functional transformation, we obtain a prior estimate of the solution norm in the functional space L2 as a function of the integral time estimates of the right side, and the initial condition. Thus, the stability of the solution to the initial problem from the change of the initial and boundary conditions, the right-hand side function, is established.

Discussion and Conclusions. The model can be of value for predicting the spread of contaminants and changes in the bottom topography, both under an anthropogenic impact and due to the natural processes in the coastal area.

Introduction. The technique of numerical modeling of the transverse flow over span structures of bridges on the basis of the two-dimensional URANS (Unsteady Reynolds-averaged Navier-Stokes) approach used in the modern methods and software packages for computational fluid dynamics is verified. The work objective was debugging and experimental substantiation of this technique with the use of the database on the aerodynamic characteristics of the cross-sections of span structures of girder bridges of standard shapes pre-developed by the authors.

Materials and Methods. A numerical simulation of the transverse flow of low-turbulent (smooth) and turbulent air flows around the bridge structures in a range of practically interesting attack angles is carried out. SST  k − ω turbulence model was used as the closing one. The technique was preliminarily tested on the check problem for the flow of the rectangular crosssection beams. Calculations were carried out using the licensed ANSYS software.

Research Results. The calculated dependences on the attack angle of the aerodynamic coefficients of forces (drag and lift) and the moment of the cross sections of the girder bridges of standard shapes are obtained. These data refer to the span structures at the construction phase (without deck and parapets, without parapets) and operation phase, under the conditions of model smooth and turbulent incoming flow. The latter allows us to outline the boundaries for more weighted estimates of the aerodynamic characteristics of thegirder bridges in a real wind current. The best agreement with the experimental data was obtained from the drag of the cross-section. The magnitude of the lifting force is more sensitive to the presence and extent of the separation regions, so its numerical determination is less accurate. The reproduction of the angle-of-attack effect on the aerodynamic moment of the cross-section is the most challenging for the majority of configurations.

Discussion and Conclusions. Comparison of the calculated and experimental data indicates the applicability of the URANS approach to the operational prediction of the aerodynamic characteristics of the single-beam span structures. In the case of multi-beam span structures, where the aerodynamic interference between separate girders plays an important role, the URANS approach must apparently give way to more accurate eddy-resolving methods. The results obtained can be used in the aerodynamic analysis of structures and in practice of the relevant design organizations in the field of transport construction.

Introduction. Methods of energy saving in pneumatic drive are considered. The method of braking by creating back pressure in the exhaust cavity of the pneumatic actuator is of interest. Under braking, the compressed air energy is stored in the recuperative volume. It is possible to control the braking dynamics through setting the initial parameters of the recuperative volume. The work objective is to create a mathematical model describing the dynamic processes taking place in the pneumatic drive under braking by backpressure, with a constant mass enclosed in the cavities of the air motor, and considering variation of the initial parameters of the braking volume.

Materials and Methods. A mathematical model is proposed that describes the speed change of the output link, pressures and temperatures in the cavities of the pneumatic drive depending on the initial parameters of the recuperative volume. The solution to the mathematical model is carried out by the numerical integration method.

Research Results. The dependences of the output link velocity, pressures and temperatures in the pneumatic drive cavities on the initial parameters of the recuperative volume are obtained. Adequacy of the built mathematical model is confirmed by Fisher's criterion.

Discussions and Conclusions. The results obtained can be used to solve the problems of energy saving in pneumatic drives under the organization of backpressure braking. The use of recuperative volume increases the technological flexibility of the drive during its readjustment and extends the possibilities of energy saving.

Introduction. Heuristic synthesis is used to improve the efficiency of reception and processing of discrete signals under aprior information pressure. The analysis of the decisionmaking algorithm for the linear-logical processing of discrete signals in case of the incomplete aprior data on their parameters is presented. The work objective is to develop and analyze the efficiency of the linear-logical algorithms.

Materials and Methods. New mathematical algorithms for the signal reception and processing, effective under conditions of a priori uncertainty, are proposed. They are based on the consideration of the structure of emissions and process exceedance in the signal processing channels.

Research Results. Linear-logical algorithms for processing discrete signals are developed. They are based on the consideration of one, two and more detailed characteristics of emissions or exceedance of random processes.

