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Scientific Seminar
"Problems of Continuum Mechanics"
The abstracts of the reports 2000

22 March 2000
Nikiphorov A.I. On modeling suffosian in aquifer. A new mathematical model of release of solid particles by an aqueous flow from a porous bed is proposed. The porous medium is modeled as two overlapping continuous media, one of which is associated with the moving fluids and particles and another with those fixed. Equations defining changes of the function of pore size distribution and particle size distribution are derived. These equations include parameters which are estimated on model presentation of the porous medium as parallel capillary tubes. The appropriate expressions for dynamic porosity and permeability are obtained.

22 March 2000
Soultanov R.A. On some problems of numerical simulation of nonlinear fluid flow. Two-phase fluid flow is considered, one of which is a non-Newtonian fluid. It is known that for small fluid flow velocities Darcy law (linear dependence between fluid flow velocity and pressure gradient) is violated. Numerical simulation in these conditions encounters some problems that are characteristic of only nonlinear fluid flow. Some approaches for their solution are considered. Results obtained are analyzed.

22 March 2000
Gainetdinov R.R. The hydrodynamic investigation of vertical gas wells. As experimental investigations show, the dependence of permeability on pressure is well approximated by monotonous and convex functions. In this work a numerical algorithm is proposed for estimating dependence of permeability on pressure in non-stationary filtration of a gas in porous medium. The inverse problem is solved with the help of the additional a priory information about the structure of the required solution (monotony and convexity of the function).

5 April 2000
Gabidullina A.N, Elesin A.V, Kadyirova A.Sh, Mazurov P.A. On identification filtration coefficient of three-dimensional anysotropic confined aquifier. A preliminary results are given related to constructing regularizational algorithms for identification of filtration coefficient of three-dimensional anysotropic confined aquifier in stationary case.

19 April 2000
Malakhov V.G. An algorithm of the additional-viscosity method for axisymmetrical deformation of shells of revolution. A variant of the additional-viscosity method to solve the problem of large axisymmetrical deflections and stability of elastic and elastoplastic shells of revolution has been proposed. The canonical system of equations for unknown forces, momenta and deflection velocities has been derived. To solve the system an iteration method in combination with the orthogonal sweep method is employed. Results of computations are presented.

19 April 2000
Shikhranov A.N. Nonlinear asymmetric deforming of the shallow shells of revolution with imperfections in the form under the thermal load. Influence of asymmetric initial irregularities in the form of the flexible elastic shallow shells of revolution under the action of moderate heating on the character of deforming is investigated. The problem is considered in geometrically nonlinear statement within the medium-bend theory. Computations presented have been performed for a shallow spherical shell under the linear distribution of the temperature over the shell thickness.

26 April 2000
Malikov A.I. Matrix comparison systems in the dynamic analysis and state estimation of nonlinear continuous and discrete control systems. The modern state-of-the-art in matrix comparisons systems method offered by E.F.Sabaev and advanced during last years in laboratory of stability and control IME KSC RAS is considered. The results obtained are systematized and discussed in comparison which other methods of qualitative analysis of nonlinear systems. Connection of matrix comparison systems with square-law Lyapunov functions and, for linear non autonomous systems, with the evolutionary equations is established. Approaches for construction of matrix comparison systems for adjustable systems with uncertainties and structural changes are given. Prospects of development and application of a matrix comparison systems method for the qualitative analysis and state estimation of nonlinear systems in the light of using opportunities of the modern applied programs MathCad and Matlab are considered.

26 April 2000
Zakirov U.N. Stability of orbits in the frame of Kaluza-Klein's five-dimensional theory. Basing on the concept of the world as energy density (included in the fifth a coordinate), space and of time, the Einstein's five-dimensional equations are solved for the Vaidja-Kerr's metrics (for the case when the gravitational radius depends on the fifth coordinate). Equations of deviation with effective component dependent on the fifth coordinate are obtained. As a result, the stability of orbits for tested particles is investigated relatively bodies with variable energy density. In particular, the Kaplan's stable orbit, nearest to the centre, appears to depend on the fifth coordinate, unlike the classical case.

31 May 2000
Danilaev P.G. The identification of transport processes in inhomogeneous porous mediums. Kazan Technical University. On materials of thesis for Doctor of Sciences Degree, speciality: 05.13.16 - Application of computer facilities, mathematical modeling and mathematical methods in scientific researches. Reviewer DrSc M.KH.Khairullin. Ill-posed problems of the underground hydrodynamics and the heat conduction are investigated. The main attention is given to the coefficient inverse problems for parabolic type equations in connections with their applications. Results derived from corresponding uniqueness theorems are taken as the basic for the algorithms construction.

31 May 2000
Vishnyakova I.V. Modelling of circulation water cooling process and reconstruction of the industrial cooling towers. Kazan Technological University. On materials of thesis for Candidate of Sciences Degree, speciality: 05.17.08 - Processes and apparatuses of chemical technology. Reviewer PhD Fedyaev V.L. Operation of the fills of the industrial cooling towers is considered. A closed mathematical description of their cooling water process is assumed. Results of calculation of the temperature fields are given, the influence of the type and thickness of the fill layer on heat efficiency of the cooling tower is estimated. The empirical dependencies for estimation of coefficients of reverse stirring, mass transfer and wetting of the fill walls are presented. On the basis of the presented investigations recommendations on reconstruction of the considered cooling towers are developed.

7 June 2000
Gainetdinov R.R. Hydrodynamic methods of investigation on the basis of theory of ill-posed problems for gas vertical and horizontal wells. On materials of thesis for Candidate of Sciences Degree, speciality: 01.02.05 - Mechanics of liquid, gas and plasma. Reviewer PhD Shamsiev M.N. Recent progress of oil and gas fields projection theory is closely connected to the development and analysis of mathematical models of the investigated flow processes. An important stage in mathematical models is the solution of the inverse problem. The distinctive feature of inverse problems connected to the research of mathematical models of real oil and gas reservoirs is that the character of the additional information is determined by the possibilities of field experiment.

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