Uchenye Zapiski Zabaikalskogo Gosudarstvennogo Universiteta. Seriya Fizika, Matematika, Tehnika

12-23

Authors: Vladimir A. Tolpayev, Mariya A. Bondarenko, Vladimir V. Zaharov, Aleksandr M. Kravtsov, Musheg T. Petrosyants

A filtration law with kinematic correction for compressible fluid filtered in a porous medium is proposed. In the approximation of a plane wave, asymptotic solutions of the filtration equations were obtained in a closed form according to the Darcy law and according to the amended law with a kinematic correction. The illustrations are presented with graphs of the distribution of pressure and density of the flow of elastic energy in a stream of compressible fluid. The calculated estimates of the size of the filtration area are given for a practical example.

31-40

Authors: Svyatoslav Ye. Kholodovskii, Mariya G. Honina

Boundary value problems for the Poisson equation in a circle bounded by a weakly or strongly permeable on films are derived. Derived boundary conditions on films. The derived theorems of existence and uniqueness are proved. Solutions of boundary value problems are obtained in quadratures.

49-57

Authors: Sergey Ya. Berezin

The article deals with the theoretical provisions and experimental studies of contact stresses of plastic deformation by pressing a conical indenter. Empirical dependences of indicators of plastic properties in the form of contact stresses and yield stress on temperature, speed and degree of deformation for the main types of non-ferrous alloys are obtained. The method of analogy with the process of ball indenter indenta-tion is used to determine the degree of deformation during cone indenta-tion. The correlation of contact stresses with the Brinell hardness and relative weight parameters of the material is established. The nature of the influence of independent factors on the level of contact stresses is de-termined on the basis of empirical dependences.

67-74

Authors: Alexandr A. Gurulev

Due to the wide distribution of salt solutions in nature (in water bodies, in soils, in vegetation, etc.), an urgent task is to study the physicochemical processes taking place in them not only at positive temperatures, but also at negative ones. In the present work, the study of electrokinetic effects accompanying the crystallization of water-salt solutions was carried out using the example of sodium chloride solution. The measurements were performed with a monotonic change in the temperature of the sodium chloride solution at a rate of 0:28C/min with simultaneous measurement of the EMF arising between the platinum and copper electrodes, and temperature. As a result of the experiments, a correlation of the EMF signals in the sodium chloride solution with the process of crystallization of the sample at the eutectic temperature was found. At this moment, the magnitude of the EMF signal increases and then sharply tends to the minimum value. Also, by the rate of change of the sample temperature, it is possible to determine phase transitions in liquid and solid media. With joint thermometry and measurements of electric potentials, it is possible to study the features of the processes of formation and destruction of crystals in solutions.

11-16

Authors: Fedor A. Kovalev

A Cauchy problem for an unbounded rod consisting of two parts with different weight and thermal parameters is considered. An explicit solution of the problem in one-time quadratures is constructed. For instant heat source the solution of the problem is obtained in the final form. Temperature function graphs with a certain time step for different composite rods are constructed.

24-32

Authors: Vladimir A. Tolpayev, Kurban S. Akhmedov, Aleksandr M. Kravtsov, Musheg T. Petrosyants

The article proposes a simplified dynamic statement of the linear filtration problem with the replacement of the classical static condition at the bottom of the well with the dynamic boundary conditions of the steady-state regime of harmonic pressure pulsations. The estimation of the oscillation correction to the static solution for pressure and flow rate is obtained. Analytical dependencies for well flow rates allow us to describe more accurately the filtration processes in the reservoir system, taking into account the dynamic character of the processes at the bottom of the well.

42-50

Authors: Svyatoslav Ye. Kholodovskii, Pavel A. Chuhrii

A Cauchy problem for an unbounded string consisting of two homogeneous parts with different density is considered. We give the linear formulation of the problem. The solution of the problem in explicit form in single quadratures is obtained. String graphs with a certain time step for different combinations of composite string densities are constructed.

