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Sibirskii Zhurnal Industrial'noi Matematiki
2017, vol. 20, No 3 (71)Contents
UDC 514.862
DOI 10.17377/sibjim.2017.20.301Astrakov S. N., Golushko S. K., Korolenko L. A.
Isoepiphanic forms of pressure vesselsWe consider the generalized statements of the optimization problems of the geometric shape of simple and composed domains under given constrains. Alongside the condition of the minimality of the boundary of the domain, some additional constraints are introduced on pointwise or contour ``fastening'' of the domain. The obtained results can be used for the optimal design of tanks and pressure vessels including multisection ones.
Key words: pressure vessels, isoperimetric problems, the minimum weight.
Pp. 3-10.
Astrakov Sergei Nikolaevich
Design Technological Institute of Digital Techniques SB RAS
Acad. Rzhanov str., 6
Novosibirsk State University
Pirogova str., 2
Golushko Sergei Kuzmich
Design Technological Institute of Digital Techniques SB RAS
Institute of Computational Technologies SB RAS
Acad. Lavrentyev ave., 6
Novosibirsk State University
Korolenko Leonid Aleksandrovich
Novosibirsk State University
630090 Novosibirsk
E-mail: astrakov90@gmail.com; s.k.golushko@gmail.com; lakorolenko@gmail.com
UDC 517.95 539.3
DOI 10.17377/sibjim.2017.20.302Beskrovnykh A. V.
Global solvability of the regularized problem of the volumetric growth of hyperelastic materialsWe present a model of volumetric growth of biological materials in the framework of finite elasticity. Surface effects on the boundary with the environment are taken into account. New mathematical results are obtained for the model, the main of which is a complete proof of global existence of a solution. The results can be used in further scientific developments at the juncture of biology and mechanics.
Key words: volumetric growth, existence of global solutions.
Pp. 11-23.
Beskrovnykh Andrey Vladimirovitch
Novosibirsk State University
Pirogova str. 2
630090 Novosibirsk
E-mail: andrey.beskrovnykh@yandex.ru
UDC 517.9
DOI 10.17377/sibjim.2017.20.303Germider O. V., Popov V. N., Yushkanov A. A.
Mathematical modeling of transfer processes in an elliptical channel in the free molecular regimeThe article considers heat and mass transfer in a long channel of constant elliptical cross-section as a part of the free molecular regime. We use a diffuse reflection model as the boundary condition. The distributions are found of the mass velocity of the gas and the heat flux vector over the cross-section of the channel. An analytical method is proposed for finding the heat flux and the mass flux of the gas through the cross-section in an elliptical channel.
Key words: diffuse reflection model, rarefied gas, free molecular regime, heat and mass transfer processes in a channel.
Pp. 24-30.
Germider Oksana Vladimirovna
Popov Vasily Nikolaevich
Northern Arctic Federal University M. V. Lomonosov
Severnaya Dvina Emb., 4
163002 Arkhangelsk
Yushkanov Aleksandr Alekseevich
Moscow State Regional University
Radio str., 10a
107005 Moscow
E-mail: o.germider@narfu.ru; v.popov@narfu.ru; yushkanov@inbox.ru
UDC 519.676
DOI 10.17377/sibjim.2017.20.304Ivanov A. A.
Analysis of the stochastic motion of a charged particle in a magnetic field by the Monte Carlo method on supercomputersWe study the influence of random noises on the motion of a charged particle in a magnetic field using statistical modeling for solving the emerging stochastic differential equation. Numerical results of experiments are given. For the analysis of numerical solutions, we use the frequency characteristics that generalize an integral curve and the phase portrait.
Key words: stochastic differential equation, cumulative frequency curve, frequency phase portrait, generalized Euler method, charged particle, magnetic field.
Pp. 31-38.
Ivanov Aleksandr Aleksandrovich
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Akad. Lavrentyev, 6,
630090 Novosibirsk
E-mail: 6ppp@mail.ru
UDC 517.929
DOI 10.17377/sibjim.2017.20.305Korobov A. A.
