Principles of the analytic description of fluid flow in network models of porous media

A method of calculating the conductivity of capillary networks which combines percolation concepts of conductivity in the neighborhood of the flow threshold with the results obtained using the effective medium model is proposed. The conductivity calculated theoretically is compared with experimental data. Water and oil phase permeabilities for combined flow through a capillary network are determined as an example of the use of the relations obtained. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 79–83, January–February, 2000.     

Stability analysis of non-autonomous stochastic Cohen–Grossberg neural networks

This paper is concerned with pth moment exponential stability of stochastic Cohen–Grossberg neural networks (SCGNN) with time-varying connection matrix and delays. With the help of Lyapunov function, stochastic analysis technique and the generalized Halanay inequality, a set of novel sufficient conditions on pth moment exponential stability for SCGNN is given. These results are helpful to design exponentially stable non-autonomous Cohen–Grossberg neural networks when stochastic effects are taken into consideration in practice. This work was supported in part by the High-Tech Research and Development Program of China under Grant No. 2006AA04A104, the National Natural Science Foundation of China under Grant No. 50677014, China Postdoctoral Science Foundation under Grant No. 20070410300, the Hunan Provincial Natural Science Foundation of China under Grant No. 07JJ4001.     

Vertical impact on a thin torus of elliptic cross-section floating on the surface of an ideal incompressible fluid

The logarithmic-exponential asymptotics for a thin torus are constructed using the boundary integral equation method. The asymptotics of the main impact characteristics, including the added mass and moment of inertia, are found. Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 144–152, March–April, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (projects Nos. 96-15-96 81 and 99-01023).     

Determination of the shape of the shocks ahead of a transverse jet injected into a supersonic flow

The three-dimensional shape of the shock wave formed ahead of a sonic jet flowing out into a supersonic flow through the surface of a sharp cone is determined. The shape of the wave in the longitudinal and transverse cross-sections of the model is constructed using schlieren photographs taken for various angles of rotation and freestream Mach numbers M=1.75–3. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 41–44, March–April, 1998. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 95-01-00709a).     

Study of stable and unstable jet flows on the basis of the boltzmann equation

Free supersonic underexpanded jets are studied using a direct method conservative splitting scheme for solving the Boltzmann equation. Numerical solutions for a jet flowing into a vacuum and into a fluid-filled space are presented for the following ranges of the parameters: Knudsen number 10⁻⁶<Kn<∞ and pressure ratio 10<n<∞. The solutions are compared with experimental data. Instabilities associated with free turbulence effects in the mixing layer are detected for low Kn numbers. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 153–157, March–April, 1998. The work was carried out with support from the Russian Foundation for Fundamental Research (project No. 96-01-00829).     

Properties of the nonequilibrium high-velocity “Tails” of the molecular distribution function in plane couette flow of a compressible gas

The results of an analytic and numerical investigation of the properties of the high-velocity “tails” of the distribution function are given for the solution of the BGK model of the kinetic Boltzmann equation for plane Couette flow of a compressible gas. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 183–190, July–August, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00573; grant in support of leading science schools No. 96-15-9603).     

Nonlinear regimes of convection of an elasticoviscous fluid in a closed cavity heated from below

The two-dimensional thermal convection of a elasticoviscous fluid in a horizontal cylinder with a square cross-section heated from below is investigated. For describing the rheological properties of the fluid the Oldroyd model with the upper convective derivative is used. The investigation is carried out numerically using the finite-difference method. The instability limits of mechanical equilibrium with respect to monotonic and oscillatory perturbations are determined. Supercritical convection regimes are investigated numerically. Perm. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 5–11, July–August, 2000. This work was carried out with financial support from the Program of State Financial Support for Leading Science Schools (grant No. 96-15-96084).     

