Coupling of order parameter collective modes to spin density in3He-B

We derive a general expression for the dynamic spin susceptibility of³He-B which is valid for all magnetic fields. The coupling of real and imaginary modes by particle-hole asymmetry is taken into account. Then we calculate the contribution of the mode at frequency =2 – 1/4 ( is the effective Larmor frequency) to the transverse susceptibility. The spectral weight of this mode in magnetic resonance absorption is proportional to (/)^1/2 (–)², where and are particle-hole asymmetry parameters. From the experimental coupling strength of the real squashing mode to sound we estimate (–)²10^–4. The dynamic susceptibility satisfies the sum rules of Leggett. Finally we point out the difficulties in calculating the transverse NMR frequency of³He-B. These difficulties arise from theS _z =0 Cooper pairs and from the coupling ofJ _z =±1 modes forJ=1 andJ=2.     

Some electrical characteristics of lithium and yttrium sialons

Some electrical properties of hot-pressed lithium sialons, Li _x/8Si_6–3x/4Al_5x/8O _x N_8–x havingx<5 and an yttrium sialon were measured between 291 and 775 K; the former consisted essentially of a single crystalline phase whereas the latter contained 98% glassy phase. For lithium sialons, the charging and discharging current followed al(t) t ^–nlaw withn=0.8 at room temperature. The d.c. conductivities were about 10^–13 ohm^–1 cm^–1 at 291 K and rose to 5×10^–7 ohm^–1 cm^–1 at 775 K. At high temperatures electrode polarization effects were observed in d.c. measurements. The variation of the conductivity over the frequency range 200 Hz to 9.3 GHz followed the () ⁿ law. The data also fitted the Universal dielectric law,() ^n–1 well, and approximately fitted the Kramers-Kronig relation()/()– =cot (n/2) withn decreasing from 0.95 at 291 K to 0.4 at 775 K. The temperature variations of conductivities did not fit linearly in Arrhenius plots. Very similar behaviour was observed for yttrium sialon except that no electrode polarization was observed. The results have been compared with those obtained previously for pure sialon; the most striking feature revealed being that _d.c. for lithium sialon can be at least 10³ times higher than that of pure sialon. Interpretation of the data in terms of hopping conduction suggests that very similar processes are involved in all three classes of sialon.     

Thermodynamic properties of superconducting niobium

The thermodynamic properties of superconducting Nb are calculated numerically from the solution of the Eliashberg equations on the imaginary axis for several possible electron-phonon spectral densities ²()F(). Comparison with experiment is made in order to see which spectrum gives the best agreement, and functional derivatives with respect to ²()F() are used to estimate how this agreement might be improved by small changes in ²()F(). Possible gap anisotropy effects are also considered with the help of a simple model anisotropy for the interaction.Research supported by Natural Science and Engineering Research Council of Canada.     

AC electrical conductivity of electron beam evaporated Cu-GeO2 thin cermet films

AC electrical properties of 410 nm think 30 at.wt% Cu-70 at.wt% GeO₂ thin films are reported for the frequency range 10⁴ to 10⁶ Hz and temperature range 150 to 425 K. The loss tangent (tan ) and the dielectric loss (/₀) are found to show striking minima around a cut-off frequency 10⁵ Hz. In the lower frequency range (10⁵ Hz), ₁() ^s T ⁿ is obeyed with s (0 to 0.51) increasing as a function of temperature and n (0.10 to 0.14) showing a very weak temperature dependence. In the higher frequency region (10⁵ Hz), ₁() and /₀ increase sharply leading to the quadratic behavior of ₁() with s equal to 2. These processes are discussed by analyzing an equivalent circuit which shows that at lower frequencies, the effects of series resistance in leads and contacts can be neglected, while at higher frequencies such effect give rise to spurious ² dependance for the conductance. A weakly activated AC conductivity and a frequency exponent s that increases with increasing temperature suggest that the low frequency behavior originates from carrier migration by tunneling process.     

A model with length scales for composites with periodic structure. Steady state heat conduction problem

A new high-order model for analysing distribution of temperature in periodic composites is proposed. The original scalar elliptic problem with Y-periodic coefficients (Y is a cube) is replaced with a vectorial elliptic problem of constant coefficients. The unknown fields are: the averaged distribution of temperature and the vector field which stands for perturbation of the temperature within the cells of periodicity. The recovery of temperature in the original composite is given by the approximation: 0(x)=0(x) +h ^a (x/) _a (x) analogous with the first terms of the two-scale asymptotic expansion known from the homogenization theory. The functions h are defined as approximations of the solutions to the basic cell problems. In contrast to the two-scale expansion the expression for satisfies the boundary condition.     

