Unsteady motion of a fluid near a disk rotating in a magnetic field

The effect of a magnetic field on the velocity distribution in a fluid close to an unsteadily rotating disk is investigated.Notation r, , and z coordinates in the radial, circular, and axial directions - t time - u, v, and w radial, circular, and axial velocity components - u₀ radial velocity of external potential flux - v₀ circular velocity of the disk - (t) angular velocity of the disk - p pressure - density - v kinematic viscosity - B₀ characteristic of the applied magnetic field - electrical conductivity of fluid - R and Z dimensionless coordinates in the radial and axial directions - =Z/2 dimensionless coordinate - T dimensionless time - U, V, and W radial, circular, and axial components of dimensionless velocity - P dimensionless pressure - a, , and ₀ constants with dimensionality t^–1 - m, n, and positive numbers - k =a constant - = = B ₀ ² / parameter characterizing the magnetic field     

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     

Response of differently axially excited spinning liquid columns

Summary A solidly rotating finite liquid column consisting of frictionless liquid is subjected to various axial excitation modes. The response of the free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic range (<2₀). Differences of the various cases are presented.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - axial excitation amplitude - elliptic case (>2₀) - hyperbolic case (<2₀) - liquid density - surface tension - liquid surface displacement - _n damping factor - phase angle - acceleration potential - ₀ rotational speed - , ₁,₂ axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response     

Preparation of YBa2Cu3O7 ? δ Thin Films by the Self-Template Sputtering Method

Using the self-template technique, c-axis-oriented epitaxial YBa₂Cu₃O_{7 –} thin films have been prepared in situ on LaAlO₃ substrate by the d.c. magnetron sputtering method. The properties of thin film dependence on the deposition conditions of the two-step self-template method have been systematically investigated. By optimizing the parameters, high-quality YBCO thin films with T _c0 90 K, T _c 1 K, R _s (77 K, 10 GHz)500 were reproducibly obtained. The best sample grown under optimal conditions gave a low R _s of 330 at 77 K, 10 GHz, which can be used in a microwave field.     

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.     

Electron-phonon coupling as a mechanism for high-temperature superconductivity

We have solved the Eliashberg gap equations which are valid for arbitrary phonon frequency, (_ph), electron-phonon coupling constant, (), and screened Coulomb interaction, ( ^*). We have used values of (_ph),, and ( ^*) appropriate to the cuprate superconductors, and calculated the density of states, the pair potential., and the value of the gap at T=0 K. Using the linearized Eliashberg equations in the matrix representation, we have calculatedT _c and 2/k T _c . We have found that we can account for the highT _c 's in the cuprates with reasonable values for, ^*, and _ph.     

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.     

Response of a spinning liquid column to axial excitation

Summary The response of a solidly rotating finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀).Notation a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - P liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _02n –1 natural frequency of harmonic axial response With 8 Figures     

Temperature field in a plate containing a system of heat sources

The temperature field is determined in a circular plate with a system of thin extrinsic heat sources.Notation T temperature in the plate with the inclusions - r polar radius - polar angle - time - (r,) coefficient of thermal conductivity - (r,) heat transfer coefficient - C(r,) volume heat capacity - W(r,, ) specific intensity of the heat sources - half thickness of the plate - (x) Dirac's delta function - ¯T finite Fourier cosine transform of the temperature - p parameter for this transformation - T Laplace transform of the temperature - s its parameter - Iv(x) Bessel function with imaginary argument of order - K _v (x) the MacDonald function of order - and dimensionless temperature - Po Pomerantz number - Bi Biot number - Fo Fourier's number - dimensionless polar radius - b₁ ^* dimensionless radius of the circle on which the inclusions are placed - R^* dimensionless radius of the plate Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 495–502, March, 1981.     

