Kerr constant of water

Measurements are conducted of the Kerr constant of ultrapure water with resistivity 10⁷ · cm. Values of the Kerr constant of (3.26 ± 0.10) · 10^-7 and (2.29 ± 0.07) · 10^-7 esu were obtained at a temperature of 30 °C for wavelengths of 441.6 nm and 632.8 nm.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 157–160, January–February, 1976.The authors wish to express their appreciation to D. D. Ryutov for useful discussion.     

Waves in a plasma with Hall dispersion

In a magnetohydrodynamic approximation, an investigation is made of the propagation of waves in a plasma, whose characteristic frequency is much less than the collision frequency of the electrons _e ^–1. It is assumed that the magnetic field is sufficiently strong so that the equality _ee1 will be satisfied, where _e is the cyclotron frequency of the rotation of the electrons. With large magnetic Reynolds numbers (R_m1), which are characteristic for many astrophysical problems, this latter condition leads to a need to take account of dispersion effects connected with Hall currents, in the absence of Joule dissipation. The dispersion equation for the propagation of small perturbations is analyzed in the limiting cases of weak dispersion and of a wave propagating along the magnetic field. In the case of weak dispersion, an equation is derived for nonlinear waves. The solutions are found in the form of stationary solitons. The region of such solutions is analyzed. A typical example of a medium with Hall dispersion is an interplanetary plasma, in which the parameter _ee is generally great.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 108–113, May–June, 1974.     

An experimental study on vortex breakdown in a differentially-rotating cylindrical container

The vortex breakdown phenomenon in a closed cylindrical container with a rotating endwall disk was reproduced. Visualizations were performed to capture the prominent flow characteristics. The locations of the stagnation points of breakdown bubbles and the attendant global flow features were in excellent agreement with the preceding observations. Experiments were also carried out in a differentially-rotating cylindrical container in which the top endwall rotates at a relatively high angular velocity _t, and the bottom endwall and the sidewall rotate at a low angular velocity _sb. For a fixed cylinder aspect ratio, and for a given relative rotational Reynolds number based on the angular velocity difference _t–_sb, the flow behavior is examined as |_sb/_t| increases. For a co-rotation (_sb/_t>0), the breakdown bubble is located closer to the bottom endwall disk. However, for a counter-rotation (_sb/_t<0), the bubble is seen closer to the top endwall disk. For sufficiently large values of _sb, the bubble ceases to exist for both cases.     

Influence of rotation of the body and exterior vorticity on the heat transfer near the stagnation point of a blunt body in a supersonic stream

A study is made of the influence of longitudinal vorticity on the hypersonic viscous shock layer near an axisymmetric cooled surface that rotates about the longitudinal axis with angular velocity ₁ [1, 2]. The equations of the viscous shock layer for the neighborhood of the stagnation point are simplified on the basis of the theory of a thin three-dimensional shock layer [1, 2]. The results are given of some calculations of the influence of the parameters and ₁ on the heat transfer and the structure of the shock layer in the case of steady flow. An iterative numerical method proposed by the author [1] is used, and a modification to accelerate the convergence of the iterations is proposed. It is noted that the parameters and ₁ have characteristic ranges of variation, which depend on the Mach and Reynolds numbers, for which the distributions of the streamlines in the shock layer are qualitatively different.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 179–182, May–June, 1984.I thank V. Ya. Neiland and Yu. D. Shevelev for helpful discussions of this paper.     

Spectral and correlation characteristics of the turbulent boundary layer on an extended flexible cylinder

In marine geophysical seismological prospecting extensive use is made of towed receiving systems consisting of extended flexible cylinders containing acoustic sensors over which the water flows in the longitudinal direction. The boundary layer pressure fluctuations on the cylinder surface are picked up by the sensors as hydrodynamic noise. This paper is concerned with the study of the energy and spacetime characteristics of the pressure fluctuations in the turbulent boundary layer on an extended flexible cylinder in a longitudinal flow. The pressure fluctuations on the cylinder surface have been investigated experimentally for Re_X=(2–4)·10⁷, a dimensionless diameter of the pressure fluctuation sensors d _p ⁺ =d_pu^*/=500, where d_p is the sensor diameter, u^* the dynamic viscosity, and the viscosity coefficient, and frequencies 0.02311.259 (=^*/U). The spectral and correlation characteristics of the pressure fluctuations on the surface of the flexible cylinder are found to differ from the corresponding characteristics for a rigid cylinder [1–4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i aza, No, 5, pp. 49–54, September–October, 1989.     

Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions

In this paper, we show that the maximum principle holds for quasilinear elliptic equations with quadratic growth under general structure conditions.Two typical particular cases of our results are the following. On one hand, we prove that the equation (1) {ie77-01} where {ie77-02} and {ie77-03} satisfies the maximum principle for solutions in H ¹()L(), i.e., that two solutions u ₁, u ₂H¹() L() of (1) such that u ₁u₂ on , satisfy u ₁u₂ in . This implies in particular the uniqueness of the solution of (1) in H ₀ ¹ ()L().On the other hand, we prove that the equation (2) {ie77-04} where fH^–1() and g(u)>0, g(0)=0, satisfies the maximum principle for solutions uH¹() such that g(u)¦Du|{²L¹(). Again this implies the uniqueness of the solution of (2) in the class uH ₀ ¹ () with g(u)¦Du|{²L¹().In both cases, the method of proof consists in making a certain change of function u=(v) in equation (1) or (2), and in proving that the transformed equation, which is of the form (3) {ie77-05}satisfies a certain structure condition, which using ((v₁ -v ₂)⁺)ⁿ for some n>0 as a test function, allows us to prove the maximum principle.     

Instability of a plane axisymmetric flow with a shear discontinuity in the velocity profile

It is proposed to investigate the stability of a plane axisymmetric flow with an angular velocity profile (r) such that the angular velocity is constant when r < r_O – L and r > r_O + L but varies monotonically from ₁ to ₂ near the point r_O, the thickness of the transition zone being small L r_O, whereas the change in velocity is not small ¦₂ – ₁¦ ₂, ₁. Obviously, as L O short-wave disturbances with respect to the azimuthal coordinate (k=m/r_O 1/r_O) will be unstable with a growth rate-close to the Kelvin—Helmholtz growth rate. In the case L=O (i.e., for a profile with a shear-discontinuity) we find the instability growth rate _O and show that where the thickness of the discontinuity L is finite (but small) the growth rate does not differ from _O up to terms proportional to kL 1 and 1/m 1. Using this example it is possible to investigate the effect of rotation on the flow stability. It is important to note that stabilization (or destabilization) of the flow in question by rotation occurs only for three-dimensional or axisymmetric perturbations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 111–114, January–February, 1985.     

Messung der Gewebetemperatur mit infrarotem Thermometer in einer Trockenanlage

Zusammenfassung Es wurde eine theoretische Analyse der kontaktlosen Temperaturmessung des an der Spann-, Trocken- und Fixiermaschine bearbeiteten Gewebes vorgenommen. Der Einfluß der Trocknerwand ist durch die Korrektive Funktion ausgedrückt, zu deren Festlegung ein allgemein anwendbares Diagramm zusammengestellt wurde. Dabei wird die Tatsache berücksichtigt, daß die Messung in einem beschränkten Teil des Spektrums durchgeführt wird, welcher außerhalb der Wasserdampfabsorptionsbänder liegt.

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Measuring temperature of textiles in driers with infrared thermometer

The paper undertakes a theoretical analysis of contactless temperature measurement of textiles processed on a stretching, drying and fixation machine. The effect of the drier wall is expressed through a corrective function for whose determination a universal diagram has been established. The measurements have been performed in a narrow part of the spectrum lying outside the water vapour absorption bands.

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Formelzeichen B W· m^–2 Effektive Wärmestromdichte durch Strahlung - K _i Radiationskoeffizient für Oberflächei - q W · m^–2 Wärmestromdichte durch Strahlung - T K Temperatur - t °C Temperatur - dtj Kroneckersches Symbol - Emissionsgrad der Oberfläche - m Wellenlänge - _ij Radiationskoeffizient - _T W·m ^–2 ·K ^–4 Koeffizient in der Gleichung (2) - Winkelkoeffizient für Strahlung zwischen Oberflächen 1, 2 - – Korrektionsfunktion - W·m ^–2 Wärmestromdichte des schwarzen Körpers Indizes c Gewebe - M Meßwert - w Trocknerwand     

Existence theorem for a minimum problem with free discontinuity set

We study the variational problem Where is an open set in ⁿ ,n2gL ^q () L (), 1q<+, O<, <+ andH _n–1 is the (n–1)-dimensional Hausdorff Measure.     

Qualitative behavior of dissipative wave equations on bounded domains

The qualitative behavior of solutions of the mixed problem u_tt = u-a(x)u_t in IR x , u=0 on IR x , is studied in the case when a>0 and IRⁿ is bounded. Roughly speaking, if aa_min>0, then solutions decay at least as fast as exp t( –1/2a_min), with the possible exception of a finite dimensional set of smooth solutions whose existence is associated with a phenomenon of overdamping. If a_max is sufficiently small, depending on , then no overdamping occurs.Partially supported by NSF grant NSF GP 34260.This work was partially supported by the National Science Foundation under Grant No. GP 34260     

Mixed convection flow over a vertical plate with localized heating (cooling), magnetic field and suction (injection)

An analysis is carried out to study the effects of localized heating (cooling), suction (injection), buoyancy forces and magnetic field for the mixed convection flow on a heated vertical plate. The localized heating or cooling introduces a finite discontinuity in the mathematical formulation of the problem and increases its complexity. In order to overcome this difficulty, a non-uniform distribution of wall temperature is taken at finite sections of the plate. The nonlinear coupled parabolic partial differential equations governing the flow have been solved by using an implicit finite-difference scheme. The effect of the localized heating or cooling is found to be very significant on the heat transfer, but its effect on the skin friction is comparatively small. The buoyancy, magnetic and suction parameters increase the skin friction and heat transfer. The positive buoyancy force (beyond a certain value) causes an overshoot in the velocity profiles.A mass transfer constant - B magnetic field - C_fx skin friction coefficient in the x-direction - C_p specific heat at constant pressure, kJ.kg^–1.K - C_v specific heat at constant volume, kJ.kg^–1.K^–1 - E electric field - g acceleration due to gravity, 9.81 m.s^–2 - Gr Grashof number - h heat transfer coefficient, W.m².K^–1 - Ha Hartmann number - k thermal conductivity, W.m^–1.K - L characteristic length, m - M magnetic parameter - Nu_x local Nusselt number - p pressure, Pa, N.m^–2 - Pr Prandtl number - q heat flux, W.m^–2 - Re Reynolds number - Re_m magnetic Reynolds number - T temperature, K - T_o constant plate temperature, K - u,v velocity components, m.s^–1 - V characteristic velocity, m.s^–1 - x,y Cartesian coordinates - thermal diffusivity, m².s^–1 - coefficient of thermal expansion, K^–1 - , transformed similarity variables - dynamic viscosity, kg.m^–1.s^–1 - ₀ magnetic permeability - kinematic viscosity, m².s^–1 - density, kg.m^–3 - buoyancy parameter - electrical conductivity - stream function, m².s^–1 - dimensionless constant - dimensionless temperature, K - w, conditions at the wall and at infinity     

Steady axisymmetric flow with vorticity of an inviscid fluid in multistage turbomachines

The direct problem of steady axisymmetric flow of a gas with vorticity through a multistage turbomachine is formulated precisely and a generalized solution is constructed by a variational-difference method. The turbomachine is represented schematically by an annular channel in which there are fixed (₁) and rotating (₂) three-dimensional cascades and channels free of them (₀).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–15, October–December, 1981.     

Rheological properties of skim milk gels at various temperatures; interrelation between the dynamic moduli and the relaxation modulus

The rheological properties of rennet-induced skim milk gels were determined by two methods, i.e., via stress relaxation and dynamic tests. The stress relaxation modulusG _c (t) was calculated from the dynamic moduliG andG by using a simple approximation formula and by means of a more complex procedure, via calculation of the relaxation spectrum. Either calculation method gave the same results forG _c (t). The magnitude of the relaxation modulus obtained from the stress relaxation experiments was 10% to 20% lower than that calculated from the dynamic tests.Rennet-induced skim milk gels did not show an equilibrium modulus. An increase in temperature in the range from 20° to 35 °C resulted in lower moduli at a given time scale and faster relaxation. Dynamic measurements were also performed on acid-induced skim milk gels at various temperatures andG _c (t) was calculated. The moduli of the acid-induced gels were higher than those of the rennet-induced gels and a kind of permanent network seemed to exist, also at higher temperatures. G storage shear modulus,N·m^–2; - G loss shear modulus,N·m^–2; - G _c calculated storage shear modulus,N·m^–2; - G _c calculated loss shear modulus,N·m^–2; - G _e equilibrium shear modulus,N·m^–2; - G _ec calculated equilibrium shear modulus,N·m^–2; - G(t) relaxation shear modulus,N·m^–2; - G _c (t) calculated relaxation shear modulus,N·m^–2; - G ^*(t) pseudo relaxation shear modulus,N·m^–2; - H relaxation spectrum,N·m^–2; - t time,s; - relaxation time,s; - angular frequency, rad·s^–1. Partly presented at the Conference on Rheology of Food, Pharmaceutical and Biological Materials, Warwick, UK, September 13–15, 1989 [33].     

Homogenization of the Robin problem in a thick multilevel junction

We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction that is the union of a domain ₀ and a large number 2N of thin rods with variable thickness of order = (N ^–1). The thin rods are divided into two levels, depending on their length. In addition, the thin rods from each level are -periodically alternated. We investigate the asymptotic behavior of the solution as 0 under the Robin conditions on the boundaries of the thin rods. By using some special extension operators, a convergence theorem is proved.Published in Neliniini Kolyvannya, Vol. 7, No. 3, pp. 336–355, July–September, 2004.     

Scalar Minimizers with Fractal Singular Sets

Lack of regularity of local minimizers for convex functionals with non-standard growth conditions is considered. It is shown that for every >0 there exists a function aC() such that the functional admits a local minimizer uW^1,p() whose set of non-Lebesgue points is a closed set with dim()>N–p–, and where 1<p<N<N+<q<+.     

Untersuchungen des Blasensiedens einiger verflüssigter Gase und ihrer binÄren Mischungen

Zusammenfassung Die Arbeit behandelt das Blasensieden an einer ebenen, horizontalen, 64·10^–4m² gro\en KupferoberflÄche von Stickstoff, Methan, Aethan und Gemischen aus Stickstoff/Methan und Methan/Aethan bei verschiedenen Drücken. Die Messwerte und empirischen Ausgleichskurven sind angegeben. Die Daten für die binÄren Gemische bestÄtigen die Gleichung von Happel und Stephan.

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Heat transfer in nucleate boiling of liquified gases and their binary mixtures

The paper deals with pool boiling of nitrogen, methane, ethane and mixtures of nitrogen/methane and methane/ethane at different pressures. The boiling surface was a horizontal, plan copper disk of 64·10^–4m²· The measured data points and their fit by an empirical correlation are given. For mixtures the correlation of Happel and Stephan provides a good agreement with the results.

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Formelzeichen a₁, a₂, a₃ Konstanten - b₁,b₂ Konstanten - K Konstante - n,n₁,n₂ Konstanten - p Druck Pa, M Pa - p_red reduzierter Druck (p/p_kritisch) - q^* WÄrmestromdichte W/m² - R_p Rauhtiefe m - x Molanteil der leichter flüchtigen Komponente in der Flüssigkeit - y Molanteil der leichter flüchtigen Komponente im Dampf - WÄrmeübergangskoeffi-W m^–2 K^–1zient - _i idealer WÄrmeüber-W m^–2K^–1 - _i gangskoeffizient - realer WÄrmeübergangs-W m^–2K^–1 - _r koeffizient - T Temperaturdifferenz K     

Existence and Uniqueness of Time-Periodic Physically Reasonable Navier-Stokes Flow Past a Body

Let be a three-dimensional exterior domain of class C^2,, 0<<1. Assume that a Navier-Stokes liquid is moving in under the action of a body force F that is time-periodic of period T, and that the velocity of the liquid is zero at spatial infinity. In this paper we show that, if F satisfies suitable conditions, and its norm, in appropriate function spaces, is sufficiently small, there is at least one time-periodic strong solution. Furthermore, the velocity field v of such a solution decays to zero for large |x| as |x|^–1 and its spatial gradient decays as |x|^–2, both uniformly in time. In addition, the pressure p decays like |x|^–2 and its gradient like |x|^–3, for almost all t[0,T]. In the special case where F is time-independent, these solutions are also time-independent and coincide with Finns physically reasonable solutions [4]. Moreover, we show that our time-periodic solutions are unique in a very large class, namely, the class of time-periodic weak solutions satisfying the energy inequality and with corresponding pressure fields verifying mild summability conditions in ×[0,T].     

