Effects of phase fluctuation on a mixture of rotating superfluids

It is shown that if the root-mean-square of the gradient of the phase fluctuation of either of the components exceeds the corresponding inverse of the coherence length or if the chemical potential exceeds ₁ ⁰ or ₂ ⁰ , where is the volume integrals of the interaction function between the components, and ₁ ⁰ , ₂ ⁰ are the densities of the two components, the mixture of two rotating superfluids has an instability.     

Metal-Insulator Transition and Cu K-Edge XANES Studies for Pr1.85Ce0.15CuO4+δ High-Tc Superconductors

Metal-insulator transition near oxygen content parameter –0.018 was observed for electron-doped Pr_1.85Ce_0.15CuO₄₊ (–0.0030.03) cuprates. Cu K-edge X-ray absorption near-edge structure (XANES) studies with nearly identical threshold edge energy E₀ of 8980.8 eV indicate a Cu formal valence smaller than 2 for all samples, which is consistent with the estimated Cu valence of 1.84 for 20.5 K superconductor Pr_1.85Ce_0.15CuO_3.997 and 1.91 for Pr_1.85Ce_0.15CuO_4.03 insulator. The XANES spectrum reflects the Cu 3d ⁿ character where low energy peak A ₁ reflects the 3d ¹⁰ configuration of Cu(I) oxidation state and A ₂ peak reflects the 3d¹⁰ ( for a oxygen ligand hole) configuration for Cu(II) oxidation state. The variation of energy separation E(A ₂–A ₁) is consistent with the observed metal-insulator transition, increases sharply from 2.42 eV for Pr_1.85Ce_0.15CuO_4.018 insulator to 2.74 eV for 15 K underdoped superconductor Pr_1.85Ce_0.15CuO_4.015.     

On a stability theory of non-selfadjoint mechanical systems

Summary The concept of the Hamiltonian functional is generalized in such a way that a bilinear functional results, which plays the role of the Hamiltonian for non-selfadjoint systems. For this generalized Hamiltonian the condition leads to the so called hybrid Galerkin's equations, and the condition , to the load-frequency reationship. This relationship can be interpreted as a surface in the load-frequency space, the projection of which on the load-planes yields the stability boundaries, i.e. the buckling loads.

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Zu einer Stabilitätstheorie nicht-selbstadjungierter mechanischer Systeme

Zusammenfassung Der Begriff des Hamiltonschen Funktionals wird in solcher Weise verallgemeinert, daß ein bilineares Funktional bei nicht-selbstadjungierten Systemen an seine Stelle tritt. Für dieses verallgemeinerte Hamiltonsche Funktional führt die Bedingung auf die sogenannten hybriden Galerkinschen Gleichungen und die Bedingung auf die Last-Frequenz-Funktion. Diese Funktion kann im Last-Frequenz-Raum als eine Fläche aufgefaßt werden, deren Projektion auf die Last-Ebenen die Stabilitätsgrenzen und damit die Knicklasten liefert.

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Dedicated to Professor Kurt Magnus in honor of his sixtieth birthday.     

Viscous response of an anchored spinning liquid column to various axial excitations

Summary For a solidly rotating viscous cylindrical liquid column of finite length the response to axial synchronous, counter- and one-sided excitation is determined for anchored contact lines at the disc-rim. For a rotating column additional responses of inertial waves (hyperbolic range) appear for < 2 ₀, while in the elliptic range < 2 ₀ the sloshing response occurs. The various responses for the free surface displacement have been numerically evaluated. Only in the one-sided exitation case all resonance peaks appear, while for synchronous excitation only the odd resonances and for counter-excitation only the even resonance peaks occur.Notation a radius of column - h length of liquid bridge - I _n modified Bessel function - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution - Weber number - z ₀ excitation amplitude - liquid density - surface tension - surface tension parameter - Ohnesorge number - liquid surface displacement - kinematic viscosity - ₀ rotational speed - dimensionless rotational speed - forcing frequency - dimensionless forcing frequency - dimensionless forcing frequency for non-viscous liquid - a= root of bi-cubic Eq.(33) - root of bi-cubic Eq.(33)     