Discussion and Conclusion. The results obtained can be useful in the synthesis of algorithms and devices for the signal reception and processing. Algorithms and devices are implemented both in an analog form and in the form of algorithms for computers. The simulation programs for the signal processing under conditions of the considerable uncertainty of aprior information on the signals and the channels of their distribution are developed.

Introduction. The issues on standardization of reliability indices in the early stages of machine design are considered. This approach maintains thetarget level of reliability when developing parts that are critical in view of stable operation. The work objective is to study design problems in this area. The analysis of the reliability regulation methods suggests that they are insufficient to design. Besides, there are some contradictions associated with the use of the exponential failure law in design.

Materials and Methods. At the stage of the task order, the numerical values of the operation time and reliability of the machine are determined. Then the values of the reliability probabilities or failures of the system and its elements are shown by exponential expressions. In them, degrees are the ranking parameters of the system reliability indices.

Research Results. The alternative approach to normalization is synthesized; it enables to complete a full structural analysis. Thus, the reliability indices of the entire system or parts, whose operational safety determines the machine reliability, can be assessed. Parts and other components, whose failures are not sudden, are considered without using the exponential law. This preserves the inherent simplicity of mathematical operations.

Discussion and Conclusions. The numerical value of the reliability probability (RP) of the machine as a whole, taken at the stage of the task order, is insufficient for the reliability target design. The specified RP and running time of the system elements, which are sources of failures developing according to different laws, are required. The results obtained can be used both in designing new mechanical systems with the reliability target, and in the modernization of machines.

Introduction. The effect of variable parameters of the electroacoustic sputtering (ELAS) process on the characteristics of the crystalline structure of hardening coatings is studied. The ELAS parameter values providing nanostructured cover coatings for machine parts and cutting tools are determined. Hardening through using such coatings allows achieving a significant (5-10 times) increase in the life of hardenable machine parts and various tools designed for mechanical processing. To obtain coatings with the desired properties of the surface layer, nanocrystalline materials should be selected. In this case, a certain content of the amorphous phase is permissible.

Materials and Methods. To carry out the X-ray structural analysis, the X-ray diffraction Russian-made device DRON-3M was used. The Scherrer-Wilson method was applied to determine the granularity of particle blocks from the value of the intrinsic broadening of the diffractogram peaks. The conclusions obtained in this paper are based on the method of separation of the affecting factor contributions into broadening the diffraction reflection peaks (the Warren-Averbach method).

Research Results. Depending on the process conditions and the technique for obtaining nanostructured materials, a nonuniquely interpretable change in the indices of the diffraction peaks broadening occurs, which is generally characteristic of nanocrystalline metals. One of the possible explanations for this phenomenon is the presence of a nanosized effect in the hardened layer. The occurrence of the nanocrystalline structure in the sputtered layer verifies the calculated values of the dimensions of the coherent scattering regions (CSR). The occurrence of affecting values of the misorientation angle of the crystal structure is verified by the CSR value for the investigated 110 and 220 reflexes, which is supported by a high percentage of the amorphous phase.

Discussion and Conclusions. The electroacoustic scattering method is promising for obtaining nanocrystalline structures in the surface and subsurface layers of the sprayed samples. The ELAS process variables variation leads to the parameter spread of the crystal lattice and coherent scattering areas. In this case, there is no definite trend. In the future it is expected to solve the given problem. First, experiments will be conducted to determine the optimal sputtering regimes that could stimulate the formation of nanocrystalline structures. Secondly, visual observation and evaluation of the sprayed layer structure using electron microscopy is planned.

Introduction. Rational parameters and modes of an inclined batch screw mixer are validated to achieve the lowest energyintensive feed mixing under observance of the zootechnical requirements for the feed quality on uneven mixing. The establishment of functional dependences between parameters and modes enables to design power-efficient equipment for the on-farm feed production.

Materials and Methods. Experimental studies of the feed mixing were implemented on an inclined screw batch feed mixer. The experimental design included variation of four independent factors: mixer shaft speed, filling ratio of the mixing chamber, mixing time, and mixing chamber angle. Mixing irregularity and energy intensity of the process were taken as optimization criteria characterizing the mixing efficiency.