Properties of hypersonic separated flows at moderate reynolds numbers

The hypersonic rarefied flow past a flat plate with a transverse barrier and past a plate with a bend in the generator (a compression angle) is studied at Reynolds numbers Re≤10⁴. Direct statistical modeling (Monte Carlo method) is used to investigate the characteristics of the separated flow formed on the plate as a function of the Reynolds number, the surface temperature, the barrier dimensions, and the internal degrees of freedom of the molecules. The results obtained are compared with those for analogous high-Re flows. The possibility of using the similarity criteria derived for the continuum flow regime is considered. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 134–144, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 97-01-00577) and the Program of State Support for Leading Scientific Schools (grant No. 96-15-9606).     

Two-parameter model of a turbulent flow with a dispersed-particle admixture

Using a two-point probability density function for the particle distribution over velocities and coordinates, a closed model of the particle effect on the turbulent flow characteristics is formulated. The processes of turbulent dissipation and turbulent energy transfer across the spectrum are studied. Different models of two-phase turbulence are compared. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 40–56, July–August, 1998. The work received financial support from INTAS (grant No. 94-4348) and the Russian Foundation for Basic Research (project No. 98-01-00-353).     

Pulse testing of wells in reservoirs with a nonlinear seepage law

Non-steady-state flows through porous media generated by pulse excitation are studied for flows following obeying a law with a limiting pressure gradient. The phenomena of approach to the steady-state and steady-state hysteresis due to the limiting pressure gradient are investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 104–110, May–June, 1998. The study was supported by the Russian Foundation for Basic Research (project No. 96-01-0748).     

Transition to turbulence in supersonic jets of nitrogen and argon

Laminar-turbulent transition in the mixing layer of supersonic nitrogen and argon jets has been studied experimentally using a local pulse diagnostic technique based on the Rayleigh light scattering effect. It was found that, in the argon jet, the transition to turbulence occurs at smaller Reynolds numbers than in the nitrogen jet. Among the possible reasons for this, the effects of the specific heat ratio and the second viscosity on the transition to turbulence are discussed. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 196–200, May–June, 1998. The work received financial support from the Russian Foundation for Basic Research (project No. 96-01-01565).     

Nonequilibrium kinetics of the gas-phase reactions of high-velocity molecules: Description by perturbation methods and simulation by statistical methods

Data on the numerical solution of a system of kinetic Boltzmann equations for a homogeneous multicomponent mixture of reacting gases with molecules of different “colors” that change in the reactions are given. The solution is obtained using a well-known version of the direct statistical simulation (Monte-Carlo) method, namely, the majorant frequency method, under conditions when the molecules belonging to the high-velocity “tails” of the corresponding distribution functions enter into the color change reaction. The properties of the numerical solution are compared with solutions obtained within the framework of the usual perturbation methods. It is shown that to obtain correct solutions over the range of threshold molecular velocities it is necessary to modify substantially the procedure of the perturbation method, while the traditional approach can be used only on the range of thermal particle velocities. Earlier, this was definitely established for distributions of the reacting molecules over their internal degrees of freedom and for the distributions of reactant-molecules participating in a high-threshold reaction. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 176–184, May–June, 2000. The work was carried out with financial support from the Russian Foundation for Fundamental Research (project No. 96-01-00573) and the Government Program for Leading Science Schools (grant No. 96-15-9603).     

Passivity of uncertain neural networks with both leakage delay and time-varying delay

In this paper, the passivity problem is investigated for a class of uncertain neural networks with leakage delay and time-varying delay as well as generalized activation functions. By constructing appropriate Lyapunov–Krasovskii functionals, and employing Newton–Leibniz formulation and the free-weighting matrix method, several delay-dependent criteria for checking the passivity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.     

Delay-independent exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms

Different from the approaches used in the earlier papers, in this paper, the Halanay inequality technique, in combination with the Lyapunov method, is exploited to establish a delay-independent sufficient condition for the exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms. Moreover, for the deterministic delayed Cohen–Grossberg neural networks, with or without reaction–diffusion terms, sufficient criteria for their global exponential stability are also obtained. The proposed results improve and extend those in the earlier literature and are easier to verify. An example is also given to illustrate the correctness of our results.     