Order parameters and energies of analytic and singular vortex lines in rotating3He-A

We present the expressions of the generalized Ginzburg-Landau (GL) theory for the free energy and the supercurrent in terms of thed vector, the magnetic fieldH, and operators containing the spatial gradient and the rotation. These expressions are then specialized to the Anderson-Brinkman-Morel (ABM) state. We consider eight single-vortex lines of cylindrical symmetry and radiusR=[2m/]^–1/2: the Mermin-Ho vortex, a second analytic vortex, and six singular vortices, i.e., the orbital and radial disgyrations, the orbital and radial phase vortices, and two axial phase vortices. These eight vortex states are determined by solving the Euler-Lagrange equations whose solutions minimize the GL free energy functional. For increasing field, the core radius of the texture of the Mermin-Ho vortex tends to a limiting value, while the core radius of the texture goes to zero. The gap of the singular vortices behaves liker forr 0, where ranges between and . The energy of the radial disgyration becomes lower than that of the Mermin-Ho vortex for fieldsH6.5H*=6.5×25 G (atT=0.99T _c and forR=10L*=60 µm, or=2.9 rad/sec). ForR 2 _T ( _T is the GL coherence length) or _c2 (upper critical rotation speed), the energies of the singular vortices become lower than the energies of the analytic vortices. This is in agreement with the exact result of Schopohl for a vortex lattice at _c 2. Finally, we calculate the correction of order (1 -T/T _c ) to the GL gap for the axial phase vortex.     

Heat transfer in plane film formation

A mathematical model is obtained for the process of cooling with formation of a planar film. The solution obtained is verified experimentally.Notation mean axial velocity gradient - v_x current axial velocity - v_o initial polymer velocity - v₁ sampling velocity - K draw ratio - deformation rate tensor - x, y, z spatial coordinates - X, Y dimensionless coordinates - L() differential operator - T temperature - T_o initial temperature - T_c temperature of surrounding medium - dimensionless temperature - dimensionless temperature averaged over film thickness - thermal-diffusivity coefficient - 2_o initial film thickness - thermal conductivity - heat-transfer coefficient - f(X) distance function - Bi Biot criterion, Bi_o, Biot criterion calculated for initial film thickness - Gz* modified Graetz criterion - V dimensionless velocity - ₁, ₂, ₃ heat-transfer coefficients produced by radiation, free convection, and forced convection - v_c, _c mean velocity and film half-thickness in formation zone - T₁ calculated temperature value - T₂ experimental temperature value - l formation zone length Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 854–858, November, 1979.     

Nonlinear axisymmetric response of orthotropic thin truncated conical and spherical caps

Summary An approximate analytical solution of the large deflection axisymmetric response of polar orthotropic thin truncated conical and spherical shallow caps is presented. Donnell type equations are employed. The deflection is approximated by a one term mode shape satisfying the boundary conditions. The Galerkin's method is used to get the governing equation for the deflection at the hole. Nonlinear free vibration response and the response under uniformly distributed static and step function loads are obtained. The effect of various parameters is investigated.Notations A, A ^* Inward and outward amplitudes - a, b, h Base radius, inner radius and thickness of the cap - D M h ³/[12(–v ² )] - E ,E Young's moduli - H ^*,H Apex height, dimensionless apex heght:H ^*/h - N _, Stress resultants - p ^1/2 - q Uniformly distributed load - Q,Q₀ Dimensionless load: , dimensionless step load - Q, Q ₀ Dimensionless load: , step load - t, Time, dimensionless time: t - T _A Ratio of nonlinear periodT for inward amplitudeA and the linear periodT _L - w ^* Normal displacement at middle surface - w Dimensionless displacement:w ^*/h - ₁ Linear parameter of static response - Orthotropic Parameter:E /E - Mass density - ₂,₃ Quadratic and cubic nonlinearity parameters - b/a - v ,v Poisson's ratios - Dimensionless radius:r/a - ^*, Stress function, dimensionless stress function: - ₀ ^* ,₀ Linnear frequency, dimensionless frequency: With 7 Figures     

The effect of a circumferential stiffener on the stress in a pressurized cylindrical shell with a longitudinal crack

From a numerical analysis of the Marguerre complex stress function in an integral representation, the effect of a continuous uniform circumferential stiffener upon the stress singularities at the crack tips of a nearby longitudinal crack and the maximum load concentration in the stiffener are calculated and presented in graphical parametric form.

