Effect of phase fluctuations upon penetration depth

The temperature dependence of the static penetration (T) has been used as a guide to the nature of the superconducting state in high-T _c materials. It has been argued that an algebraic temperature dependence in the ratio (T)/(0) [(T) — (0)]/(0) at low temperature is evidence for d-wave pairing. This paper examines the effect of superconducting phase fluctuations upon (T) and finds an algebraic dependence over a broad range of temperature.     

Dependence of helium II viscosity properties on oscillation frequency

The causes of a discrepancy in the results of measurements of He II viscosity below T 1.6 k obtained with different measurement methods are investigated. It is shown that to obtain correct results in oscillation experiments, the condition _ph should obtain, where is the depth of viscous wave penetration and _ph is the phonon free path length. Results of viscosity measurements at different ratios /_ph (by a wire viscometer) are presented. It is shown that for the condition _ph, the results obtained are in good agreement with the results of Andronikashvili (in which /_ph > 100). If the mentioned relation is not satisfied, then, as the value of the ratio /_ph is decreased, the value measured for the viscosity is increasingly lower than the results of Andronikashvili.     

Measurements of Critical Current of Superfluid 4He through An Array of Submicron Apertures very near Tλ

Far from the lambda transition the critical flow of superfluid ⁴ He through a small orifice is determined by thermal nucleation of quantized vortices. Between 300 mK and 2 K linearly decreasing critical flow velocity has been observed earlier. As the temperature approaches T the size of the vortex core increases and becomes comparable to that of the orifice. We report here measurements of the critical mass current in this temperature range. An array of 24 3×0.17 m holes in parallel with a macroscopic parallel path and flexible-diaphragm Helmholtz resonator have been used. The temperature range explored was from 80 mK to 20 K below T. Preliminary analysis of the data shows that for a reduced temperature t=(T–T)/T1·10 ^–4 the critical current scales approximately as t ^1.25 . Closer to T the critical phase difference across the array becomes comparable to 2 and the results have to be analyzed in terms of Josephson effect. The superfluid density has been measured at the same time as the critical current.     

A note on the similarity solutions for free convection on a vertical plate

Summary The similarity solutions for free convection on a vertical plate when the (non-dimensional) plate temperature is x and when the (non-dimensional) surface heat flux is –x are considered. Solutions valid for 1 and 1 are obtained. Further, for the first problem it is shown that there is a value ₀, dependent on the Prandtl number, such that solutions of the similarity equations are possible only for >₀, and for the second problem that solutions are possible only for >–1 (for all Prandtl numbers). In both cases the solutions becomes singular as ₀ and as –1, and the natures of these singularities are discussed.     

Asymptotic behavior of the vector potential and the order parameter for an isolated vortex

Eilenberger's formulation of the theory of inhomogeneous superconductors is used to study an isolated vortex in a type-II superconductor. Exact integral expressions for the vector potential and the order parameter are obtained and used to determine the asymptotic behavior of these quantities. Far from the axis of the vortex, the vector potential approaches its BCS value in an approximately exponential fashion, the decay constant being equal to the quantity obtained by Eilenberger and Büttner in the local case, and equal to {2[(k _BT)²+ _BCS ² ]^1/2/v_F+(1/v _F)}^–1 in the case where nonlocal effects dominate. The order parameter also approaches its BCS value approximately exponentially, the decay constant being equal to the quantity of Eilenberger and Büttner when <2, and equal to 1/2 when >2.Supported in part by the National Research Council of Canada.Sole affiliation is now the University of Toronto.     

The penetration depth of HgBa2CuO4+δ with 0.07 ≤ δ ≤ 0.35

The magnetic penetration depth (T) of three HgBa₂CuO₄₊ samples with 0.16 < 0.27 has been determined from the reversible magnetization. The obtained follows a BCS-like correlation of 1/² 1–(T/T_c)² over whole measured temperature range in an underdoped sample with T_c 90 K, but deviates significantly from similar fits in an overdoped sample with the same T_c and an optimum doped sample, whose 1/² 's depends on T nearly linearly below T_c/2. This asymmetry between the underdoped and overdoped samples suggests that the T-dependence of 1/² is affected by doping in a complicated way.     

Anisotropic Pair-breaking by Impurity Doping in High-Tc Cuprates: Modification of Interlayer Coupling

Impurity (Zn/Ni) doping effects on the superconducting coherence length and the penetration depth have been studied for the in-plane and the out-of-plane directions of YBa ₂ Cu ₃ O _y single crystals. We determined from diamagnetic susceptibility in the reversible region and from optical conductivity spectra. It was found that both in and the ac-anisotropy ratio is reduced with impurity doping. Both changes can be explained by assuming an increase in Josephson coupling strength due to impurity doping.     

