Localized single-particle excitations and the density of states for superconducting composites

The problem of localized single-particle excitations and the density of states (DOS) for an inhomogeneous system consisting of a spherical superconductor (with radius a and order parameter ₁) embedded in another superconductor (order parameter ₂) of infinite size is considered. With the assumption of constant values of ₁ and ₂, the Bogoliubov equations are solved for general values of l (the orbital angular momentum quantum number). For a fixed value of ₁/₂ and different values of ₂/E _F, the dependence of the excitation energy (l=0)/₂ on the particle sizek _F a is shown (k _F is the Fermi wave vector andE _F is the Fermi energy). Fork _F a=300, 450, and 800 and a fixed value of ₂/E _F, the variations in the DOS by changing ₁/₂ are also shown.     

Investigation of Permittivity Dispersion in the Infralow-Frequency Band by Time-Domain Dielectric Spectroscopy

The transient-current method of time-domain dielectric spectroscopy, used to investigate the dispersion of the dielectric parameters of materials in the 10^–4–1 Hz frequency band, and apparatus based on it, are considered. A program is developed for the mathematical processing of the results of an experiment using the numerical Fourier transformation method employing cubic splines for approximation, interpolation and extrapolation of data. The frequency spectra of ' and ' of certain solid materials are presented.     

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.     

Fracture stress difference of notched polycarbonate between atmospheric pressure and a hydrostatic pressure

Experimental data on fracture stress of polycarbonate (PC) with and without various artificial notches have been obtained at atmospheric pressure and a high hydrostatic pressure (400 MPa). The difference in fracture stress, _F, between both pressures was directly proportional to the intensity of pressure,P, and was inversely proportional to the stress concentration factor of the notch,K _n such that _F following the form of the Kaieda-Oguchi formula, _F. By using the combined stress concentration factor,K _nc, of superposed notch and craze, and by considering the change in elastic modulus due to pressure, the experimental data agreed with the modified Kaieda-Oguchi formula. The stress concentration factor of the craze was calculated by using the Dugdale model.     

Methodic error of conversion of analog signals into frequency-modulated pulse signals

Conclusions For an equiprobable distribution of the position of the beginning of interval T_i on the time axis, _m manifests itself as an uncorrelated random error.If the pulse duration is negligible in comparison with the time interval between adjacent pulses, the ME of the error _m is equal to zero for AFC's with uniform or nonuniform pulse sequences.The RMSD of the error _m varies with T_i, assuming a number of extremum values [_m]_max. For the same values of T_i andf, [_mn]_max exceeds [_mu]_max by a factor of not more than 2. If the maximum allowable values of the RMSD of the methodic error _m are assigned on the basis of experimental conditions, the minimum allowable measurement time of the secondary instrument which receives the AFC signal can be found by means of (7) and (11).Translated from Izmeritel'naya Tekhnika, No. 12, pp. 53–55, December, 1972.     

An apparatus for measuring the thermal conductivity and diffusivity of solid materials

An apparatus is described for measuring the thermal conductivity and diffusivity on small specimens of solid materials; also the results are shown which have been obtained for refractive high-alumina concrete by such measurements.Notation thermal conductivity at the mean temperature of specimens, W/m· °C - Q power of the central heater, W - F cross section area of a specimen, m² - t_1,2 temperature drop across the specimens, °C - ₁, ₂ difference in heights between the thermocouple beads, center-to-center, in the first and in the second specimen respectively, m - t temperature, °C - time coordinate, min - d₁= (d_1u+d_1l )/2 mean distance between specimen contact plane and nearest thermocouple beads, for the upper and lower specimen, m - d₂= (d_2u+d_2l )/2 mean distance between specimen contact plane and farthest thermocouple beads, for the upper and lower specimen, m - dt(d₁,)/d rate of temperature rise at section d₁ of the specimen at time, °C/h - t=t₁+t₂ sum of temperature drops in the specimens at time, °C - m heating rate, h^–1 - a thermal diffusivity of specimens, referred to their mean temperature, m²/h - =m/a, m^–1 b=¦(t_u–t_l)/t_u¦ heating nonuniformity factor Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 1049–1054, June, 1972.     

Anisotropic spin diffusion and multiple spin echoes in3He-4He solutions

We propose a ₁-t₁-₂ pulse-NMR experiment to detect the spin-diffusion anisotropy, =D-D, in degenerate spin-polarized³He-⁴He mixtures, where D and dare the transverse and longitudinal spin diffusion coefficients. In such an experiment the nonlinearity of the dynamics produces multiple spin echoes (MSE). At the ³He concentration x₃ 4% the spinrotation parameter vanishes (M 0), so that the nonlinearity of the equations of motion is entirely due to the anisotropy. In this situation, detection of MSE amounts to observation of D. For slight anisotropy, i.e. D/D 0.25, we use a perturbation scheme similiar to that developed by Einzel et al. (in that case, for small M and small demagnetizing field) to calculate the second and third echo heights. For larger anisotropy we numerically calculate the echo heights. We find that for D/D = 0.5 the heights are 2 % of the first echo, and should be detectable. The (₁, ₂) tip-angle dependence of the D echoes is different from that of the M and demagnetization echoes, and furthermore, they occur at right angles to these echoes (in spin space). Thus, even when small spin-rotation and demagnetization effects are present, the ₁-t₁-₂ experiment provides a sensitive means of detecting the anisotropy.     

