Home • Editorial Board • Contents • Russian page

Sibirskii  Zhurnal  Industrial'noi  Matematiki
2011,  vol. 14,  No 4 (48)

Contents
 

UDC 532.542.86
Basok B. I., Gotsulenko V. V.
Auto-oscillations in a distributed model of a Rijke tube

We consider a Rijke tube as a distributed autooscillating system. We analyze self-excitation conditions theoretically, obtain relations that determine the amplitude of steady-state autooscillations, and study their stability. The approach rests on the previously justified mechanisms of negative resistances: viscous along the tube and thermal, which is a local hydraulic resistance of the heat source zone.

Keywords: Rijke tube, auto-oscillations, distributed system, mechanisms of auto-oscillations, negative resistances.
Pp. 3–13.

Basok Boris Ivanovich
Gotsulenko Vladimir Vladimirovich
Technical Thermophysics Institute of the NAS of the Ukraine, 2a Zhelyabov str. Kiev 03057, Ukraine. E-mail: gosul@ukr.net

 

UDC 539.37
Burenin A. A., Dudko O. V., Lapteva A. A.
About the laws of propagation of shape deformations

We consider a one-dimensional automodel problem of an impact onto a deformed half-space in an incompressible elastic medium. Basing on the solution we study the one-dimensional interaction of flat shear shock waves coming toward each other from opposite directions and polarized in different planes.

Keywords: nonlinear elasticity, incompressible medium, shock waves, Riemann waves, automodel problems.
Pp. 14–23.

Burenin Anatoly Aleksandrovich
Dudko Ol'ga Vladimirovna
Lapteva Anastasiya Aleksandrovna
 Institute of Automatics and Control Processes,  Far East Division of the RAS, 5 Radio str. Vladivostok 690041 Russia. E-mail: burenin@iacp.dvo.ru;  dudko@iacp.dvo.ru; lanastal@mail.ru

 

UDC 517.956.3:517.968:519.237.5
Kokurin M. Yu.
On a correlation method for studying random wave fields

We consider the problem of reconstructing the probabilistic characteristics of a group of random acoustic sources from the measured space-time acoustic field coherence function on manifolds of various dimensions. We establish the unique solvability of this inverse problem in various formulations.  

Keywords: random wave field, hyperbolic equation, coherence function, inverse problem, integral  equation.
Pp. 24–31.

Kokurin Mikhail Yur'evich
 Mari State University, 1 Lenin sq. Yoshkar-Ola, 424001 Russiaþ E-mail: kokurinm@yandex.ru


 

UDC 539.311
Lazarev N. P.
An equilibrium problem for a Timoshenko plate with a through crack

We study the equilibrium problem for an elastic plate (Timoshenko model) with a vertical crack. On the curve defining the through crack we impose a boundary condition as an inequality describing the nonpenetration of the opposite crack edges. We prove the unique solvability of the variational statement of the problem. From the variational statement we deduce a complete system of boundary conditions, which we use to obtain an equivalent differential statement. We establish additional smoothness of the solution in comparison with that given in the variational statement. We prove that the solution functions are infinitely smooth under additional assumptions on the function of external loads and the functions of displacements near the curve describing the through  crack.
Pp. 32–43.

Lazarev Nyurgun Petrovich
 Mathematics Research Institute, Northeastern Federal University. 48 Kulakovskogo str. Yakutsk 677000 Russia
Lavrent'ev Institute of Hydrodynamics Siberian Division of the RAS, 15 Lavrent'ev av. Novosibirsk 630090 Russia E-mail: nyurgun@ngs.ru

 

UDC 533:517.958
Mamontov Ye. V.
On the stability of the stationary solution to the shallow water equation on a rotating gravitating sphere

We discuss the question of stability of the constant solution to the shallow water equation on a rotating gravitating sphere. The problem reduces to finding eigenvalues in a singular boundary value problem for a system of four first-order ODEs. We show that the eigenvalues are pure imaginary; thus, the solution in question is stable under small perturbations of arbitrary kinds.

