Influence of Saffman's lift force on the motion of a particle in a Couette layer

The article is concerned with the study of the effect of E. S. Asmolov's corrections to Saffman's lift force for the wall vicinity and a nonzero ratio of Reynolds numbers. It is shown in what way these corrections change the particle paths in a Couette layer and the conditions of deposition.Notation x=X/D, y=Y/D dimensionless longitudinal and transverse coordinates - u=U _p /U , =V _p /U dimensionless projections of particle velocity on the longitudinal and transverse axes - =tU /D dimensionless time - U ²/(18D) Stokes number - = _g / _p , coefficient of the gas kinematic viscosity - particle diameter - /D - _g , _p densities of the gas and particle material - du/d - dv/d - P _s Saffman's force - C coefficient in the formula for Saffman's force - yRe _d ^1/2 - A v _r Re _d ^1/2 - 3.08 - Re V _r / - Re _k ²/)U _g /Y - A Re/Re _k ^1/2 - Re _d U D/ - V _r ((U _g –U _p )²+V _p ² )^1/2 Indices g refers to gas parameters - p refers to the parameters of particles - 0 at the time momentt=0 - S Saffman's force - k Reynolds number based on the velocity gradient - based on velocity - r relative velocity - x projection on thex axis     

Coarsening of δ′ (Al3Li) and composite precipitates in an Al-2.5% Li-0.15% Zr alloy

The early stage coarsening behaviour of (Al₃Li) precipitates and composite precipitates, consisting of (Al₃Zr) core enveloped by a shell, in an Al-2.5% Li-0.15% Zr alloy has been studied at 443, 473 and 503 K by conventional transmission electron microscopy using superlattice dark-field images. Coarsening kinetics of precipitates was found to exhibit considerable deviation from the t ^1/3 law corresponding to diffusion control at 473 and 503 K. This deviation may be explained either by the operation of a surface-reaction controlled coarsening mechanism represented by t ^1/2 law, or by the presence of a slower precoarsening stage preceding diffusion-controlled coarsening. The particle-size distributions of precipitates were not in accordance with either the earlier theoretical predictions or the normal distribution. They were symmetrical or slightly skewed to the left, and particle sizes twice the average were observed. The coarsening kinetics of composite precipitates, was found to be rather different from that of ; a diffusion model which yields t ^1/n law with n changing from 1/4 to 1/6 as the coarsening progresses, was predicted. The composite precipitates have exhibited quite a narrow and rather symmetrical size distribution.     

Effective Łojasiewicz inequalities in semialgebraic geometry

The main result of this paper can be stated as follows: letV ⁿ be a compact semialgebraic set given by a boolean combination of inequalities involving only polynomials whose number and degrees are bounded by someD > 1. LetF, G[X₁,, X_n] be polynomials with degF, degG D inducing onV continuous semialgebraic functionsf, g:VR. Assume that the zeros off are contained in the zeros ofg. Then the following effective ojasiewicz inequality is true: there exists an universal constantc ₁ and a positive constantc ₂ (depending onV, f,g) such that for allxV. This result is generalized to arbitrary given compact semialgebraic setsV and arbitrary continuous functionsf,g:V . An effective global ojasiewicz inequality on the minimal distance of solutions of polynomial inequalities systems and an effective Finiteness Theorem (with admissible complexity bounds) for open and closed semialgebraic sets are derived.     

On the temperature dependence of the London penetration depth in a superconductor

In the framework of the electron-phonon theory of superconductivity [1], it is shown that the magnetic field penetration depth _L increases like a certain power of temperature atTT _c due to the low-lying excitations in the phonon spectrum. For the acoustic phonons with the density of states ² the penetration depth increases T ⁵. The origin of such a high power ofT is the same as that in the case of resistivity of the normal metal: the phonon corrections to the electromagnetic vertex should be taken into account, and major terms (T ³) cancel, the surviving ones having a higher power ofT. The possibility of linear and quadratic terms in _L(T) is discussed in a model of electrons interacting with two-level centers [2].     

Theory of the Surface Tension Maximum of Liquid 3He

Recently Matsumoto et al. performed very precise measurements of the surface tension of liquid ³He, (T), at low temperatures and found that (T) exhibits a small maximum at about 100 mK. Existing theories are unable to explain this anomaly. On the basis of a local approximation for the entropy in which the Fermi liquid effect is included, we can evaluate the variation of (T), (T)=(T)–(0), as a function of T and of the number density (or the interaction strength). It is found that (T) consists of two terms; a T² term and T⁴ ln T term. We predict that, for the density of real liquid ³He, exhibits a tiny minimum and a small but relatively larger maximum. This prediction explains qualitatively and quantitatively all salient features of the observed (T).     

