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The article is devoted to the numerical study of shock-wave flows in inhomogeneous media–gas mixtures. In this work, a two-speed two-temperature model is used, in which the dispersed component of the mixture has its own speed and temperature. To describe the change in the concentration of the dispersed component, the equation of conservation of “average density” is solved. This study took into account interphase thermal interaction and interphase pulse exchange. The mathematical model allows the carrier component of the mixture to be described as a viscous, compressible and heat-conducting medium. The system of equations was solved using the explicit Mac-Cormack second-order finite-difference method. To obtain a monotone numerical solution, a nonlinear correction scheme was applied to the grid function. In the problem of shock-wave flow, the Dirichlet boundary conditions were specified for the velocity components, and the Neumann boundary conditions were specified for the other unknown functions. In numerical calculations, in order to reveal the dependence of the dynamics of the entire mixture on the properties of the solid component, various parameters of the dispersed phase were considered — the volume content as well as the linear size of the dispersed inclusions. The goal of the research was to determine how the properties of solid inclusions affect the parameters of the dynamics of the carrier medium — gas. The motion of an inhomogeneous medium in a shock duct divided into two parts was studied, the gas pressure in one of the channel compartments is more important than in the other. The article simulated the movement of a direct shock wave from a high-pressure chamber to a low–pressure chamber filled with a dusty medium and the subsequent reflection of a shock wave from a solid surface. An analysis of numerical calculations showed that a decrease in the linear particle size of the gas suspension and an increase in the physical density of the material from which the particles are composed leads to the formation of a more intense reflected shock wave with a higher temperature and gas density, as well as a lower speed of movement of the reflected disturbance reflected wave.

The paper analyzes the methods of studying the process of interaction of soil environments with the tillage tools of soil processing machines. The mathematical methods of numerical modeling are considered in detail, which make it possible to overcome the disadvantages of analytical and empirical approaches. A classification and overview of the possibilities the continuous (FEM — finite element method, CFD — computational fluid dynamics) and discrete (DEM — discrete element method, SPH — hydrodynamics of smoothed particles) numerical methods is presented. Based on the discrete element method, a mathematical model has been developed that represents the soil in the form of a set of interacting small spherical elements. The working surfaces of the tillage tool are presented in the framework of the finite element approximation in the form of a combination of many elementary triangles. The model calculates the movement of soil elements under the action of contact forces of soil elements with each other and with the working surfaces of the tillage tool (elastic forces, dry and viscous friction forces). This makes it possible to assess the influence of the geometric parameters of the tillage tools, technological parameters of the process and soil parameters on the geometric indicators of soil displacement, indicators of the self-installation of tools, power loads, quality indicators of loosening and spatial distribution of indicators. A total of 22 indicators were investigated (or the distribution of the indicator in space). This makes it possible to reproduce changes in the state of the system of elements of the soil (soil cultivation process) and determine the total mechanical effect of the elements on the moving tillage tools of the implement. A demonstration of the capabilities of the mathematical model is given by the example of a study of soil cultivation with a disk cultivator battery. In the computer experiment, a virtual soil channel of 5×1.4 m in size and a 3D model of a disk cultivator battery were used. The radius of the soil particles was taken to be 18 mm, the speed of the tillage tool was 1 m/s, the total simulation time was 5 s. The processing depth was 10 cm at angles of attack of 10, 15, 20, 25 and 30°. The verification of the reliability of the simulation results was carried out on a laboratory stand for volumetric dynamometry by examining a full-scale sample, made in full accordance with the investigated 3D-model. The control was carried out according to three components of the traction resistance vector: $F_x$, $F_y$ and $F_z$. Comparison of the data obtained experimentally with the simulation data showed that the discrepancy is not more than 22.2%, while in all cases the maximum discrepancy was observed at angles of attack of the disk battery of 30°. Good consistency of data on three key power parameters confirms the reliability of the whole complex of studied indicators.

The reconstruction of charged particle trajectories in tracking detectors is a key problem in the analysis of experimental data for high energy and nuclear physics.

The amount of data in modern experiments is so large that classical tracking methods such as Kalman filter can not process them fast enough. To solve this problem, we have developed two neural network algorithms of track recognition, based on deep learning architectures, for local (track by track) and global (all tracks in an event) tracking in the GEM tracker of the BM@N experiment at JINR (Dubna). The advantage of deep neural networks is the ability to detect hidden nonlinear dependencies in data and the capability of parallel execution of underlying linear algebra operations.

In this work we generalize these algorithms to the cylindrical GEM inner tracker of BESIII experiment. The neural network model RDGraphNet for global track finding, based on the reverse directed graph, has been successfully adapted. After training on Monte Carlo data, testing showed encouraging results: recall of 98% and precision of 86% for track finding.

