Abstract The paper is devoted to numerical simulation of multicomponent gas flows based on extended Euler equations using a modified explicit Godunov-type scheme. A feature of the used algorithm is to take into account strong shock waves and occurrence of pressure oscillations at contact boundaries. This is expressed by the use of exact solutions of the corresponding Riemann problem and special double-flux

Abstract The paper considers the problem of a flow around a thin plate of infinite span. The frontal surface of the plate absorbs gas. For the calculations we use the mathematical flow model containing a combination of the Navier–Stokes–Fourier model and the model kinetic equation of polyatomic gases. The calculations are performed for a supersonic flow with a Mach number of 2.31 for a Knudsen number

Abstract A conservative version of the entropy stable discontinuous Galerkin method is proposed for the Euler equations in variables: density, momentum density, and pressure. For the equation describing the dynamics of the mean pressure in an FE, a special difference approximation in time and conservative in total energy is constructed. The entropy inequality and the requirements for the monotonicity

Abstract Based on the discrete sources method, a mathematical model of the plasmon nanolaser resonator deposited on the prism surface in an active ambient medium is developed and implemented, which allows taking into account the non-local effect (NLE) in the plasmon material. The resonator’s characteristics are optimized, which makes it possible to obtain a field enhancement on the external surface

Abstract A method is proposed for the numerical modeling of acoustic processes in solids, representing a solid in the form of an array of particles in a cubic body-centered crystal lattice. The particle dynamics is described by Newton’s equations of motion. It is shown that the developed numerical model makes it possible to describe resonance phenomena and the process of wave propagation. The results

Abstract— A numerical method proposed in the authors’ previous work to solve the Schrödinger equation is developed. Ambiguity remains in the method described earlier in identifying the average positions of quantum particles in a molecular system, which were prescribed from external considerations without taking into account the Schrödinger equation itself. In this paper, a list of procedures for the

Abstract This study is devoted to the construction and software implementation of a computational algorithm for modeling the process of anomalous diffusion. The mathematical model is formulated as an initial-boundary value problem for a semilinear partial differential equation of fractional order. An implicit finite-difference scheme is constructed based on the approximation of a higher order of accuracy

Abstract A method is proposed to solve the linearized ellipsoidal-statistical Holway equation in the classical problem of a rarefied gas flow between two parallel planes. To approximate the desired solution, the function is expanded in a series in Chebyshev polynomials of the first kind for each variable. The Holway model kinetic equation is reduced by the collocation method to a linear matrix equation

Abstract The perspective n-point problem (PnP), or a three-point photogrammetric resection in space, consists of the problem of finding the position and the orientation of the model of the camera of the central projection by the assigned spatial coordinates of the given points and by the corresponding coordinates of their projections on the image. Due to the available applications in robotics and machine

Abstract We consider random changes in the standard genetic code, in which its structure is preserved, and small variations in the genetic code, in which the structure is preserved or changed. The assumption is substantiated that the standard genetic code provides the best possible overlap of genes. The structure and content of the standard genetic code is determined by the condition of the maximum

Abstract Based on the equations of thermodynamic balances, a model of a stationary non-equilibrium distillation process is proposed. It is shown that the heat consumption for any given efficiency of a distillation column depends monotonically on the parameters of the reversible distillation. Using this result, the authors propose an algorithm for choosing the optimal separation sequence for a system

Abstract We develop/propose the method reducing the dimension of a data matrix, based on its direct and inverse projection, and the calculation of projectors that minimize the cross-entropy functional, remove. We introduce the concept of information capacity of a matrix, which is used as a constraint in the optimal reduction problem, is introduced. The proposed method is compared with known methods

Abstract A family of difference schemes on an explicit five-point stencil for the numerical solution of the linear transfer equation is considered. To construct and study the properties of difference schemes, a generalized approximation condition is used. Difference schemes in the space of undefined coefficients are analyzed. In this case, the problem of constructing the optimal difference scheme is

Abstract— This study carries out the numerical simulation of the propane pyrolysis process in a flow-through chemical reactor where chemical conversions are induced by the external heating of the reaction zone. Navier–Stokes equations in the approximation of small Mach numbers are used for the mathematical description of the studied processes, since the velocity of the gas mixture is much lower than

Abstract— A numerical algorithm is presented for solving the multicomponent gas dynamics equations by the discontinuous Galerkin method on locally adaptive grids. The numerical algorithm uses a data structure and a dynamic local grid adaptation algorithm from the p4est library. We use Lax–Friedrichs–Rusanov and HLLC numerical flows. To get rid of unphysical oscillations, the Barth–Jespersen limiter