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Zusammenfassung Eine geschlossene zylindrische Hülle unter gleichmässigem inneren Druck hat einen Riß entlang einer Portion einer von ihren Erzeugern. Die Hülle hat auch einen kontinuierlich angefesteten Ringversteifer ringsum ihren Umfang und dicht am Riß. Eine Integraldarstellung ist gefunden worden für die komplexe Spannungsfunktion der Flach-Hülle-Theorie von Marguerre. Die Integralgleichungen sind abgeleitet und gelöst worden durch den IBM 7094 Komputer. Eine Darstellung ist gegeben der Wirkung des Versteifers auf die Spannungseigenheiten an den Riß-Spitzen, und auch der Höchstbelastungskonzentration im Versteifer.

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Résumé Un corps creux cylindrique fermé scus pression intérieure uniforme est supposé d'avoir une fissure dans le sens d'une part d'un de ses générateurs. Le corps creux soit aussi pourvu d'un contrefort annulaire continuellement attaché au corps sur sa circonférence près de la fissure. Une représentation intégrale a été trouvée pour la fonction de tension complexe de la théorie de Marguerre du corps creux sans profondeur. Les équations intégrales sont dérivées et résolues par l'ordinateur IBM 7094. Une démonstration est donnée de l'effet du contrefort sur les particularités de la tension aux pointes de la fissure, aussi bien de la. concentration minimum de charge dans le contrefort.

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Notation A() S+(3+)(1–)[1/3(1–²)]^–1/2B: composite singularity strength defined by Copley [6]. - constant cross-sectional area of the stiffener - a / - B bending singularity strength for =0. (See footnote to (30)) - B , B values of B at x=, x= for 0 - b (Rh)^1/2[3/4(1–²)]^1/4: length scale in shell, with respect to which distances are made dimensionless - c half crack length - CA (),CA() . See footnote to (30) - CS ,CS, CB, CB correction factors S /S, S /S, B /B, B /B - d cut-off distance for integrations on -axis - E modulus of elasticity of shell - E _s modulus of elasticity of stiffener - G Green's function, (22) - h thickness of shell - M _x, M _y dimensionless bending moment resultants - M _x, M _y (p ₀b²)(M _x, M _y): bending moment resultants - M _xy dimensionless twisting moment resultant - M _xy p ₀b²M_xy: twisting moment resultant - M _inf ^sup* see (23a) - N _x, N _y, N _xy dimensionless stress resultants - N _x, N _y, N _xy (p0R)·(N _x, N _y, N _xy): membrane stress resultants - N ₀ tension in stiffener at infinity - N tension in stiffener for perturbation problem - N _inf ^sup* see (23b) - p ₀ pressure inside shell - Q _x, Q _y dimensionless transverse shear resultants - Q _y, Q _x (p ₀b)·(Q _x, Q _y): transverse shear resultants - R radius of shell - S stretching singularity strength for =0 (see footnote to (30)) - S , S values of S at x=, x= for 0 - V Kirchhoff transverse shear (see Fig. 2) - V _x, V _y see Appendix - u, dimensionless displacements in x, y-directions - , v ·(u, ): displacements in x, y-direction - _inf ^sup* see (23c) - dimensionless displacement in z-direction - w {it{p₀R²}/(Eh)}: displacement in z-direction - x dimensionless coordinate along generator - x bx: coordinate along generator - y dimensionless coordinate perpendicular to x-direction in plane of shallow shell - z bx: coordinate perpendicular to x- and y-directions - z dimensionless coordinate normal to shell - z (b ²/R)z: coordinate normal to shell - dimensionless distance of near crack tip from stiffener - b: distance of near crack tip from stiffener - dimensionless distance of far crack tip from stiffener - b: distance of far crack tip from stiffener - strain in stiffener - _x, _y dimensionless strains in x, y-directions in shell - poR/(Eh)( _x , _y ):strains in x, y-directions in shell - (/bh)(E _s/E):defines rigidity of stiffener - · - c/b: dimensionless half crack length - dimensionless stress function - p ₀ Rb ²: stress function - +i: complex stress function This work was supported in part by the National Aeronautics and Space Administration under Grant NsG-559, and by the Division of Engineering and Applied Physics, Harvard University.Now Mary E. Fama.     

