Abstract— The article presents a matrix model of natural language texts and a model for the quantitative assessment of the similarity in the content of text documents. The use of the model to identify text documents with similar contents is considered. The differences between the proposed models—the matrix model and the model of the similarity of the content of text documents constructed based on it—and

Abstract The angular motion of a CubeSat-type nanosatellite with a passive magnetic attitude control system is mathematically modelled. The attitude control system consists of a permanent magnet and hysteresis dampers in the form of a plate or a set of rods. The parameters of the hysteresis dampers are studied using a laboratory facility. A comparative analysis of the damping time using the plate and

Abstract The variational approach to obtaining equations of the entropy stable discontinuous Galerkin method is generalized. It is shown how the monotonicity property can be incorporated into this approach. As applied to Euler equations, the entropic slope limiter, a new effective approximate method for the studied approach, is designed. It guarantees the monotonicity of the numerical solution, as

Abstract In this paper, we consider the construction of a generalized algorithm for calculating diffuse radiation configuration factors (CFs). The generalized algorithm is based on dividing the existing computational algorithms into two groups (paired and one-to-many), as well as the results of studying the possible combinations of grid and computational methods (exact, special, numerical integration

Abstract The problem of the sunlight transfer equation in the atmosphere in a gas absorption band is considered. The structure of the spectral dependence of the brightness coefficient (reflectance) of the radiation, reflected by the atmosphere–surface system is studied. The low-parametrical approximations of the reflectance as an expansion of the inverse logarithm of the reflectance by the degrees

Abstract The models of text corpora, formed on the basis of the matrix model of texts in natural languages, are presented. As methods to form models of collections we consider the techniques of computational identification of the thematic structure of the collections. We suggest to use the models for searching for thematically similar text collections and thematic categorization of texts based on text

Abstract We consider the difference approximation of the one-dimensional Liouville equation for modeling the evolution of the sample distribution density (of the nonstationary time series) estimated by a histogram. It is shown that the change in the sample density of the distribution over a certain period of time can be numerically described as a solution of the Liouville equation if the initial density

Abstract Modification of Pride’s equations, describing the interrelated process of acoustic and electromagnetic waves’ propagation in saturated porous medium, arising due to the electrokinetic effect, is proposed. This modification allows taking into account Joule heating during the propagation of acoustic oscillations, generated by electromagnetic source, and is implemented by adding “thermoelastic

Abstract An algorithm for the numerical solution of the equations of magnetic gas dynamics (MGD) approximated by a fully conservative Lagrangian–Euler difference scheme (FCDS) is considered. The complete system of equations for the dynamics of a high-temperature medium is solved taking into account the conductive (electronic, ionic) and radiative heat transfer. The calculation stage related to computations

Abstract The requirements on the models for computing volumes and areas of contaminated zones of water reservoirs by suspended materials and other admixtures imply that multiscale turbulence, suspension sedimentation, attachment conditions for suspended particles at the water–bottom boundary, jet effects, and salvo discharge of soil must be taken into account, which allows more accurately evaluating

Abstract A dynamic theory of the linear reaction from nonextensive quasi-equilibrium multibody systems to an external time-dependent perturbation is developed in quantum statistical mechanics based on the Tsallis parametric nonadditive entropy associated with the density matrix. For nonextensive quantum systems, a modification of the Kubo theory developed in quantum mechanics is proposed. The linear

Abstract The convergence and accuracy of a method for solving high-order accurate bicompact schemes having the fourth order of approximation in spatial variables on a minimum stencil for a multidimensional inhomogeneous advection equation are investigated. The method is based on the approximate factorization of difference operators of multidimensional bicompact schemes. In addition, it uses iterations

Abstract The article presents the results of the mathematical modeling of the flow of the electric current in a lamellar graphite polycrystal in a magnetic field. In contrast to the simple model, which takes into account only the contact resistance between the flakes, this model also takes into account the ohmic resistance along and across the layers of graphite based on the chain model of the flow

Abstract The features of navigation devices based on fiber-optic gyroscopes cause problems in their practical applications and require calibration prior to being used. The algorithms for accumulating and processing the information of strapdown inertial blocks (SIBs) based on fiber-optic gyroscopes and units determining the stars’ coordinates (UDSC) are given. The calibration algorithms are modified

Abstract A complex model for supercomputing the parameters of radiation-induced thermomechanical fields in heterogeneous media of a complex dispersed structure is developed. A technique for calculating the parameters of the photon-electron cascade generated in the object by the interaction of radiation with matter is constructed. A geometric model of the medium with a direct resolution of its microstructure