Optical thermophysical characteristics of the condensed phase of combustion products and heatproof materials

An unconventional unit for experimentally studying the optical thermophysical properties of materials over a wide temperature range is described. Results are presented of studying the temperature function and dispersion of the absorption index for the condensed phase of the combustion products of a metalbearing fuel and of the emittance of fiber fireproof materials.Notation K spectral absorption coefficient - D spectral transmission coefficient - spectral absorption index - wavelength - d sample thickness - d_s surface layer thickness - I spectral intensity of radiation - , spectral and total emittances Kirov Polytechnical Institute. Kazan Chemical Engineering Institute, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 3, pp. 330–336. March, 1993     

Die Entwicklung von Längswirbeln in zeitlich anwachsenden Grenzschichten an konkaven Wänden

Zusammenfassung Messungen des Anwachsens von Längswirbeln in zeitlich anwachsenden Grenzschichten an konkav gekrümmten Wänden (Görtler-Taylor-Wirbel) ergaben drei deutlich getrennte Bereiche: Es traten zunächst Wirbel mit der Wellenläge 0,9 auf (=Grenzschichtdicke, =Höhe einer Zelle, die zwei gegensinnig drehende Wirbel enthält). Je nach Größe der mit der Verdrängungsdicke ₁ der Grenzschicht gebildeten Reynolds-Zahl erschienen dann kurze Zeit später Wirbel mit 2,5, wenn war. Im Bereiche dagegen traten stattdessen bei den hier durchgeführten Versuchen immer Wirbel mit der Wellenlänge 6,5 auf. Bei werden die ersten Tollmien-Schlichting-Wellen mit der Wellenlänge _TS 6· angefacht. In ihren wandnahen Bereichen der Wellentäler könnten sich dann die oben genannten Längswirbel der Wellenlänge 6,5· ausbilden, die die zwei-in eine dreidimensionale Störung allseits gleicher Größenordnung verwandeln können.

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The development of longitudinal vortices in boundary layers growing with time along concave walls

Summary Measurements of the growth of longitudinal vortices in boundary layers growing with time along concave walls (Görtler-Taylor vortices) rendered three distinctly separated regions. First, vortices with a wave-length 0.9 appeared (-boundary layer thicness, =height of a cell containing two counterrotating vortices). Then, depending on the Reynolds number R _{a 1}/v ₁=displacement thickness), vortices with 2.5 appeared shortly afterwards, provided . In the region , however, the wave-length was 6.5. For the first Tollmien-Schlichting waves with _TS 6 were excited. In the wave-throughs close to the wall the abovementioned longitudinal vortices with wave length 6.5 may then be formed. This might transform the two-dimensional into a three-dimensional flow of equal order of magnitude in all directions.

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Zeichenerklärungen R _a Innenradius - Re _a Reynolds-Zahl gebildet mit dem InnenradiusR _a - Reynolds-Zahl gebildet mit der Verdrängungsdicke ₁ - kritische Taylor-Zahl - h Standhöhe der Flüssigkeit im Zylinder - t Zeit - z Anzahl - Steigungswinkel der Geraden - Grenzschichtdicke - ₁ Verdrängungsdicke - Wellenlänge (enthält ein gegensinnig rotierendes Längswirbelpaar) - v kinematische Zähigkeit - Winkelgeschwindigkeit Indizes K Knickpunkt der Geradensteigung - L unterhalb des Knickpunktes der Geradensteigung - TS Tollmien-Schlichting - e Einsatz der Wirbelentstehung     

Normal-State Optical Response Functions of MgB2 Superconductor

The reflectivity of superconducting MgB₂ (T _c = 39 K) has been measured on a randomly oriented thin film at room temperature over a wide-range of frequencies, 20 < 100000 cm^–1. The conductivity shows highly metallic behavior but cannot be explained with a simple Drude model alone. The electronic contribution is analyzed by a generalized Drude model. The scattering rate 1/() and the mass renormalization ratio m*()/m = 1 + () exhibit clear frequency dependence. The electron–phonon coupling strength is estimated to be 1.5 ± 0.5 while the plasma frequency _p is 2.4 eV.     

