A technique is proposed for determining the regional differentiation coefficients on the basis of regional price differentiation, taking into account substitution effects for goods and services. The approach is based on a generalized nonparametric method for constructing a pair of the Konus–Divisia indices. For the Konus–Divisia indices to exist, consumer behavior must be consistent with the Pareto model of a single representative rational agent. The technique has been applied to trade statistics data for regions and groups of regions in Russia for 2020–2024. Significant price differentiation among regions has been detected. The differences in per capita expenditure between non-capital groups of regions are shown to be due to different price levels, since the purchasing power of the population of these groups is similar.
This study aims to develop a robust algorithm for the classification of images with interval attributes to used under significant interference and data uncertainty. The algorithm is based on the transformation of attributes of reference images into an interval form with a given error and subsequent comparison with classified images using two purpose-built metrics based on interval intersection analysis. Computer simulation was performed on samples of 680 to 68 000 images with interference levels ranging from 0 to 100
A mathematical model and a calculation algorithm for numerical studies of physical and chemical processes in the engines with prechamber ignition have been developed. This type of ignition is currently the subject of active research due to its potential to improve the combustion efficiency, especially in case of the hybrid powertrain configuration. A new approach for modeling the prechamber ignition is proposed, which combines the control-volume method, predefined turbulence parameters, and direct coupling calculations on the basis of the fictitious domain method. This makes it possible to significantly simplify the geometry of the computational domain and the model preparation as well as to reduce the computing time due to the use of a relatively coarse grid. The model of ignition requires only one empirical parameter (if the turbulence field is known) to be tuned up. Modeling is conducted in a direct coupling way. The prechamber, the connecting passage, and the main combustion chamber are considered as a single computational domain. The prechamber volume is separated on the basis of the fictitious domain method. The mesh for the main combustion chamber has a moving boundary. The local flow parameters are calculated using the control volume method with staggered grids for components of the velocity vector and scalar variables. The mathematical model can be used for preliminary planning of three-dimensional calculations of the operating process or their verification in the case when no experimental data are available (at the stage of conceptual design). The results of calculations can be used as initial conditions for estimating the engine knock probability. The model can be used for calibration of the engine control unit.
The modeling approach based on the concept of a fuzzy cognitive map for studying complex processes occurring in the permafrost zone has been specified. The corresponding complex system is represented as an oriented graph, where the vertices correspond to factors and the edges are causal relationships between them. Mathematical properties related to the distribution of influence of input factors in the cognitive map have been described. The concept of influence has also been generalized for interactions between internal factors. A specialized model of the relationship between climate factors and the factors of permafrost soil structure and state has been developed. The model weights have been calibrated using available observational data to establish correlations mediated through the complex system.
For the Fredholm equations of the first and second kinds, difference schemes with super-power convergence are proposed. They are dramatically more accurate than previously known ones. For the equation of the first kind, a new regularization method is proposed based on adding a stabilizer directly to the matrix of the difference scheme. For the non-self-adjoint problem, the proposed approach reduces the complexity and improves the conditionality of the matrix of the linear system. A new procedure for selecting the regularization parameter is proposed. It is selected so that the systematic error introduced by the stabilizer and the random error due to rounding errors are comparable. A new calculation algorithm with precision control is designed based on grid refining and simultaneously increasing the number precision. The proposed approaches were verified on representative test problems with a known exact solution.
We consider the fundamentals of the Ray Tracing Method with a detailed description of its algorithmic implementation. This method is widely used and plays a principal role in investigating acoustic properties of the rooms where the acoustic quality is essential. As an example, the fundamental properties of the method are demonstrated by estimating the acoustic properties of a tested room.
Experimental technique of the Central Aerohydrodynamic Institute as well as various methods and programs for calculating heat fluxes in the area of a separated flow due to shock wave on a flat plate with a mounted vertical sharp wedge are described. A series of test calculations have been conducted. The physical features of the flow have been investigated as well as calculated and experimental data have been compared. Estimates of the tested programs accuracy have been obtained.