On the resonance of acoustic waves in slightly deformed and slowly moving slabs

The stability is studied of acoustic waves generated by a time harmonic force in slabs described by: 0z1±g(x, y). By using a recently developed method, the exact solution of the Dirichlet problem is found for =0. It is shown that the solution is unstable against values of the frequency: =n,n. This is in agreement with the result already known in the literature, but found by other means. In a slightly deformed slab, 0<1, it is shown that stabilization of the resonant wave occurs at a time of order ^–. This is valid if the upper boundary is a concave surface. In case of a slab with slowly moving upper boundary, only the growth rate of the amplitude of the resonant wave is reduced. This holds for a non-oscillating motion of the upper boundary. In the case of an oscillating motion a further resonance is produced.     

Universal simulation of degenerating homogeneous turbulence

The problem of universal simulation of the dynamics of a turbulent velocity field (universal in the sense of arbitrary values of the Reynolds turbulence number) is treated on the basis of the moment model in the second approximation.Notation ¯q² _i ² double the kinetic turbulence energy - _u ² =5v¯q²/_u Taylor turbulence scale squared - _u=v1/x_k)²> kinetic-energy dissipation function - N_Re,=¯q²_u / Reynolds turbulence number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 46–52, January, 1982.     

Thermal response of a3He-superfluid-4He mixture

The response of a layer of superfluid mixture to an ac heat source,Q(t)=Q ₀ exp(it), is determined. In the low-frequency regime, the temperature response at the heated side of a superfluid layer is essentially identical to that of an ordinary fluid having a thermal conductivity _eff and a thermal diffusion coefficient ₀ /2. Here _eff is the effective conductivity of Khalatnikov, and ₀ is the diffusion coefficient of Griffin. At much higher frequencies, the results are more complicated. The low-frequency regime is defined in terms of the second sound velocityu ₂ by u ₂ ² / ₀ . The ac response function is valuable in a number of ways. It can be used to obtain the system response to more complicated time-dependent variations inQ such as step changes inQ. A knowledge of the response function in the low-frequency regime provides a mechanism for directly determining the Kapitza resistance in mixtures. Finally, a knowledge of the response function provides an additional opportunity to test two-fluid hydrodynamics. Alternative tests of superfluid hydrodynamics are of particular interest in light of recent experiments that show anomalous values for _eff in the low ³ He concentration limit     

Isochoric specific heat of sulfur hexafluoride at the critical point: Laboratory results and outline of a spacelab experiment for the d1-mission in 1985

The specific heat at constant volume c_v shows a weak singularity at the critical point. Renormalization group techniques have been applied, predicting a universal critical behavior which has to be experimentally confirmed for different systems. In this paper an experiment is presented to measure the specific heat of SF₆ along the critical isochore (_c=0.737 g·cm^–3), applying a continuous heating method. The results cover a temperature span of –1.5×10^–2< <1.70×10^–2 [=(T–T _c)/T _c] and were strongly affected by gravity effects that emerge in the sample of 1-mm hydrostatic height near the critical point. Using regression analysis, data were fitted with functions of the form c _v/R=A × ¦¦^– + B for the one-phase state and c _v/R=A × ¦¦^– + B for the twophase state. Within their error bounds the critical values (==0.098, A/A=1.83) represent the measurements for the temperature span 3.5×10^{–5< ¦¦<2.0×10 –3}, in good agreement with theoretical predictions. In order to exclude density profiles in the specimen, which are unavoidable in terrestrial experiments due to the high compressibility of fluids at the critical point and the gravity force, a space-qualified scanning ratio calorimeter has been constructed, which will permit long-term c_v measurements under microgravity (-g) conditions. The experiment will be part of the German Spacelab mission in October 1985. The significant features of the apparatus are briefly sketched.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

A method of joint determination of the effective coefficients of horizontal mixing of large particles and of external heat exchange in an organized fluidized bed

