Scientific Journal of KubSAU

Polythematic online scientific journal
of Kuban State Agrarian University
ISSN 1990-4665
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604 kb

SIMULATION OF TURBULENT FLOW IN A CAVITY ON THE NAVIER-STOKES EQUATIONS

abstract 1191605079 issue 119 pp. 1111 – 1133 31.05.2016 ru 414
The article deals with the numerical solution of the Navier-Stokes equations describing turbulent flow in a rectangle cavity or in a cuboid with one open face at high Reynolds numbers. It is known, that there is a mechanism of turbulent mixing in natural systems, leading to an increase in the viscosity of the continuous medium. In this regard, we suggest methods of regularization of the Navier-Stokes equations, similar to the natural mechanisms of mixing. We proposed the models based on the properties of the turbulent environment. For this we modified the continuity equation taking into account the pressure fluctuations. It is shown that the incompressibility condition is can be violated due to pressure fluctuation even for flows with low Mach numbers. Modification of continuity equation by the introduction of turbulent viscosity allows the regularization of the Navier-Stokes equations to solve the problems with rapidly changing dynamic parameters. It was shown that the modification of the continuity equation taking into account turbulent fluctuations leads to a system of nonlinear equations of parabolic type. A numerical model of turbulent flow in the cavity with the rapid change in the parameters of the main flow developed. Discovered type of instability of the turbulent flow associated with the rapid changes in the main flow velocity. In numerical simulations found that due to the acceleration of the main flow there is the unsteady vortex flow in the cavity, which is characterized by the integral of energy not vanishing with time, vibrations that have a certain period, depending on the turbulent viscosity
216 kb

TO THE RESEARCH METHODS OF FAULTS UNDER THE VIBRATION IMPACTS

abstract 1211607033 issue 121 pp. 647 – 659 30.09.2016 ru 421
We propose an approach to the modeling of stressstrain state of lithospheric structures near faults by modeling them as Kirchhoff plates on threedimensional elastic foundation. We describe an efficient method of solving problems for plates with rectilinear fractures, based on the transformation of the differential operator, which allows us to analyze the solutions obtained for different contact conditions in the area of the fracture. The method is presented on the example of the vibration problem of two elongated plates on the surface of the elastic layer under the effect of concentrated surface load. The results of numerical implementation of the developed algorithm make it possible to identify the influence of the substrate properties, characteristics of the plates and the nature of their border interactions on the picture of wave process in the test structure. At the same time obtained configurations of the harmonic signal passage through the fracture can serve as an indicator of its type. The proposed approach should be used to determine the presence and type of fractures based on measurements of signals from vibration sources in cases when geophysical environment can be modeled by the previously described structure. The problems of studying objects we reviewed in this paper also occur in various areas of technology, and, therefore we can apply the proposed method for their solution
520 kb

CRYSTALL SPACE METRIC

abstract 1271703072 issue 127 pp. 1010 – 1044 31.03.2017 ru 424
In the present article, we investigate the metric of the crystal space in the general theory of relativity and in the Yang-Mills theory. It is shown that the presence of a lattice of gravitational ether has observable macroscopic consequences. Earlier, the influence of the gravity of the celestial bodies of the solar system on the electrical conductivity, inductance, the rate of radioactive decay of atomic nuclei, on seismic activity, the magnetic field and the motion of the pole of our planet, and on the rate of biochemical reactions was established. In all cases, a similar behavior of the physicochemical characteristics of materials and processes is observed, depending on the universal parameters characterizing the seasonal variations of the gravitational field of the solar system. The relationship between lattice parameters and the properties of materials, elements, atomic nuclei, and elementary particles is discussed. Possible metrics of the crystal space are constructed: a metric that depends on the Weierstrass function, derived in the Yang-Mills theory and analogous metrics found in Einstein's theory. Such metrics, which have a central symmetry, can be used to justify the structure of elementary particles, the properties of atomic nuclei, atoms and matter. Periodic metrics are constructed that admit an electromagnetic field, as well as metrics associated with the assumed structure of the crystal space. These metrics are of particular interest, since the properties of the substance are related to the metric parameters. We proposed the model of electron beam as a streamer of preons
540 kb