Abstract— This paper considers an approach to approximating the sensor data of an autonomous navigation system installed on the Russian segment of the International Space Station (ISS) based on the application of a mathematical model simulating the orbital motion of a spacecraft (SC) in which the midship area is computed with allowance for the aerodynamic drag forces using a geometric model of the

Abstract The problem of optimizing air passenger transport schedules is investigated. It is required to minimize renting and operating costs taking into account heterogeneous fleet, the possibility of multiple visits to the same location, inaccessibility of specified air corridors, etc. Two formalizations of this problem are presented in the form of multi-index problems of binary linear programming

Abstract— The paper considers a three-dimensional gas-dynamic model of a protoplanetary disk that revolves around a gravitating center. The dynamics of small perturbations in a rotational shear flow are modeled. The development of the initial azimuthal perturbations of the rotation speed leads to the formation of spiral density arms, while self-gravity increases its local maxima and creates gravitational

Abstract We consider the problem of modeling hydroelastic oscillations of liquid fuel in the tanks of launch vehicles with the use of mechanical analogs. Here, it is important to ensure the applicability of the computational model with mechanical analogs to the real object in terms of the mass-inertial and dynamic characteristics. In addition, it is necessary to ensure the correct modeling of the external

Abstract The paper presents a modification of the asymptotic averaging method for solving the homogenization problem of elastic properties for composite materials. The elasticity of the phase interface is taken into account. The conditions of a soft imperfect interface are considered, which account for a displacement jump on the phase boundary. A review of the interface-modeling methods in composite

Abstract— The issues of the mathematical modeling of a thermoporoelastic medium taking its damage into account are considered. The employed model generalizes the classical Biot model simulating the behavior of a poroelastic medium taking the thermoelastic effects into account. In order to describe the damage of the medium, the approach of continual damage mechanics is used, in which the state of the

Abstract The possibility of introducing a nonlinear correction to the Dirac equation for graphene in order to adequately describe collective electronic phenomena is considered. In contrast to the other papers on this topic the interaction term includes the sum of the spinor components’ squares instead of their difference. Particular attention is paid to the equality of the spatial coordinates. We investigate

Abstract— The paper is devoted to the simulation of oil displacement by water and the formation of the Saffman–Taylor instability. The problem is solved in two-dimensional formulation. A circular domain with one injection well and eight production wells located along the contour around the injection well is considered as geometry. To study the patterns of oil displacement by water, hydrostatic pressure

Abstract In this paper, a mathematical model of a neural network defuzzificator is presented. It is a two-layer perceptron and serves to convert a fuzzy solution to a numerical form in fuzzy-logic output procedures. The model allows optimizing the computational load that occurs when using the standard center-of-gravity method, through the use of a neural network. Training and testing are conducted

Abstract This paper considers continuous models of informational warfare based on the traditional neurological scheme. Using the method of substituting differential equations by cellular automata we propose a discrete version of the information warfare model. This model is used to simulate a propaganda campaign by two parties and to carry out a number of computational experiments. It is shown that

Abstract This paper provides a vector autoregression model with an additional regularization problem similar to the Hodrick–Prescott filter problem to model a single, i.e., balanced, growth rate of the structural component of the main macroeconomic indicators of the Russian economy. This model includes the real GDP without government expenditure, the real household consumption, real fixed capital investment

Abstract— This article considers interpretation of matrix models of texts and models of text collections based on them. Examples of computationally generated models of text collections are presented to demonstrate the high quality of the modeling results and practical applicability of the proposed approaches. An original method of the experimental verification of the text models’ applicability to problems

Abstract A numerical solution method based on the reduction of systems of ordinary differential equations to the Shannon form is considered. Shannon’s equations differ in that they contain only multiplication and summation operations. The absence of functional transformations makes it possible to simplify and unify the process of numerical integration of differential equations in the form of Shannon

Abstract The study of the development of perturbations under the influence of various hydrodynamic instabilities, as well as the transition to turbulent mixing and turbulence, has been a subject of considerable interest over the past decades. This is primarily due to the importance of these phenomena in various fields of science and engineering. In addition, it should be noted that studies of the characteristics

Abstract— The aim of this work is to study and compare various approximations for the system of radiative heat transfer equations (TEs) in optically dense and transparent media. For this purpose, in optically dense media, asymptotic analysis is used; and in optically transparent media, an approach that allows reducing the solution of diffusion equations to solve a kinetic equation. The performed studies

Abstract The results of a study of the oscillations of microcantilevers (MCs) made of nanoporous anodic aluminum oxide and constituting the base of biochemical sensors are described. Finite-element modeling of an MC’s vibrations reveal the sources of resonances in the frequency spectrum that do not correspond to the cantilever’s oscillations and complicate the development of sensors. It is shown for

Abstract— Steady-state solutions for the problem of magnetohydrodynamic motion of an incompressible polymer fluid over an infinite rotating disk are considered. The representation of the solution used here is similar to the Von Kármán self-similar solution for a viscous fluid. Examples of the numerical steady-state solutions for various values of the problem parameters are presented.

