Universality and the scaling laws in the superfluid phase transition of3He-4He mixtures

From the second-sound velocityU ₂ near the superfluid transition point, the superfluid densities in³He-⁴He mixtures, _s (X) and _s (), were deduced along the paths of constant³He concentrationX and of constant chemical potential difference of³He and⁴He. The following critical exponents of _s are determined: (a) =XX for _s (X) in the(X, T) plane,(b) X for _s (X) in the(, T) plane, and(c) for _s () in the(, T) plane. It is found that and _X change by about 4–6% relative to with increasing³He concentration up toX=0.4 and by 8–10% up toX=0.53. It seems that, belowX=0.53, universality hold for . Values of have been found to be in good agreement with the critical exponent of _s in pure⁴He under constant pressure. The values of and _X forX0.53 are also found to be consistent with the scaling relations in the (,T) plane of³He-⁴He mixture.Work performed in part while at the Electrotechnical Laboratory.     

Computation of particle settling speed and orientation distribution in suspensions of prolate spheroids

A numerical technique for the dynamical simulation of three-dimensional rigid particles in a Newtonian fluid is presented. The key idea is to satisfy the no-slip boundary condition on the particle surface by a localized force-density distribution in an otherwise force-free suspending fluid. The technique is used to model the sedimentation of prolate spheroids of aspect ratio b/a=5 at Reynolds number 03. For a periodic lattice of single spheroids, the ideas of Hasimoto are extended to obtain an estimate for the finite-size correction to the sedimentation velocity. For a system of several spheroids in periodic arrangement, a maximum of the settling speed is found at the effective volume fraction (b/a)²04, where is the solid-volume fraction. The occurence of a maximum of the settling speed is partially explained by the competition of two effects: (i) a change in the orientation distribution of the prolate spheroids whose major axes shift from a mostly horizontal orientation (corresponding to small sedimentation speeds) at small to a more uniform orientation at larger , and (ii) a monotonic decrease of the the settling speed with increasing solid-volume fraction similar to that predicted by the Richardson–Zaki law (1–)⁵⁵ for suspensions of spheres.     

Rheological properties of aqueous silicon nitride suspensions

The effect of surface modification of Si₃N₄ particle on the colloidal behavior and the rheological properties of aqueous Si₃N₄ suspensions under steady and oscillatory conditions are investigated in detail. Due to the decrease of the oxidizing level, the isoelectric point (IEP) of the modified particle shifts to basic region gently. Attempts have been made to apply rheological models to the suspensions with various solid volume fraction (). For the as-received suspensions, the Sisco model provides the best fit in the range of 0.30 while the Casson model in 0.35 0.45. The shear behavior of modified suspensions fits to Sisco model in the range of 0.40 and Casson model in 0.45 0.54. The rheological behavior of modified suspensions is improved efficiently. The critical strain decreases and the linear viscoelastic regime narrows continuously with increasing solid concentration. For the modified suspensions, the linear viscoelastic regime broadens and the corresponding elastic modulus decreases sharply. With increasing solid concentration, the characteristic frequency shifts toward lower frequencies and the suspension transforms from more viscous to more elastic.     

Interfacial spring model for ultrasonic interactions with imperfect interfaces: Theory of oblique incidence and application to diffusion-bonded butt joints

The quasi-static distributed spring model is used to derive the ultrasonic reflectivity of an imperfectly-bonded interface as a function of frequency and angle of incidence. The results are then incorporated in a model for the corner reflection from a diffusion-bonded joint between two abutting plates, the corner being defined by the bond plane and the common lower surface plane of the plates. An immersion-inspection geometry is assumed, and seven categories of corner reflections are identified and examined in detail. These fall into two classes: those having parallel incident and exiting rays in water (=), and those having nonparallel water rays ( ). The = categories are suitable for single probe (pulse-echo) inspections of the joint. Based on the amplitude of the outgoing corner-reflected signal, two = geometries appear promising. These employ, respectively, a corner reflection involving only longitudinal waves with the interface illuminated at near-grazing incidence (LLL), and a corner reflection involving only transverse waves with the interface illuminated at near 45° incidence (TTT). In addition, two practical geometries are indicated; these both involve mode conversion upon reflection from the interface, with the incident or outgoing longitudinal wave traveling nearly parallel to the interface. Model predictions for LLL and TTT reflections are compared to measurements on diffusion-bonded Inconel specimens, and techniques for applying the model results to more complicated bond geometries are discussed.     