56-68

Authors: Oleg N. Shablovsky, Dmitry G. Kroll, Ivan A. Kontsevoy

The growth of a dendrite in a unicomponent overcooled melt is studied. The phase boundary is considered as a strong rupture surface complying the conditions of dynamical compatibility subjected to the integral conservation laws. We studied the class of movements with the phase boundary velocity depending on the angle between the normal and the growth line. The time evolution of the two-dimensional contour of the phase boundary was studied both analytically and numerically. The shape of the growth line, its curvature, velocity and heat flux in the solid phase were studied as well. With respect to the problem of the vibration effect on the crystallization process, the influence of phase boundary velocity fluctuations on the heat transfer intensification is considered. The calculations showed strong sensitivity of the heat flux to changes in the vibration amplitude. The uniform (with account to the special time coordinate) growth of a two-dimensional axially symmetric contour of dendrite is considered. The case when the original line suffers a perturbation localized at a final distance from the vertex is analyzed. It is established that the perturbation of the growth line curvature (a protrusion or a dent) induces a harbinger of a side branches of an axon. Its geometrical image is the point of intersection of the time-evolving the contour line. The applied aspects of the report refer to the methods of high-speed solidification of melts and obtaining new functional materials.

110-117

Authors: Sergei D. Krylov

The possibility of using microwave measurement technique to study the processes taking place in ice and porous media containing water during cooling and heating was investigated. Two methods were considered: waveguide and radiometric. The basis of these methods is the following: there is a significant difference in the absorption coefficient of electromagnetic waves for water and ice, and it is not difficult to study the water – ice phase transitions. It is also possible to study media in a different state in a confined space, in a waveguide and in free space by a radiometric method. Two examples of the application of these techniques are presented. As follows from the results of the experiments carried out, there are differences in the nature of the eutectic processes that can occur due to the stressed state of the sample when ice forms in the closed space and free space.

127-132

Authors: Nikolay P. Stepanov

In semiconductor materials Bi2Te3

6-10

Authors: Irina A. Efimova

We consider two boundary value problems for semi bounded string with non-uniform boundary conditions of type elastic contact and a point mass, which simulates non-ideal contacts of extended objects with the external environment. The equation and the initial conditions are homogeneous. Solving the considered task is given explicitly. Specific examples for which the solution of tasks is received in final form are given.

11-14

Authors: Anatoly A. Zabelin

The article describes the task of selecting the moment of the beginning of the working day, unified for the whole calendar year, in order to minimize the total annual time of intersection the dark time of the day and working time. The solution consists of constructing an optimization nonlinear model and finding the approximate result by numerical methods.

10

Authors: Svyatoslav Ye. Kholodovskii

The article considers a mathematical model of processes of heat conduction, diffusion, fltration, etc. in the cylindrical regions D = (x 2 R)  (y; z 2 Q  R2), separated by a film into two half-cylinders D1(x < 0) and D2(x > 0). The film consists of three strongly and weakly permeable layers in an arbitrary combination, in problems of biology it corresponds to the multilayered membranes, the drainage tubes, filter and protective screens, etc. The differential equation in the zones Di can be of any type (elliptic, parabolic, hyperbolic). Using the method of Convolution of Fourier expansions, the solution of boundary value problems with the films is expressed through the solution of a similar classical problem without films.We obtained analytical solutions to specific problems in different areas with three-layer films.

12

Authors: Oleg I. Viytovych

Technical operating costs by way of charges per unit of products (we take necessary received electricity for the consumer as products) can be direct or indirect. Direct costs are called expenses which include: payroll for staff, costs for lubricants, maintenance operation (i. e., the number of failures before the first maintenance), current and capital repairs, transportation and procurement of works and depreciation deductions. Indirect costs include: overhead and general running.