Research Results.The optimization criteria versus the variability level factor, which are two-dimensional sections of the second-order response surfaces, are plotted. The rational values at mixing irregularity of less than 5% were as follows: mixer shaft speed was 27.5-36.5 min^-1 , filling ratio of the mixing chamber was 0.43–0.51, mixing time was 3.0–4.2 min, mixing chamber angle was 22°–25°. At such parameter values, the mixing irregularity will be minimal, and it will be 4.10– 4.18%, and the process intensity is from 2.08 to 2.16 kW • h/t.

Discussion and Conclusions. The dependences obtained as a result of the experimental studies allowed establishing the domain of rational design parameters and modes of an inclined batch screw mixer. The results obtained can be used in further studies under the development of initial requirements for the creation of new technical means with a gravitation effect of intensive mixing.

Introduction. The work objective is to increase the reliability of the prediction methods for the lithium hydroxide behavior in the steam-water circuit at the thermal power plants and nuclear power plants, and for the operational monitoring of the pH index of steam solutions. A method of operational control is developed on the basis of the conductometric measurements of the hydrogen index of the corrosion inhibitor vapor solutions for construction materials of lithium hydroxide used at the TPP and NPS.

Materials and Methods. A mathematical model method is used for the practical implementation of the high-temperature operational control of the steam solution pH index.

Research Results. A method for monitoring the pH of vapor solutions of lithium hydroxide based on the determination of vapor concentration through the steam condensation in the coolable conductivity sensor located in the vapor space of the steam generator is developed. This has significantly improved the accuracy of determining the lithium hydroxide concentration. Equations describing the change in the limiting molar equivalent conductance and dissociation constants of lithium hydroxide in a wide range of state change parameters are proposed.

Discussion and Conclusions. The proposed on-line technique of testing the pH value of steam solutions, and mathematical models for calculating the limiting molar equivalent conductance and dissociation constants provide an acceptable error level calculations and the capability of measurements automation. With an increase in the vapor temperature up to 573.15 K, the necessity arises to fortify lithium hydroxide in the vapor to 10^-2 mol/kg.

Introduction. It is known that the quality of products from sintered hardmetals, if the fabrication technique is not violated, is determined by the phase composition and an average grain size of the carbide phase. However, hard alloys have a disadvantage inherent in all products of powder metallurgy - the inhomogeneity of the structure and the corresponding variation of properties. Traditional methods of monitoring the structure and phase composition according to the results of selective destructive tests prevent from receiving quality data under the production conditions and do not guarantee the identity of the properties of all batch products under study. The major method of non-destructive quality control of hard alloys is coercimetry, but domestic coercimeters are currently not produced. In this regard, the work objective is to create a domestic data measurement system for non-destructive quality testing of hard alloys and an assessment of the reliability of the results obtained with its help.  Materials and Methods. Cylindrical and spherangular rods with the diameter of 4 to 10 mm, made of alloys of VK8 and VK10HOM grades, were used in the work. The method of comparison with a certified product was used to determine the coercitive force in the data measuring system. Research Results. The coercive force of two batches of products from hard alloys of VK10HOM and VK8 grades was measured using the developed data measuring system and KOERZIMAT 1.097 HcJ coersimeter. Discussion and Conclusions. The experimental studies show that the values of the coercitive force of the samples obtained on different equipment have approximately the same level. 

The inhomogeneity of the structure characteristic of sintered hardmetals being a fabrication technique effect is confirmed. Providing that the relative error of measuring the coercitive force for each sample should be within ± 6%, the results obtained can be considered satisfactory. It is shown that the measurement algorithm proposed and implemented in the data measurement system through comparing the characteristics of the tested and certified samples with the known coercitive force, allows the manufacturer of hard alloy products to expand the sample of inspected products up to 100%, and to significantly reduce the costs for non-destructive testing of products. 

Introduction. The theoretical description of the ion transport in membrane systems in the galvanostatic mode is presented. A desalting channel of the electrodialysis apparatus is considered as a membrane system. The work objectives are the development and verification of a two-dimensional mathematical model of the stationary transport of salt ions in the desalting channel of the electrodialysis apparatus for the galvanostatic mode.