The local neural network model TrackNETv2 was also adapted to BESIII CGEM successfully. Since the tracker has only three detecting layers, an additional neuro-classifier to filter out false tracks have been introduced. Preliminary tests demonstrated the recall value at the first stage of 99%. After applying the neuro-classifier, the precision was 77% with a slight decrease of the recall to 94%. This result can be improved after the further model optimization.

The numerical model of sedimentation and suspension filtration is proposed in this paper. The model is based on dynamic variant of discrete element method. This model represents the particles behavior on microand meso-scales: pores, arches, flocks formation. In addition, the proposed model qualitatively reproduces macro phenomenon: sedimentation of particle layer, slow shrinkage of the layer, sealing of the layer under its own weight of the particles and the external applied force.

In the present paper the application of the kinetic methods to the blood flow problems in elastic vessels is studied. The Lattice Boltzmann (LB) kinetic equation is applied. This model describes the discretized in space and time dynamics of particles traveling in a one-dimensional Cartesian lattice. At the limit of the small times between collisions LB models describe hydrodynamic equations which are equivalent to the Navier – Stokes for compressible if the considered flow is slow (small Mach number). If one formally changes in the resulting hydrodynamic equations the variables corresponding to density and sound wave velocity by luminal area and pulse wave velocity then a well-known 1D equations for the blood flow motion in elastic vessels are obtained for a particular case of constant pulse wave speed.

In reality the pulse wave velocity is a function of luminal area. Here an interesting analogy is observed: the equation of state (which defines sound wave velocity) becomes pressure-area relation. Thus, a generalization of the equation of state is needed. This procedure popular in the modeling of non-ideal gas and is performed using an introduction of a virtual force. This allows to model arbitrary pressure-area dependence in the resulting hemodynamic equations.

Two test case problems are considered. In the first problem a propagation of a sole nonlinear pulse wave is studied in the case of the Laplace pressure-area response. In the second problem the pulse wave dynamics is considered for a vessel bifurcation. The results show good precision in comparison with the data from literature.

This paper demonstrates the advantages of using artificial intelligence algorithms for the design of experiment theory, which makes possible to improve the accuracy of parameter identification for an elastostatic robot model. Design of experiment for a robot consists of the optimal configuration-external force pairs for the identification algorithms and can be described by several main stages. At the first stage, an elastostatic model of the robot is created, taking into account all possible mechanical compliances. The second stage selects the objective function, which can be represented by both classical optimality criteria and criteria defined by the desired application of the robot. At the third stage the optimal measurement configurations are found using numerical optimization. The fourth stage measures the position of the robot body in the obtained configurations under the influence of an external force. At the last, fifth stage, the elastostatic parameters of the manipulator are identified based on the measured data.

The objective function required to finding the optimal configurations for industrial robot calibration is constrained by mechanical limits both on the part of the possible angles of rotation of the robot’s joints and on the part of the possible applied forces. The solution of this multidimensional and constrained problem is not simple, therefore it is proposed to use approaches based on artificial intelligence. To find the minimum of the objective function, the following methods, also sometimes called heuristics, were used: genetic algorithms, particle swarm optimization, simulated annealing algorithm, etc. The obtained results were analyzed in terms of the time required to obtain the configurations, the optimal value, as well as the final accuracy after applying the calibration. The comparison showed the advantages of the considered optimization techniques based on artificial intelligence over the classical methods of finding the optimal value. The results of this work allow us to reduce the time spent on calibration and increase the positioning accuracy of the robot’s end-effector after calibration for contact operations with high loads, such as machining and incremental forming.

In this paper particularities of the swirling turbulent flow of monodisperse suspension in the hydrocyclone with injector are investigated on the base of the numerical simulation. The 2D axisymmetric approximation of Reynolds Stresses Model and model of mixture is used to describe the swirling turbulent flow field of suspension and particles parameters in the hydrocyclone. Special attention is paid to the clarification of mechanisms of injection influence on the reorganization of hydrodynamic field and finally on classification mechanisms. It is shown that tangential injection method stronger effects separation curve compared to the radial one.

