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     

Phase relationships in Si3N4-AIN-MxOy systems and their implications for sialon fabrication

Phase relationships in Si₃N₄-AIN-M_xO_y systems involving -sialon, where M represents lithium, magnesium, calcium, yttrium, neodymium, samarium, gadolinium, dysprosium, erbium and ytterbium are outlined. Their implications for the formation and fabrication of single-phase -sialon and two-phase : sialon ceramics are discussed.     

Theory of the hall effect in strongly correlated Fermi systems

The anomalous properties of the Hall constant in the normal state of high-T_c superconductors are investigated within the Hubbard model. In Mori theory, the frequency dependent Hall constant is given as the sum of its infinite frequency limit and a memory function contribution. The first term (R _H ) was already considered by Shastry et al.¹ In perturbation theory and in the limit of infinite spatial dimensions, the memory function contribution causes the Hall constant to change sign as a function of doping () and to decrease as a function of temperature, if we allow U to be 2W (U: Coulomb repulsion; W: bandwidth). In the limit U , the memory function is calculated via its moments. For frequencies W U, this leads to a decrease of R _H by a factor of (1 + )/2.     

A dilatometric method to measure the thermal diffusivity of nonmetallic liquids

A new method to measure the thermal diffusivity of liquids is presented. It requires determination of the time dependence of the thermal expansion of the liquid when it is subjected to a heat source at the top of the cell containing the liquid. The high accuracy of the method (about 3%) is due to an essential reduction of convective currents and also to the absence of temperature detectors, which generally introduce unwanted perturbations on the thermal Field.Nomenclature Thermal conductivity - c Specific heat - Density - c = specific heat x density - h Newton coefficient - Thermal diffusivity - T, 0 Temperature - tV Electric signal - Calibration coefficient - _exp, _th Volume change of the liquid     

Microstructure and crystallographic texture of rolled polycrystalline Fe3Al

An imperfectly B₂ ordered Fe₃Al aggregate was cast, thermomechanically hot rolled and finally annealed at 870 K. Subsequently, the specimen was rolled at 800–830 K to a strain of 80%. The microstructure and the crystallographic texture of the rolled polycrystalline sample was investigated within the range =20–80%. The microstructure consisted of flat, elongated grains. In numerous grains straight slip lines were detected. Even after =80% recrystallization was not observed. The rolling texture of Fe₃Al considerably deviates from that of non-ordered body centered cubic (b.c.c.) alloys and pure b.c.c. metals. The {111}uvw texture fibre (7-fibre) was very pronounced, while the {hkl}110 fibre (-fibre) was very weak. The {112}110 orientation which represents the strongest texture component in non-ordered b.c.c. alloys did not occur at all. The textures are discussed in terms of the {110}111, {112}111, {112}111 and {123}111 slip systems. The contribution of crystallographic slip of the various types of potential slip systems was simulated by means of the Taylor theory.     

The critical curve in an antiferromagnetic superconductor with nonmagnetic impurities

The critical curve of a transition of the second kind in an antiferromagnetic superconductor (AFS) with nonmagnetic impurities has been studied. The AFS is described by using the mean-field model given by Nass, Levin, and Grest and assuming a one-dimensional electron band. We find that the points on the critical curve satisfy the thermodynamic stability condition for 0₁/₀5.04 and 0.49H_Q/₀1.64.Here ₁ is the inverse lifetime of a conduction electron for nonmagnetic impurity scattering,H _Q is the antiferromagnetic molecular field, ₀ is the zero-temperature order parameter of a superconductor in the absence ofH _Q and impurities. Further, ₁ and H_Q denote the values of these quantities for points on the critical curve. For ₁/₀>5.04 and H_Q/₀>1.64, the phase transition from the superconducting to the normal state is always of the second kind. Some thermal properties of the system near the critical curve have also been investigated and we find that these depends dramatically on the impurity concentration.     

Analysis of the effect of the decomposition of char-forming heat-insulating materials on the free discharge of a gas mixture

The article presents results of a numerical solution of a nonsteady problem on the free discharge of a mixture of gases from a hemispherical volume with allowance for thermal decomposition of heat-insulating materials.Notation V volume - S area - t - P p - T - u v - Q q, dimensional and dimensionless time, pressure, temperature, TIM decomposition rate, and heat flux - adiabatic exponent - R gas constant - density - H specific enthalpy - c specific heat - thermal conductivity - , , _s dimensionless complexes - coefficient expressing the radiative properties of the gas medium and the heat-transfer surface - Stefan-Boltzmann constant Indices 0 initial state and scale factors - s surface - coke - M TIM material - P pyrolysis front - A ablation front - v volatile degradation products - adiabatic conditions - c completion of discharge Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 787–793, May, 1988.     

In-Plane Fourfold Symmetry of the Upper Critical Field Observed in La(Sr)214 Single Crystals

In order to establish the existence of in-plane anisotropy of the upper critical field H _c2 (), the out-of-plane resistivity _c measurements were performed on La(Sr)214 single crystals with rectangular and cylindrical shape under rotating magnetic field applied within the ab-plane. Although observed _c shows non-sinusoidal twofold symmetry, clear fourfold symmetry was obtained after subtracting twofold sinusoidal component in _c which is due to the unavoidable misalignment of the magnetic field with respect to ab-plane. H _c2 () is estimated from the extracted fourfold component of _c with the flux flow theory. Angular dependence of H _c2 () was well fitted by cos(4). Since the fourfold component of H _c2 () was largest at = n/2, which corresponds to the a-axis direction, the present results strongly suggest the type symmetry in La(Sr)214. In addition, the difference in fourfold component of H _c2 at = n/2 and n/2+/4 was found to increase with decreasing temperature.     

Crack growth in lamellar titanium aluminides containing beta phase precipitates

Mode-I fracture behavior of fully-lamellar polycrystalline -TiAl + ₂-Ti₃Al intermetallic alloys and the role of Ti-V base -phase precipitates of different thermodynamic stability have been studied using a finite element method. A rate-dependent, finite-strain, crystal-plasticity based materials constitutive model is used to represent the deformation behavior of both the -TiAl + ₂-Ti₃Al lamellar matrix and the -phase precipitates. Within the matrix colonies, fracture is assumed to take place throughout the ₂-Ti₃Al lamellae. In addition, fracture along colony boundaries and matrix/precipitate interfaces is considered. The constitutive behavior of all fracture interfaces is modeled using a cohesive-zone formulation. The analysis is carried out using the commercial finite element program Abaqus/Standard within which the material state is integrated using an Euler-backward implicit formulation. The results obtained show that the main mechanism of crack growth is nucleation of secondary cracks along ₂-Ti₃Al lamellae ahead of the main crack and their subsequent link-up with the tip of the main crack. The resulting fracture resistance curve acquires the characteristic step-wise shape. Both stable and metastable -phase precipitates are found to have a beneficial effect on the fracture resistance of the material. However, the effect is not very significant and metastable -phase precipitates appear to be a little bit more beneficial. All these findings are consistent with their experimental counterparts.     

Experimental study of the boundary between single-phase convection and boiling in underheated cryogenic liquids

The effect of pressure and underheating on the position of the boundary between heat-transfer regimes in liquid helium and hydrogen is investigated.Notation q heat flux - p pressure - =T_s–T underheating - T_s saturation temperature - T temperature of liquid - T=T_wa – T T_s=T_wa – T_s - T_wa temperature of heat-emitting surface - A,a, B, b, C constants - m, n indices - Nu Nusselt number - Ra Rayleigh number - thermal conductivity - coefficient of cubical expansion - kinematic viscosity - g acceleration - standard deviation Indices 01 conditions of convection-boiling transition - 02 conditions of boiling-convection transition Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 5–11, January, 1982.     

Evolution of transient thermal processes in layer counterflow apparatuses and heat exchangers

Results are given of an analytic investigation of transient processes inside counterflow apparatuses and heat exchangers with temperature disturbance in one of the heat carriers at the entry to the apparatus.Notation =(t–t₀)/(T₀–t₀),=(T–t₀)/(T₀ s-t₀) relative temperatures - t, T temperatures of material and gas respectively - t₀, T₀ same for the initial state - Z=[ _Vm₁/c(1–w/w_g)] [–(y₀–y)/w_g] dimensionless time - m₁=1/(1+Bi/) solidity coefficient - B₁=( _FR/) Biot number - _{F V} heat-exchange coefficients referred to 1 m² surface and 1 m³ layer - R depth of heat penetration in a portion - portion heat conductivity coefficient - shape coefficient (=0 for a plate,=1 for a cylinder,=2 for a sphere) - c, C_g heat capacities of material and gas respectively - , _g volumetric masses - w, W_g flow velocities of material and gas - y distance from the point of entry to the heating heat carrier - y₀ heat-exchanger length - Y= _Vm₁y/W_gC_{g g} dimensionless coordinate - m=cw/C_g– _gW_g water equivalent ratio Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, vol. 20, No. 5, pp. 832–840, May, 1971.     

Structure and Magnetism of the Composite Crystal Ca0.824CuO2

We have studied the magnetic state from a viewpoint of crystallographic features of the 1-D chain compound Ca_0.824CuO₂. A possible spin-hole arrangement in the magnetically coexisting state was determined by analyzing the local structural distortion in the CuO₂ chain by means of a modulated-crystal-structure analysis. The essential periodic sequence expected is (: up- and down-spin, : hole), which can be regarded as a kind of spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain.     

o′-β′ sialon ceramics

Powders of Si₃N₄, Al₂O₃ and SiO₂ were mixed with Y₂O₃ as sintering aid and hot-pressed to form o- sialon. During sintering, the o phase preferentially precipitated in the temperature region of 1550 to 1600 °C, and the phase precipitated at temperatures of 1700 °C and above. The resultant microstructure consisted of dual phases of o and . The mechanical properties of o- sialon were improved with increasing amount of the phase. When SiO₂ required for the formation of the o phase was all included in the grain boundary phase, o- sialon exhibited a three-point bending strength as much as 1400 MPa. The oxidation resistance of o- sialon is expected to improve due to the presence of the o phase, but actually was not so good due to the presence of the grain-boundary glassy phase and impurities.     

An extension of the theory of oscillating cup viscometers

The theory of the fluid motion in the interior of an oscillating or rotating cup is reexamined. The quantity of interest in viscometry is the torque exerted by the fluis on the sides and rims of the cup. In this paper expressions for the torque are obtained for geometries for which the cup height approaches a fluid boundary layer thickness. Interest in such geometries is due to viscosity measurements made in mixtures in the critical region where cups of small height are used in order to minimize gravity effects.Nomenclature D() Torque on the cup, Eq. (5) - E() Truncation error term, Eq. (24) - h Internal half-height of a filled cup or the height of the liquid in a partially filled cup - I Moment of inertia of cup and suspension system - I Moment of inertia of fluid inside cup - I _n Modified Bessel function of order n - J _{i, n} Defined in Eq. (13) - R Radius of the cup - S _n Defined in Eq. (7) - S _n Defined in Eq. (10) - x Variable 2 ₀/ - z Variable 2 ₀^1/2 - () Angular displacement of the cup - Boundary layer thickness - Logrithmic decrement - Laplace transform variable - ₀ Dimensionless height h/ - Frequency ratio / ₀ - Kinematic viscosity - ₀ Dimensionless radius R/ - Density of liquid - Dimensionless time ₀ t - Phase angle of oscillation - Angular frequency of oscillation with liquid present in cup - ₀ Angular frequency of oscillation in a vacuum     

Effect of Gamma Irradiation on the Piezoelectric Properties of K2Sr4Nb10O30–K6Li4Nb10O30 Solid Solutions

The effect of gamma irradiation on the dielectric ( ₃₃/₀, tan) and piezoelectric (d ₃₁, g ₃₁, K _p, Q _m) properties of ₂Sr₄Nb₁₀O₃₀–K₆Li₄Nb₁₀O₃₀ solid solutions (tetragonal tungsten bronze structure) was studied as a function of K₆Li₄Nb₁₀O₃₀ content. The results demonstrate that increasing the gamma dose to 9 × 10⁵ Gy reduces ₃₃/₀ and tan. With increasing Li⁺ content (filling of triangular channels), d ₃₁, g ₃₁, K _p, and Q _m increase. The results are interpreted in terms of the generation of stable defects and effective redistribution of the energy of gamma radiation over the ceramic sample.     

Tilted and Crossing Vortex Chains in Layered Superconductors

No Heading In presence of the Josephson vortex lattice in layered superconductors, small c-axis magnetic field penetrates in the form of vortex chains. In general, structure of a single chain is determined by the ratio of the London [] and Josephson [_J] lengths, = /_J. The chain is composed of tilted vortices at large s (tilted chain) and at small s it consists of crossing array of Josephson vortices and pancake-vortex stacks (crossing chain). We study chain structures at the intermediate s and found two types of phase transitions. For 0.6 the ground state is given by the crossing chain in a wide range of pancake separations a [2–3]_J. However, due to attractive coupling between deformed pancake stacks, the equilibrium separation can not exceed some maximum value depending on the in-plane field and . The first phase transition takes place with decreasing pancake-stack separation a at a = [1 – 2]_J, and rather wide range of the ratio , 0.4 0.65. With decreasing a, the crossing chain goes through intermediate strongly-deformed configurations and smoothly transforms into the tilted chain via the second-order phase transition. Another phase transition occurs at very small densities of pancake vortices, a [20 – 30]_J, and only when exceeds a certain critical value 0.5. In this case small c-axis field penetrates in the form of kinks. However, at very small concentration of kinks, the kinked chains are replaced with strongly deformed crossing chains via the first-order phase transition. This transition is accompanied by a very large jump in the pancake density.PACS numbers: 74.25.Qt, 74.25.Op, 74.20.De     

Notch tip stress distribution in strain hardening materials

Using the results of elastic-plastic stress analyses for notched bars, it is shown that a modified form of slip-line field solution can satisfactorily explain the variation of longitudinal stress ahead of notch tips in strain hardening materials.

---

Résumé En utilisant les résultats d'analyses de contrainte élastoplastique dans le cas de barres entaillées, on montre qu'il est possible d'utiliser une forme simplifiée de solution du champ des lignes de glissement pour expliquer de façon satisfaisante la variation des contraintes longitudinales en avant d'extrémités d'entaille dans des matériaux susceptibles d'un écrouissage.

---

Nomenclature _yy longitudinal tensile stress in the notch tip plastic zone - _xx transverse stress in the x-direction - _zz transverse stress in the z-direction - k yield stress in shear - ₀ yield stress in tension - ₀ ^* strain hardened yield stress (flow stress) - _{0/* c} flow stress at notch tip - _total total strain _pl plastic strain _l principal strain - _{1 c} maximum principal strain at notch tip - _1pl plastic strain in they-direction - _{1 cp1} E_{1 pl} at notch tip - _eff effective plastic strain - _{c eff eff} at notch tip - ₀ yield strainC Stress decay constant in the notch tip region - /e_pl linear strain hardening rate - n strain hardening exponent in power hardening law - 2 flank angle of notch - distance from notch tip - p notch tip radius - k _I applied stress intensity for Mode I loading - E Young's modulus - V _c crack tip opening displacement     

Deformation behaviour of retained β phase inβ-eutectoid Ti-Cr alloys

Plastic deformation mode and its relation to tensile properties were investigated in retained phase of-eutectoid type Ti-Cr alloys. A plate-like single variant phase is induced during deformation of the most unstable phase having a minimum chromium content required to suppress martensitic transformation. A selected area electron diffraction pattern taken from a boundary region of the stress-induced phase plate can be explained by the idea that a single variant of phase is induced in a {3 3 2} 1 1 3 twin produced during deformation. Anisotropy in population of four phase variants decreases with increasing chromium content. On further increasing chromium content, deformation occurs by slip. Enhanced ductility is obtained in as-quenched Ti-Cr alloys accompanied by phase transformation or {332} 1 1 3 twinning during deformation, phase of as-quenched Ti-Cr alloys changes continuously from commensurate structure with sharp reflections to incommensurate structure with diffuse reflections with increasing chromium content. The obtained results in-eutectoid type Ti-Cr alloys are quite similar to those in-isomorphous type Ti-V alloys.     

Precipitate strengthening mechanisms in magnesium zinc alloy single crystals

The mechanical behaviour of Mg-5.1 wt % Zn alloy single crystals was studied in the 4.2 to 300° K temperature range. Quenched crystals have activation energies and volumes best associated with the cutting of small clusters of Zn atoms by dislocations. Fully hardened crystals contain fine ₁ and occasional ₂ precipitates with an average ₁ interparticle spacing of 330 to 660 Å. Strengthening in these crystals is mainly ascribed to the cutting of ₁ particles by dislocations. In the overaged condition ₁, ₂ and equilibrium particles are present and lead to a considerable temperature-dependence unusual for an overaged condition. Analysis of this temperature-dependence suggests that below 77° K the relatively easy cutting of ₁ particles by dislocations takes place in addition to the cutting of ₂ and particles. Above 77° K the difficult cutting of ₂ and particles alone controls the deformation, ₁ being more easily cut with the aid of thermal fluctuations.     

High-accuracy bench mark solutions to natural convection in a square cavity

A fourth-order high-accuracy finite difference method is presented for the bouyancy-driven flow in a square cavity with differentially heated vertical walls. The two bench mark solutions against which other solutions can be compared were obtained. The present solution is seemed to be accurate up to fifth decimal. The proposed scheme is stable and convergent for high Rayleigh number, and will be applicable to general problems involving flow and heat transfer, especially in three dimensions.List of symbols a thermal diffusivity - g gravitational acceleration - h mesh length in the x-direction - k time step - L side length of cavity - Pr Prandtl number - Ra Rayleigh number = gTL ³/a - t time - T _c, T _h surface temperatures (see Fig. 1a) - T temperature - T temperature difference = T _h - T _c - u, v velocity in the x and y directions, respectively - x, y coordinates - x, y mesh lengths in the x- and y-directions, respectively Greek symbols volumetric expansion coefficient - kinematic viscosity - stream function - vorticity