Effect of wall conductances on hydromagnetic flow and heat transfer in a rotating channel

Summary Wall conductance effects on the hydromagnetic flow and heat transfer between two parallel plates in a rotating frame of reference has been studied when the liquid is permeated by a transverse magnetic field. An exact solution of the governing equations has been obtained. It is found that the velocity, current density and the temperature depend only on the sum of the wall conductances ₁ + ₂ = but magnetic field depends on the individual values of ₁ and ₂, where ₁ and ₂ are respectively the wall conductance ratios of the upper and lower walls.

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Einfluß der Wandleitfähigkeit auf die hydromagnetische Strömung und den Wärmeübergang in einem rotierenden Kanal

Zusammenfassung In der Arbeit wird der Einfluß der Leitfähigkeit der Wände auf die MHD-Strömung sowie auf den Wärmeübergang untersucht für den Fall, daß sich das zähe Medium zwischen zwei rotierenden Platten befindet und ein Magnetfeld parallel zur Rotationsachse angelegt wird. Es wird eine exakte Lösung des Problems gegeben. Es zeigt sich, daß die Geschwindigkeit, die Stromdichte und die Temperatur nur von der Summe der Leitfähigkeiten der Wände + ₂ = abhängen, dagegen hängt die magnetische Feldstärke von den individuellen Werten ₁ und ₂ ab, wobei ₁ und ₂ die Leitfähigkeiten der oberen bzw. unteren Wand bezeichnen.

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With 5 Figures     

Vanadium sesquioxide-polymer composites: the study of electrical conductivity

The electrical conductivity of V₂O₃-polymer composites were studied by examining the dependence of resistivity (conductivity) on the volume fraction of V₂O₃. The experimental data (_m versus ) were fitted (using a computer program) to the GEM equation with satisfactory accuracy. The critical volume fraction and other parameters evaluated by fitting (t, _h and _c) and calculated after fitting L and m , L _f and m _f were analysed by taking into account the geometry, orientation and arrangement of the two components. The physical meanings of L, m and t are further illustrated on the basis of their definitions.     

Disappearance of Bose-Glass Behavior in Transport Properties of YBa2Cu3O y Films with Columnar Defects

The glass transitions of the vortex system in Au-ion irradiated YBa₂Cu₃O _y films have been studied by the measurements of transport properties as a function of magnetic field B and angle of B to the direction of columnar defects. At =0°, we find an anomalous upturn behavior of the glass transition line B _g(T) at BB /3, where B is the matching field. In B>B /3, the dependence of glass transition temperature T _g reveals cusplike behavior with a peak at =0°, which is consistent with the Bose glass theory. In B<B /3, on the other hand, T _g is almost independent of , suggesting the system undergoes the vortex glass transition induced by the inherent point-like defects.     

A new application of the reciprocity relations to the study of fluid flows through fixed beds

Creeping flow through an array of spheres with small volume fraction is studied theoretically. It is observed that it can be described macroscopically by Brinkman's equation. A generalized version of the reciprocity relations is used to determine the viscous term up to O(²) for the case of random configuration and up to O(³) for the case of periodic, cubic configurations of the fixed bed.     

Collective oscillations at long wavelengths in liquid4He

The recent successful calculation of the lower collective branch of the excitation spectrum in liquid ⁴ He by Sunakawaet al. contains a phenomenological parameter (k) whose relation to microscopic theory is obscure. To clarify matters, an exact identity is presented for the absorptive part of the density-density correlation function and is employed to show that Pines' zero-sound concept of the phonon in liquid ⁴ He is accurate in the limit of infinitely long wavelengths. Since the zero-sound theory can be made to produce an explicit relation between (k) and the two-particle potential in the liquid, the foundation has been laid for a microscopic expression for the excitation spectrum in the range of very low wave numbers, where the classic Feynman theory of the phonon is known to be accurate. A numerical calculation of (k) using this expression results in a theoretical excitation spectrum which is in excellent agreement with neutron scattering measurements in the regionk0.4 Å ^–1 .     