The rheological behavior of aqueous suspensions based on nanoscale silicon dioxide particles strongly depends on the dynamic viscosity, which affects directly the use of nanofluids. The purpose of this work is to develop and validate models for predicting dynamic viscosity from independent input parameters: silicon dioxide concentration SiO₂, pH acidity, and shear rate $\gamma$. The influence of the suspension composition on its dynamic viscosity is analyzed. Groups of suspensions with statistically homogeneous composition have been identified, within which the interchangeability of compositions is possible. It is shown that at low shear rates, the rheological properties of suspensions differ significantly from those obtained at higher speeds. Significant positive correlations of the dynamic viscosity of the suspension with SiO₂ concentration and pH acidity were established, and negative correlations with the shear rate $\gamma$. Regression models with regularization of the dependence of the dynamic viscosity $\eta$ on the concentrations of SiO₂, NaOH, H₃PO₄, surfactant (surfactant), EDA (ethylenediamine), shear rate γ were constructed. For more accurate prediction of dynamic viscosity, the models using algorithms of neural network technologies and machine learning (MLP multilayer perceptron, RBF radial basis function network, SVM support vector method, RF random forest method) were trained. The effectiveness of the constructed models was evaluated using various statistical metrics, including the average absolute approximation error (MAE), the average quadratic error (MSE), the coefficient of determination $R^2$, and the average percentage of absolute relative deviation (AARD%). The RF model proved to be the best model in the training and test samples. The contribution of each component to the constructed model is determined. It is shown that the concentration of SiO₂ has the greatest influence on the dynamic viscosity, followed by pH acidity and shear rate γ. The accuracy of the proposed models is compared to the accuracy of models previously published. The results confirm that the developed models can be considered as a practical tool for studying the behavior of nanofluids, which use aqueous suspensions based on nanoscale particles of silicon dioxide.

We consider a one-dimensional three velocity kinetic lattice Boltzmann model, which represents a secondorder difference scheme for hydrodynamic equations. In the framework of kinetic theory this system describes the propagation and interaction of three types of particles. It has been shown previously that the lattice Boltzmann model with external virtual force is equivalent at the hydrodynamic limit to the one-dimensional hemodynamic equations for elastic vessels, this equivalence can be achieved with use of the Chapman – Enskog expansion. The external force in the model is responsible for the ability to adjust the functional dependence between the lumen area of the vessel and the pressure applied to the wall of the vessel under consideration. Thus, the form of the external force allows to model various elastic properties of the vessels. In the present paper the physiological boundary conditions are considered at the inlets and outlets of the arterial network in terms of the lattice Boltzmann variables. We consider the following boundary conditions: for pressure and blood flow at the inlet of the vascular network, boundary conditions for pressure and blood flow for the vessel bifurcations, wave reflection conditions (correspond to complete occlusion of the vessel) and wave absorption at the ends of the vessels (these conditions correspond to the passage of the wave without distortion), as well as RCR-type conditions, which are similar to electrical circuits and consist of two resistors (corresponding to the impedance of the vessel, at the end of which the boundary conditions are set and the friction forces in microcirculatory bed) and one capacitor (describing the elastic properties of arterioles). The numerical simulations were performed: the propagation of blood in a network of three vessels was considered, the boundary conditions for the blood flow were set at the entrance of the network, RCR boundary conditions were stated at the ends of the network. The solutions to lattice Boltzmann model are compared with the benchmark solutions (based on numerical calculations for second-order McCormack difference scheme without viscous terms), it is shown that the both approaches give very similar results.

In this work, we analyze the system of contracts made by Russian defense enterprises in the process of state defense order execution. We conclude that methods of statistical mechanics can be applied to the description of the given system. Following the original grand-canonical ensemble approach, we can create the statistical ensemble under investigation as a set of instant snapshots of indistinguishable contracts having individual values. We show that due to government regulations of contract prices the contract system can be described in terms of nonextensive Tsallis statistics. We have found that probability distributions of contract prices correspond to deformed Bose – Einstein distributions obtained using nonextensive Tsallis entropy. This conclusion is true both in the case of the whole set of contracts and in the case of the contracts made by an individual defense company as a seller.

In order to analyze how deformed Bose – Einstein distributions fit the empirical contract price distributions we compare the corresponding cumulative distribution functions. We conclude that annual distributions of individual sales which correspond to each company’s contract (order) can be used as relevant data for contract price distributions analysis. The empirical cumulative distribution functions for the individual sales ranking of Concern CSRI Elektropribor, one of the leading Russian defense companies, are analyzed for the period 2007–2021. The theoretical cumulative distribution functions, obtained using deformed Bose – Einstein distributions in the case of «rare contract gas» limit, fit well to the empirical cumulative distribution functions. The fitted values for the entropic index show that the degree of nonextensivity of the system under investigations is rather high. It is shown that the characteristic prices of distributions can be estimated by weighing the values of annual individual sales with the escort probabilities. Given that the fitted values of chemical potential are equal to zero, we suggest that «gas of contracts» can be compared to photon gas in which the number of particles is not conserved.