Keywords: shallow water, sphere, eigenvalues, stability.
Pp. 44–49.

Mamontov Yevgeniy Vladimirovich
Lavrent'ev Institute of Hydrodynamics Siberian Devision of the RAS, 15 Lavrent'ev av. Novosibirsk 630090 Russia E-mail: mamontov@hydro.nsc.ru

 

UDC 519.718
Nagul N. V.
The dynamical properties of a discrete event model of a public transportation network

We consider the  well-known model of a public transportation network described by linear equations in the algebra on the set of real numbers whose operations are maximum and addition. In order to study the stability properties of the train schedule in this network we suggest a representation of the model as a discrete event system. The available stability theorems for invariant sets of the discrete event systems describing the situation of trains going on schedule enable us to make some statements concerning the properties of a schedule in this model of railroad transport.

Keywords: discrete event system, Lyapunov stability, railroad network, (max, +)-algebra.
Pp. 50–62.

Nagul Nadezhda Vladimirovna
 Institute of Systems Dynamics and Control Theory Siberian Division of the  RAS, 134 Lermontova, Irkutsk 664033 Russia E-mail: sapling@icc.ru

 

UDC 517.956.8:517.958:531.34
Nazarov S. A., Slutsky A. S.
The buffer boundary layer in a mixed boundary value problem  with contrasting coefficients

We construct asymptotics for the solution to a mixed boundary value problem in a thin compound cylinder   Wh0 È Wh1 È … È WhJ for a scalar second-order differential equation with piecewise   linear coefficients of orders hm in Wh0 and h0 in Wh j , j = 1,… , J, where h > 0 is a small parameter, and m = 0, 1, 2 (the typical cases).  For m = 1 and J >1 we discover the new phenomenon of a one-dimensional buffer boundary layer, which enables us to combine smooth-type expansion to a higher-dimensional boundary layer concentrated in the immediate vicinity of the bases of the cylinder.

Keywords: thin region, contrasting coefficients, asymptotics, buffer boundary layer.
Pp. 63–75.

Nazarov Sergey Aleksandrovich
Slutsky Andey Semenovich
 Institute of Machine Construction RAS, 61 Bol'shoi av., Vasil'evsky Island, Saint-Petersburg 199178 Russia. E-mail: srgnazarov@yahoo.co.uk; slutskij@gmail.com

 

UDC 517.9
Romanovsky R. K., Ivanchenko T. V.
A hyperbolic model of neutron diffusion in a one-dimensional moderator

We consider some boundary value problem describing the diffusion of thermal neutrons in a homogeneous one-dimensional medium accounting for absorption and breeding in the framework of a hyperbolic model of diffusion. We prove a unique existence theorem. The construction of a solution reduces to solving successively systems of  linear integral equations of the second kind.

Keywords: generalized Fick's law, thermal neutrons, one-dimensional medium, Riemann matrices of the first and second kinds, reduction of a mixed problem to a Cauchy problem.
Pp. 76–85.

Romanovskiy Rem Konstantinovich
Ivanchenko Tatyana Viktorovna
 Omsk State Technical University, 11 Mira av. Omsk 644050, Russia. E-mail: little-one@mail.ru

 

UDC 534.18
Romenskiy Ye. I.
A thermodynamically consistent system of conservation laws for the flow of a compressible fluid in an elastic porous medium

Basing on the method of thermodynamically consistent systems of conservation laws we develop a model of the isoentropic flow of a compressible fluid in an elastically deformable porous medium in the case of finite deformations, whose defining equations are hyperbolic and has divergence form. We also derive equations for the propagation of small amplitude waves in a motionless medium and analyze the dependence of the speed of sound on porosity.

Keywords: conservation laws, hyperbolic system, elastic porous medium.
Pp. 86–97.