14

Authors: Vladimir A. Tolpayev., Kurban S. Akhmedov., Aleksandr M. Kravtsov., Musheg T. Petrosyants

The article deals with the problem of calculating the bottom hole pressure in the gas well, subject to risk of self-loading by condensation water. Correct choice of the bottom hole pressure is important to determine the steady state operation mode of the well. Its calculation in the case of presence of liquid in the well production is complicated by the fact that the pressure gradient calculation formulas for single-phase flows in this case do not apply. The paper analyzes the experimental data on the pressure gradients in the gas-liquid flows and proposes an approximation model for analytical calculations of pressure gradients. Approximation model for analytical calculations of pressure gradients was used for the integration of the differential equation for the pressure distribution along the wellbore. The results of numerical solutions of technological problems of well operation in conditions of water seepage are presented.

77-84

Authors: T. A. Vompe., A. S. Ustyukhin., I. M. Milyaev., V. A. Zelensky

In the present work, hard magnetic Fe-Cr-Co alloys containing 12 and 16 wt. % cobalt were obtained by powder metallurgy method. Molybdenum and silicon were used as alloying additives. Vacuum sintering of this alloys allows us to obtain specimens with relative density 96.598.5 %. Comparison of magnetic hysteresis properties of Fe-26 % Cr-16 % Co-2 % Mo- 0,5 % Si and Fe-26 % Cr-12 % Co-3 % Mo-0,5 % Si alloys indicated that alloy with 16 wt. % cobalt content usually has a higher coercivity, while alloy with 12 wt. % cobalt content has a higher residual induction. It was found that magnetic hysteresis properties depend on treatment start temperature and cooling rate in a magnetic field. It is possible under certain settings of thermal treatment to obtain an alloy containing 12 wt. % cobalt magnetic hysteresis properties comparable to standards for alloys with 15–16 wt. cobalt. Using alloys with low cobalt content will reduce the economic cost production of permanent magnets and rotors for hysteresis motors.

99 - 106

Authors: I. E. Kalashnikov., L. K. Bolotova., P. A. Bykov., N. B. Podymova., S. F. Zabelin

Physical, mechanical and tribological characteristics of composite materials based on SnSbCu alloy have been investigated. The paper presents the manufacturing technique by the extrusion method of the composite filler rods based on SnSbCu alloy, namely on babbit alloy B83. The manufactured filler rods were obtained with the uniform distribution of high-strength reinforcing particles of SiC. It was found that the hardness and the density of these filler rods are comparable with those of the cast babbit alloy B83 whereas their wear resistance exceeds that of this alloy.

14-22

Authors: Mikhail Sergeevich Voronin, Lev Alekseevich Merzhievskiy

A model of viscoelastic body of Maxwell’s type is developed to describe behavior of loaded polytetrafluoroethylene. The characteristic feature of the model are the defining relations: relaxation time of shear stresses and equation of state (EoS) with non-spherical deformations tensor. Relaxation time function is developed taking into account the fact that there are a number of thermo-fluctuating relaxation processes in polymers. The results of EoS calculations are also compared with available data of shock temperature. The model is used for simulating of propagation, interaction and reflection from a free surface of shock and unloading waves.

29-31

Authors: Irina Anatol’evna Efimova

The first boundary value problem in the inner part of the area limited by parabola is considered. Using a convolution method of Fourier expansions, the problem solution is expressed in the form of a series through the solution of the classical Dirichlet problem in the half-plane.

36-42

Authors: Zelenskiy V.A, Tregubova I.V., Ankudinov A.B., Zabelin S.F.

A new technology of porous material production from silver powders is offered.Technology combining the principles of colloid chemistry and powder metallurgy allows us to synthesize nanopowders of silver with the particles of mainly platelet shape and small areas of confluence of round shape particles.The method involves synthesis of precursors on the basis of silver with the use of organic compounds and their low temperature(175 ◦С) postreduction in a hydrogen-nitrogen atmosphere. Compacting methods with a pore forming element(food sugar) and follow-up sintering allowed us to get open porous structure of silver with the maximum porosity value up to 73 %. The study found that slip casting technology with the use of paraffin as a connecting element provides production of a homogeneous porous structure of the material.