Magnetic penetration depth measurements with the microstrip resonator technique

The microstrip resonator technique is a convenient way to sensitively measure the temperature dependence of the magnetic penetration depth (T) in superconducting thin films. Because the method relies on measuring the resonant frequency of a high-Q transmission line resonator at microwave frequencies, one can very precisely measure small changes in (T). This technique is applied to studying the low-temperature dependence of (T), since that is in principle a measure of the low-lying pair-breaking excitations of the superconductor. We find that the penetration depth in niobium films is consistent with the predictions of weak coupled BCS theory. The low-temperature dependence of (T) inc-axis YBa₂Cu₃O_7– films can be interpreted as either a weak exponential or as a power law. In addition, the measured value of (0) is found to be strongly dependent on the form of the temperature dependence for (T) used in fitting the data. Best fits over the entire temperature range are obtained with a BCS temperature dependence having values for 2(0)/k _BT_c strictly less than 3.5, consistent with our measurements of the temperature dependence of (T) at low temperatures in YBa₂Cu₃O_7– .     

Estimation of the Mean Thermal Conductivity of Anisotropic Materials

An estimation method of the plane directional thermal conductivity of fibrous insulations using the cyclic heat method and the transient hot-wire method is proposed. By assuming that the thermal conductivity _h of anisotropic materials measured by the transient hot-wire method is equivalent to that of the isotropic materials which have the same bulk density and specific heat c as the anisotropic materials, the thermal conductivity _h is shown to be equal to , which is a geometrical mean of the thermal conductivities in the direction of the plane _x and the thickness _y of the anisotropic materials. For an alumina silica blanket (=125 kg·m^–3), the thermal conductivities _h , _x , and _y were measured in the temperature range between –140 and 300°C using the transient hot-wire method for _h and the cyclic heat method for _x and _y . In the same way, the thermal conductivities _h , _x , and _y of a rock wool (=121 kg·m^–3) insulation were also measured in the temperature range, 100 to 600°C. From a comparison of the measured results with the estimated values of _x , it is confirmed that the proposed method can estimate the measured values reasonably well.     

Superfluid fraction of4He from 1.5 K toT λ(P) and from vapor pressure to the melting curve

New measurements of the first-, second-, and fourth-sound velocities are reported and used to obtain the superfluid fraction _s / at pressures from vapor pressure to the melting curve and from 1.5 K to within 1% of the superfluid transition temperatureT (P). Close toT , the new results agree very well with previous measurements by Greywall and Ahlers. At low temperatures they agree well with the tabulations by Maynard; but in the range within 10% or so ofT (P) and at the higher pressures they differ from Maynard's values by several percent.     

Branching of the Falkner-Skan solutions for λ<0

Summary The Falkner-Skan equation f+ff+(1-f²)=0,f(0)=f(0), is discussed for <0. Two types of problems, one with f()=1 and another with f()=-1, are considered. For =0^- a close relation between these two types is found. For <-1 both types of problem allow multiple solutions which may be distinguished by an integer N denoting the number of zeros of f-1. The numerical results indicate that the solution branches with f()=1 and those with f()=-1 tend towards a common limit curve as N increases indefinitely. Finally a periodic solution, existing for <-1, is presented.     

Thermodynamics of the quasiequilibrial growth of crazes

By comparing the morphology and physical properties (averaged over the scale of 1 to 10m) of a crazed and uncrazed polymer, it can be concluded that crazing is a new phase development in the initially homogeneous material. The present study is based on recent work on the general thermodynamic explanation of the development of a damaged layer of material. The treatment generalizes the model of a crack-cut in mechanics. The complete system of equations for the quasiequilibrial craze growth follows from the conditions of local and global phase equilibrium, mechanical equilibrium and a kinematic condition. Constitutive equations of craze growth-equations are proposed that are between the geometric characteristics of a craze and generalized forces. It is shown that these forces, conjugated with the geometric characteristics of a craze, can be expressed through the known path independent integrals (J, L, M,). The criterion of craze growth is developed from the condition of global phase equilibrium. F Helmholtz's free energy - G Gibb's free energy (thermodynamic potential) - f density ofF - g density ofG - T absolute temperature - S density of entropy - strain tensor - components of - stress tensor - components of - _y stress along the boundary of an active zone (yield stress) - _b stress along the boundary of an inert zone - applied stress - value of at the moment of craze initiation - K stress intensity factor - C tensor of elastic moduli - C ^–1 tensor of compliance - internal tensorial product - V volume occupied by sample - V ₁ volume occupied by original material - V ₂ volume occupied by crazed material - V boundary ofV - (V) vector-function localized on V - (x) characteristic function of an area - (x) variation of(x) - (x) a finite function - tensor of alternation - components of the boundary displacement vector - l components of the vector of translation - n components of the normal to a boundary - _k components of the vector of rotation - e symmetric tensor of deviatoric deformation of an active zone - expansion of an active zone - J ⁽ⁱ⁾ ,L _k ⁽ⁱ⁾ ,M ⁽ⁱ⁾,N ⁽ⁱ⁾ partial derivatives ofG ⁽ⁱ⁾ with respect tol , _k, ande , respectively - [ ] jump of the parameter inside the brackets - thickness of a craze - 2l length of a craze - 2b length of an active zone - l _c distance between the geometrical centres of the active zone and the craze - ^* craze thickness on the boundary of an active and the inert zone - l ^* craze parameter (length dimension) - A craze parameter (dimensionless) - ^* extension of craze material     

