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We present a physico-mathematical statement of coupled geometrical and gas dynamics problem of intrachamber processes simulation and calculation of main internal ballistics characteristics of solid rocket motors in axisymmetric approximation. Method and numerical algorithm of solving the problem are described in this paper. We track the propellant burning surface using the level set method. This method allows us to implicitly represent the surface on a fixed Cartesian grid as zero-level of some function. Two-dimensional gas-dynamics equations describe a flow of combustion products in a solid rocket motor. Due to inconsistency of domain boundaries and nodes of computational grid, presence of ghost points lying outside the computational domain is taken into account. For setting the values of flow parameters in ghost points, we use the inverse Lax – Wendroff procedure. We discretize spatial derivatives of level set and gas-dynamics equations with standard WENO schemes of fifth and third-order respectively and time derivatives using total variation diminishing Runge –Kutta methods. We parallelize the presented numerical algorithm using CUDA technology and further optimize it with regard to peculiarities of graphics processors architecture.

Created software package is used for calculating internal ballistics characteristics of nozzleless solid rocket motor during main firing phase. On the base of obtained numerical results, we discuss efficiency of parallelization using CUDA technology and applying considered optimizations. It has been shown that implemented parallelization technique leads to a significant acceleration in comparison with central processes. Distributions of key parameters of combustion products flow in different periods of time have been presented in this paper. We make a comparison of obtained results between quasione-dimensional approach and developed numerical technique.

Authors describe a two-stage traffic assignment model. It contains of two blocks. The first block consists of a model for calculating a correspondence (demand) matrix, whereas the second block is a traffic assignment model. The first model calculates a matrix of correspondences using a matrix of transport costs (it characterizes the required volumes of movement from one area to another, it is time in this case). To solve this problem, authors propose to use one of the most popular methods of calculating the correspondence matrix in urban studies — the entropy model. The second model describes exactly how the needs for displacement specified by the correspondence matrix are distributed along the possible paths. Knowing the ways of the flows distribution along the paths, it is possible to calculate the cost matrix. Equilibrium in a two-stage model is a fixed point in the sequence of these two models. In practice the problem of finding a fixed point can be solved by the fixed-point iteration method. Unfortunately, at the moment the issue of convergence and estimations of the convergence rate for this method has not been studied quite thoroughly. In addition, the numerical implementation of the algorithm results in many problems. In particular, if the starting point is incorrect, situations may arise where the algorithm requires extremely large numbers to be computed and exceeds the available memory even on the most modern computers. Therefore the article proposes a method for reducing the problem of finding the equilibrium to the problem of the convex non-smooth optimization. Also a numerical method for solving the obtained optimization problem is proposed. Numerical experiments were carried out for both methods of solving the problem. The authors used data for Vladivostok (for this city information from various sources was processed and collected in a new dataset) and two smaller cities in the USA. It was not possible to achieve convergence by the method of fixed-point iteration, whereas the second model for the same dataset demonstrated convergence rate $k^{-1.67}$.

The work is devoted to the construction of efficient and applicable to real tasks first-order methods of convex optimization, that is, using only values of the target function and its derivatives. Construction uses OGMG, fast gradient method which is optimal by complexity, but requires to know the Lipschitz constant for gradient and the strong convexity constant to determine the number of steps and step length. This requirement makes practical usage very hard. An adaptive on the constant for strong convexity algorithm ACGM is proposed, based on restarts of the OGM-G with update of the strong convexity constant estimate, and an adaptive on the Lipschitz constant for gradient ALGM, in which the use of OGM-G restarts is supplemented by the selection of the Lipschitz constant with verification of the smoothness conditions used in the universal gradient descent method. This eliminates the disadvantages of the original method associated with the need to know these constants, which makes practical usage possible. Optimality of estimates for the complexity of the constructed algorithms is proved. To verify the results obtained, experiments on model functions and real tasks from machine learning are carried out.

The paper provides a method for selecting the composition of a refrigerant with a given isobaric cooling curve using an artificial neural network (ANN). This method is based on the use of 1D layers of a convolutional neural network. To train the neural network, we applied a technological model of a simple heat exchanger in the UniSim design program, using the Peng – Robinson equation of state.We created synthetic database on isobaric boiling curves of refrigerants of different compositions using the technological model. To record the database, an algorithm was developed in the Python programming language, and information on isobaric boiling curves for 1 049 500 compositions was uploaded using the COM interface. The compositions have generated by Monte Carlo method. Designed architecture of ANN allows select composition of a mixed refrigerant by 101 points of boiling curve. ANN gives mole flows of mixed refrigerant by composition (methane, ethane, propane, nitrogen) on the output layer. For training ANN, we used method of cyclical learning rate. For results demonstration we selected MR composition by natural gas cooling curve with a minimum temperature drop of 3 К and a maximum temperature drop of no more than 10 К, which turn better than we predicted via UniSim SQP optimizer and better than predicted by $k$-nearest neighbors algorithm. A significant value of this article is the fact that an artificial neural network can be used to select the optimal composition of the refrigerant when analyzing the cooling curve of natural gas. This method can help engineers select the composition of the mixed refrigerant in real time, which will help reduce the energy consumption of natural gas liquefaction.