Determination of the thermophysical characteristics of alternatively freezing and thawing dispersed media by the method of solving inverse problems of heat conduction

The article explains an algorithm for determining the thermophysical characteristics of dispersed media with phase transitions based on the method of solving inverse problems of heat conduction.Notation r space coordinate - time - T temperature of the specimen - T₀ initial temperature - c_i, c_w, c_sk specific heat of ice, water, and of the organic-mineral skeleton, respectively - c_f, c_m, _f, _m specific heat and thermal conductivity in the frozen and melted zones, respectively - c effective heat capacity - thermal conductivity - p density - ₀, _sb bound and strongly bound moisture, respectively - (T) amount of nonfrozen water - R radius of the cylinder - q() heat flux - I functional - u₁(), U₂() measured temperatures of the specimen at the points r = 0 and r = R, respectively, at the instant - ₁, ₂ degree of confidence of the supplementary information - final instant of time - a, b, k, _s positive constants - L specific heat of melting - N number of grid nodes over space - n number of grid nodes over time - h grid step over space - grid step over time - solution of the conjugate system - s number of iteration Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 292–297, August, 1980.     

Transient two-dimensional diffusion along a high-diffusivity lamina which bisects a half-space

Summary The right half-space is bisected by a high-diffusivity planar sheet which lies along the x-axis. A sudden increase in the potential on (y-axis) causes longitudinal diffusion along coupled with transverse diffusion from into . Restricting to the case of large diffusivity ratio, to , it is demonstrated that the problem possesses a sequence of three distinct time domains in which self-similar solutions become asymptotically valid. The early, intermediate, and late solutions are each functions of only two independent variables; they are universally valid for all parameter values; and they are easily computed and readily applied. Transitions between asymptotics are described by expansions in time, the perturbations being regular in the early-intermediate period but singular in the intermediate-late period. The considered problem is a linear example which affords the opportunity for comparison with Fourier-Laplace analysis, and has application to thermal or electric conduction, diffusion mass transfer, and Darcy-flow of fluid in a fractured or layered porous medium. Methodology and qualitative observations are applicable to more complex nonlinear problems of the same class.This work supported by the U.S. Department of Energy under Contract DE-ACO4-76D00789.A U.S. DOE Facility.     

Paramagnetic resonance in a “dirty” spin-glass

For a spin-glass with nonmagnetic defects (n _m ^1/3l 1, where n _m is the magnetic impurity concentration and l is the mean free path) an absorption function () is derived. Three ranges of temperature and external magnetic field are considered. In the vicinity of the transition the value of () d is estimated as a function of temperature and field.     

Axi-symmetric natural frequencies and response of a spinning liquid column under strong surface tension

Summary The response of a solidly rotating anchored finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined analytically in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀). For the liquid surface displacement the response has been evaluated numerically as a function of the forcing frequency/2 ₀. In addition the first natural stuck-edge frequency has been determined and compared with the slipping case.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - Weber number - z₀ axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response     

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.     

Structure of unidimensional temperature stresses

Using the structural approach, the temperature stresses are examined in a semiinfinite rod, insulated on the lateral faces and rigidly fixed at the end. A comparative analysis is made for three heat-transfer models.Notation k(t) heat flux relaxation function - (t) internal energy relaxation function - T rod temperature - ambient temperature - t time - x coordinate along the rod - _xx(x, t) stress - u(x, t) displacement - (x, t) deformation - c₀=(E/)^1/2 speed of sound in the rod under isothermal conditions - E elasticity modulus - density of the material - _t coefficient of thermal expansion - thermal-conductivity coefficient - a thermal-diffusivity coefficient - b thermal-activity coefficient - c_q=(a/_r)^1/2 velocity of heat propagation - _r heat flux relaxation time - (t) unique Heaviside function Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 5, pp. 912–921, November, 1977.     

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     

Radiation of internal waves during vertical motion of a body through a nonuniform liquid

Energy losses to radiation of internal waves during the vertical motion of a point dipole in two-dimensional and three-dimensional cases are computed.Notation _o(z), p_o(z) density and pressure of the ground state - z vertical coordinate - v, p, perturbed velocity, pressure, and density - H(d 1n _o/dz)^–1 characteristic length scale for stratification - N=(gH^–1–g²c _o ^–2 )^1/2 Weisel-Brent frequency - g acceleration of gravity - c_o speed of sound - vertical component of the perturbed velocity - V vector operator - k wave vector - frequency - d vector surface element - W magnitude of the energy losses - (t), (r) (x)(y)(z) Dirac functions - v_o velocity of motion of the source of perturbations - d dipole moment of the doublet - _o,l length dimension parameters - _o intensity of the source Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 619–623, October, 1980.     

The optical properties and a.c. conductivity of magnesium phosphate glasses

Magnesium phosphate [X MgO-(100–X) P₂O₅] glasses in the composition range [X=20, 25, 30, 40, 45, 50 mol %] have been made. The optical properties and a.c. conductivities were measured and their amorphous nature confirmed by X-ray diffraction technique. The variation of relative density with x was anomalous. In the ultraviolet/visible regions it was found that the fundamental absorption edge is a function of glass compositions and lower absorption coefficients, () follow the so-called Urbach edge. At lower absorption levels (1<<10⁴cm^–1), the width of the tail of localized states in the band gap, E _g, did not vary significantly with glass composition and lay in the range (0.26–0.343) eV. In the high absorption region (()>10⁴ cm^–1), the behaviour of () suggests that there are two different transition energies for electrons in k-space, namely direct allowed transitions and non-direct transitions. In the infrared region at wavelengths =2.5–30 m, the transmission spectrum has four absorption bands. Using the Kramers-Kronig theory, the optical constants (refractive index n and extinction coefficient k) have been determined from the transmission spectrum. The a.c. conductivity, (), real and imaginary dielectric constants, ₁, ₂, and loss factor, tan , have been determined at room temperature in the frequency region, = 2×10⁴–10⁶ Hz. It has previously been established theoretically that () ^s and s was found to be in the range 0.64–0.73, depending on glass composition.     

Functional derivative ofT c with α2(ω)F(ω) for weak coupling anisotropic superconductors

Approximate analytic calculations of the functional derivative ofT _c with respect to ²()F() for anisotropic superconductors are presented, with the primary purpose of identifying the determining material parameters. The square-well model for the phonon-mediated electron-electron interaction, the weak coupling limit ( _c /2T _c 1), and separable anisotropy are used. The general behavior of T _c /²()F() is the same as that found in numerical calculations for the case of small anisotropy, a ²/(–*)1; the regime of * is also discussed.     

Breakup of an anomolously viscous liquid film in a centrifugal force field

An equation is obtained for the breakup radius with consideration of tipping moments and Laplacian pressure forces acting on the liquid ridge at the critical point.Notation K, n rhenological constants - density - surface tension - r current cup radius - R maximum cup radius - r_c critical radius for film breakup - ¯r=¯r=r/R dimensionless current radius - ¯r_c=r_c/R dimensionless critical radius - ₀, _c actual and critical film thicknesses - current thickness - R_r ridge radius - h₀ ridge height - h current ridge height - ₀ limiting wetting angle - current angle of tangent to ridge surface - angle between axis of rotation and tangent to cup surface - angular velocity of rotation - q volume liquid flow rate - v₁ and v meridional and tangential velocities - =4vv _lm/r,=4v_m/r dimensionless velocities - M moments of surface and centrifugal forces - M_v moment from velocity head - p_r pressure within ridge - P_vm pressure from velocity head - p_m, p_pm pressures from centrifugal force components tangent and normal to cup surface - deviation range of breakup radius from calculated value - ¯r_max, ¯r_min limiting deviations of breakup radius - _c angle of tangent to curve _c/°₀=f(¯r) at critical point - t random oscillation of ratio _c/_c Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 51–56, July, 1980.