Thermal boundary resistance in superfluid4He nearT λ

New measurements of the boundary resistivity in superfluid⁴He (2ppb³He) nearT are reported as a function of ¦¦ ( =T/T (Q) — 1) and of heat flux Q in a cell with parallel polished copper surfaces. Here we call T(Q) the temperature where the superfluid state abruptly disappears. In this design, the sidewall gaps between the copper pieces and the stainless steel spacer were eliminated. In contrast to several previous experiments but in agreement with those of Li and Lip a, no largeQ-dependent boundary resistivity anomaly was detected. However, as ¦¦ 0 the small weakly divergent resistivity was observed and its dependence onQ over the experimental range 1 <Q < 80 W/cm² was found to be very small. These new results are compared with previous experiments and predictions. An explanation of the previously observed anomalous transport phenomena is presented in terms of a heat flow through the sidewall gaps in these cells, and its limitation by a critical flow value _c. This phenomenological model can be fit satisfactorily to the observations. In the appendix we calculate _c from mutual friction.     

A molecular theory of the fracture toughness of low molecular weight polymers

Recent experiments by Robertson show that the fracture toughness G _IC of glassy polystyrene PS does not decrease to the ideal brittle value 2 (where is the surface energy for PS) at molecular weights M _w below M _c the entanglement molecular weight. Instead G _IC is more than an order of magnitude above 2 at M _c and decreases slowly below M _c. It is postulated that a small craze exists at the crack tip in such low molecular weight glassy polymers. However, since entanglements do not occur single molecules must span this craze; if they do not the craze becomes unstable and the crack advances. Under these conditions a critical craze surface displacement exists and G _C can be computed to be G _IC=S _c(–1) R ^21/2, where and S _c are the craze fibril extension ratio and craze surface drawing stress observed in high molecular weight crazes (both quantities should be only weak functions of M _w) and R ^21/2 is the root mean square end-to-end distance of the PS molecule in the glass from neutron scattering measurements. The fracture toughness is predicted to decrease as M _w ^1/2 ; this prediction and the absolute magnitude of G _IC are in excellent agreement with experiment.     

Nonequilibrium gap instability and phase transition under intense tunnel injection in superconducting lead films

We report on lead energy gap measurements made under intense tunnel current injection near the gap edge at various temperatures in terms of the differential tunnel resistance at zero bias voltage using the double-junction configuration. It is shown that the behavior is significantly different below T and above T . For T < T , a first-order transition occurs and the result is close to the prediction by the ^* model, although the estimated phonon trapping factor may be large. For T > T , an instability similar to that of Chang and Scalapino is observed. The gap reduction behavior, however, is complicated, and cannot be interpreted in terms of present theories. In addition, a new structure which indicates an abrupt enhancement of the gap is observed.     

Errors in measuring the reflection coefficient of ground

Conclusions The ground reflection factor can be determined in the range of 25–400 Mc from relative measurements of field strength in a vertical plane.In order to raise the accuracy of measurements it is necessary that the load impedance of the receiving dipole should be considerably larger than its input impedance and that its height should vary in the range of 0.5h₂2 (for h₁5=const).     

Transport properties of helium near the liquid-vapor critical point. II. Thermal conductivity of a3He-4He mixture

Measurements of the thermal conductivity are reported for an 80%³He-20%⁴He mixture above the critical point along several isotherms and near-critical isochores, using the same techniques and apparatus described for a study of³He. Using again the assumption that the observed conductivity can be decomposed into a sum of a regular and a singular contribution _reg and _sing, it is shown that along two near-critical isochores, _sing diverges. In particular, along the isochore showing the largest at the phase transition, the divergence is nearly the same as for³He and can be roughly characterized by a simple power law (T-T_c)^– with 0.58. This observation is contrary to predictions that foresee _sing0 asT _c is approached. The relaxation times characterizing the attainment of steady state conditions after switching the heat flux on and off show a similar behaviour as a function of reduced temperature as do those for pure³He. This result might indicate a substantial coupling between concentration and entropy diffusion. In the Appendix, the correlation length for³He nearT _c is calculated from heat conductivity, viscosity, and specific heat data.Work supported by Grant DMR 8024056 of the National Science Foundation.