A problem of numerical modeling of wave reflections that occur during localization of natural and hydraulic fractures is considered using borehole acoustic logging methods. For numerical calculations, we use the spectral element method implemented in the SPECFEM3D software library. The accuracy of numerical solutions for problems of wave propagation from a point source in inhomogeneous anisotropic media is analyzed. An implementation of the Schoenberg linear slip model was added to SPECFEM3D. Calculations for the model scenario of hydraulic fracture identification yield almost identical responses in the borehole for reflected waves from fractures obtained with the Schoenberg model and with an explicit internal structure specification by a fine grid. A significant reduction in the required computational resources is achieved, since explicit fracture calculations require several times more the number of time steps and a larger number of grid points due to the very small transverse cells sizes near and inside the fracture. The use of the spectral element method in combination with the Schoenberg fracture model is one of the promising approaches for modeling the process of borehole acoustic reflections from hydraulic fractures.
A numerical approach based on the orthogonal central composite design is proposed. This approach allows one to study the mechanism of acoustic wave scattering on the system of sound-permeable spheres and analyze the sensitivity of this multiparameter system to a small change in several main parameters (factors). The method is implemented for a three-factor computational experiment using the example of systems with strong interaction between scatterers. For the resulting regression equation, the significance of the coefficients and the adequacy of the model are checked for two simple configuration types and three values of the number of spheres in them, as well as optimal values of two objective functions are found. For each case, essential and insignificant factors are established, the parameters at which the objective functions achieve the maximum (minimum) value are determined, and the sensitivity of this function to a small change in the variable parameters is determined.
Statement of an unsteady thermoelasticity problem in terms of stresses is considered. General equations of deformation compatibility in terms of stressaes for an isotropic thermoelastic medium in an arbitrary curvilinear coordinate system are obtained. These equations are generalizations of the Beltrami–Mitchell equations for the case of unsteady loads taking into account the finite velocity of heat flux propagation. The advantage of the proposed model when using numerical algorithms for solving initial boundary value problems of coupled thermoelasticity based on the finite difference method is briefly analyzed. Fundamental solutions to one-dimensional thermal elasticity problems in a Cartesian coordinate system are obtained.
A vertex-centered scheme is considered that is based on monotonicity-preserving edge-based reconstruction of variables for solving the Euler equations on unstructured meshes. Unlike a similar scheme that is based on quasi-one-dimensional WENO-reconstructions, the new method provides less dissipation and consequently a higher accuracy of the numerical solution. This property is demonstrated by solving two-dimensional model problems on uniform, quasi-uniform, and compressing triangular meshes.
Numerical simulation of supersonic (M∞ = 2.5) flow of viscous heat-conducting gas past a flying vehicle model for various attack angles and wall temperatures was carried out on the basis of an unsteady Reynolds averaged Navier–Stokes equations system (URANS) with Spalart–Allmaras (SA) and Menter’s SST turbulence model as well as with the hybrid IDDES+SA method. Three-dimensional features of the flow and surface heat flux dependence on wall temperature were investigated. The dependence of the base flow on the chosen turbulence model was studied. Comparison of simulation results with experimental data was carried out.
Recently, rumors regarding election postponement in Indonesia became a controversy on Twitter. To analyze how much the rumors spread on social media, the ignorance–discussant–spreader–remover (IDSRI) model was applied to actual data from February 27, 2023 to March 8, 2023, contained in Drone Emprit academic open data. Using the stability theorem, the type of endemic equilibrium point obtained for the condition E_1^* = ( I_1^*, D_1^*, S_1^*) = (0.0016; 0; 0.9886) is asymptotic stable. Furthermore, using the next generation matrix method, a basic reproduction number obtained was R0 = 152.09, indicating each person can spread rumors to 152 other people. This reveals that rumors of postponing the elections will continue to increase and spread rapidly within the population. The Indonesian government can use these results as a basis for preventive actions against rumor spread that disturbs the community.
The description of nonlinear characteristics of sea surface waves by models based on the Stokes expansion is discussed. The limitations of existing models are noted, which do not allow describing the variety of waveforms present on the sea surface. The necessity of introducing an additional parameter is justified. A modified second-order nonlinear model is proposed that allows obtaining negative values of skewness, which are observed in field experiments but are not described by existing models. The proposed model also allows obtaining horizontal asymmetry of waves.