Negative self-inductance in superconducting thin wires and weak links

One of the most promising implications of the phenomenological Ginzburg—Landau (GL) theory of superconductivity is the possible existence of current-carrying metastable states with a negative effective self-inductance. Microscopically this phenomenon can be explained as a result of the depairing mechanism which, when the center-of-mass velocityv _s of the Cooper pairs is sufficiently large, can be so strong that a further increase ofv _s will lead to a decrease of the total current. Using a one-dimensional formulation of the GL theory we investigate the thermodynamic stability of these states for different external constraints and obtain the result that a negative self-inductance can only be stable if the length of the system in the direction of the current is smaller than a critical value comparable to the GL coherence length /. It is an experimental fact that states of negative self-inductance are realized in Josephson junctions and other types of superconducting weak links because the dc supercurrent can be a decreasing function of the phase variable . The thermodynamic stability theory can therefore explain why weak links have to be short, and it also provides us with a unifying point of view by treating the phase and the current as a pair of thermodynamically conjugate variables for arbitrary one-dimensional systems. An important point is the operational phase definition as a thermodynamic parameter that can be controlled by the experimentalist. This requirement is essential for the general validity of the ac Josephson equation and it implies that must depend on the magnetic self-inductance of the system. By applying the GL theory to weak links we can delimit the validity of the usual dc Josephson equationI sin and see that deviations from this functional form are most likely to be found in thin-film bridges of the Anderson-Dayem (AD) type. When the currentI is the controlled variable the conjugate phase variable will fluctuate and the magnitude of these fluctuations depends strongly on the functional formI(). The phase fluctuations for constantI lead to a reduction of the critical current which will be absent when is the controlled variable. The observed microwave enhancement of the critical current in AD bridges, the so-called Dayem effect, can be explained as a result of a switch from current control to phase control, and the fluctuation formulae explain why the effect is negligible in structures exhibiting the classical Josephson sine law for the current-phase relation.     

Recovery of a creep-deformed Type 316 stainless steel

The recovery of the dislocation structures produced in a Type 316 steel during creep has been examined by annealing over a range of temperatures and times, both in the presence and in the absence of stress. The influence of dislocation recovery on subsequent reloading behaviour has also been examined.Initial dislocation recovery occurs rapidly but the rate of recovery subsequently decreases as precipitate effects become more important. Dislocation recovery in the early, rapid stage appears to be controlled by vacancy diffusion between the dislocation links. The application of stress during recovery leads to an enhancement of the recovery rate in agreement with the network coarsening model whilst the incremental strains observed on reloading after recovery correlate well with the changes in dislocation structure produced during the recovery periods.List of symbols and appropriate values l dislocation link length - D _s self diffusion coefficient - b Burgers vector (2.5×10^–1 m) - C _j equilibrium jog concentration - dislocation link tension - k Boltzman's constant (1.38×10^–23 J atom^–1 K^–1) - T absolute temperature - t recovery time - M mobility term - Z frictional term associated with particles - _d dislocation density determined from micrographs - N _d number of dislocation intersections on test line - p length of test line - S foil thickness - ¯l mean dislocation link length - _c mean intragranular particle (carbide) spacing - r ₀ mean intragranular particle radius at timet=0 - r _t mean intragranular particle radius at timet - D solute diffusion coefficient - B solubility of M₂₃C₆ in austenite - particle-matrix interface energy - atomic volume (10^–29m³) - change in dislocation density during recovery period - incremental strain associated with reloading after recovery period - K constant - dislocation density - ₀ dislocation density at timet=0 - _t dislocation density at timet - ₀ friction stress associated with particles - constant (1) - shear modulus - angle between dislocation segments as dislocation breaks through a particle - A 1 cos (/2) - E constant - creep rate - F Taylor factor - L mean slip distance of dislocations - rate of dislocation recovery - stress - _y yield stress - J strength coefficient - _p plastic strain     

A new iterative technique of the finite element method for the analysis of the steady state incompressible viscous flow based on the transformation of variables

In this paper the convergence acceleration for solving steady-state incompressible flows, by using iterative solvers, is explored. The variable transformation: u = u – , p = –r, where u and are the rotational velocity and the velocity potential, respectively, is applied to the finite element discretized equations so as to get diagonal-dominant equations. The effectivity of the present techniques is demonstrated on the 2D lid-driven flow and the 3D flow in a disk-cylinder system.     