Abstract The generation of an electromagnetic field in a region with a perfectly conducting boundary by a long duration pulse of ionizing radiation is considered. The problem of calculating the field by numerically solving the complete system of Maxwell equations is posed. The approximations of the large and small radiation conductivity of the medium in the region are formulated. Analytical estimates

Abstract The era of the development of fundamentally new materials began with the discovery of graphene. Their unique properties already allow us to create many useful products in electronics, biomedicine, and other high-tech industries. However, the study of graphene and its derivatives is continuing. The mechanism of the formation of the graphene lattice and the state parameters of its individual

Abstract The problem of the propagation of deformations and stresses in a thin fiber under a dynamic mechanical load, as well as the destruction of the fiber, is considered. High-speed interactions in which the striker’s speed is comparable to the speed of sound in the fiber are considered. The numerical results are compared with an analytical solution for a point impact. Various loading modes are

Abstract— The impact of the choice of the proximity measure for the numerical and reference solutions is discussed in terms of the verification of the calculations and software. If no reference solution is available, the deterministic and stochastic options for estimating computational errors are considered using an ensemble of solutions obtained by different numerical algorithms. The relation between

Abstract The method of Lebesgue moments for simulating the reversal of resonances, resonance self-shielding, and block effect in the neutron spectra of extended heterogeneous objects, such as nuclear reactors, radiation shielding, and installations for studying the properties of matter, is developed. The method uses a more accurate averaging procedure over neutron energy than the group averaging. The

Abstract— The multicriteria problem of optimizing the state regulation of the quality of human capital in an information society is considered. A discrete dynamic model of human capital is described taking into account the age dynamics of the awareness and cognitive abilities possessed by an individual as a carrier of information. On trajectories, The lifelong indices of human capital are considered

Abstract A numerical simulation of the evolution and interaction of flow discontinuities in a channel caused by a pulsed volume discharge is performed. The algorithm is based on a system of quasi-gasdynamic equations in compact form. A comparison is made with the experimental data and calculation results based on the Euler and Navier-Stokes equations.

Abstract— A general equilibrium model, which describes the interaction of heterogeneous agents who choose between the labor market and self-employment and the state, which plays the role of an inspection body (auditor) in a model that controls the fact of tax evasion, is considered. It is shown that in the case of information asymmetry, the tax rate that maximizes the amount of tax revenues increases

Abstract A semiempirical mathematical model of motion of the center of mass of a spinning projectile in the atmosphere is proposed. This model takes into account the effects of the derivation and change in the frontal resistance due to variation in the angle of attack. These effects are accounted for without a detailed description of spinning in our model, which allows using a large integration step

Abstract An approach to mathematically model the nucleation and growth of soot particles during the diffusion combustion of hydrocarbon fuel is presented. The chain of transformations of hydrocarbon fuel is modeled using a Markov process with a finite number of states, which is described by a stiff system of Kolmogorov’s ordinary differential equations (ODEs). As a result of numerical modeling, the

Abstract This paper proposes a new stochastic transport model formalized in differential equations with random parameters. Explicit formulas for the mathematical expectation and the second-moment function for solving the corresponding equations are given. The estimation of the influence of random factors on the system, in the case of replacing the random coefficient of the equation by its mathematical

Abstract Injection of plasma flow generated by a quasi-stationary plasma accelerator into a region with a magnetic field created by a series of ring current-carrying conductors forming a solenoid is considered. Numerical studies are carried out based on the set of magnetogasdynamic (MGD) equations represented in terms of the vector potential of the magnetic field, taking into account electrical conductivity

Abstract Results are presented of scale-resolving computations of mean and turbulent (including the dissipation rate of turbulent kinetic energy) characteristics of the turbulent wake of a flat plate subjected to adverse pressure gradient (APG). The computations are performed in the framework of a zonal RANS-LES model for two configurations. In the first one, APG is created by a plane symmetric diffuser