Experimental investigation of the effects of stress rate and stress level on fracture in polystyrene

The effects of stress rate and stress level on fatigue crack propagation in compression-moulded single-edge notched specimens (0.25 mm in thickness) of polystyrene are reported. Values of the stress rate are obtained from the formula = 2v(_max – _max),, wherev is the frequency and _max, _min are the maximum and minimum stresses of the fatigue cycle. Different levels of are achieved by changing the frequency while keeping _max, _min at fixed values. The effect of the stress level is investigated by keeping and _min constant and varying _max andv. The results show that when the kinetic data are plotted as l/t against the energy release rateG ₁, a relatively small effect of the stress rate is observed. If the same data are treated as l/N againstG ₁, a decrease in l/N with test frequency is seen. The increase in the level of _max results in a higher crack speed. The critical crack length is found to be practically the same for all stress-rate experiments. A decrease in the critical crack length is observed with the increase in stress level. Analysis of craze distribution around the crack path shows that the extent of crazing decreases with the increase in stress rate and increases with the increase in stress level. For all experimental conditions, the ratio of the second moment to the square root of the fourth moment of the histograms of craze density along directions normal to the crack path is found to be constant throughout the slow phase of crack propagation. This result supports a self-similarity hypothesis of damage evolution proposed in the crack layer model.     

Torsional boundary layer effects in shells of revolution undergoing large axisymmetric deformation

Numerical and asymptotic solutions are developed to the equations governing large torsional, axisymmetric deformation of rubberlike shells of revolution. The shell equations include large-strain geometric and material nonlinearities, transverse shear deformation, transverse normal stress and strain, and torsion. Both analyses allow ready incorporation of different strain-energy density functions. In the asymptotic analysis, the interior solution corresponds to that of nonlinear membrane theory and contains a primary boundary layer. The edge-zone solution gives a secondary boundary layer that, for large strain, divides into a bending-twisting moment component and a torsional-membrane component. The boundary layer behavior is illustrated for a clamped neo-Hookean cylinder subjected to internal pressure and axial torque.List of symbols Latin symbols a General dependent variable - a ^(mn) Terms of the asymptotic expansion of a(x) - b Characteristic length - c Scalar curvature components in the normal direction - c , c , , c Cosine of , respectively - C Material constant with units of a Young's modulus - e _i Deformed local orthonormal basis associated with (, s, n)(x ₁, x ₂, x ₃) coordinates - Undeformed cylindrical coordinate basis - Intermediate coordinate basis - g Shear correction factor - H Horizontal stress resultants - l ₁ Strain invariant - k Scalar curvature components - L Undeformed cylinder length - M Moment resultants - M _r, M , M _z Moment resultant components in the basis - N Membrane stress resultants - p Internal pressure - p _H, p _v Horizontal and vertical surface loads, respectively - p _i Thickness-averaged surface tractions - Q Transverse shear stress resultants - , r Radial coordinate prior to, after deformation - R Undeformed cylinder radius - , s Meridional coordinate prior to, after deformation - s , s _x, , s Sine of , respectively - , S Reference surface prior to, after deformation - S ₁, S ₂ Shear stress resultants parallel to the reference surface - S ₃ Average transverse normal stress resultant - t Undformed shell thickness - T Axial torque - V Vertical stress resultants - w Two-dimensional strain-energy density function - w _n Terms in expansion for w - W Three-dimensional strain-energy density function - x Undeformed axial coordinate in cylinder - , z Axial coordinate prior to, after deformation     

First and Second Order Phase Transitions and Magnetic Hysteresis in a Superconducting Plate

The self-consistent solutions of the nonlinear Ginzburg–Landau equations, which describe the behavior of a superconducting plate of thickness 2D in a magnetic field H parallel to its surface (provided that there are no vortices inside the plate), are studied. We distinguish two classes of superconductors according to the behavior of their magnetization M(H) in an increasing field. The magnetization can vanish either by a first order phase transition (class-I superconductors), or by a second order (class-II). The boundary S _I–II, which separates two regions (I and II) on the plane of variables (D,), is found. The boundary (D,) of the region, where the hysteresis in a decreasing field is possible (for superconductors of both classes), is also calculated. The metastable d-states, which are responsible for the hysteresis in class-II superconductors, are described. The region of parameters (D,) for class-I superconductors is found, where the supercooled normal metal (before passing to a superconducting Meissner state) goes over into a metastable precursor state (p-). In the limit 1/2 and D( is the London penetration depth) the self-consistent p-solution coincides with the analytic solution, found from the degenerate Bogomolnyi equations. The critical fields H ₁, H ₂, H _p, H _r for class-I and class-II superconducting plates are also found.     