On pointwise degenerate linear delay-differential systems with nonnilpotent passive matricesComplete description is given of pointwise degenerate fourth-order linear systems of delay differential equations (with constant coefficients) with semisimple active matrix and nonnilpotent passive matrix. These systems are described in the language of the geometrical invariants of certain elements of the semigroup generated by the matrices of the system.
Key words: controlled delay linear system, relatively zero controllable system, pointwise completeness of a delay system of ordinary differential equations, degeneration direction, minimal moment of degeneration.
Pp. 39-50.
Korobov Alexey Alexandrovich
Sobolev Institute of Mathematics SB RAS
Acad. Koptyug ave., 4
Novosibirsk State University
Pirogova str., 2
630090 Novosibirsk
E-mail: korobov@math.nsc.ru
UDC 532.546
DOI 10.17377/sibjim.2017.20.306Lutsenko N. A., Fetsov S. S.
Stationary regimes of cooling porous objects with periodically distributed sources of energy releaseWe study a one-dimensional steady-state regime of a gas flow through porous objects with periodically distributed intensity of energy release under a given pressure difference on the open boundaries of the object, i.e., under self-regulation of the gas moving through the object. The obtained numerical-analytical solution to the problem is analyzed in a large range of the defining parameters; and the basic regularities of the studied process are revealed. It is shown that, under a periodical distribution of energy release sources, the dependencies of the phase temperatures, the filtration velocity, and the density on the height of the object are oscillatory but the pressure changes monotonically. It is found that the local maxima of the temperature of the solid medium and energy release differ, and their local minima can coincide only at those points where there is no energy release. We show that, the highest heating and other parameters under a periodical distribution of energy release can differ substantially from those under uniform energy release with the same total heat release. We also found that when the frequency of the heat-release intensity oscillations increases, the values of all sought parameters converge to those of the uniform energy release with the same total heat release as in the case of any integer even frequencies.
Key words: porous medium, gas filtration, heat release.
Pp. 51-62.
Lutsenko Nickolay Anatolyevich
Fetsov Sergey Sergeyevich
Institute of Automation and Control Processes Far Eastern Branch of the RAS
Radio str., 5
690041 Vladivostok
Far Eastern Federal University
Sukhanova str., 8
690091 Vladivostok
E-mail: nickl@inbox.ru; fetc95@mail.ru
UDC 536.423.4:532.22
DOI 10.17377/sibjim.2017.20.307Marchuk I. V., Barskii A. A., Kabov O. A.
Modeling of filmwise condensation on curvilinear fins with condensate suction from interfin groovesUnder numerical study is the nonsteady filmwise vapor condensation on curvilinear fins with condensate suction from the interfin grooves with account taken of the surface tension and gravity. The problem is reduced to solving a nonlinear evolution equation for the condensate film thickness. We carry out the calculations of the ethanol vapor condensation at the atmospheric pressure on fins of constant curvature with for various temperature differences between the fin surface and the vapor saturation temperature and at different values of condensate suction rate from the interfin grooves. Numerical calculations show that the condensation process in the condenser with condensate suction is stable. The filling of the interfin groove leads to a decrease in the zone of intense condensation and reduces the condensate inflow, and so it leads to a stable equilibrium between the condensate suction rate and the condensate inflow. Small changes in the temperature of the condenser under constant condensate suction rate lead to a change of the filling level of the interfin grooves and to the establishement of a stationary process if the temperature of the fin becomes constant.
Key words: vapour condensation, finning, heat exchange, condensate suction.
Pp. 63-69.
Marchuk Igor V.
Institute of Thermophysics SB RAS
Lavrentyev ave., 1
Barskii Artem A.
Novosibirsk State University
Pirogova str., 1
Kabov Oleg A.
Institute of Thermophysics SB RAS
630090 Novosibirsk
E-mail: marchuk@itp.nsc.ru; artemiy.barskiy@gmail.com; kabov@itp.nsc.ru
UDC 539.3
DOI 10.17377/sibjim.2017.20.308Puris V. A.