Abstract For technical applications, it is important to be able to solve the radiation transport equation under reflection conditions rather than under free boundary conditions. The reflection conditions lead to the situation when all angular directions for which the transport equation is calculated are dependent on each other even in the case of the absence of scattering. The angular directions are

Abstract The paper describes a block for calculating the Earth’s natural atmospheric radiation in the IR range developed for the general circulation model simulating the lower and middle atmosphere. This block uses the new parametrization of molecular absorption in the frequency range from 10 to 2000 cm−1 at the altitude ranging from the Earth’s surface to 76 km. The algorithm for constructing this

Abstract A mathematical model of proton transport in matter is considered. The interaction of protons with the electron subsystem of the medium’s atoms is modeled in the approximation of the average energy loss during ionization scattering. Nuclear interactions are considered in the model of individual collisions. An algorithm for modeling proton transfer in piecewise-homogeneous media is developed

AbstractIn this paper, we consider the problem of modeling viscous incompressible fluid flow using the quasi-hydrodynamic (QHD) system of equations. The use of this approach makes it possible to avoid instability in the pressure calculation when using the classical formulation of the Navier–Stokes equations, which is manifested when using cellular numerical schemes. For the numerical implementation

AbstractDiabetes Mellitus (DM) during pregnancy is a major global public health burden with various adverse outcomes. In this paper, a mathematical model of the population dynamics of DM during pregnancy is developed and analyzed. Four independent variables have been considered, namely the numbers of nonpregnancy nondiabetic women, diabetic nonpregnant women, diabetic pregnant women and diabetic pregnant

AbstractThis article presents a method of collaborative one-dimensional (1D)–three-dimensional (3D) modeling of computational fluid dynamics. The method is based on the simultaneous calculation of 3D and 1D areas and linking the two parts of the problem by transferring the boundary conditions. The 3D approximation region is modeled based on the solution of Navier-Stokes equations. The 1D regions are

AbstractThe angular motion of a mockup of a satellite’s attitude control system on an air bearing is considered. The general purpose of the work is to verify the one-axis magnetic attitude control algorithm. This control is designed to maintain the satellite’s solar panels attitude towards the Sun. Specific mockup motion patterns are found. These patterns allow comparing the ground-based control performance

AbstractThe paper describes the features and capabilities of the software to simulate the dynamics of near-Earth satellites. The software package allows the passive and controlled angular and orbital motion simulation of both single satellites and formations. The software also allows using the mathematical models of varying precision and complexity while performing the computations. The user-friendly

Abstract—The work is aimed at determining parameters of a deuterium-tritium mixture expanding into a vacuum with an external magnetic field, the output of thermonuclear energy from which compensates or exceeds the initial thermal energy of the plasma. This type of assessment is usually based on the Lawson criterion. In the paper the parameters are determined on the basis of the model of adiabatic expansion

AbstractIn the present work, a numerical modified Verlet scheme (MVS) is obtained. This scheme is intended to solve the equations of motion of charged particles immersed in an external stationary environment and a uniform magnetic field, for example, charged particles of a condensed substance in a buffer plasma (dusty plasma). The influence of the environment on the particle dynamics is described by

AbstractThis article presents the results of generalizing the existing methods for determining the diffuse radiation configuration factors for the radiation transfer calculation in the zone model of the system of bodies with complex-shaped surfaces. Such problems arise in determining construction temperatures, surface illumination, and construction of realistic images in various fields of science and

Abstract—A mathematical model of nonequilibrium crystallization of a binary aluminum alloy (Al-Si) with modifying refractory nanoparticles, which are the centers of nucleation of the crystalline phase, is proposed. The model describes thermodynamic processes, as well as heterogeneous nucleation and crystallization of the α-component and the β-component of a melt. The crystalline phase nucleates on

AbstractA variational problem for a radial gas journal bearing with two sectors is considered. The pressure field in the gas layer can be described by the nonlinear Reynolds equation for arbitrary compressibility numbers. The magnitude of the resultant pressure force vector is used as a functional of the variational problem. The system of necessary conditions of the extremum is qualitatively analyzed

Abstract—A theoretical analysis has been to draw out the flow characteristics of natural convective nanofluid flow along an exponentially accelerating vertical plate in the presence of magnetic field. Three different types of water-based nanofluids containing copper, silver and copper oxide are considered. The governing equations are transformed into dimensionless form and tackled with the usual time-frequency

AbstractThe random variable of passenger journeys between any two stopping points on a route (passenger correspondence) represents a discrete variable. For each value of the discrete random variable, its probability is calculated. As a solution to the problem of determining the number of corresponding passengers between two stopping points on a route, we take the most probable value of the random variable

AbstractA description of two methods for simulation of the flow around complex test configurations is considered. One method implements a well-known approach to solving the Reynolds-averaged Navier-Stokes equations with a closing differential turbulence model. Another method is based on scale-resolving wall-modelled LES approach (WMLES). The classical problem of the flow around the inclined backward-facing

AbstractThe paper presents a dynamical stochastic general equilibrium (DSGE) model for key indicators of the Russian economy. A special feature of the approach is the Keynesian microeconomic foundation, which takes into account market failures such as imperfect competition, as well as inflexible prices and wages. The second specific feature is the hypothesis of rational expectations. The model consists

AbstractAn original algorithm is developed for vortex methods of computational fluid dynamics for determining the intensity of the vortex sheet on the surface of a body in the flow of an incompressible medium. Unlike the common in the vortex methods approach to satisfying the no-slip boundary condition on a streamlined surface, which is based on ensuring that the normal velocity component of the medium

AbstractA mathematical model of the Alfvén wave absorption is proposed, the study of which is based on the equations of two-fluid electromagnetic hydrodynamics (EMHD) having taken the electron inertia and bremsstrahlung into account. Special attention is paid to the research of the additional effects of photorecombinational and synchrotron radiation. The investigation revealed, in particular, the finite

AbstractBased on the application of conservation laws, a compact quasi-gasdynamic system, which was previously obtained using a kinetic model, is derived. The possibility of using algorithms previously used to solve the Navier–Stokes equations to solve this system is discussed.

AbstractThe article is devoted to a description of a mathematical model of a tethered high-altitude unmanned platform in which the power of propulsion systems and payload is supplied from a ground-based energy source via cable. The magnitudes and directions of the forces acting on the unmanned vehicle by the cable are determined from the derived system of differential equations which allows calculating

Abstract—A method is presented for solving interior boundary-value problems for second-order elliptic equations by transition to ray variables. The domain is divided into cells within which the coefficients and sources have the smoothness and continuity properties necessary for the existence of a regular classical solution in the cell. The finite discontinuities of the coefficients (if any) are located

AbstractThe microlevel dynamics of the age-limited production capacities differentiated by the moments of creation set the macrolevel production function. The microdescription is based on the hypothesis of the capacity loss at a constant rate and constant number of jobs from the moment of the creation of the production unit to its closure, when the age limit is exceeded. An analytical expression for

AbstractThe flow in a four-stage axial compressor is investigated by numerical modeling using the Numeca FINE/Turbo software. A few approaches to modeling the rotor-stator interaction are considered: the steady statement with the use of the Mixing Plane boundary condition, the fully unsteady statement (URANS), and the non-linear harmonic (NLH) method. These approaches are compared by considering the

AbstractThe methodology of turbulent combustion simulation is presented. The methodology is based on large eddy simulation coupled with a global reaction. The numerical simulation of a flow in a laboratory combustion chamber is performed. The effect of the constants of the model’s rate of chemical reactions on the results of the calculations is analyzed. It is shown that the methodology ensures close

Abstract—The problem of actively shielding a conversation inside a room with an open window from street noise is considered as an example of a more general problem actively shielding a specified domain in real-time from external noise. Active shielding is understood as protection based on additional sound sources installed on the boundary of the domain. These sources are supplemented by measuring the

AbstractThe Reynolds-averaged Navier–Stokes (RANS)/Implicit Large Eddy Simulation (ILES) method is applied to analyze the effect of variable heat capacity on the flow characteristics and pressure pulsation spectra for various operation modes of a model high-speed air intake. The dependence of the heat capacity on temperature is described by a fourth-degree polynomial. The calculation method and the

AbstractThe paper is devoted to the RANS/ILES high-resolution method application for studying the influence of a nonuniformity of the inflow temperature field on the throttle characteristics of a supersonic mixed compression inlet, and the intensity and spectral characteristics of pressure pulsations in the inlet duct. Five cases of inflow parameters are investigated, three of which have a nonuniform

AbstractThe paper presents two computational techniques that do not require a change in the topology of the mesh to simulate the flow around oscillating bodies. The first technique uses the immersed boundary method, the second technique uses the method of deformed meshes. The capabilities of these two approaches are demonstrated by solving model problems in a two-dimensional formulation for simulating

AbstractDual-stream nozzle jet computations conducted using different numerical algorithms developed at Zhukovsky Central Aerohydrodynamic Institute (TsAGI) and Keldysh Institute of Applied Mathematics, Russian Academy of Sciences (KIAM RAS) are presented. The scale-resolving approaches of the DES family based on higher accuracy numerical methods are applied. The flow considered is studied experimentally

