Critical and tricritical dynamics in3He-4He mixtures

A new formalism is presented to study the critical and tricritical dynamics of³He-⁴He mixtures near the superfluid transition for arbitrary concentration. In this fluid two conserved variables, the molar concentrationX and the entropys, are twofold coupled to a complex order parameter ψ first in the dynamic equations reversibly and second in the free energy dissipatively. However, at an intermediate concentrationX=X _D (which is 0.37 at the saturated vapor pressure) a linear combination ofX ands is found to be asymptotically decoupled from ψ both reversibly and dissipatively. There, dynamic renormalization group equations reduce to those of pure⁴He (or those of the F model) and some dynamic properties are common to those of pure⁴He. For example, atX≈X _D , the gradient ?(T?T _λ ) under heat flow goes to zero without³He mass flow, whereT _λ is the critical temperature, dependent onX, and the thermodiffusion ratio loses the singularity with the critical exponent α. Our dynamic renormalization group equations take into account the above two nonlinear couplings and can be used for any concentrations. Furthermore, using a linear response scheme, general relations are obtained among the kinetic coefficients. As a result the thermal conductivity on the λ line is found to be exactly proportional toX ^?1 at smallX. The coefficient in front ofX ^?1 can be expressed in terms of the diffusion constant of an isolated³He molecule in⁴He.     

High Frequency Transport Properties of YBCO: Extrinsic Versus Intrinsic d-Wave Properties

In good superconducting YBCO films, the surface impedance Z(T,ω,B)=Z_int(T,ωB)+Z_res(T,ωB) is dominated for T T _c/2 and B～0 by intrinsic properties, which are difficult to improve. Below T _c/2, Z _res usually dominates over Z, and below 0.9 T _c, Z(T,ω,B) increases with field, both are, up till now, explained by extrinsic properties related to extrinsic and intrinsic surfaces. The latter are named weak or strong links (WSL), into which around B _c1J for ω₀ ^J » ω₀ ^A Josephson fluxons (JF) enter, where B_c1J « B_c1 holds with B_c1 the lower critical field of Abrikosov fluxon (AF) with ω₀ ^A ～ MHz their nucleation or pinning frequency. Below fields ?B _C1 and below the pinning or nucleation frequency ω₀ ^J ～ THz hysteresis losses increase Z=R+iX nonlinearly with r(T,ω)=δ X/δ R～2 with the surface resistance R and the surface reactance X. The nonlinearities decrease toward B _c1J to (small) oscillation of JF yielding r(T,ω) δ ω₀ ^J (T)/ω . Those Z nonlinearities yield harmonics or intermodulation products IMD(T). Below B _c1J new types of nonlinearities relate to d-wave properties of HTS. Either nonlinear Meissner effect (NME) and anomalous Meissner effect (AME) at internal or external surfaces are proposed with r ? 1, observed by harmonic generation and by specific IMD(T, B) dependencies being identified recently. New developments in theory and experiment and procedures to separate extrinsic from intrinsic properties will be analyzed.     

Evaluation of Shewhart time-between-events-and-amplitude control charts for correlated data

In recent years, several techniques based on control charts have been developed for the simultaneous monitoring of the time interval T and the amplitude X of events, known as time-between-events-and-amplitude (TBEA) charts. However, the vast majority of the existing works have some limitations. First, they usually focus on statistics based on the ratio $\frac{X}{T}$, and second, they only investigate a reduced number of potential distributions, that is, the exponential distribution for T and the normal distribution for X. Moreover, until now, very few research papers have considered the potential dependence between T and X. In this paper, we investigate three different statistics, denoted as Z₁ , Z₂ , and Z₃ , for monitoring TBEA data in the case of three potential distributions (gamma, normal, and Weibull), for both T and X, using copulas as a mechanism to model the dependence. An illustrative example considering times between machine breakdowns and associated maintenance illustrates the use of TBEA control charts.     

On the effect of noisy measurements of the regressor in functional linear models

We consider the estimation of the slope function in functional linear regression, where a scalar response Y is modelled in dependence of a random function X, when Y and only a panel Z ₁,…,Z _L of noisy measurements of X are observable. Assuming an i.i.d. sample of (Y,Z ₁,…,Z _L ) of size n we propose an estimator of the slope which is based on a dimension reduction technique and additional thresholding. We derive in terms of both the sample size n and the panel size L a lower bound of a maximal weighted risk over a certain ellipsoid of slope functions and a certain class of covariance operators associated with the regressor X. It is shown that the proposed estimator attains this lower bound up to a constant and hence it is minimax-optimal. The results are illustrated considering different configurations which cover in particular the estimation of the slope as well as its derivatives.     