A method is proposed for the joint determination of the coefficients of horizontal particle diffusion and external heat exchange in a stagnant fluidized bed.Notation c_f, c_s, c_n specific heat capacities of gas, particles, and nozzle material, respectively, at constant pressure - D effective coefficient of particle diffusion horizontally (coefficient of horizontal thermal diffusivity of the bed) - d equivalent particle diameter - d_t tube diameter - H₀, H heights of bed at gas filtration velocities u₀ and u, respectively - H_a height of active section - l width of bed - L tube length - l _o width of heating chamber - N number of partition intervals - p=H/H₀ expansion of bed - s_n surface area of nozzle per unit volume of bed - S_h, S_v horizontal and vertical spacings between tubes - t_c, t₀, t_s, t_n, t_w initial temperature of heating chamber, entrance temperature of gas, particle temperature, nozzle temperature, and temperature of apparatus walls, respectively - u₀, u velocity of start of fluidization and gas filtration velocity - y horizontal coordinate - ^*, coefficient of external heat exchange between bed and walls of apparatus and nozzle - ₁, ₁, ₂, ... coefficients in (4) - thickness of tube wall - _b bubble concentration in bed - ₀ porosity of emulsion phase of bed - _n porosity of nozzle - =(t_s – t₀)/(t_c – t₀) dimensionless relative temperature of particles - _n coefficient of thermal conductivity of nozzle material - f, _s, _n densities of gas, particles, and nozzle material, respectively - _be=_s(1 – ₀) (1 – _b) average density of bed - time - _max time of onset of temperature maximum at a selected point of the bed - R =l _o/l Fourier number - Pe = ₁ l ²/D Péclet number - Bi = /_n Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 457–464, September, 1981.     

Precipitate strengthening mechanisms in magnesium zinc alloy single crystals

The mechanical behaviour of Mg-5.1 wt % Zn alloy single crystals was studied in the 4.2 to 300° K temperature range. Quenched crystals have activation energies and volumes best associated with the cutting of small clusters of Zn atoms by dislocations. Fully hardened crystals contain fine ₁ and occasional ₂ precipitates with an average ₁ interparticle spacing of 330 to 660 Å. Strengthening in these crystals is mainly ascribed to the cutting of ₁ particles by dislocations. In the overaged condition ₁, ₂ and equilibrium particles are present and lead to a considerable temperature-dependence unusual for an overaged condition. Analysis of this temperature-dependence suggests that below 77° K the relatively easy cutting of ₁ particles by dislocations takes place in addition to the cutting of ₂ and particles. Above 77° K the difficult cutting of ₂ and particles alone controls the deformation, ₁ being more easily cut with the aid of thermal fluctuations.     

Response of a spinning liquid column to pitch excitation

Summary The response of a solidly rotating liquid bridge consisting of inviscid liquid is determined for pitch excitation about its undisturbed center of mass. Free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic (<2₀) excitation frequency range.List of symbols a radius of liquid column - h length of column - I ₁ modified Besselfunction of first kind and first order - J ₁ Besselfunction of first kind and first order - r, ,z cylindrical coordinates - t time - u, v, w velocity distribution in radial-, circumferential-and axial direction resp. - mass density of liquid - free surface displacement - velocity potential - ₀ rotational excitation angle - ₀ velocity of spin - forcing frequency - _1n natural frequency - surface tension - acceleration potential - for elliptic range >2₀ - for hyperbolic range >2₀     

The dielectric properties of glass-ceramic-on-metal substrates for microelectronics packaging

The dielectric properties of some glass-ceramic-on-metal substrates have been determined over the frequency range 500 Hz to 5 MHz using a.c. bridge techniques. The substrates consisted of cordierite-based glass-ceramics screen printed on molybdenum. For glass layers of thickness greater than 100 m both the permittivity, and the dielectric loss, , are frequency independent over this frequency range at room temperature giving the value of =6.5 and tan =8×10^–3; the room-temperature data are consistent with the universal law of dielectric response. The variation of permittivity with temperature has also been examined and, below 120 °C, the temperature coefficient [(–1) (+2)]^–1 (/T)_p, was found to be 1.3×10^–5 K^–1. The results are compared with those previously reported for Al₂O₃ and AIN substrates.     