Differential-flow-induced instability in a cubic autocatalator system

The formation of spatio-temporal stable patterns is considered for a reaction-diffusion-convection system based upon the cubic autocatalator, A + 2B 3B, B C, with the reactant A being replenished by the slow decay of some precursor P via the simple step P A. The reaction is considered in a differential-flow reactor in the form of a ring. It is assumed that the reactant A is immobilised within the reactor and the autocatalyst B is allowed to flow through the reactor with a constant velocity as well as being able to diffuse. The linear stability of the spatially uniform steady state (a, b) = (µ^–1, µ), where a and b are the dimensionless concentrations of the reactant A and autocatalyst B, and µ is a parameter reflecting the initial concentration of the precursor P, is discussed first. It is shown that a necessary condition for the bifurcation of this steady state to stable, spatially non-uniform, flow-generated patterns is that the flow parameter > _c(µ, ) where _c(µ,) is a (strictly positive) critical value of and is the dimensionless diffusion coefficient of the species B and also reflects the size of the system. Values of _c at which these bifurcations occur are derived in terms of µ and . Further information about the nature of the bifurcating branches (close to their bifurcation points) is obtained from a weakly nonlinear analysis. This reveals that both supercritical and subcritical Hopf bifurcations are possible. The bifurcating branches are then followed numerically by means of a path-following method, with the parameter as a bifurcation parameter, for representatives values of µ and . It is found that multiple stable patterns can exist and that it is also possible that any of these can lose stability through secondary Hopf bifurcations. This typically gives rise to spatio-temporal quasiperiodic transients through which the system is ultimately attracted to one of the remaining available stable patterns.     

Hydrodynamic reaction to accelerated onedimensional motion of gas bubbles of variable volume in an unbounded liquid

A solution is given for the problem of the hydrodynamic reaction of an ellipsoidal gas bubble of variable volume to accelerated motion and the relation between the value of the apparent mass and the eccentricity of the bubble.Notation (,) velocity potential - V velocity of motion of the bubble with respect to the liquid - (, ) velocity potential of the near field - T₂ kinetic energy of the liquid due to the variation in bubble volume - F_r reaction force of the liquid - B₁ momentum of the liquid - _e apparent mass of the ellipsoid - density of the liquid - V_e volume of the ellipsoidal bubble Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 47–50, July, 1980.     

Estimation of the drawing efficiency of hot spinning of co-polyester fibres in producing high degrees of preferred orientation

A range of liquid crystalline polyester fibres varying in diameter from 65 to 440m were produced by spinning from a hot melt. These were analysed for preferred orientation by flatplate X-ray diffraction to produce equatorial azimuthal densitometry scans/() which were processed to produce the corresponding planar orientation profiles/() corresponding to a Bragg separation of 0.448nm. A further mathematical analysis was applied to these to produce the respective molecular orientation profiles/() which may be more directly related to fibre mechanical properties,/() profiles from this analysis were matched against theoretical/() calculated by assuming an idealized mechanism of affine deformation with no orientation losses due to thermal perturbations. The theoretical draws ratios corresponding to the experimentally observed cos² were matched against experimentally observed draw ratios to produce ratios which indicate drawing efficiencies. Although preferred orientation increased with increasing draw ratios, the drawing efficiency diminished with draw ratio.     

Correlations and effective potential in the ground state of a one-dimensional model for solid helium and deuterium

The ground-state energyE can be calculated exactly by the transfer-integral method if the total wave function is assumed to be a product of single-particle functions and nearest-neighbor correlation functionsf. The variation ofE with respect tof for fixed leads to a Schrödinger equation for the relative motion of two particles which is coupled to the transfer integral equation by an effective potential V. For the case of a Gaussian the optimalf, the one- and two-particle probability amplitudes, and other quantities are computed by iteration of the Schrödinger equation with the transfer integral equation until self-consistency is achieved. The minimum ofE as a function of the Gaussian width is obtained for different values of the lattice parameter. The shape of V andf is discussed. The self-consistentf describes both short- and long-range correlations.     

Effect of Normal-State Pseudogap on Physical Quantities in Hubbard Model for Underdoped High-T c Cuprates

We develop the strong-coupling theory of coexisting charge-density-wave (CDW) and superconductivityd-wave gaps within the framework of the FLEX (fluctuation exchange) approximation for the two-dimensional Hubbard model. For nested sections of the Fermi surface these equations reduce to the previous FLEX equations for superconductivity where the squared energy gap _s ² in the denominator of the Green's function is replaced by ( _s ² + _c ² ) (here _s is the superconductivity and _c the CDW gap). We solve these equations by taking for _c a phenomenologicald-wave gap. The resulting neutron scattering intensity, spin-lattice relaxation rate 1/T₁ , Knight shift, resistivity, and photoemission intensity are in qualitative agreement with the data on underdoped high-T_c cuprates. TheT_c for superconductivity decreases and the crossover temperature T_* for 1/T₁Tincreases with increasing gap amplitude of _c which is in qualitative agreement with the phase diagram for underdoped cuprates.     

Bounding-surface plasticity: Stress space versus strain space

Summary A bounding-surface plasticity model is formulated in stress space in a general enough manner to accommodate a considerable range of hardening mechanisms. Conditions are then established under which this formulation can be made equivalent to its strain-space analogue. Special cases of the hardening law are discussed next, followed by a new criterion to ensure nesting. Finally, correlations with experimental data are investigated.Notation (a) centre of the stress-space (strain-space) loading surface; i.e., backstress (backstrain) - ^* (a ^*) centre of the stress-space (strain-space) bounding surface - (a ) target toward which the centre of the stress-space (strain-space) loading surface moves under purely image-point hardening - (b) parameter to describe how close the loading surface is to nesting with the bounding surface in stress (strain) space; see (H10) - (c) elastic compliance (stiffness) tensor - (d) parameter to describe how close the stress (strain) lies to its image point on the bounding surface; see (H10) - (D) generalised plastic modulus (plastic compliance); see (1) - function expressing the dependence of the generalised plastic modulus on (plastic complianceD ond) - ^* (D ^*) analogue to (D) for the bounding surface - function expressing the dependence of ^* on (D ^* ond) - () strain (stress) - ' (') deviatoric strain (stress) - ^P ( ^R ) plastic strain (stress relaxation); see Fig. 1 - () image point on the bounding surface corresponding to the current strain (stress) - _iso (f _iso) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change of radius; i.e., fraction of isotropic hardening in the stress-space theory - _kin (f _kin) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change in the backstress (backstrain); i.e., fraction of kinematic hardening in the stress-space theory - _nor (f _nor) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - _ima (f _ima) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - function relating _iso to , , and (f _iso tob,d, andl) - function relating _kin to , , and (f _kin onb,d, andl) - function relating _nor to , , and (f _nor onb,d, andl) - function relating _ima to , , and (f _ima onb,d, andl) - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change of radius - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change in the centre - function relating _iso ^* to (f _iso ^* tod) - function relating _kin ^* to (f _kin ^* tod) - (l) parameter to describe the full extent of plastic loading up to the present, giving the arc length of plastic strain (stress relaxation) trajectory; see (H10) - function relating the direction for image-point translation of the loading surface to various other tensorial directions associated with the current state; see (H5). With 6 Figures     

Comparison of energy and phase relaxation in metallic wires

We have determined the phase coherence time, , frommagnetoresistance measurements of long, narrow wires ofAu, Ag, and Cu, over the temperature range40 mK-6 K. In the Cu and Au wires, saturates at low temperature. In the Ag wire, continues to increase down to the lowesttemperatures measured; moreover, its temperature dependencebelow about 1 K is consistent with theoreticalpredictions of Altshuler, Aronov and Khmelnitskii published in1982. These results cast doubt on recent assertions thatsaturation of at low temperature is a universalphenomenon in metal wires. We compare these results with thoseof recent experiments on energy relaxation in similar metallicwires. The results of the two experiments are stronglycorrelated, suggesting that a single (unknown) mechanism isthe cause of the enhanced phase and energy relaxation observedin some samples.     

Non-linear liquid motion in conical containers

Summary The non-linear behavior of an incompressible and frictionless liquid with a free surface in an annular conical sector frustrum container has been determined. All special cases of conical tanks may be obtained from the results. Some configurations have been evaluated numerically. It was found that the oscillating liquid system exhibits softening behavior, showing for increased free surface amplitudes decreased natural frequencies as compared to the linearized frequencies. This non-linear behavior is more pronounced for larger vertex angles and smaller frustrum heights.Notation a, b radius (describing the free surface,r=a the container bottomr=b) - k=b/a ratio of radii - g gravity constant or acceleration along the axis of the container - h liquid height - P ^m ,Q ^m associated Legendre functions of first and second kind and orderm - r, , spherical coordinates - p liquid pressure - t time - 2, 2 outer- and inner vertex angle resp - 2 sector angle of container - (r, , ,t) velocity potential - liquid density - zeros of associated Legendre function or cross product Legendre functions with respect to the degree - non-linear frequency - _mn ⁽⁰⁾ linearized natural frequencies of liquid - free surface elevation With 7 Figures