A thermally stimulated current technique for measuring the molecular parameters of Pebax,a polyether-block amide copolymer

The primary relaxation peaks of Pebax copolymer having a soft segment, poly (tetramethylene glycol) (PTMG) and a hard segment, polyamide 12 (PA12) are located at –69.5 and 18° C for a raw sample and at –71.5 and 4° C when the sample is recrystallized after fusion using the thermally stimulated current (t.s.c.) method. A comparison is made of rapid and slow cooling t.s.c. on hard-segment molecules. Applying the fractional polarization method, the modes _PTMG and _PA have been analysed. The parameters (such as activation energy and relaxation time) associated with the dipolar relaxation process of Pebax have been calculated. The maximum energy observed for modes _PTMG and _PA is 1.47 eV at – 66° C and 1.34 eV at 1° Q respectively. The elementary processes that constitute the modes _PTMG and _PA obey a compensation law with compensation temperatureT _c = –43° C and compensation relaxation time _c, = 3.4 x 10^–2 sec for mode _PTMG, andT _c = 66° C and _c = 2.8 x 1 0^–4 sec for mode _PA.     

Shear viscosity of the B phase of superfluid3He

The shear viscosity (T) in the Balian-Werthamer (BW) state of superfluid ³ He is calculated variationally throughout the region 0t 1(t=T/T _c) from the transport equation for Bogoliubov quasiparticles. Coherence factors are treated exactly in the calculation of the collision integral. The numerical result for =_s= _s(T)/_n(T_c) agree very well with experiment in the range 0.8t1.0. Analytic expressions = 0.577 (1–1.0008t) and =1–(23/64) [=(T)/k _B T] are obtained in the low-temperature region and in the vicinity ofT _c, respectively. From the numerical analysis it is shown that the latter equation is valid only in the temperature range 0.9997t1.0.Supported by the Research Institute for Fundamental Physics, Kyoto University.     

Die Herleitung von Schalengleichungen über ein erweitertes Variationsprinzip bei Berücksichtigung der Querschubverzerrungen

Ohne ZusammenfassungBezeichnungen L Bezugsgrößen für dimensionslose Koordinaten - L charakteristische Schalenabmessung - t Schalendicke - Schalenparameter - körperfeste, krummlinige, dimensionslose Koordinaten der Schalenmittelfläche - Dimensionslose Koordinate in Richtung der Schalennormalen - i, j,...=1,2,3 Indizierung des dreidimensionalen Euklidischen Raumes - ,,...=1,2 Indizierung des zweidimensionalen Riemannschen Raumes - (...), Partielle Differentiation nach der Koordinate - (...), Kovariante Differentiation für Tensorkomponenten des zweidimensionalen Raumes nach der Koordinate - (...)| Kovariante Differentiation für Tensorkomponenten des dreidimensionalen Raumes nach der Koordinate - Variationssymbol - a ,a ₃ Basisvektoren der Schalenmittelfläche - V Verschiebungsvektor - U ,U ₃ Verschiebungskomponenten des Schalenraumes - v ,w,w ,W Verschiebungskomponenten der Schalenmittelfläche - Verhältnis der Metriktensoren des Schalenraumes und der Schalenmittelfläche - _ik Verzerrungstensor des Raumes - _{(, )}, Symmetrische Verzerrungstensoren der Schalenmittelfläche - _{[, ]} Antimetrischer Term des Verzerrungsmaßes - ^, Spannungstensor - n ,m ,q Tensorkomponenten der Schnittgrößenvektoren - p ,p,c Tensorielle Lastkomponenten     

Slip flow past an approximate spheroid

Summary Creeping axisymmetric slip flow past a spheroid whose shape deviates slightly from that of a sphere is investigated. An exact solution is obtained to the first order in the small parameter characterizing the deformation. As an application, the case of flow past an oblate spheroid is considered and the drag experienced by it is evaluated. Special well-known cases are deduced and some observations made.Notation A _n, B_n, C_n, D_n, E_n, F_n, b₂, d₂ Constants - a, b radii of spheres - coefficient of sliding fraction - D drag - , _m parameters characterizing the deformation of the sphere - c a(1+) - viscosity coefficient - - dimensionless coordinate - I _n Gegenbauer function - P _n Legendre function - Stream function - U stream velocity at infinity     

Thermomechanic behavior of a polymer upon its formation in a crystallization process: Theoretical principles,hypotheses, and mathematical model

A model of thermomechanic behavior of a polymer upon its formation in a crystallization process is proposed. Based on methods of nonequilibrium thermodynamics governing relationships are obtained which make it possible to establish the dependence of the final degree of crystallicity of the material on the history of the crystallization process and to explain the mechanism of formation of the remanent stresses in a polymer article.Notation u translation vector - v velocity vector - acceleration vector - absolute temperature - density - c specific heat capacity - deformation tensor - strain tensor - specific enthropy - U ^* internal energy - z specific free enthalpy - _i internal parameters of state - t time - q heat flux vector - matrix of heat conduction coefficients - W ^* energy dissipation - F vector of mass forces - the 4th rank tensor of elastic pliabilities - matrix of heat expansion coefficients - tensor of contribution of structural variations to deformation - function of equilibrium value ^* - p mean pressure - deviator of the tensor of deformations - spherical part of the deformation tensor - deviator of the tensor of stresses - K volume modulus - unity tensor - Q enthalpy of the crystallization process - Q _eq enthalpy of the equilibrium crystallization process - _g glass transition temperature - ^*() the curve obtained in the equilibrium crystallization process - f final degree of crystallicity Institute of Mechanics of Continuous Media of the Ural Branch of the Russian Academy of Sciences, Perm', Russia. Institute of Technical Chemistry of the Ural Branch of the Russian Academy of Sciences, Perm', Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 479–485, May–June, 1995.     

Thermodynamic Functions of Fermi Gas with Quadruple BCS-Type Binding Potential with dx2 - y2 d_{x^2 - y^2 } -Wave-Pairing Symmetry

A gas of spin 1/2 fermions with an interaction V+W = -||^-1 _k,k g _k,k(k)(k) b _k b _-k - 2 _k(k)n _k+ n _k-, where n _k± = a _k±, b _k = a _k+ a _k- and a _k, satisfy Fermi anticommutation relations, is investigated in the -pairing case. W+V₄ is nonzero only within a thin layer of one-fermion energies around the chemical potential , and (k) denotes the characteristic function of the corresponding range of momenta. Two cases are studied: 1⁰ = 0, 2⁰ = 0.10025 eV. In the first case the system exhibits a first order transition, in the second, the transition is second order. Temperature dependence of the system's thermodynamic functions is examined and compared with that of the s-pairing case.     

Structural Changes in the Surface Layers of PdHx Alloys Caused by the Hydride Phase Decomposition

By the method of optical microscopy, we perform the in-situ investigation of the plane polished surfaces of PdH _x alloys (with video recording of the processes of transformation) in the case of their rapid cooling at a rate of 11–20°C·sec^–1 from T _c = 292°C ( = 1.97MPa) with simultaneous lowering of the pressure of hydrogen within the temperature range 100–160°C. In the course of decomposition of the PdH_0.24 alloy according to a scheme ₀ + , the formation of nuclei of the - and -phases and their growth were not detected. However, we observe a simultaneous coherent transformation of the entire surface accompanied by the formation of a surface topography similar to the modulated structures formed as a result of the spinodal decomposition. We discuss the possibility of realization of spinodal decomposition under the described experimental conditions.     

Analytical Theory of DC SQUIDS Operating in the Presence of Thermal Fluctuations

A comprehensive analytical theory of symmetric DC SQUIDs is presented taking into account the effects of thermal fluctuations. The SQUID has a reduced inductance < 1/ where = 2LI_c/₀, L is the loop inductance, ₀ is the flux quantum, and I_c is the critical current of the identical Josephson junctions which are assumed to be overdamped. The analysis, based on the two dimensional Fokker–Planck equation, has been successfully performed in first order approximation with considered a small parameter. All important SQUID characteristics (circulating current, current-voltage curves, transfer function, and energy sensitivity) are obtained. In the limit 1( = 2k_BT/I_c0 is the noise parameter, k_B is the Boltzmann constant, and T is the absolute temperature) the theory reproduces the results of numerical simulations performed for the case of small thermal fluctuations. It was found that for < 1 the SQUID energy sensitivity is optimum when is higher than 1/, i.e., outside the range for which the present analysis is valid. However, for 1 the energy sensitivity has a minimum at L = L_F , where L_F = ( ₀ /2) ²/k_B , and therefore, in this case, the optimal reduced DC SQUID inductance is _opt = 1/, i.e., within the range for which the present analysis is valid. In contrast to the case of an RF SQUID, for a DC SQUID the transfer function decreases not only with increasing L/L_F but also with increasing (as 1/). As a consequence, the energy sensitivity of a DC SQUID with < 1/ degrades more rapidly (as ⁴ ) with the increase of than that of an RF SQUID does (as ² ).     

Mixed convection flow of micropolar fluid over an isothermal plate with variable spin gradient viscosity

Summary A steady two-dimensional mixed convection flow of viscous incompressible micropolar fluid past an isothermal horizotal heated plate with uniform free stream and variable spin-gradient viscosity is considered. With appropriate transformations the boundary layer equations are transformed into nonsimilar equations appropriate for three distinct regimes, namely, the forced convection regime, the free convection regime and the mixed convection regime. Solutions of the governing equations for these regimes are obtained by an implicit finite difference scheme developed for the present problem. Results are obtained for the pertinent parameters, such as the buoyancy parameter, in the range of 0 to 10 and the vortex viscosity parameters, =0.0, 1.0, 3.0, 5.0 and 10.0 for fluid with Prandtl number Pr=0.7 and are presented in terms of local shear-stress and the local rate of heat transfer. Effects of these parameters are also shown graphically on the velocity, temperature and the couple stress distributions. From the present analysis, it is observed that both the momentum boundary layer and the thermal boundary layer increase due to an increase in the vortex viscosity of the fluid.List of symbols f, F, dimensionless stream function for forced convection free convection and mixed convection, respectively - g acceleration due to gravity - Gr_x local Grashof number - j micro-inertia density - m ₂₃ distribution of couple stress - N microrotation component normal to (x, y)-plane - p pressure of the fluid - q dimensionless rate of heat transfer - Re_x local Reynolds number - T temperature of the fluid in the boundary layer - T temperature of the ambient fluid - T temperature at the surface - u, v thex andy-components of the velocity field - U free stream velocity - x, y axis in direction along and normal to the plate Greek thermal diffusivity - coefficient of volume expansion - vortex viscosity parameter - stream function - , , nondimensional similarity variables - buoyancy parameter (=Gr _x Re _x ^/5/2 ) - vortex viscosity - density of the fluid - v kinematic coefficient of viscosity - spin-gradient viscosity - stream function - dimensionless skin-friction - fluid viscosity     

Structural features of Σ = 19, [110] GaAs tilt grain boundaries

= 19, [110] tilt grain boundaries have been observed to facet parallel to particular planes; the facets lie along _A/ _B, ( )_A/ )_B and ( )_A/( )_B. The structural unit of the = 19 ( )_A/( )_B [110] boundaries consists of 5- and 7-member rings, which are similar to the core structure of a/2[110] edge dislocations. The polarities in each grain on either side of the boundaries has been confirmed by CBED methods; a lower number of anti-site type cross-boundary bonds occur along the boundaries compared to when the polarity of one grain is reversed. The presence of 7-member rings and anti-site cross-boundary bonds results in a more open atomic structure at the boundary, shortening the distance between the first and the second {331} atomic planes from the boundary plane by 40%.     

Pressureless sintering of SiC-TiC composites with improved fracture toughness

Composites of SiC-TiC containing up to 45 wt% of dispersed TiC particles were pressureless sintered to 97% of theoretical density at temperatures between 1850°C and 1950°C with Al₂O₃ and Y₂O₃ additions. An in situ-toughened microstructure, consisted of uniformly distributed elongated -SiC grains, matrixlike TiC grains, and yttrium aluminum garnet (YAG) as a grain boundary phase, was developed via pressureless sintering route in the composites sintered at 1900°C. The fracture toughness of SiC-30 wt% TiC composites sintered at 1900°C for 2 h was as high as 7.8 MPa·m^1/2, owing to the bridging and crack deflection by the elongated -SiC grains.     

Response of a spinning liquid column to pitch excitation

Summary The response of a solidly rotating liquid bridge consisting of inviscid liquid is determined for pitch excitation about its undisturbed center of mass. Free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic (<2₀) excitation frequency range.List of symbols a radius of liquid column - h length of column - I ₁ modified Besselfunction of first kind and first order - J ₁ Besselfunction of first kind and first order - r, ,z cylindrical coordinates - t time - u, v, w velocity distribution in radial-, circumferential-and axial direction resp. - mass density of liquid - free surface displacement - velocity potential - ₀ rotational excitation angle - ₀ velocity of spin - forcing frequency - _1n natural frequency - surface tension - acceleration potential - for elliptic range >2₀ - for hyperbolic range >2₀