In a number of fundamental and practical problems, it is necessary to describe the dynamics of the motion of complexshaped particles in a high-speed gas flow. An example is the movement of coal particles behind the front of a strong shock wave during an explosion in a coal mine. The paper is devoted to numerical simulation of the dynamics of translational and rotational motion of a square-shaped body, as an example of a particle of a more complex shape than a round one, in a supersonic flow behind a passing shock wave. The formulation of the problem approximately corresponds to the experiments of Professor V. M. Boiko and Professor S. V. Poplavski (ITAM SB RAS).

Mathematical model is based on the two-dimensional Euler equations, which are solved in a region with varying boundaries. The defining system of equations is integrated using an explicit scheme and the Cartesian grid method which was developed and verified earlier. The computational algorithm at the time integration step includes: determining the step value, calculating the dynamics of the body movement (determining the force and moment acting on the body; determining the linear and angular velocities of the body; calculating the new coordinates of the body), calculating the gas parameters. To calculate numerical fluxes through the edges of the cell intersected by the boundaries of the body, we use a two-wave approximation for solving the Riemann problem and the Steger – Warming scheme.

The movement of a square with a side of 6 mm was initiated by the passage of a shock wave with a Mach number of 3,0 propagating in a flat channel 800 mm long and 60 mm wide. The channel was filled with air at low pressure. Different initial orientation of the square relative to the channel axis was considered. It is found that the initial position of the square with its side across the flow is less stable during its movement than the initial position with a diagonal across the flow. In this case, the calculated results qualitatively correspond to experimental observations. For the intermediate initial positions of a square, a typical mode of its motion is described, consisting of oscillations close to harmonic, turning into rotation with a constant average angular velocity. During the movement of the square, there is an average monotonous decrease in the distance between the center of mass and the center of pressure to zero.

A method for studying the dispersion characteristics of photonic crystals — media with a dielectric constant that varies periodically in space — is considered. The method is based on the representation of the wave functions and permittivity of a periodic medium in the form of Fourier series and their subsequent substitution into the wave equation, which leads to the formulation of the dispersion equation. Using the latter, for each value of the wave vector it is possible determined a set of eigen frequencies. Each of eigen frequency forms a separate dispersion curve as a continuous function of the wave number. The Fourier expansion coefficients of the permittivity, which depend on the vectors of the reciprocal lattice of the photonic crystal, are determined on the basis of data on the geometric characteristics of the elements that form the crystal, their electrophysical properties and the density of the crystal. The solution of the dispersion equation found makes it possible to obtain complete information about the number of modes propagating in a periodic structure at different frequencies, and about the possibility of forming band gaps, i.e. frequency ranges within which wave propagation through a photonic crystal is impossible. The focus of this work is on the application of this method to the analysis of the dispersion properties of metallic photonic crystals. The difficulties that arise in this case due to the presence of intrinsic dispersion properties of the metals that form the elements of the crystal are overcome by an analytical description of their permittivity based on the model of free electrons. As a result, a dispersion equation is formulated, the numerical solution of which is easily algorithmized. That makes possible to determine the dispersion characteristics of metallic photonic crystals with arbitrary parameters. Obtained by this method the results of calculation of dispersion diagrams, which characterize two-dimensional metal photonic crystals, are compared with experimental data and numerical results obtained using the method of self-consistent equations. Their good agreement is demonstrated.

When recognizing workers on images of a construction site obtained from surveillance cameras, a situation is typical in which the objects of detection have a very different spatial scale relative to each other and other objects. An increase in the accuracy of detection of small objects can be achieved by using the Feature-Fused modification of the SSD detector. Together with the use of overlapping image slicing on the inference, this model copes well with the detection of small objects. However, the practical use of this approach requires manual adjustment of the slicing parameters. This reduces the accuracy of object detection on scenes that differ from the scenes used in training, as well as large objects. In this paper, we propose an algorithm for automatic selection of image slicing parameters depending on the ratio of the characteristic geometric dimensions of objects in the image. We have developed a two-pass version of the Feature-Fused SSD detector for automatic determination of optimal image slicing parameters. On the first pass, a fast truncated version of the detector is used, which makes it possible to determine the characteristic sizes of objects of interest. On the second pass, the final detection of objects with slicing parameters selected after the first pass is performed. A dataset was collected with images of workers on a construction site. The dataset includes large, small and diverse images of workers. To compare the detection results for a one-pass algorithm without splitting the input image, a one-pass algorithm with uniform splitting, and a two-pass algorithm with the selection of the optimal splitting, we considered tests for the detection of separately large objects, very small objects, with a high density of objects both in the foreground and in the background, only in the background. In the range of cases we have considered, our approach is superior to the approaches taken in comparison, allows us to deal well with the problem of double detections and demonstrates a quality of 0.82–0.91 according to the mAP (mean Average Precision) metric.