Specific heat measurements of intercalation compounds M x TiS2 (M=3d transition metals) using ac calorimetry technique

Specific heats of 3d transition metal intercalates of 1T-CdI₂-type TiS₂, M _x TiS₂ (M=V, Cr, Mn, Fe, Co, and Ni; 0x1), have been measured in the temperature range 1.6–300 K using an ac calorimetry technique. The electronic specific heat coefficient (2–100 mJ/mole K²) and the Debye temperature _D (240–430 K) are found to depend on the guest 3d metals and their concentrations. All the intercalates show anomalous specific heat at low temperatures following an – lnT dependence ( and are constants), as found in dilute alloys.     

Investigations of the copper isotope effect in oxygen-deficient YBa2Cu3O7−δ

We present data on the copper isotope effect (⁶³Cu-⁶⁵Cu), C_u =-nT_c/nm_Cu, for two isotopic pairs of oxygen-deficient YBa₂Cu₃O_7–, where varies between 0.06 and 0.52. _Cu is below 0.01 at =0.06 (fully oxygenated), it takes values between –0.14 and –0.34 in the 60 K plateau. Larger negative values of _Cu are observed away from the plateau. The dependence of _Cu is similar to that of the pressure effect dnT_c/dP.     

The dispersion of3He quasiparticles in He II from neutron scattering

In an inelastic neutron scattering (INS) experiment on³He-⁴He mixtures one observes, besides the photon-roton mode which is barely modified by the admixture of³He, an additional excitation at lower energies which is interpreted as quasi-particle-hole excitations of a nearly free Fermi gas. We reanalyse INS data ofx ₃=1% and 4.5% mixtures at various pressures to extract the mean energy of the fermions. In the momentum range 9<q<17 nm^–1 (above 2k _F ) follows very closely the relation =A ₂ q ²+A ₄ q ⁴ at all concentrations, pressures and temperatures observed. In a 4.5% mixture (T _F 0.3 K), measurements were performed for temperatures in the range 0.07<T<0.9 K. We find bothA ₂ andA ₄ to be strongly temperature dependent. For the interpretation of thermodynamical properties, the single particle energy _k is parametrized as _k =_o+1/(2ms*) ·k ₂ · (1+k ²). Neglecting interactions between fermions, we calculate from the free-particle _k the scattering functionS(q, ) and the mean value of the fermion peak energy _q = S ₃(q, )d/S ₃(q, )d. We find that follows closely _q , deviating at most by 10%. A comparison to the measuredA ₂ andA ₄ directly yieldsms* (x ₃,p, T) and (x ₃,p, T). In the limitx ₃=0,p=0 andT=0, the density and concentration dependence of the inertial mass is in excellent agreement with values found by Sherlock and Edwards. The temperature dependence of the specific heat data from Greywall and Owers-Bradleyet al. are well represented by our model atT<0,5 K.     

Tangent modulus tensor in plasticity under finite strain

Summary The tangent modulus tensor, denoted as , plays a central role in finite element simulation of nonlinear applications such as metalforming. Using Kronecker product notation, compact expressions for have been derived in Refs. [1]–[3] for hyperelastic materials with reference to the Lagrangian configuration. In the current investigation, the corresponding expression is derived for materials experiencing finite strain due to plastic flow, starting from yield and flow relations referred to the current configuration. Issues posed by the decomposition into elastic and plastic strains and by the objective stress flux are addressed. Associated and non-associated models are accommodated, as is plastic incompressibility. A constitutive inequality with uniqueness implications is formulated which extends the condition for stability in the small to finite strain. Modifications of are presented which accommodate kinematic hardening. As an illustration, is presented for finite torsion of a shaft, comprised of a steel described by a von Mises yield function with isotropic hardening.Notation B strain displacement matrix - C=F ^T F Green strain tensor - compliance matrix - D=(L+L ^T )/2 deformation rate tensor - D fourth order tangent modulus tensor - tangent modulus tensor (second order) - d VEC(D) - e VEC() - E Eulerian pseudostrain - F, F _e ,F _p Helmholtz free energy - F=x/X deformation gradient tensor - f consistent force vector - residual function - G strain displacement matrix - h history vector - h time interval - H function arising in tangent modulus tensor - I, I ₉ identity tensor - i VEC(I) - k ₀,k ₁ parameters of yield function - K _g geometric stiffness matrix - K _T tangent stiffness matrix - k _k kinematic hardening coefficient - J Jacobian matrix - L=v/x velocity gradient tensor - m unit normal vector to yield surface - M strain-displacement matrix - N shape function matrix - n unit normal vector to deformed surface - n ₀ unit normal vector to undeformed surface - n unit normal vector to potential surface - r, R, R ₀ radial coordinate - s VEC() - S deformed surface - S ₀ undeformed surface - t time - t, t ₀ traction - t VEC() - VEC( ) - t VEC() - t _r reference stress interior to the yield surface - t t–t _r - T kinematic hardening modulus matrix - u=x–X displacement vector - U permutation matrix - v=x/t particle velocity - V deformed volume - V ₀ undeformed volume - X position vector of a given particle in the undeformed configuration - x(X,t) position vector in the deformed configuration - z, Z axial coordinate - vector of nodal displacements - =(F ^T F–I)/2 Lagrangian strain tensor - history parameter scalar - , azimuthal coordinate - elastic bulk modulus - flow rule coefficient - twisting rate coefficient - elastic shear modulus - iterate - Second Piola-Kirchhoff stress - Cauchy stress - Truesdell stress flux - deviatoric Cauchy stress - Y, Y yield function - residual function - plastic potential - X, Xe, Xp second order tangent modulus tensors in current configuration - X, Xe, Xp second order tangent modulus tensors in undeformed configuration - (.) variational operator - VEC(.) vectorization operator - TEN(.) Kronecker operator - tr(.) trace - Kronecker product     