53-59

Authors: Korchagina A. N., Merzhievskiy L. A.

Derivatives of a fractional order are used for modeling of anomalous diffusion. Various definitions of fractional derivatives are considered, comparison of numerical solutions of a number of problems of diffusion by various numerical methods is carried out. The most perspective definitions and methods of the numerical decision are specified.

70-75

Authors: Mencher A. E.

We consider a non-cooperative zero-sum game. The players, the Labor and the Manager, negotiate an improvement in the wage rate. In a conflict situation the players appeal to the arbitrator. The arbitrator’s solution is a discrete random variable. In this paper we use two arbitration schemes with quadratic payoff function. A mixed strategy Nash equilibrium in this game is found.

83-88

Authors: Orlov A. O., Bordonskiy G. S.

The experimental investigation of supercooled water in nanoporous silica at the temperatures down to −140◦ C was carried out. Nanoporous silica MCM-41 with 3.5 nm diameter cylindrical pores and SBA-15 (8.5 nm pores) were investigated using the methods of dielectric spectroscopy and measuring proper electrical fluctuations at low frequencies. Occurrence of non-linear media properties at the temperature below −40◦ C was found, which was revealed in the form of the registered cell capacity dependence on voltage amplitude in it, as well as noise increase. The effect observed is supposed to be related to the earlier predicted ferroelectric phase transition close to −40◦ C.

93-98

Authors: Sidorov A. A., Starchenko E. V., Matyuta A. A., Kul’chenkov E. A.

The dependence of the radii of the atoms in binary ionic crystals with cubic lattice on the charge of the nucleus is inveshigated. Using the postulate of the stability of the crystal lattice, we determine the ratio between the radii of the ions and the lattice parameter in binary cubic crystals with the structure of NaCl, CsCl, and fluorite.

105-109

Authors: Tokareva Yu. S., Mazalov V. V.

This paper considers the multi-stage game of three persons. A cake of unit size is divided between the three players. To resolve the problem, an arbitrator who is represented by a random number from the Dirichlet distribution is invited. The analytical expression of each of the three winning players as recurrence formulas is found. The optimal behavior of the negotiators is obtained in the class of threshold strategies.

117-120

Authors: Tolpaev V. A., Evenko I. A.

The article provides derivation of an equation for the study of unsteady flat-radial gas discharge according to the Forchheimer law for the purpose of its further application with the data on pressure recovery curves and pressure drop curves. They can more accurately determine reservoir pressure in the drainage area of the well as compared with the stationary studies.

132-139

Authors: Kholodovskiy S. E.

The paper considers the Cauchy problem of the motion of an unbounded string (a rod), consisting of two pieces, the ends of which are connected by an elastic gasket type of spring. Using the method of convolution of Fourier expansions, the problem solution is expressed in terms of the classical solution of the Cauchy problem maintaining the initial functions. The paper gives an example of the problem solution in a closed form for which the graphs in the vicinity of the elastic contact with a constant time step are drawn.

146-150

Authors: Shchegrina K. A., Petrov O. I., Krylov S. D.

The research of the microwave properties of salty ice containing NaCl, Na2CO3 and natural ice from the ice lake Doroninskoye at temperatures ranging from −20◦ C to −190◦ C was carried out. We used the following techniques: dielectric measurement of ice samples placed in a waveguide at a frequency of 15 GHz, as well as measuring the radio thermal radiation of ice against a cloudless sky at 5 GHz, 13.5 GHz and 37.5 GHz. Dependences of the real ε′ and ε′′ imaginary parts of the relative permittivity of the samples of salted ice for the temperatures below −60◦ C were found for the first time. The temperature of freezing liquid in the pores of the salty ice was experimentally determined as −145◦ C.