On fundamental groups of compact Hausdorff spaces

We discuss which groups can be realized as the fundamental groups of compact Hausdorff spaces. In particular, we prove that the claim ``every group can be realized as the fundamental group of a compact Hausdorff space' is consistent with the Zermelo-Fraenkel-Choice set theory.

     

On an adjoint functor to the Thom functor

We construct a right adjoint functor to the Thom functor, i.e., to the functor which assigns the Thom space to a vector bundle .

     

Application of new numerical algorithm for solving the Navier—Stokes equations for modelling the work of a viscometer of the physical pendulum type

A model is proposed, which describes the work of the viscometer sensor of the physical pendulum type. The model enables the obtaining of data on fluid viscosity directly from the measurement of the settling frequency of sensor oscillations or the amplitude of these oscillations. To describe the sensor operation a numerical computational algorithm is developed. This method enables the solution of a wide class of three-dimensional laminar fluid flow problems involving moving solids of arbitrary geometry. The results of testing the proposed numerical technique are presented.     

Moment and forces exerted on the inner cylinder in eccentric annular flow

This paper presents results of numerical modeling for analysis of the moment and forces exerted on an eccentrically positioned rotating inner cylinder due to the annular flow between two cylinders with parallel axes. Laminar stationary fully developed flows of Newtonian and power law fluid flows are considered. An impact of annulus geometry, flow regime, and fluid characteristics are studied. The study indicates that the moment exerted on the inner cylinder increases monotonically with the eccentricity. Forces acting on the inner cylinder include pressure and viscous friction. The pressure forces provide a predominant contribution. When eccentricity does not exceed a certain critical value, the radial force pushes the inner cylinder to the channel wall. When eccentricity is large enough, the radial force reverses its sign, and the inner cylinder is pushed away from the outer wall. Circumferential component of the force has always the same direction and induces precession of the inner cylinder.     

Kinetic equations for a finely dispersed rarefied gas suspension

Starting from the Liouville equation, the kinetic equations for a finely dispersed rarefied gas-particle medium are derived. The size of the suspension particles is assumed to be much less than the free path of the gas molecules, while their density is so small that interaction between the particles can be neglected. It is shown that in general the dynamics of this gas suspension can be described by a system of two kinetic equations, which differ radically from the Boltzmann equations. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 165–171, March–April, 1994.     

Experimental and theoretical investigation of boundary layer perturbations on a low-aspect-ratio wing

Laminar-turbulent transition in a boundary layer of low-aspect-ratio wing was investigated. Experiments clarifying the flow structure, its mean and oscillatory characteristics were carried out accompanied by linear stability analysis of the wind tunnel data on the laminar flow velocity profiles. Theoretical results obtained in a parallel flow approximation are in a good agreement with the experimental data on disturbances evolution at the initial stage of transition to turbulence. The study was supported by the Ministry of Education and Science of the Russian Federation (Grant No. RNP 2.1.1.471) and Russian Foundation for Basic Research (Grant No. 03-01-06145)