μ+SR Study on Bi2Sr2Ca1−x Y x (Cu1−y Zn y )2O8+δ around the Hole Concentration of \frac{1} {8} per Cu

In order to study the effect in different high-T _c oxides from the La-system, muon spin relaxation measurements were applied to the Zn-substituted Bi-2212 system, Bi ₂ Sr ₂ Ca _1–x Y _x (Cu _1–y Zn _y ) ₂ O ₈₊ , around the hole concentration p= per Cu. It has been revealed that the magnetic correlation between Cu spins is anomalously enhanced in the Zn-substituted samples at per Cu, proving the existence of the effect" in the Bi-2212 system as well.     

Correlation between magnetic hysteresis and magnetic relaxation in YBaCuO single crystals

The dependence of the magnetic momentm obtained from the hysteresis loops on the speed of the magnetic field sweep =dH _ext/dt is explained on the basis of Anderson's interpretation of the magnetic flux creep. In addition, a phenomenological model is suggested which predicts a linear dependence ofm on ln with the slope m/ ln , numerically equal to the relaxation rate m/ ln(t) from the usual magnetic relaxation. Such linear relations betweenm and ln were observed experimentally in single crystals of YBaCuO. Preliminary experiments on the complementary time dependent relaxation ofm after a simulated step change ofH _ext gave mostly relaxation rates close to the predicted values. The model here presented also enables one to compare the critical state in the superconductor at a field sweep rate with the critical state at some timet _eff after a step change ofH _ext. The values of analyzed in our experiments actually correspond to the critical state at timest _eff between0.04 and4 sec after an imaginary large step change ofH _ext.     

On strong Dickson pseudoprimes

It is known that the Lucas sequenceV _n(,c)=aⁿ + bⁿ,a, b being the roots ofx ² – x + c=0 equals the Dickson polynomial .^n–2i Lidl, Müller and Oswald recently defined a number b to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [itg_n(b, c)b modn for all b. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined.     

Natural damped frequencies and axial response of a rotating finite viscous liquid column

Summary For a finite solidly rotating cylindrical liquid column the damped natural axisymmetric frequencies have been determined. The liquid was considered incompressible and viscous. The cases of freely slipping edges and that of anchored edges have been treated. It was found that instability appears in a purely aperiodic root for the spinning liquid bridge. This is in contrast to the instability appearing in the damped oscillatory natural frequency of a nonspinning liquid column at . The spinning viscous liquid column exhibits the same instability as the frictionless liquid. It appears at for axisymmetric oscillations.List of symbols a radius of liquid column - I _m modified Bessel function of first kind and orderm - s complex frequency ( ) - r, ,z polar cylindrical coordinates - p pressure - t time - u, v, w radial-, azimuthal- and axial velocities of liquid, respectively - Weber number - h height of liquid column - dynamic viscosity of liquid - v kinematic viscosity of liquid (v=/) - density of liquid - surface tension of liquid - _r , _rz shear stress - (r, z, t) circulation - (r, z, t) streamfunction - ₀ angular velocity of liquid column about the axis of symmetry - (,t) free surface displacement     

Angular dependence of the critical magnetic field in granular superconducting films

The critical magnetic fieldH _c () of granular Al films has been measured as a function of the angle between the field direction and the plane of the film at temperatures nearT _c0 .The film thicknessd is smaller than the temperature-dependent coherence length (T), the bulk electron mean free path1 is smaller than the BCS coherence length ₀, and 1 d. The experimental data onH _c () are well fitted by the Tinkham formula. However, the observed values ofH _c/H _care not always consistent with and increase with1/d. This fact suggests that the boundary scattering of electrons at the film surface enhancesH _c () and that the enhancement ofH _cis larger than that ofH _c.On leave from Department of Physics, Faculty of Science, Kyushu University, Fukuoka, Japan.     