New Universal Relations for Liquid-Vapor Phase Equilibrium

Universal relations between the saturation pressure p _LV and the value of =h _LV/ _LV–p _LV, where h _LV .is the latent heat of evaporation and _LV is the volume change of the vapor-liquid transition, and the product of the orthobaric densities _L and _V of the liquid and vapor at coexistence have been discovered. In the temperature range from the triple point to T/T _c0.9, these relations obey a power law with universal exponents. At temperatures 0.9<T/T _c1, p _LV and depend linearly on ln( _{L V}) with retention of universality for substances of different nature.     

Ageing characteristics of cast Zn-Al based alloy (ZnAl7Cu3)

Microstructure and ageing characteristics of a cast Zn-Al based alloy (ZnAl7Cu3) were studied using X-ray diffraction, electron scanning microscopy and back-scattered diffraction techniques. Two stages of phase transformation, i.e., decomposition of zinc rich phase and four phase transformation, + T + , were detected during ageing at 150°C. Electron back-scattered diffraction technique was applied in distinguishing both zinc rich and phases.     

The effect of Ag additions on the microstructure of aluminium–lithium alloys

Minor quantities of Ag have been added to Al–Li–Cu–Mg–Zr alloys. Their microstructure has been studied by means of optical metallography, transmission electron microscopy and X-ray diffraction. In the high Li, low Cu:Mg ratio alloys the main phases found were , , S and T1, while fewer T2 and Al7Cu2Fe precipitates were also observed. The addition of up to 0.5 wt% Ag diminishes the and T1 precipitates size. This is attributed to a small increase of Li solubility in the matrix. In the low Li, high Cu:Mg ratio alloy the addition of 0.2 wt% Ag resulted in the precipitation of phase simultaneously with , , S and T1 phases. Due to the low Li concentration an unusual growth of the / precipitates at the expense of the precipitates was also observed. © 1998 Kluwer Academic Publishers     

Streamline curvature effects in side-channel spillway flow

Summary Steady flow in side channel spillways is investigated, thereby accounting for the effects of the streamline slope and curvature on the free surface profile. The governing system of equations is linearized in order to discuss the main features of the solutions. Subsequently, the non-linear version is solved by an implicit numerical procedure; particular attention is paid to the stability of the chosen scheme. Finally, the solutions are compared to observations and an almost perfect agreement is found.Notation a reference flow depth - b channel width - F Froude number - g gravitational acceleration - h flow depth - J average energy gradient - K Strickler's roughness coefficient - L lateral inflow length - m root of characteristic polynomial - n Manning's roughness coefficient - p lateral inflow intensity per unit channel width - q lateral inflow intensity - Q discharge - R hydraulic radius - S specific momentum - S _f frictional slope - S ₀ bottom slope - V average cross-sectional velocity - x longitudinal coordinate - X normalized longitudinal coordinate - y normalized flow depth - factor, 01 - factor, 01 - perturbative change in flow depth - relative discharge intensity - relative specific momentum With 7 FiguresSeveral symbols may appear with indices u, d, N, c and then refer to the up-and downstream end of the lateral inflow zone, and to uniform and critical flow conditions, respectively. Primes indicate derivatives with respect to the longitudinal coordinate.     

Third sound in a restricted geometry

Bergman's general treatment of third sound waves has been extended to a (restricted) parallel plate geometry. In a parallel plate geometry two independent third sound modes can propagate: a symmetric and an antisymmetric one. Calculations show that at temperatures below 1 K the antisymmetric mode carries the most important part of the temperature amplitude. Because of the relatively strong substrate influence the temperature amplitude of the symmetric mode is suppressed. The T/h versus T measurements by Laheurteet al. ¹ and of the T/h versus measurements by Elliset al. ² are explained.     

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.     