The conjugation problem for thin elastic and rigid inclusions in an elastic bodyWe consider the problem of the conjugation of a thin elastic inclusion and a thin rigid inclusion that are in contact at one point and are placed in an elastic body. Depending on what kind of conjugation conditions are given at the contact point of the inclusions, we consider the two cases: the case of no fracture, where as the conjugation conditions we take the coincidence of the displacements at the contact point and the preservation of the angle between the inclusions, and the case with a fraction, where only the coincidence of the displacements is given. At the conjugation point, we obtain boundary conditions for a differential statement of the problem. Delamination happens at the positive face of the rigid inclusion. On the crack faces, inequality-type nonlinear boundary conditions are given to prevent the mutual penetration of the crack faces. Existence and uniqueness theorems for a solution to the equilibrium problem are proved for each of the cases.
Key words: thin rigid inclusion, crack, nonlinear boundary conditions, Kirchhoff—Love beam, conjugation conditions.
Pp. 70-79.
Puris Vadim Alekseevich
Lavrentyev Institute of Hydrodynamics SB RAS
Acad. Lavrentyev ave., 15
630090 Novosibirsk
Å-mail: purisvadim@gmail.com
UDC 517.958:532.582.92
DOI 10.17377/sibjim.2017.20.309Starovoitov V. N., Starovoitova B. N.
Solvability of the unsteady problem of the motion of a rigid body in a flow of a viscous incompressible fluid in a pipe of arbitrary sectionWe prove the existence of a generalized weak solution to an unsteady problem of a motion of a rigid body in a flow of a viscous incompressible fluid. The flow of the fluid obeys the Navier—Stokes equations and tends to a Poiseuille flow at infinity. The body moves in accordance with the laws of classical mechanics under the action of the ambient fluid and the gravity force directed along the cylinder. Collisions of the body with the boundary of the flow domain are not allowed, and hence the problem is considered until the body approaches the boundary.
Key words: Navier—Stokes equations, solid body, cylindrical pipe, noncompact boundary.
Pp. 80-91.
Starovoitov Victor N., Starovoitova Botagoz N.
Lavrentyev Institute of Hydrodynamics SB RAS
Acad. Lavrentyev ave., 15
Novosibirsk State University
Pirogova str., 2
Starovoitova Botagoz N.
Lavrentyev Institute of Hydrodynamics SB RAS
630090 Novosibirsk
E-mail: starovoitov@hydro.nsc.ru; botagoz@hydro.nsc.ru
UDC 531.36
DOI 10.17377/sibjim.2017.20.310Chaikin S. V.
One-axis equilibrium orientations to an attracting center of a symmetric prolate orbital gyrostat with an elasctic beamWe study the motion of a symmetric prolate stationary gyrostat along a Keplerian circular orbit in a Newtonian central field of forces in the restricted formulation. An elastic beam is clamped by one end in the body of the gyrostat along its axis of symmetry. The beam has a point mass at the free end. The inextensible elastic beam (which is, for simplicity, of constant circular cross-section) performs infinitesimal space vibrations in the process of the motion of the system. Moreover, we neglect the terms nonlinear with repect to the displacements of the points of the beam in the tensor of inertia of the system. We consider the following (so-called semi-inverse) problem: Under what kinetic moment of the gyrostat among its relative equilibria (the states of rest in the orbital coordinate system) is an arbitrary coordinate axis defined in the coordinate system associated with the gyrostat collinear to the local vertical? In the discretization of the problem, we give the values of the Lagrange coordinates defining the deformation of the beam in these equilibria and the value of the gyrostatic moment guaranteeing the presence of the equilibrium.
Key words: orbital prolate symmetric gyrostat, circular orbit, central Newtonian force field, elastic beam, point mass, one-axis orientation.
Pp. 92-100.
Chaikin Sergey Vasil'evich
Institute for System Dynamics and Control Theory SB RAS
Lermontov str., 134
664033 Irkutsk
E-mail: schaik@yandex.ru