The Boltzmann equation for the electron gas in a dielectric is constructed. Equations for the moments of the electron distribution function—concentration, drift velocity and energy density of the electron gas—are obtained. Closed equations for the electromagnetic field, concentration, and temperature of nonequilibrium electrons are derived in the drift approximation. Under the assumption that the electron gas is nondegenerate and the density of energy states of electrons is quasi-classical, the rate of the impact ionization reaction of the dielectric near the ionization threshold is calculated.
This paper presents a new traffic flow model based on cellular automata theory, taking into account the effects of overacceleration and speed adaptation inherent in real traffic flows. The focus is on the choice of driving strategies, reflected in the safe distance and acceleration values during acceleration and braking. The behavior of individual drivers may differ when changing lanes, moving forward along a lane, or entering the main road from a secondary one. These features are taken into account in the developing of the model. To verify the model, test calculations are carried out and the simulation results are presented.
This paper investigates the effect of numerical perturbations arising in the simulation of symmetric radiation-hydrodynamic flows on rectangular grids. Various methods for stabilizing the numerical solution are described. For problems involving dense shell dynamics in supernovae and their remnants, a combined reconstruction procedure is proposed, which significantly suppresses the influence of grid perturbations on the symmetry of the solution.
The paper presents approaches for constructing thermodynamic relationships for a mixture of noninteracting substances without resorting to labor-intensive molecular modeling. The main practically applicable approximations are the requirements of thermodynamic equilibrium (pT-approximation) and mechanical equilibrium (p-approximation). It is assumed that the motion of the components is described by a single velocity. For these approximations, the corresponding systems of nonlinear equations and approaches for solving them are presented. Using the example of solving a Riemann problem at the contact interface between two substances with significantly different properties, it is demonstrated that the requirement of temperature equilibrium between components is not always justified and can lead to incorrect results.
The problem of the end-to-end calculation of the flow of a weakly compressible fluid flowing in a porous body–free flow system is considered. This problem is relevant to the design of hydrocarbon processing systems, pollution purification plants, etc. As an example, the problem of the flow of an aqueous fluid through a cylindrical region containing a porous insert formed by spherical sorbent granules is chosen. This model problem is analyzed by two mathematical methods. The first method is based on direct mathematical modeling of a flow in a medium with discontinuous porosity determined by a system of granules. The second method involves the introduction of a continuous porous medium and consists of averaging the flow parameters over a representative volume under the specified fluid velocity and filtration rate. Within the framework of each method, the basic model is a quasi-hydrodynamic system of equations. Approximation of the proposed systems is based on the finite volume method for unstructured three-dimensional grids. The constructed computational algorithm is programmatically implemented using geometric parallelism. Based on the results obtained in direct mathematical modeling, permeability coefficients for the averaged model are selected. Computational experiments carried out within the framework of the averaged representation of porosity demonstrated the correctness of the used model, computational algorithm, and its software realization.
This article develops a mathematical model of an unsteady process in a catalyst layer with cylindrical grains. The model includes diffusion–reaction–convection equations, an equation for calculating the rate of forced convection in grain pores, the heat conductivity equation for the catalyst skeleton, and the equations of heat and mass transfer of gas in the catalyst layer. A computational algorithm based on splitting by physical processes is constructed for the developed model. The tasks of chemical kinetics are separated into an isolated integration stage and solved by the RADAU5 method with an adaptive step. The diffusion–reaction–convection equations are hyperbolized to reduce the estimated time of slow diffusion processes in grain pores. A three-layer scheme explicit in time is used for these equations. The heat conductivity equation is also explicitly integrated, and the integral source term in it is calculated using the trapezoid method. The transport equations along the length of the catalyst layer are integrated implicitly to expand the range of the algorithm’s stability in the case of sharp temperature and concentration fluctuations in the layer. The boundary conditions for the catalyst grain are approximated by second-order spatial accuracy. The constructed algorithm is tested on a problem with a known analytical solution and compared with the solution of the Dirichlet problem in a mathematical package. The developed model and algorithm are used to study the modes of a real unsteady process in the catalyst layer.