An algorithm is proposed to identify parameters of a 2D vortex structure used on information about the flow velocity at a finite (small) set of reference points. The approach is based on using a set of point vortices as a model system and minimizing a functional that compares the model and known sets of velocity vectors in the space of model parameters. For numerical implementation, the method of gradient descent with step size control, approximation of derivatives by finite differences, and the analytical expression of the velocity field induced by the point vortex model are used. An experimental analysis of the operation of the algorithm on test flows is carried out: one and a system of several point vortices, a Rankine vortex, and a Lamb dipole. According to the velocity fields of test flows, the velocity vectors utilized for identification were arranged in a randomly distributed set of reference points (from 3 to 200 pieces). Using the computations, it was determined that: the algorithm converges to the minimum from a wide range of initial approximations; the algorithm converges in all cases when the reference points are located in areas where the streamlines of the test and model systems are topologically equivalent; if the streamlines of the systems are not topologically equivalent, then the percentage of successful calculations decreases, but convergence can also take place; when the method converges, the coordinates of the vortices of the model system are close to the centers of the vortices of the test configurations, and in many cases, the values of their circulations also; con-vergence depends more on location than on the number of vectors used for identification. The results of the study allow us to recommend the proposed algorithm for identifying 2D vortex structures whose streamlines are topologically close to systems of point vortices.

This article proposes the sumo-atclib framework, which provides a convenient uniform interface for testing adaptive control algorithms with different limitations, for example, restrictions on phase durations, phase sequences, restrictions on the minimum time between control actions, which uses the open source microscopic transport modeling environment SUMO. The framework shares the functionality of controllers (class TrafficController) and a monitoring and detection system (class StateObserver), which repeats the architecture of real traffic light objects and adaptive control systems and simplifies the testing of new algorithms, since combinations of different controllers and vehicle detection systems can be freely varied. Also, unlike most existing solutions, the road class Road has been added, which combines a set of lanes, this allows, for example, to determine the adjacency of regulated intersections, in cases when the number of lanes changes on the way from one intersection to another, and therefore the road graph is divided into several edges. At the same time, the algorithms themselves use the same interface and are abstracted from the specific parameters of the detectors, network topologies, that is, it is assumed that this solution will allow the transport engineer to test ready-made algorithms for a new scenario, without the need to adapt them to new conditions, which speeds up the development process of the control system, and reduces design overhead. At the moment, the package contains examples of MaxPressure algorithms and the Q-learning reinforcement learning method, the database of examples is also being updated. The framework also includes a set of SUMO scripts for testing algorithms, which includes both synthetic maps and well-verified SUMO scripts such as Cologne and Ingolstadt. In addition, the framework provides a set of automatically calculated metrics, such as total travel time, delay time, average speed; the framework also provides a ready-made example for visualization of metrics.

The article is devoted to modeling the shallow water hydrodynamic processes using the example of the Azov Sea. The article presents a mathematical model of the hydrodynamics of a shallow water body, which allows one to calculate three-dimensional fields of the velocity vector of movement of the aquatic environment. Application of regularizers according to B.N.Chetverushkin in the continuity equation led to a change in the method of calculating the pressure field, based on solving the wave equation. A discrete finite-difference scheme has been constructed for calculating pressure in an area whose linear vertical dimensions are significantly smaller than those in horizontal coordinate directions, which is typical for the geometry of shallow water bodies. The method and algorithm for solving grid equations with a tridiagonal preconditioner are described. The proposed method is used to solve grid equations that arise when calculating pressure for the three-dimensional problem of hydrodynamics of the Azov Sea. It is shown that the proposed method converges faster than the modified alternating triangular method. A parallel implementation of the proposed method for solving grid equations is presented and theoretical and practical estimates of the acceleration of the algorithm are carried out taking into account the latency time of the computing system. The results of computational experiments for solving problems of hydrodynamics of the Sea of Azov using the hybrid MPI + OpenMP technology are presented. The developed models and algorithms were used to reconstruct the environmental disaster that occurred in the Sea of Azov in 2001 and to solve the problem of the movement of the aquatic environment in estuary areas. Numerical experiments were carried out on the K-60 hybrid computing cluster of the Keldysh Institute of Applied Mathematics of Russian Academy of Sciences.