Convective instability of a plane horizontal layer of weakly conducting fluid in alternating and modulated electric fields

The electrothermoconvective instability of a plane horizontal layer of weakly conducting fluid in a modulated vertical electric field is investigated. The analysis is based on the electrohydrodynamic approximation. The stability threshold in the linear approximation is found using Floquet’s theory. The effect of periodic modulation on the fluid behavior is studied in both the presence and the absence of the constant component of the electric field. It is shown that modulation can stabilize the unstable ground state or destabilize fluid equilibrium, depending on the amplitude and frequency. In addition to a synchronous or subharmonic response to an external forcing, the instability may be associated with two-frequency (quasiperiodic) perturbations. The cases of weightlessness and a transversely stratified fluid in a static gravity field are considered. Madrid, Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 31–38, May–June, 2000. The investigations whose results are presented in this paper were supported by the Russian Foundation for Basic Research (project No. 98-01-00507).     

Contact holographic interferometer for studying the deformation of small-curvature shells of revolution

The strains of a curvilinear surface are determined using holographic interferometry. Equations are derived to interpret the interference fringes for a shell of revolution. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 176–182, May–June, 2006.     

Nonlocal turbulent transport in a buoyant vortex ring during the ascent of a thermal in a stratified atmosphere

The flow initiated by a hot gas cloud (thermal) in a stratified atmosphere is calculated on the basis of theκ-ε turbulence model and the transport model for the Reynolds stresses and turbulent fluxes and the results obtained are compared The nonlocal nature of the turbulent transport in a vortex ring and its effect on certain flow characteristics are explained In particular, the calculations carried out using the Reynolds stress model show much slower cooling of the temperature-vortex torus than those based calculated on theκ-ε-model Modification of theκ-ε-model to take the effect of curvature of the streamlines approximately into account makes it only partially possible to reproduce the results obtained on the basis of the Reynolds stress model Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 12–20, January–February, 1999. The research was carried out with support from the Russian Foundation for Basic Research (project No. 95-01-00544a).     

Propagation of a thermal detonation wave in a water-corium system

The problem of the unsteady propagation of a thermal detonation wave in a high-temperature-melt-water system up to the steady-state regime is considered on the basis of the three-dimensional and three-temperature vapor explosion model. The basic laws of wave evolution are analyzed and the wave structure is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 115–125, July–August, 2000. The work was supported by the Russian Foundation for Basic Research (project No. 98-02-17766) and the International Science and Technology Center (project No. 408).     

Three-dimensional supersonic turbulent flows past conical bodies

The results of the numerical simulation of supersonic three-dimensional flow past sharp-nosed cones with circular and elliptic cross-sections in the turbulent shock-layer flow regime are presented. The calculations are performed in the local conical approximation using the system of Reynolds equations and the differential one-equation turbulence model. The numerical solutions are obtained by means of an implicit constant-direction finite-difference scheme. The emphasis is placed on the investigation of the transverse flow separation and the flow features associated with the turbulent flow regime. St.Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 99–105, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 99-01-00735).     

Observation of standing waves of large amplitude in harmonic Faraday resonance

Stationary two-dimensional gravity waves on the free surface of a homogeneous fluid in a rectangular vessel in the presence of vertical oscillations excited in harmonic Faraday resonance with identical frequencies are investigated. For the second mode, the dependence of the amplitude on the excitation frequency is found and the wave profiles are obtained. The experimental results are compared with the theoretical model. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 185–188, January–February, 2000. The work was supported by the Russian Foundation for Basic Research (project No. 99-01-01080) and CONACYT (Mexico, Catedra Patrimonial, S. Ya. Sekerzh-Zen’kovich, Ref. 489100-2, Exp. 950060).