Materials and Methods. A new model of ion transfer is proposed. It is based on the Nernst –Planck – Poisson equations for the electric potential and on the equation for the electric current stream function. A numerical solution to the boundary value model problem by the finite element method is obtained using the Comsol Multiphysics software package.

Research Results. The developed mathematical model enables to describe the stationary transfer of binary salt ions in the desalting channel of the electrodialysis apparatus. Herewith, the violation of the solution electroneutrality and the formation of the dilated domain of space charge at overlimiting currents in the galvanostatic mode are considered. A good agreement between the physicochemical characteristics of the transfer calculated by the models for the galvanostatic and potentiostatic modes implies adequacy of the constructed model.

Discussion and Conclusions. The developed model can interpret the experimental study results of ion transfer in membrane systems if this process takes place in the galvanostatic mode. Some electrokinetic processes are associated with the appearance of a dilated domain of space charge at overlimiting currents. When describing the formation of this domain, it is possible to find out how the processes dependent on it affect the ion transfer in the galvanostatic mode.

Introduction. A special case of synthesizing the same electromechanical control system by the Pontryagin maximum principle and by the synergetic synthesis method is considered. The task was to solve the synthesis problem of the time optimal electromechanical position control system; herewith the travel resistance modulus linearly depended on the output coordinate of the system. This approach to the selection of the synthesis problem was because the synthesis of time optimal systems is one of the most widespread problems, and it is solved by increasing the efficiency of the existing control systems.

Materials and Methods. Synthesis of the time optimal linear control system based on the maximum principle is a widely accepted problem in the modern control theory. However, the procedure of synergistic synthesis does not have such formalization. This being the case, the paper suggests an approach that brings together these two methods, which, in our opinion, will increase the efficiency of the synergistic synthesis method through adding some features of the synthesis methodology for optimal systems.

Research Results. The paper formulates two key concepts. The first one is as follows: the application of the maximum principle for an object of the DC motor class when synthesizing the positioning algorithm under the conditions of linear loading functionally dependent on the engine rotation angle allows the time optimal system to be optimized. The second concept states that synthesis of a control system based on the synergistic approach enables to obtain a system close to optimal (quasioptimal), but after modifying the synergetic synthesis method itself. A hypothesis is formulated on the possible connection between the introduced (when implementing the procedure of state space extension in the synergetic synthesis method) time constants with the optimal switching time of control defined in the maximum method.

Discussion and Conclusions. The synthesis through the maximum control technique and the ADAR method is performed. In virtue of the comparison of efficiency of these methods, a hypothesis is put forward on the possible compatibility of the studied methods.

Introduction. Algorithms for the parallel binary tree construction are developed. The algorithms are based on sorting and described in a constructive form. For the Nelement set, the time complexity has T(R) = O(1) and T(R) = O(log₂ N) estimates, where R = (N²-N)/2 is the number of processors. The tree is built with the uniqueness property. The algorithms are invariant with respect to the input sequence type. The work objective is to develop and study ways of accelerating the process of organizing and transforming the tree-like data structures on the basis of the stable maximum parallel sorting algorithms for their application to the basic operations of information retrieval on databases.

Materials and Methods. A one-to-one relation between the input element set and the binary tree built for it is established using a stable address sorting. The sorting provides maximum concurrency, and, in an operator form, establishes a one-to-one mapping of input and output indices. On this basis, methods for the mutual transformation of the binary data structures are being developed.

Research Results. An efficient parallel algorithm for constructing a binary tree based on the address sorting with time complexity of T(N²) = O(log₂ N) is obtained. From the well-known analogues, the algorithm differs in structure and logarithmic estimation of time complexity, which makes it possible to achieve the acceleration of O(N^α), α≥1 order analogues. As an advanced version, an algorithm modification, which provides the maximum parallel construction of the binary tree based on a stable address sorting and a priori calculation of the stored subtree root indices is suggested. The algorithm differs in structure and estimation of T(1) = O(1) time complexity. A similar estimate is achieved in a sequential version of the modified algorithm, which allows obtaining the acceleration of known analogs O(N^α), α>1 order.

Discussion and Conclusions. The results obtained are focused on the creation of effective methods for the dynamic database processing. The proposed methods and algorithms can form an algorithmic basis for an advanced deterministic search on the relational databases and information systems.