AbstractVarious methods for the accurate approximation of the gradients entering the diffusion fluxes are considered. Linear combinations of the 2nd order difference schemes for a non-uniform mesh that transform into 4th order schemes in the uniform case are investigated. We also consider 3rd and 4th order schemes for approximating gradients on a non-uniform mesh in the normal and tangential directions

AbstractThe features of a flow generated during the injection of a supersonic small body (pellet) from the channel of a spherically blunted cylinder into a supersonic flow are studied. The cylinder’s diameter is 35 times larger than the diameter of the injected body. The numerical simulation is carried out using multilevel Cartesian grids with the local adaptation based on the wavelet analysis. The

Abstract—This paper considers modeling the processes of cleaning air from finely dispersed solid contaminants clustered in the form of nanoparticles. The purification technology chosen for the study involves the use of a system consisting of nanofilters and sorbents. Both cleaning methods used in it are currently in high demand and are often combined in appropriate devices. The first cleaning method

AbstractWe describe contrast structures (CSs) arising from the simulation of reaction–diffusion (RD) processes in inhomogeneous media with the power dependence of the source density on the concentration in the vicinity of the roots. The results obtained earlier for homogeneous media are generalized to the case of inhomogeneous media. Sufficient conditions for the existence of a solution of the type

AbstractTo compute controlled fusion problems, four nuclear reactions are conventionally used. In the paper, cross sections of many thermonuclear reactions between the lightest elements are compared. We show that, along with the traditional four reactions, a tangible contribution can be made by the reaction \({\text{T}} + {\text{T}} \to 2n + \,{}^{{\text{4}}}{\text{He}}\). At low temperatures, the

AbstractThis work studies a stochastic method for the generation of artificial three-dimensional, divergence-free, homogeneous, and isotropic velocity fields. The technique is based on the randomized spectral method. The statistical and spectral properties of turbulent fields constructed by this generator are analyzed. A validation LES-based computation which uses the obtained turbulent fields as initial

AbstractThe results of the direct numerical simulation of a supersonic flow around a cylindrical blunt body with tail expansion are presented. The data obtained are compared with the results of laboratory experiments for the Mach numbers 3 and 4 and the angles of attack of 10 and 20 degrees. The results are obtained by using the quasi-gas-dynamic (QGD) equations.

AbstractThe paper is devoted to the development and implementation of a hybrid stochastic fractal-based approach for modeling electron-induced kinetics of polarization switching in ferroelectrics as the self-similar memory physical systems. The mathematical model of fractal dynamic system includes the initial value problem for the fractional order differential equation. Computational schemes for solving

AbstractThis study considers discontinuous Galerkin schemes with a Legendre polynomial basis of degree K = 0, …, 5. The schemes built for the convection equation are studied in terms of the amplitude and dispersion error. The relation between wave number and cell size is determined to provide the desired accuracy of the solution in the task with a harmonic wave. The computations for an acoustic wave

AbstractThe paper considers bicompact schemes for HOLO algorithms to solve the transport equation. To accelerate the convergence of scattering iterations not only the solution of the transfer equation with respect to the distribution function of a high order (HO) is used but also the quasi-diffusion equation of a low order (LO). For both systems of kinetic equations semidiscrete bicompact schemes with

AbstractActive users have appeared who require the solution of inverse problems on a graph with conditions of uncertainty for modeling processes in the economic sphere. Such tasks were not considered by mathematicians earlier. This article provides an analogy with mathematical models which are described by a replicator system (RS) of equations related to the stated theme. The exact and asymptotic solutions

AbstractA new class of models of hysteretic converters, generalizing the classical backlash definition to the case where the curves defining it are non-deterministic and have a random distribution, is proposed. In this case, the output of the stochastic converter is defined as a random process. The correctness of the definition of the corresponding converter in terms of a special limit construction

AbstractThe software for the topological optimization of parts with different constraints of the objective function, as well as for the generation and use of different types of lattice structures for filling the parts, is developed within the project Development of the Atlas of Standard Forms for Topological Optimization of Structures Formed by Selective Laser Melting and Their Production Verification

AbstractUsing the support operator technique for two-dimensional problems of the elasticity theory we constructed integrally consistent approximations of the components of the strain tensor and the elastic energy of the medium for the equations of the elasticity theory in terms of displacements. Approximations are constructed for the case of irregular difference grids in the R–Z plane of a cylindrical

AbstractDifferential relations include both differential operators and solvers for boundary value problems. The formulas of compact finite difference approximations for first- and second-order differential relations of the form \({{P}_{1}}[u] = {{P}_{2}}[f]\) are obtained. An approximation on three-point stencils is used. Its implementation, as in the case of classical difference schemes, requires