Measurement of temperature in a non-steady-state gas flow

A method is described for measuring the temperature of a non-steady-state gas flow with a thermocouple which is an inertial component of the first order.Notation T*_f non-steady-state gas flow temperature - T_t thermosensor temperature - thermal inertia factor of thermosensor - time - C total heat capacity of thermosensor sensitive element - S total heat-exchange surface between sensitive element and flow - heat-liberation coefficient - temperature distribution nonuniformity coefficient in sensitive element - Re, Nu, Pr, Bi, Pd hydromechanical and thermophysical similarity numbers - P^* total flow pressure - P static flow pressure - T^* total flow temperature - d_t sensitive element diameter - w gas flow velocity - flow density - flow viscosity - _f flow thermal conductivity - k gas adiabatic constant - R universal gas constant - M Mach number - T thermodynamic flow temperature - _o, _o and values at T=288°K - A, m, n, p, r coefficients - _c heat-liberation coefficient due to colvection - _r heat-liberation coefficient due to radiation - _b emissivity of sensitive element material - Stefan-Boltzmann constant - T_e temperature of walls of environment - _c, _r, _tc thermosensor thermal inertia factors due to convective, radiant, and conductive heat exchange - L length of sensitive element within flow - a thermal diffusivity of sensitive element material - _t thermal conductivity of sensitive element material Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 59–64, July, 1984.     

Critical dynamics of a sheared micellar solution

We have investigated the dynamic behavior of a nonionic micellar solution of tetra-ethylene glycoln-decylether (C₁₀ E₄) in water near its critical point in the presence of shear. The non-Newtonian behavior of the viscosity can be represented by * = [ 1 +a(S₄)=]², where* is the viscosity in the absence of shear,S is the shear rate. ₄ is the lifetime of the critical Iluctuations,a is a system-dependent constant, and = 0.02 In addition, we have found that, before attaining a steady state, the sheared mixture undergoing phase separation shows significant shear-dependent rheological effects due to the presence of concentration domains.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24. 1994, Boulder, Colorado, U.S.A.     

Metal-Insulator Transition (MIT), Defects, and Percolative Transport in HTS

HTS as layered, doped Mott insulators close to the Metal-Insulator Transition (MIT) become insulating at 6.5 k per CuO-plane at n _L 10²¹/cm³ localized states. The MIT occurs exponentially around point defects and at weak links, the latter interrupt the metallic CuO-plane current flow by insulating seams becoming most prominent in transport. Below T _c, weak links are parameterized by a reduced critical Josephson current j _cJ(A/cm²) and by a boundary resistance dominated by a resonant, leakage resistance R _bl( cm²) by Mott insulating seams yielding j _cJ R _bl 10^–12 V cm²/R_b1 /e for natural junctions and j _cJ R _bl ² > 10^–11 V cm² for artificial, bicrystal junctions. Both junction types enhance rf residual losses R _res ²/j _cJa_J(j_cJR² _b1)^1/2 with a _J as mean distance betwen weak links and enforce nonlinearities R _hys H/j _cJ by their reduced j _cJ a _J reducing H _c1J j _cJ allowing easy Josephson fluxon penetration.