Abstract In this paper possible scenarios of pattern formation in nonlinear media with diffusion and differential operators of a noninteger order are studied for the abstract Brusselator model. Through the standard linear analysis exact critical values for different types of instabilities are derived. It is shown that the stability criteria significantly depend on the order of the fractional derivative

Abstract A model of the medium, which makes it possible to use information more rationally for solving inverse problems in comparison with the well-known models of a layered and quasi-layered medium is introduced. A two-dimensional medium in which the fields are described by the Helmholtz equation is studied. A linearized statement of the problem of reconstructing the parameters of the medium, the

Abstract This paper presents an approach to construct an interactive geometric model of a spacecraft’s outer surface for solving different applied problems related to the computation of integrals over the spacecraft’s surface, with the determination of the visibility of the surface parts taking into account their mutual overlapping, and with the determination of the surface projection on an arbitrary

Abstract Euler equations for multidimensional inviscid gas flows with multispecies and multi‑reaction are considered. By using the Marchuk–Strang splitting method, an implicit numerical scheme for this system is constructed. Its convection part is computed using the bicompact scheme SDIRK3B4 of fourth order in space and third order in time, while its chemical part is computed using the L-stable Runge–Kutta

Abstract A numerical algorithm for simulating gas dynamics in rotor–stator systems based on sliding meshes and edge-based schemes is described. The paper pays particular attention to the multilevel MPI + OpenMP parallelization for cluster systems. Parallel efficiency is demonstrated on up to 1400 cores as well as on Intel Xeon Phi accelerators. The scheme is verified by solving a linear acoustic problem

Abstract We establish a relation between the class of symmetric spherical tensors and even/odd polynomials. The expansions of the scattering operator of photons or neutrons in a series of symmetric spherical tensors are obtained. Among them are expansions that have a higher rate of uniform convergence in comparison with expansions in spherical functions and Legendre polynomials. It is shown that, in

Abstract The combination of computed tomography and computational experiment is an important and promising tool in the study of the properties of various materials. State-of-the-art tomographic methods allow us to obtain a three-dimensional image of materials with a high resolution, which leads to a high dimension of discrete settings (106–109 numerical cells). They cannot be analyzed without the application

Abstract This study is devoted to the statistical method of classification based on nonlinear regression. The approaches used to implement it in solving the recognition problem of printed and handwritten characters are presented. Its implementation in assessing the health of the systems of the human body according to the parameters of peripheral blood is presented for the first time. The optimal structure

Abstract A physical and mathematical model is considered to support the investigation of the prospects of using the effect of metal’s “magnetic memory” for the nondestructive testing of items made from ferromagnetic materials located in the Earth’s magnetic field. Based on the finite-element method, an algorithm and a computer code for the 3D computations of the magnetic potential distribution in a

Abstract— Nowadays, many objects are exposed to the risks of seismic activity, either of a natural character during earthquakes or due to man-made hazards. For example, the zone of increased seismic activity includes the eastern regions of Russia located in the zone of the so-called Ring of Fire, the coastal zone of the continents of Eurasia, North America, South America, and Australia, as well as

Abstract— Physical and numerical models are developed for the analysis of the processes occurring in the multiphase flow in a well during hydrocarbon production. A detailed description of the system of equations, its numerical approximation, methods for calculating the fluid properties and phase transitions in it, and the closing relations for calculating friction and heat transfer in a two-phase flow

Abstract— Using a mathematical model of wind currents, supplemented by a module for the suspended sediment silt transfer and sedimentation, the spatiotemporal features of the accumulation of river sediments in the Don avandelta in different wind conditions (east and west wind surges and light winds of variable directions) are identified. It is shown that the exposure to an east wind of 6 to 8 m/s during

Abstract A new numerical algorithm for solving parabolic equations by balance & characteristic difference schemes is proposed. The balance and characteristic schemes combine the advantages of conservative and characteristic schemes. The main advantage of the new algorithm is that it is explicit and is implemented on the most compact computational template in one space-time computational cell. It scales

Abstract— The concept of a factor model based on frames is proposed. Factors are considered as slot values of the corresponding frames, which makes it possible to reduce the complexity of the developed model. The method for calculating the factor values by searching for the eigenvalues of the pairwise comparison matrices of the extent of the slots’ influence is proposed. A procedure allowing us to

Abstract We propose a new explicit-iterative scheme for time integrating the multidimensional Navier–Stokes equations of a compressible environment through splitting into convective and diffusive stages, which are performed sequentially at each time step. The convective stage is implemented using the Godunov scheme; and the diffusive stage, using the Chebyshev explicit-iterative LI-M scheme, which