RESTRICTED MANY-BODY PROBLEM IN THE RICCI FLOWS IN GENERAL RELATIVITY

abstract 1221608070 issue 122 pp. 1007 – 1032 31.10.2016 ru 427
In this article, the restricted problem of three and more bodies in the Ricci flow in the general theory of relativity considered. A system of non-linear parabolic equations describing the evolution of the axially symmetric metrics in the Ricci flow proposed. A model describing the motion of particles in the Ricci flow derived. It is shown that the theory describing the Ricci flow in the many-body problem is consistent with the Einstein-Infeld theory, which describes the dynamics of the material particles provided by the singularities of the gravitational field. As an example, consider the metric having axial symmetry and contains two singularities simulating particles of finite mass. It is shown that the static metric with two singularities corresponds to Newton's theory of the two centers of gravity, moving around the center of mass in circular orbits in a noninertial frame of reference, rotating with a period of bodies. We consider the statement of the problem of many bodies distributed at the initial time on the axis of symmetry of the system. In numerical calculations, we studied the properties of the gravitational potential in the problem of establishing a static condition in which multiple singularities retain the initial position on the axis of the system. This is achieved due to relativistic effects, which have no analogues in Newton's theory of gravitation. Using the properties of relativistic potentials we have justified transition from the relativistic motion of the particles to the dynamic equations in the classic theory
145 kb

THE DEVELOPMENT OF COUNTRIES' CREDIT RATING ASSESSMENT SYSTEM

abstract 1191605019 issue 119 pp. 274 – 282 31.05.2016 ru 428
This work presents a new approach to the countries’ credit rating definition, based on the advanced mathematical models, such as neural network model, multiple regression, cluster analysis and discriminant analysis. A range of the analyses such as discriminant, cluster, multiple regression models and a neural network were performed on the following economic figures: GDP per capita, GDP value, annual growth rate of GDP, FDI - foreign investment, rate of unemployment, consumer price inflation index, the size of government debt in percentage of GDP. The results, obtained for each model were combined in the countries’ credit rating estimation system called "7M"
189 kb

THE INFLUENCE OF REACTION OF DISSOCIATION / RECOMBINATION OF WATER MOLECULES ON ELECTROLYTE TRANSPORTATION 1: 1 IN MEMBRANE SYSTEMS IN THE DIFFUSION LAYER. PART 1. MATHEMATICAL MODEL

abstract 1211607122 issue 121 pp. 1929 – 1941 30.09.2016 ru 447
The influence of dissociation / recombination of water molecules is important for understanding electroconvection processes, as some authors believe that the emergence of new carriers + H and − OH , and can lead to a reduction in the space-charge and, consequently, to electroconvection disappearance. However, as shown in [5], the dissociation of water molecules, although it reduces the space charge and increases the threshold fall potential jump at which begins electroconvection, yet it persists and effectively mixes the solution. This article is devoted to mathematical modeling of electrodiffusion of four types of ions at the same time (two salt ions as well as + H and − OH ions) in the diffusion layer in electromembrane systems with perfectly selective membrane under the joint influence of violation of electrical neutrality, and the reaction of dissociation / recombination of water molecules, development of mathematical models of these processes, building efficient algorithms asymptotic and numerical analysis for different types of electrolytes. The work proposes a new mathematical model of the process of transfer of salt ions in view of the space charge and the dissociation / recombination of water in the form of a boundary value problem for a system of ordinary differential equations. This system is reduced to a form convenient for numerical solution. We have calculated the required additional boundary conditions for the electric field. Numerical and asymptotic solution of the boundary value problem and physico-chemical analysis of the influence of dissociation / recombination on the transfer of salt ions is expected to devote the next part of the work
188 kb

DERIVATION OF THE EQUATIONS OF THE KINETICS OF PLASMA CHEMICAL PROCESSES INVOLVING ISOTOPES IN A MAGNETIC FIELD

abstract 1231609123 issue 123 pp. 1864 – 1877 30.11.2016 ru 447
Specially formed mixtures of isotopes of chemical elements have better consumer properties than their natural counterparts. Therefore, the development of methods for increasing the efficiency of the known methods for producing of isotope materials is relevant. It is known that the chemical bond is formed only in the singlet state of the spins of valence electrons of the reagents. On the basis of the known representations about dispersion of spin projections on the coordinate axes and the molecular-kinetic theory of gases was obtained an expression for the constant of the chemical reaction between the radicals occurring in the magnetic field. This expression allows calculating the reactivity of the isotopic modifications of radicals. Plasma allows to transfer many of the compounds in the gas phase. It is known that a significant part of particles in low temperature plasma is in a radical form. The equations of chemical kinetics for describing the process of oxidation of the carbon isotopes in argon-oxygen plasma occurring in an external permanent magnetic field were written in the work. It was shown that the efficiency of plasma process of isotopes separation can be increased only under insufficient oxygen relative to the stoichiometric value. These equations of chemical kinetics of processes occurring in the plasma process of incomplete oxidation of carbon isotopes needed to find experimental conditions that provide the maximum isotope effect in a magnetic field
643 kb