Thermal stability of composite superconducting tape under the effect of a two-dimensional dual-phase-lag heat conduction model

Thermal stability of composite superconducting tape subjected to a thermal disturbance is numerically investigated under the effect of a two-dimensional dual-phase-lag heat conduction model. It is found that the dual-phase-lag model predicts a wider stable region as compared to the predictions of the parabolic and the hyperbolic heat conduction models. The effects of different design, geometrical and operating conditions on superconducting tape thermal stability were also studied.a conductor width, (m) - A conductor cross sectional area of, (m²) - As conductor aspect ratio, (a/b) - b conductor thickness, (m) - Bi Biot number - B dimensionless disturbance Intensity - C heat capacity, (J m^–3 K^–1) - D disturbance energy density, (W m^–3) - f volume fraction of the stabilizer in the conductor - g(T) steady capacity of the Ohmic heat source, (W m^–3) - g_max Ohmic heat generation with the whole current in the stabilizer, (W m^–3) - G_max dimensionless maximum Joule heating - h convective heat transfer coefficient, (W m^–2 K^–1) - J current density, (A m^–2) - k thermal conductivity of conductor, (W m^–1 K^–1) - q conduction heat flux vector, (W m^–2) - Q dimensionless Joule heating - R relaxation times ratio (_T/2_q) - t rime, (s) - T temperature, (K) - T_c critical temperature, (K) - T_c1 current sharing temperature, (K) - T_i initial temperature, (K) - T_o ambient temperature, (K) - x, y co-ordinate defined in Fig. 1, (m) - thermal diffusivity (m² s^–1) - dimensionless time - _i dimensionless duration time - dimensionless y-variable - _o superconductor dimensionless thickness - dimensionless temperature - _c1 dimensionless current sharing temperature - 1 dimensionless maximum temperature - dimensionless disturbance energy - numerical tolerance - x width of conductor subjected to heat disturbances, (m) - y thickness of conductor subjected to heat disturbances, (m) - dimensionless x-variable - _o superconductor dimensionless width - stabilizer electrical resistivity, () - _q relaxation time of heat flux, (s) - _T relaxation time of temperature gradient, (s) - i initial - sc current sharing - max maximum - o ambient     

Convective stability of a weakly conducting liquid in an electric field

In an inhomogeneously heated weakly conductive liquid (electrical conductivity 10^–12–1 cm^–1) located in a constant electric field a volume charge is induced because of thermal inhomogeneity of electrical conductivity and dielectric permittivity. The ponderomotive forces which develop set the liquid into intense motion [1–6]. However, under certain conditions equilibrium proves possible, and in that case the question of its stability may be considered. A theoretical analysis of liquid equilibrium stability in a planar horizontal condenser was performed in [2, 4]. Critical problem parameters were found for the case where Archimedean forces are absent [2]. Charge perturbation relaxation was considered instantaneous. It was shown that instability is of an oscillatory character. In [4] only heating from above was considered. Basic results were obtained in the limiting case of disappearingly small thermal diffusivity in the liquid (infinitely high Prandtl numbers). In the present study a more general formulation will be used to examine convective stability of equilibrium of a vertical liquid layer heated from above or below and located in an electric field. For the case of a layer with free thermally insulated boundaries, an exact solution is obtained. Values of critical Rayleigh number and neutral oscillation frequency for heating from above and below are found Neutral curves are constructed. It is demonstrated that with heating from below instability of both the oscillatory and monotonic types is possible, while with heating from above the instability has an oscillatory character. Values are found for the dimensionless field parameter at which the form of instability changes for heating from below and at which instability becomes possible for heating from above.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 16–23, September–October, 1976.In conclusion, the author thanks E. M. Zhukhovitskii for this interest in the study and valuable advice.     

Effect of latitudinal temperature gradient on spherical Couette flow

The motion of a viscous thermally stratified liquid in a spherical layer due to rotation of the boundaries of the layer at different angular velocities with nonuniform (latitudinal) heating of the outer boundary is investigated. The investigated problem can be regarded as a very simple qualitative model of some astrophysical and geophysical effects, e.g., flows in planetary atmospheres. The characteristic parameters of the problem are the Reynolds number Re=r_i ²_i/, the ratios of the angular velocities of rotation =_e/_i and of the radiia=r_e/r_i of the outer and inner spheres, and the heating nonuniformity parameter . The Boussinesq approximation is adopted in the investigation: It is assumed that the Reynolds numbers Re are fairly small and the solution is sought in the form of a series of whole positive powers of Re. The first two terms of the series are found in analytical form for arbitrary values of the other characteristic parameters. Possible types of meridional flows are established and the regions of the parameters in which a particular type of circulation takes place are determined. It is shown that a latitudinal temperature gradient on the outer boundary leads to the appearance of new (in comparison with the isothermal case) types of meridional flows. The asymptotic form of the stream function of meridional flow in very thin and very thick layers is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 15–23, March–April, 1975.