Low endurance fatigue in metals and polymers

The fatigue behaviour of commercially pure aluminium and of nylon under sequentially varying strain amplitudes is compared with a damage law of the type suggested by Miner. Aluminium obeys such a law for both cyclic and uniaxial prestrains but the behaviour of nylon is significantly affected by microcracking, which produces a marked effect of loading sequence.Appendix N Number of strain cycles at a given time - N _f Value of N at failure - True tensile stress - True stress range for a strain cycled specimen - _h Value of at half the life of the specimen - True tensile strain - Total true strain range - _p True plastic strain range (= the breadth of the hysteresis loop at = 0) - _d True diametral strain range - E Young's modulus - Linear strain hardening rate when tested at a particular value of _p - D Damage due to cycling - D _p Damage due to prestrain - _p Prestrain. C, K, K₁, , are constants     

Steady-state heat transfer through a wall with longitudinal rectangular fins and variable thermal conductivity

A method is examined of solving steady-state problems of heat transfer through a surface with longitudinal rectangular fins in the case when the thermal conductivity depends on temperature.Notation T temperature - T₀ temperature of coolant - T₁ temperature at base of fin - T_N some characteristic temperature - (T) thermal conductivity of fin material - heat transfer coefficient; F-cross-sectional area of fin - fin perimeter - h fin height - L fin length - fin thickness - Q heat flux - O_i change of temperature in i-th section - T_i mean temperature at i-th section     

Free convective flow in an enclosure with a cooled inclined upper surface

Natural convective air flow in an enclosure with a horizontal lower wall, vertical side-walls and a straight inclined top wall has been numerically studied. The lower wall is at a uniform high temperature while the top wall is cooled to a uniform lower temperature. The temperature of the side-walls varies in a prescribed way between the temperatures of the bottom and top walls. This flow situation is related to that occurring in a proposed system for use in developing countries for drying crops such as corn and rice. It has been assumed that the flow is steady, laminar, and two-dimensional and that the fluid properties are constant except for the density change with temperature that gives rise to the buoyancy forces. The governing equations have been expressed in terms of stream function and vorticity and written in dimensionless form. The finite element method has been used to obtain the solution to these dimensionless equations. Results have been obtained for enclosures with aspect ratios of between 0.25 and 1 for top surface angles of inclination of between 0 and 45° and for Rayleigh numbers, based on the enclosure width, of between 1000 and 10⁷. The results have been used to study the effect of changes in the governing parameters on the flow pattern in the enclosure and on the mean heat transfer rate to the upper surface.List of symbols A aspect ratio, h/w - h mean height of cavity - k thermal conductivity - Nu local Nusselt number based on w - mean Nusselt number for top surface based on w - n n/w - n coordinate measured normal to boundary surface considered - p pressure - Pr Prandtl number - q local dimensionless heat transfer rate - mean heat transfer rate to top surface - Ra Rayleigh number based on w - T dimensionless temperature - T temperature - T _H temperature of bottom surface - T _C temperature of top surface - u velocity component in x direction - v velocity component in y direction - w width of cavity - x dimensionless x coordinate - x horizontal coordinate position - y dimensionless y coordinate - y vertical coordinate position - thermal diffusivity This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.     

Subgap peak and Tomash-McMillan-Anderson oscillations in the density of states of SNS Bridges

The quasiparticle spectra and the densities of states of superconducting-normal-superconducting junctions are computed from the WKBJ transformed Bogoliubov-de Gennes Equations (BdGE), which are solved by Picard iteration and numerical integration. It is shown that the influence of the proximity effect on the bound states can be modeled by a rectangular pair potential well of effective normal layer thickness 2a*= _–L ^L [1–(z)/]dz, where (z) is the pair potential of the junction, is its asymptotic constant value, and 2L is the total length of the sample. The density of states exhibits a subgap peak at energies less than besides the BCS peak atE=; forE> there are geometrical resonances which are due to electron-hole interferences in finiteS layers of thicknessL-a*.     

Supercooling of In2Bi and InBi Melts

The effect of melt overheating T ⁺ on the critical supercooling T ^– of liquid In₂Bi and InBi is studied by cyclic thermal analysis. It is shown that, the T ^– for In₂Bi is 2.0 K, independent of the melt preheating temperature. In contrast, the T ^– for InBi varies jumpwise with T ⁺: T ^– 1.0–1.6 K at T ⁺ < 5 K, and T ^– 16 K at T ⁺ = 5–300 K, independent of the cooling rate (varied from 0.002 to 8.0 K/s). The solidification behaviors of In₂Bi and InBi are shown to correlate with the structures of their liquid and solid phases.     

Nucleate boiling

The study deals with the effect of the surface conditions on the nucleate boiling curve. A relation is proposed which describes the complete nucleate boiling curve.Notation q thermal flux - q* thermal flux at which the liquid boils after one-phase convection - q_c thermal flux during one-phase convection - q_cr1, q_cr2 first and the second critical thermal flux - T saturation temperature - T superheat of the heating surface relative to the saturation temperature - T* superheat prior to boiling of the liquid after one-phase convection - T_cr1 superheat during the first boiling crisis - T_cr3min minimum superheat at which the third boiling crisis can occur - P pressure - P_cr critical pressure - heat transfer coefficient during nucleate boiling - R_cr radius of a critical vapor forming nucleus - coefficient of surface tension - r latent heat of evaporation - thermal conductivity of the liquid - kinematic viscosity of the liquid - , densities of the liquid and the vapor - g gravitational constant - k Boltzmann constant - N Avogadro number - h Planck's constant Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 394–401, March, 1981.