SIMULATION OF PARTICLE DYNAMICS IN THE STERN-GERLACH APPARATUS

abstract 1171603060 issue 117 pp. 929 – 950 31.03.2016 ru 453
The model of the motion of particles in the SternGerlach apparatus in the classical and quantum mechanics was developed. The data simulation of particle trajectories and distribution of silver atoms on the surface of the plate in their deposition are discussed. It was found that for the experimentally observed distribution of two-dimensional shapes of the atoms must be assumed that the atoms are not involved in the precession motion in a magnetic field, while maintaining the direction of the magnetic moment, for example, parallel to the induction vector of the magnetic field during the time of motion in the apparatus. To obtain a realistic picture of the figure of the scattering of atoms used a classical model of movement and expression of forces compatible with the quantum picture of the motion of particles with spin ½. The magnetic field is simulated based on the original Stern-Gerlach data describing the distribution of the gradient of the induction components related to the splitting of the beam. Quantum model of particle motion is based on the Pauli equation in the boundary layer approximation. It is found that in this model, depending on the initial polarization of the particle, beam is split into either two or is deflected towards the magnet blade or in the opposite direction. It is shown that if the initial conditions for the task are reproducing the geometric dimensions and the magnetic field in the Stern-Gerlach apparatus, the figure of the scattering particles in the shape of the outline is similar to the experimentally observed shape
693 kb

SIMULATION OF PLASMOID AND STRAIMERS IN CONDUCTING ENVIRONMENT

abstract 1291705041 issue 129 pp. 471 – 497 31.05.2017 ru 460
In this work, a model is developed that describes the formation of a plasmoid and streamers in a conducting medium. To describe the contribution of the conductivity currents, we modified the standard electrostatic equation taking into account the vortex component of the electric field. As a result of this generalization, the streamer model is formulated in the form of a system of parabolictype nonlinear equations. As is known, in laboratories it is possible to create a plasmoid with a lifetime of 300- 500 ms and a diameter of 10-20 cm, which is interpreted as a ball lightning. With high-speed photography, a complex structure is detected, consisting of a plasmoid and surrounding streamers. Within the framework of the proposed model, problems are posed about the formation of a plasmoid and the propagation of streamers in an external electric field. In this model, the plasmoid is considered to be a long-lived streamer. The range of parameters in which a plasmoid of spherical shape is formed is indicated. It is established that there are three streamer branching mechanisms. The first mechanism is related to the instability of the front, which leads to the separation of the head of the streamer into two parts. The second mechanism is associated with the instability of the streamer in the base region, which leads to the branching of the streamer with the formation of a large number of lateral streamers closing the main channel of the streamer to the cathode. In numerical experiments, the third branching mechanism observed in experiments connected with the branching of the plasmoid in the cathode region with the closure of the space charge to the anode through the streamer system was observed. The similarity of ball lightning and plasmoid is discussed. If this similarity is confirmed, then the number of theoretical hypotheses concerning the nature of ball lightning, currently more than 200, can be drastically reduced to one described in this article
18043 kb

SYNTHESIS AND VERIFICATION OF MULTICRITERIA SYSTEM-COGNITIVE MODEL OF THE GUARDIAN UNIVERSITY RANKING AND ITS APPLICATION FOR THE PROPER EVALUATION OF THE EFFECTIVENESS OF RUSSIAN UNIVERSITIES WITH RESPECT TO THE DIRECTION OF PREPARATION

abstract 1071503001 issue 107 pp. 1 – 62 31.03.2015 ru 461
The article is devoted to the solution of the problem which is the fact that on the one hand, the rating of Russian universities is in demand and on the other hand it hasn’t been created yet. The proposed idea of solving the problem consists in the application of domestic licensing of innovative intelligent technologies for these purposes: we have suggested using an automated system-cognitive analysis (ASC-analysis) and its software tools – the intelligent system called "Eidos". These methods are described in detail in this context. It is proposed to consider the possibility of applying these tools on the example of the Guardian University ranking. The article discusses its private criteria (indicators of universities). We specify the sources of data and the methods of their preparation for processing in "Eidos" system. In accordance with ASC-analysis methodology the article describes the installation of "Eidos", the data input into it, and the formalization of the subject area, synthesis and verification of models, their display and use to solve problems of assessment of the Guardian rating for Russian universities and research object modeling. It also discusses the prospects and ways of development of the integrated rating of Russian universities and operation of rating in adaptive mode. We have also specified the limitations of the proposed approach and the prospects of its development
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