Studies on initial permeability and loss factor in Ni-Zn ferrites synthesized by oxalate precursors

Ni_XZn_1−XFe₂O₄ ferrites with (X = 0.28-0.40 in step of 0.2) have been synthesized by oxalate precursor method and investigated for their, initial permeability and loss factor measurements. Initial permeability has been observed to increase with the increase in Ni²⁺ up to X = 0.32, beyond which it decreases. The variation of initial permeability has been explained by considering the factors such as grain size, saturation magnetization and anisotropy constant. Thermal variation of initial permeability reveals a peak height in μ_i-T curves which tends to increase with increase in Ni²⁺ content. μ_i-T curves also exhibit thermal hysteresis, which reveals the inverse relationship between the difference in heating and cooling curves at which hysteresis falls between Hopkinson peak and T_c with value of initial permeability. Loss factor values are small which is attributed to high density of the samples and processing techniques.     

Ultrasonic propagation in3He-4He mixtures near the tricritical point

We present measurements of the singular sound attenuation _sing in liquid mixtures of³He and⁴He near the superfluid transition and at temperatures above the phase separation curve. The mole fractionX of³He ranged from 0.55 to 0.73 and the frequency /2 varied between 1 and 45 MHz. The temperature range was 0.75–1.4 K, with the greatest emphasis on the tricritical region nearX _t=0.67 andT _t=0.87 K. From the change in slopedU/dT of the sound velocityU, we present a new determination of the phase separation curve, which is compared with previous measurements. The sound attenuation peak along the superfluid transition becomes broader in temperature asT is decreased. In addition, there is also an increase in sound attenuation as the phase separation temperatureT is approached. ForX<X _t these two peaks merge into one asX _t is approached. For a given frequency, the attenuation has a maximum value at the tricritical point. Estimates of the contribution _D of mass diffusion to the attenuation for³He-⁴He mixtures with 0<X<0.55 and comparison with experimental values show that _D becomes relatively more important asX increases, and that atX=0.55 it effectively accounts for all of the observed singular attenuation, at least at megahertz frequencies. Hence we assume that for mixtures withX>0.55 the observed attenuation can be analyzed solely in terms of the diffusive relaxation mechanism. The mass diffusion parameterD is then determined from the data. AtX=0.55,D diverges asT is approached, which is consistent with theoretical expectations and experimental results. NearT _t, there is a crossover to a tricritical regime, and it is found that approximatelyD(T–T _t) ^Z withZ=0.32±0.1. Mode coupling predictions are thatZ=1/2 while recent renormalization group calculations giveZ=1/3. The attenuation curves in the tricritical region at the various frequencies can be represented satisfactorily but not perfectly by a scaling function with a characteristic relaxation time (T–T _t) ^–x withx=1.7±0.15. This time corresponds to order-parameter fluctuations. Its temperature dependence is in excellent agreement with renormalization-group calculations that givex5/3, while expectations from dynamic scaling are thatx=3/2. Our analysis also gives the variation of the amplitudes of andD with the direction of approach toT _t. A comprehensive theory for interpreting all the data, in the normal as well as in the superfluid phase, is lacking at this time.Supported by a grant from the National Science Foundation. A preliminary account of this work was presented inBull. Am. Phys. Soc. 21, 229 (1976).     

Superfluid Transition of a 4He Thin Film Pressurized by Bulk Liquid 3He

We measured transverse acoustic impedance Z of normal fluid ³He at 46.6 MHz on a surface coated with a thin ⁴He film. The real component of the impedance, Z′, in the coated samples deviates from Z′ in the pure ³He in the low temperature region. Z′ on the coated samples is almost identical with Z′ in the pure sample at high temperature and gradually deviates below a particular temperature T _onset . T _onset  is possibly the superfluid onset temperature of the ⁴He film pressurized by the bulk liquid ³He. The gradual decrease in Z′ means that the superfluid component in ⁴He film increases gradually, which is expected from the dynamic KT transition at high frequency. The thicker is the film, the higher is the T _onset . The range of T _onset we observed was between 40 and 160 mK. This is much lower than that at the saturated vapor pressure. Suppression of T _onset achieved by the applied pressure from bulk liquid ³He was presumably caused by the dissolved ³He in the film, thickening of the inert layers and/or by the strong correlation effect. The result shows that the specularity of ³He quasiparticle scattering is strongly affected by superfluidity of the ⁴He film.     

The response to ambient pressure of fuel drop combustion with surface equilibrium

The burning rate response of a fuel drop to ambient pressure is determined, using the method of activation-energy asymptotics. The combustion is assumed to be quasi-steady and spherically symmetric. Other analyses of this problem have commonly, but unrealistically, assumed that the surface temperature T_s may be prescribed a priori. By contrast, the present analysis imposes vapor-liquid equilibrium at the surface of the drop, so that T_s is determined as part of the solution. The resulting response curves differ markedly from those obtained by prescribed-T_s analyses. In particular, it is shown that the burning rate actually decreases over much of the response as the ambient pressure increases. Also, in the limit of large pressure, the reaction zone moves to the surface of the drop (the Buckmaster flame), rather than evolving into the familiar Burke-Schumann equilibrium flame.     

Critical behavior of a charged Bose gas

A fully self-consistent Hartre-Fock theory, using the Coulomb interaction screened by the polarization insertions calculated in the self-consistent random-phase approximation, is applied to thed-dimensional, dense, charged Bose gas at temperatures close to the transition temperatureT _c . The quasiparticle energy spectrum is calculated and shown to behave atT _c like ε(k)=Ak ^σ for smallk, and σ is calculated as a function of the dimensionalityd. The change in transition temperature from that of an ideal gas at the same density, and of the chemical potential are shown to be given by (T _c ?T _c0 )/T _c0 ≈Xr _s ^(d?2)/3 and μ _c ≈Yr _s ^2/3 , wherer _s is the ratio of the interparticle spacing to the Bohr radius. Approximate expressions are given for the coefficientsX andY. The critical exponents are calculated, and the system is shown to obey exact scaling.     

Band gap and structural parameter variation of CuInSe2(1-x)S2x solid-solution in the form of thin films

CuInSe_2(1-x)S_2xthin films were deposited by spray pyrolysis. Lattice parametersa andc, for all composition parametersX, were calculated from the Phillips X-ray diffractometer. The structure remained tetragonal chalcopyrite throughout. Optical band gap (E _g) was determined for the composition parameterX from the transmittance study at room temperature. Variation ofE _g,a andc withX was found to be linear.     

Two-Peak Temperature Dependence of Microwave Surface Impedance of Single-Crystalline YBCO Thin Films: Role of Pairing Symmetry and Defect Structure

Temperature dependencies of microwave surface impedance were measured for c-oriented highly perfect YBCO thin films deposited by off-axis dc magnetron sputtering onto CeO₂-buffered r-cut sapphire substrates. A distinct two-peak structure of R _s(T) and X _s(T) dependencies with peaks at 28–30, K and 50, K has been revealed. The peaks become smeared at higher frequencies or in applied dc magnetic field, while the peak positions remain almost unchanged. The two-peak Z _s(T) behavior is believed to be an intrinsic electron property of extremely perfect quasi-single-crystalline YBCO films. A theoretical model is suggested to explain the observed anomalous Z _s(T) behavior. The model is based on the Boltzman kinetic equation for quasiparticles in layered high-T _c superconductors (HTS) cuprates. It takes into account the supposed s + d wave symmetry of electron pairing and strong energy-dependent relaxation time of quasiparticles, determined mainly by their elastic scattering on extended defects parallel to the c-axis.     

The temperature dependence of the dielectric constant in solid H2, D2,4He,and Ne

The dielectric constant ε of solid hexagonal close-packed H₂ (X?0), H₂(X?0.7), D₂(X=0.33), and He ⁴ at constant volume and of H₂(X=0.75) and Ne at saturated vapor pressure is studied as a function of temperature between 1.17 and 10 K. HereX is the fraction of molecules with angular rotational momentumJ=1, the fraction 1?X havingJ=0. These are the first reported measurements on van der Waals solids at constant volume. The experiments were carried out using a thick-walled capacitance cell, the measurement frequency being 14 MHz. The observed changes of ε withT are expressed in terms of the effective polarizability α_CM defined by the Clausius-Mosotti relation. A reduced polarizability α*=α_CM (T)/α_CM (T=1.17 K) is presented as a function of temperature. The initial purpose of the measurements was to observe the effect of rotational ordering of the(J=1) molecules in H ₂ , to be detected by a change in polarizability, as suggested by A. B. Harris. With increasing temperature it was found that α_CM decreased of the order of 0.1% for H ₂ and D ₂ . Also, differences were found between H₂(X=0) and H₂(X=0.75), which are briefly discussed. For He ₄ , α_CM decreased by about 3×10 ^?5 between 1.17 K and the melting point, 3.8 K. An analysis of the results showed that the temperature variation of α_CM could not be caused by the effect of lattice vibrations. Also, a simple calculation shows that the rearrangement of molecular positions in H ₂ and D ₂ at constant volume would have to be quite substantial to account for the observed temperature change in α_CM, which change is therefore not understood. The dielectric constant of Ne was measured at saturated vapor pressure and corrections were made to obtain the change of α_CM at constant volume. Rather different results were obtained for Ne than for the other solids: α_CM rose sharply with temperature, and this behavior also is not understood. Measurements of the diectric constant of H₂(X=0) and H₂(X=0.73) near the melting curve showed that the polarizability α_CM is the same within 0.1% in both the liquid and the solid phases. In the solid and liquid phases the density differences between H₂(X=0) and H₂(X=0.75) and also the differences in the respective melting pressures are in good agreement with the previous published work.     

Damping of torsional oscillations of a quartz crystal cylinder in liquid helium at low temperatures. I. Viscosity of pure3He

Measurements have been made of the viscosity of pure liquid ³ He at the saturated vapor pressure over the temperature range 20 mK to 1 K, by observation of the decay of torsional oscillations of a crystalline quartz cylinder. The results generally confirm previous measurements by other methods, but are more accurate and extend over a wider temperature range. Careful data analysis has been carried out to determine the best fit, which is given by the equation (ηT ² )^?1 =A ₀ +A ₁ T ⁿ , withA ₀ =0.5450,A ₁ =?1.594, andn=1 (with η in micropoise) and which indicates that higher-order terms inT (n>1) are inappropriate. The coefficientA ₁ is four times larger than that given by theory which calculates it with use of only theZ ₀ Landau parameter, indicating that other interaction parameters should be included.     

Theory of the negative anode drop in low-pressure discharges

A kinetic model of the anode region with a negative anode potential drop is proposed, which explicitly takes into account the ratio of the directed velocity of electrons in plasma v ₀ to their thermal speed v _T as a parameter of the electron velocity distribution function. A transcendent equation is derived for determination of the negative anode drop as a function of the ratio v ₀/v _T . It is shown that, unlike the known Langmuir formula, the anode drop remains negative for any value of v ₀/v _T . In the case of small values (v ₀/v _T ? 1), the derived expression asymptotically reduces to the Langmuir formula. It is shown that the dependence of electron concentration on the potential differs from the Boltzmann law. The anode regions of the short high-current vacuum-arc discharge and the classical low-pressure discharge are considered as examples. For the vacuum-arc discharge, the current density distribution and the anode drop distribution over the anode surface under strong current contraction are calculated. For the low-pressure discharge, potential drops are calculated across the region of the inhomogeneous near-anode plasma and the space charge layer.     

Pulsed NMR studies in solid H2. III. Spin-lattice relaxation times

We report a systematic study of the longitudinal relaxation timeT ₁ for solid H₂ samples with ortho concentrationX between 0.15 and 0.70 and for 0.1?T?2 K. It is over this temperature region that substantial orientational ordering takes place, which drastically affectsT ₁. The measurements were made using the solid echo technique at 9 and 27 MHz. By Fourier-transforming the echo decay, it was possible to investigate the recovery from saturation of the various parts of the NMR absorption line as a function of their distance ν?ν _L from the center at the Larmor frequency ν _L .The dependence ofT ₁ on ν?ν _L is particularly noticeable in the hcp disordered (para-orientational) phase at the lowest temperatures, where the NMR absorption is broad, and this observation is qualitatively explained. An attempt is made to understand the general features ofT ₁ in the cubic ordered phase and in the hcp para-orientational phase in terms of certain relaxation mechanisms. A comparison with previous work is presented.     

NMR studies on single crystals of H2: IV. The HD impurity spectrum

Pulsed nuclear magnetic resonance and continuous wave (cw) measurements have been carried out on the proton signal of HD impurities in solid H₂ with low concentrations of ortho-H₂. The NMR absorption width is found to be appreciably smaller than that calculated for intermolecular interaction with surrounding o-H₂ in a rigid lattice, and motional narrowing via exchange is proposed to account for the observations. Detailed studies of the transverse and longitudinal relaxation timesT ₂ andT ₁ as a function of pulse width, temperature, magnetic field direction, time effects, and ortho concentrationX are described for four different samples, two of them single crystals. In particular we find thatT ₂, observed after clustering of the o-H₂ singles and pairs at temperatures below 0.1 K, is approximately twice as large asT ₂ at the start of the clustering process. We report the absorption linewidth (T ₂)^–1 after clustering as a function ofX. The width always decreases withX and the differences between the samples might be accounted for by the crystallization process and the resulting strains. The cw measurements showed a surprising shift in the Larmor frequency between the proton signal of HD and that of the isolated o-H₂ (with no nearest o-H₂ neighbors). UnlikeT ₁ andT ₂, which are isotropic in the single crystal samples, this shift was found to be anisotropic. The possible origin of this shift is discussed, but no satisfactory conclusions are reached.     

Parallel-plate resonator of variable spacer thickness for accurate measurements of surface impedance of high-T c superconductive films

Measurements of microwave surface impedance of high-T _c films at gigahertz frequencies and nitrogen temperature are performed. A simple technique employing a parallel-plate resonator with liquid nitrogen as a dielectric spaces is suggested. The use of a precise mechanical device provides smooth changing of distance between films from 200μm down to zero. Coupling to the resonator is accomplished by means of two small antennas-half-wave vibrators for frequency 10 GHz. The method for determining resistivity and magnetic field penetration depth was based on the analysis of spacer thickness dependences of the resonator quality factor and frequency. YBa₂Cu₃O₇ films produced by a laser deposition technique on CaNdAlO₄ substrates withT _c =91 K andj _c =10⁷ A/cm² and on NdGaO₃ substrates withT _c =91 K andj _c =10⁶ A/cm² are examined, and the valuesR _s =0.6 mΩ,λ=348 nm atf=8.97 GHz andR _s =0.5 mΩ,λ=250 nm atf=10.12 GHz, respectively, are obtained at 77 K.     

The theory of search from a statistical viewpoint

Summary The statistical approach to search is a subject which interfaces with many other fields. This work continues a series of papers which studies these relationship with special emphasis on geometric problems in non-sequential search. A targetT is sought using a series of testsX ₁,X ₂.... From each test there is an observationY _i=f(X _i , θ), where θ is an unknown parameter andT=T(θ). Spacing theories and the theories of Voronoi regions can be used to represent the solutions to Bayes and entropy-based formulations to the search problem by partitioning the search field intoconsistent regions where the target is known to lie, given the observations. Other examples are from integration where the target is a function. Covering theory is studied and the last section gives a brief comparison with a sequential approach. Read before the Spanish Statistical Society at a meeting organized by the Universidad de Almería on Friday, April 29, 1994     

Structural,Elastic, Electronic,and Magnetic Properties of the Full-Heusler Compounds Ti<Subscript>2</Subscript>Ni<Emphasis Type="Italic">X</Emphasis> (<Emphasis Type="Italic">X</Emphasis>= Al,Ga, and In)

We present a quantum-mechanical first-principle calculation of the structural, elastic, electronic, and magnetic properties of the full-Heusler compounds Ti₂NiX (X= Al, Ga, and In). The calculation uses the full-potential linearized augmented plane waves plus local orbital method to describe Ti₂-based Heusler alloys. The results show that these compounds exhibit half metallic characteristics over a wide range of mesh parameters and obey the Slater–Pauling rule, which states that the total magnetic moment per unit cell M _t = Z _t? 18 for half-Heusler compounds XYZ and M _t = Z _t? 24 for full-Heusler X ₂ YZ compounds. For these new alloys Ti₂NiX (X= Al, Ga, and In), we initially considered the two possible L2₁ structures AlCu₂Mn and CuHg₂Ti. However, two subsequent structural studies showed that only the CuHg₂Ti-like structure is half metallic. Over a wide range of mesh parameters, the calculations give a total magnetic moment of 3.00 μ _B. These results suggest that Ti₂NiX (X= Al, Ga, and In) are promising materials for spintronic applications.