Romenskiy Yevgenii Igorevich
Sobolev Institute of Mathematics SB RAS. 4 Acad. Koptyug av. Novosibirsk 630090, Russia. E-mail: evrom@math.nsc.ru

 

UDC 517.95
Semenko Ye. V.
Equivalence of boundary velocities and various flow schemes in the inverse boundary value problem of aerohydrodynamics

Considering the flat potential steady-state flow of  an ideal incompressible fluid past a connected contour, we describe the classes of boundary velocities corresponding to one contour for all possible parameters of the incoming flow. We present a solution to the inverse problem of  hydrodynamics: Calculate the contour from the boundary velocity for arbitrary flow schemes, including the case that the flow lacks stopping points on the contour. We consider the question of equivalence of boundary velocities, meaning their correspondence with the same contour.

Keywords: inverse problem of aerohydrodynamics, boundary velocity, flow scheme, flow parameters.
Pp. 98–110.

Semenko Yevgenii Veniaminovich
 Novosibirsk State Pedagogical University, 28 Vilyuiskaya str. Novosibirsk 630126, Russia. E-mail: semenko54@mail.ru

 

UDC 517.9:517.947:534.14:534.2
Sukhinin S. V., Yurkovsky V. S.
Tsunami waveguides  

We show that the submerged ridges that are periodic (in one direction), chains of submerged mountains and islands possess waveguide properties for long waves. We state a boundary value problem whose generalized eigensolutions describe the generalized eigenwaves on the fluid surface localized near the structure. We show the existence of generalized eigensolutions and eigenwaves localized near a periodic structure above or below the surface. We prove that in a neighborhood of zero there exists a pass band.  We study resonance phenomena near periodic in one direction tsunami waveguides and show that two types of resonance phenomena may occur in these problems: spatially localized and synchrophasotronic.  

Keywords: waveguide, periodic structures, spectral properties of the Laplacian, tsunami.
Pp. 111–124.

Sukhinin Sergey Viktorovich
Yurkovsky Vadim Sergeevich
Lavrent'ev Institute of Hydrodynamics  Siveruan Division of the RAS, 15 Acad. Lavrent'ev av. Novosibirsk 630090, Russia. E-mail: sukhinin@hydro.nsc.ru; yvs2000@gmail.com

 

UDC 517.926:517.27
Shevchenko G. V.
A numerical method for solving an optimal control problem with fixed endpoints of trajectories and a convex functional

We propose a numerical method for solving the problem of taking a nonlinear system to the zero state while minimizing a  nonnegative convex functional, whose particular cases include the problem of minimizing resource or energy consumption. The method is based on the maximum principle and approximations of solid bodies by families of simplices. The properties of coverings of solid bodies by simplices enable us to justify the convergence of the method.

Keywords: admissible control, optimal control, convex functional.
Pp. 125–135.

Shevchenko Gennadii Vasil'evich
Sobolev Institute of Mathematics, Siberian Diovision of the RAS 4 Acad. Koptyug av. Novosibirsk 630090 Russia E-mail: shevch@math.nsc.ru

 

UDC 519.865.3
Shmyrev V. I.
The method of meeting trajectories for a linear production-exchange model

We study the exchange model of economics whose participants include both consumers and companies producing goods. The production capacities of the companies are restricted by the expenses of a certain single resource. We study in detail the version of the model with fixed budgets of the participants. We present and justify a method for finding the equilibrium, which develops the original approach of polyhedral complementarity. Under a rather slight assumption of nondegeneracy we show that the algorithm enables us to obtain the equilibrium state in finitely many steps.

Keywords: exchange model, economic equilibrium, price vector, polyhedral complementarity, simplex-type algorithm.
Pp. 136–147.

Shmyrev Vadim Ivanovich
Sobolev Institute of Mathematics Siberiam Division of the RAS 4 Acad. Koptyug av. Novosibirsk 630090 Russia E-mail: shvi@math.nsc.ru

Home • Editorial Board • Contents • Russian page