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.     

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.     

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     

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.     

Kondo Impurity in a Mesoscopic Ring: Charge Persistent Current

We study the influence of a magnetic impurity or ultrasmallquantum dot on the charge persistent current of a mesoscopicring. The system consists of electrons in a one-dimensionalring threaded by spin-dependent Aharonov–Bohm/Casher fluxes,coupled via an antiferromagnetic exchange interaction to alocalized electron. By passing to a basis of electron stateswith definite parities, the problem is mapped onto a Kondomodel for the even-parity channel plus free electrons in theodd-parity channel. The twisted boundary conditionsrepresenting the fluxes couple states of opposite parityunless the twist angles satisfy =f,where f are integers, with spin index=, . For these special values of, the model is solved exactly by a Bethe ansatz.Special cases are investigated in detail. In particular weshow that the charge stiffness in the case= is insensitive to the presenceof the magnetic impurity/quantum dot.     

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.     

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.     

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.     

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.     

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.     

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.     

Low-temperature specific heat of YBa2Cu3O7, YBa2Cu3O6, Y2BaCuO5, YBa3Cu2O7, BaCuO2, and CuO

We have measured the low-temperature specific heat (1.3T20 K) and the dc magnetic susceptibility (100T250 K) of eight samples of the high-T _c superconductor Y _x Ba_3–x Cu₃O_7– (x=0.9, 1.0, 1.1) and of two samples of nonsuperconducting YBa₂Cu₃O₆₊. We have also performed specific heat measurements on the possible impurity phases: YBa₃Cu₂O₇, Y₂BaCuO₅, CuO, and BaCuO_2+x . The superconducting samples all have a nonzero, sample-dependent linear term * and an upturn inC/T at very low temperature. We show that this anomalous behavior is at least partly due to the presence of a small amount (1%) of BaCuO_2+x impurity phase in the measured samples. This is evidenced by the correlation between * and the Curie component of the susceptibility, which is proportional to the amount of paramagnetic impurities.     

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.     

Heat transfer of a semitransparent plate under conditions of a regular regime of the second kind

The kinetics of the cooling of a plane semitransparent layer under conditions of a regular regime of the second kind is analyzed.Notation time - T temperature - T_e temperature of the surrounding medium (the ambient temperature) - T° initial temperature of the layer - h_e coefficient of convective heat exchange - x coordinate - coefficient of absorption of the substance - n index of refraction - B(, T) surface density of radiation of a black body - C bulk specific heat - K thermal conductivity - wavelength of the radiation - _t range of wavelengths in which the material is partially transparent - _op range of wavelengths in which the material is opaque - degree of blackness of the surfaces in the range of _op - R() coefficient of reflection from the inner surfaces of the layer - ⁺ intensity of the rays consisting of acute angles with the inner normal to the surface x = 0 - ^– intensity of rays in the opposite direction - q thermal flux - angle measured from the inner normal to the surface x = 0 Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 541–546, September, 1981.     

Effects of Y2O3 and La2O3 addition on the crystallization of Li2O·Al2O3·4SiO2 glass-ceramic

Effects of adding Y₂O₃ and La₂O₃ on the crystallization of -quartz solid solution (ss) and the subsequent -quartz ss to -spodumene transformation of Li₂O·Al₂O₃·4SiO₂ glass-ceramic were investigated. Adding 4 mol% YO_3/2 or 8 mol % LaO_3/2 effectively improved the control of the crystallization process of the glass. Y₂O₃ did not effectively induce bulk crystallization of -quartz ss, but can reduce the rate of surface crystallization. La₂O₃ completely suppressed the surface crystallization and promoted a uniform, bulk crystallization of -quartz ss. For both the Y₂O₃- and La₂O₃-doped glasses, the kinetics for glass crystallization to -quartz ss was delayed as the doping level increased. Except for the 8 mol % LaO_3/2-doped glass in which no -spodumene was formed, the kinetics for the -quartz ss to -spodumene transformation for the doped glasses was enhanced compared with that for the undoped glass. For the 4 and 8 mol % YO_3/2-doped compositions, the relative amount of -spodumene to -quartz revealed an anomalous decrease trend with heating temperature in a particular temperature range. This can be explained by the surface crystallization characteristic, which induced an overlap of crystallization and -quartz ss to -spodumene transformation. Glass doped with 8 mol % LaO_3/2 exhibited an Avrami exponent of about 2.4 and an activation energy for crystal growth of -quartz ss of about 418 kJ mol^–1.     

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.     

Conformational and electronic band structure analysis of a new type of high performance polybenzothiazole polymers

The energy-band structure and preferred (minimum energy) conformation of the recently synthesized polybenzothiazoles (PBT; AA and AB type), representing a new class of high-performance polymers, were determined by molecular orbital calculations. In the case of the AAPBT chain, the most stable conformation was obtained at ₁ (rotation angle about the bond joining the two bibenzothiazole moieties) = 20° and ₂ (rotation angle about the bond joining the bibenzothiazole group and thep-phenylene group) = 10°. In the case of the ABPBT chain, the corresponding minimum energy rotational angle () was found to be 20°. These conformations agree fairly well with both theoretical and experimental observations. The calculated axial band gaps were 1.94 and 2.08 eV for the AAPBT and ABPBT polymers, respectively, and these values are close to the corresponding value for polyacetylene, considered a prototype electrically-conducting polymer because of its novel electronic properties and manifold applications.     

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.     

A method of reducing the severity of the thermal stress state in blades of gas turbine engines by selecting the optimum distribution of the thickness of a ceramic thermal barrier coating

On the basis of a complex solution of the problems of thermal conductivity and thermal elasticity for cooled turbine blades with ceramic thermal barrier coatings, the authors propose a method of selecting local coating thicknesses which make it possible to reduce the level of temperature and thermal stresses in the blade in both non-steady and steady operating conditions. The method is based on using LCB _T-search for multiparametric problems.The work was carried out taking into account the requirements of the project Justification of the possibility of using new high-temperature materials, including those with coatings, for increasing the economic parameters of aviation and ship engines of the program 5.2.3 Increasing the reliability, service life and preventing catastrophic failures of transport gas turbine engines of the state committee of the Ukraine for the problems of science and technology.Translated from Problemy Prochnosti, No. 1, pp. 62–67, January, 1994.