Nonlinear liquid oscillations in spherical systems under zero-gravity

Summary Nonlinear free oscillations of the interface of a concentric frictionless immiscible liquid system in a spherical container are investigated in a zero-gravity environment. The natural frequencies are determined for the axisymmetric and asymmetric oscillations of the interfacial surface with the diameter ratio and density ratio as parameters. It was found that for small outer- to inner liquid density ratio the oscillations exhibit softening, while for large density ratios it renders hardening oscillation. The asymmetric oscillations exhibit in the softening range softer and in the hardening range harder liquid oscillations. For a liquid layer around a rigid center sphere the oscillations of the free liquid surface yields softening behavior, where for thinner layers the softening effect is more pronounced.Nomenclature a radius of spherical container, or radius of rigid center sphere - b radius of undisturbed interfacial surface, or radius of undisturbed free liquid surface - k=a/b diameter ratio - pressure - pressure (dimensionless) - , , spherical coordinates - dimensionless radius - R _i main radii of curvaturei=1, 2 time - dimensionless time - v _i liquid velocity (j=1 spherical layer region,j=2 inner liquid sphere region) - V volume of the liquid - Y _nm tesseral surface harmonics - _i density of liquids - velocity potential - dimensionless velocity potential - interfacial surface- or free surface elevation - dimensionless interfacial surface- or free surface elevation - ₀ maximum elevation - circular frequency - circular frequency - _n0 axisymmetric natural frequency - _n1 asymmetric natural frequencym=1 - _nm ⁽⁰⁾ natural frequency of linearized liquid system - mean curvature - _nm Kronecker symbol With 10 Figures     

An experiment to investigate the superfluid transition in a confined planar geometry

The vibrational characteristics of the FCC–cryocrystals with substitutional impurities have been analyzed. A non–central impurity atom in environment of the central host atoms is considered. The difference between equilibrium interatomic distances and r ₀ of the impurity and host atoms, respectively, causes their non–central interaction. A very strong dependence of the impurity frequency spectra on the ratio is shown. The range of the values of this ratio which corresponds to dynamical stabitity of the system under consideration is determined.     

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.     

Natural frequencies and response of spinning liquid column with apparently sliding contact line

Summary The contact line of a liquid with a solid does in many cases—depending on the smoothness of the solid, the viscosity, the surface tension and the excitation force—apparently flow along the solid during oscillations. The influence of this effect upon the natural frequencies, the stability and the response of the system has been investigated at an oscillating and spinning cylindrical liquid column.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 - 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 - _on natural frequency of harmonic axial response     

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     

Parafluidity in helium near the λ-transition and the generalized time-dependent Landau theory

A phenomenological theory of parafluidity, i.e., an enhancement of fluidity due to order-parameter fluctuations, is presented for helium near the transition. The generalized time-dependent Landau theory of second-order phase transitions is reviewed in general and is applied to the superfluid transition in helium as a particular example. In helium, it is found that parafluidity is manifested in the divergences of the mass diffusivity , the thermal conductivity , the first-sound amplitude attenuation ||^–1, and the second-sound dampling , which are all consistent with the dynamic scaling hypothesis. Here a characteristic relaxation time ₀ ||^–1 is used, where =(T–T _c )/T _c andT _c is the transition temperature. Although there are not enough experimental data to confirm our formulas, the present approach is seen to agree in order of magnitude with available experiments. Finally, the sound absorption above a ferromagnetic transition is calculated by adding a diffusion term to the generalized time-dependent Landau equation. The result thus obtained agrees in order of magnitude with experiments in nickel.Supported in part by the National Science Foundation and the Horace H. Rackham School of Graduate Studies.     

Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains