Spin hydrodynamic equations with external disturbances and suitable Green's functions for superfluid3He-B. New onsager relations

The spin hydrodynamic equations for superfluid³He-B have been obtained for the case of external, time-dependent fields. On the basis of a microscopic approach, expressions are found for additional terms in equations containing these fields. Considering the linear response of the system to the switching on of external fields, formulas are found for suitable Green's functions (magnetization-magnetization, rotation-rotation, magnetization-rotation, rotation-magnetization). The rotation-rotation Green's function has the 1/q ² singularity characteristic of superfluid systems. Connections between Green's functions lead to relations among kinetic coefficients v, ₁, and ₂. It is also shown that there is a conserved quantityQ ^(B) = div v _s ^(B) that describes sources or magnetic type charges (monopoles) of the superfluid velocity v _s ^(B) . Comparison with the phenomenological approach suggests thatQ ^(B) is proportional to a pseudoscalar giving the projection of the spin density onto the vector describing the axis of rotation.     

Some observations on the deformation characteristics of bulk polycrystalline zirconium hydrides

The deformation behaviour of bulk polycrystalline zirconium hydrides in the composition range ZrH_1.27 to ZrH_1.66 has been investigated by compressive loading at temperatures between room temperature and 500° C. Single-phase -zirconium hydride is brittle below 100° C. Analyses of slip traces on specimens deformed at temperatures between 100 and 250° C have shown that the glide planes are {111} types. The deformation characteristics of and ( + ) alloys at temperatures between 100 and 500° C are consistent with the hydrogen vacancies in the -phase providing significant lattice friction to the movement of dislocations in the zirconium lattice of the hydride structure. The room temperature fracture stress of ( + ) alloys increases with the volume fraction of the -phase and this can be related to the resistance offered by platelets to the propagation of cleavage cracks in the matrix. In a ( + + ) alloy the resistance to crack propagation at room temperature is further increased by the soft -zirconium phase.     

The Infrared Hall Effect in YBCO: Temperature and Frequency Dependence of Hall Scattering

We measure the Hall angle, _H , in YBCO films in the far- and mid-infrared to determine the temperature and frequency dependence of the Hall scattering. Using novel modulation techniques we measure both the Faraday rotation and ellipticity induced by these films in high magnetic fields to deduce the complex conductivity tensor. We observe a strong temperature dependence of the mid-infrared Hall conductivity in sharp contrast to the weak dependence of the longitudinal conductivity. By fitting the frequency dependent normal state Hall angle to a Lorentzian _H () = _H /( _H – i) we find the Hall frequency, _H , is nearly independent of temperature. The Hall scattering rate, _H , is consistent with _H T ² up to 200 K and is remarkably independent of IR frequency suggesting non-Fermi liquid behavior.     

Localized spin fluctuations

Scaling arguments and renormalization group techniques are used in the Anderson model Hamiltonian for the nonmagnetic limit of a magnetic impurity. The range of validity of the theory is limited toU/ 1, where the electron-electron collisions can already compete strongly with the electron-hole collisions. A parquet approximation is developed; it gives for the static susceptibility in the symmetric case = ()^–1 exp (+U/). There are some hints that the exchange force might play a crucial role in the formation of localized magnetic moment. These considerations are consistent with the electron-hole symmetry in the symmetric Anderson model.     

Conical extrusion of a work-hardening material: an asymptotic analysis

We study steady-state conical extrusion of an isotropic, power-law hardening material with a Coulomb friction condition present at the die faces. An asymptotic theory is developed based on an axial velocity field which is nearly slug-like, i.e., a deformation field for which the transverse variations of the axial velocity are modest in size. However, although the velocity is slug-like, within the asymptotic limit considered the shear stresses are not negligible compared to the longitudinal deviatoric stresses. For this reason the theory accounts for the first manifestations of inhomogeneous deformation. In practical terms the validity of the asymptotic theory generally requires either the friction coefficient µ to be small or the die slope h/L to be small (where h is the radius reduction and L the die length). The primary result of the work is the set of equations (76)–(78). In addition, the present formulation enables for the first time the development of a model of inhomogeneous deformation in conical extrusion which is analogous to the very popular inhomogeneous deformation theory developed by Orowan for plane-strain sheet rolling. Results are presented for a number of examples illustrating the depature from a state of homogeneous compression which is typically found.     

Transient heat conduction in hollow spheres with a moving inner boundary

The finite integral transform method is used to obtain the solution of unsteady heat conduction problems for a hollow sphere with a moving internal boundary and various boundary conditions at the outer surface. For the solution of the problems of interest integral transform formulas are presented with kernels (16), (20), and (24) and the corresponding inversion formulas (18), (22), (26), (29) and characteristic equations (17), (21), (25), (28), (31), (33).Nomenclature a, thermal diffusivity and conductivity - t temperature of phase transformation - density - heat transfer coefficient - Q total quantity of heat passing through inner boundary - F latent heat of phase transformation - Fo(1,)=a/R ₁ ² , Fo(i,)=/r _i ² , Fo(i, _i)=a _i/r _i ² Fourier numbers - Bi₂=R₂/ Biot number     

Density Response and Equilibration in a Pure Fluid Near the Liquid-Vapor Critical Point: 3He

We report measurements of the local density response inside a quasi 1-D horizontal ³ He fluid layer to a step-like change T of the boundary temperature, where |T| 80 K and much smaller than |T – T_c| where T_c is the critical temperature. These experiments used a new cell design, described in the text, and were carried out along the critical isochore both above and below T_c. The observed temporal and spatial density response (t, z) and its equilibration time are described adequately by the relations developed from the thermodynamic theory of Onuki and Ferrell. We verify that over the temperature range of low stratification, where computer simulations and closed-form calculations can be compared, they are in exact agreement. The systematic differences of experimental results from predictions can be accounted for by the departure of the cell from the ideal 1-D geometry. The much larger disagreement between the experimental and predicted equilibration time scale in earlier experiments is also explained. Finally, deviations from linearity observed in the density response for steps |T| larger than 90 K are reported and the implications of such nonlinearity for the (t, z) profile and especially the effective relaxation time _eff are analyzed. We also discuss the predicted onset of convection near T_c for the conditions in our experiment. In the Appendix, the likely sources for systematic deviations in the density response function for the experimental cell from calculations in the ideal 1-D geometry are presented and their effects calculated. The so-obtained response function Z_F(, z) is compared with previously published data.     

Evidence for collective excitations in superconducting tin whiskers

Based on the assumption that a phase-slip center in a clean quasi-one-dimensional superconductor excites a collective oscillation, the time-averaged value of the electrochemical potential of quasiparticles is calculated. At larger distances from the phase-slip center, swings below (or above) the electrochemical potential _p of the Cooper pairs. This makes it possible to understand the unexpected results of previous measurements.     

On the “scientometric decline” of British science. One additional graph in reply to Ben Martin

With respect to the issue of whether the scientometric measurement of the decline of British science is an artifact of the specific database and underlying assumptions in methods, I argue that there are fewer analytical objections against measurement by usingSciSearch Online than against other methods (based on the fixed journal set and fractional counting). The measurement of international co-authorship, i.e. a network indicator, should not be confounded with measurement of performance of a single nation. The time series for the different subsets of UK-publications, which have been proposed, are given. None of the indicators can be shown to exhibit a trend (in contrast to a drift). The hypothesis of a decline has therefore to be rejected.     

Recovery of a creep-deformed Type 316 stainless steel

The recovery of the dislocation structures produced in a Type 316 steel during creep has been examined by annealing over a range of temperatures and times, both in the presence and in the absence of stress. The influence of dislocation recovery on subsequent reloading behaviour has also been examined.Initial dislocation recovery occurs rapidly but the rate of recovery subsequently decreases as precipitate effects become more important. Dislocation recovery in the early, rapid stage appears to be controlled by vacancy diffusion between the dislocation links. The application of stress during recovery leads to an enhancement of the recovery rate in agreement with the network coarsening model whilst the incremental strains observed on reloading after recovery correlate well with the changes in dislocation structure produced during the recovery periods.List of symbols and appropriate values l dislocation link length - D _s self diffusion coefficient - b Burgers vector (2.5×10^–1 m) - C _j equilibrium jog concentration - dislocation link tension - k Boltzman's constant (1.38×10^–23 J atom^–1 K^–1) - T absolute temperature - t recovery time - M mobility term - Z frictional term associated with particles - _d dislocation density determined from micrographs - N _d number of dislocation intersections on test line - p length of test line - S foil thickness - ¯l mean dislocation link length - _c mean intragranular particle (carbide) spacing - r ₀ mean intragranular particle radius at timet=0 - r _t mean intragranular particle radius at timet - D solute diffusion coefficient - B solubility of M₂₃C₆ in austenite - particle-matrix interface energy - atomic volume (10^–29m³) - change in dislocation density during recovery period - incremental strain associated with reloading after recovery period - K constant - dislocation density - ₀ dislocation density at timet=0 - _t dislocation density at timet - ₀ friction stress associated with particles - constant (1) - shear modulus - angle between dislocation segments as dislocation breaks through a particle - A 1 cos (/2) - E constant - creep rate - F Taylor factor - L mean slip distance of dislocations - rate of dislocation recovery - stress - _y yield stress - J strength coefficient - _p plastic strain     

Natural convection in a rectangular enclosure in the presence of a magnetic field with uniform heat flux from the side walls

Summary A numerical study is presented for magnetohydrodynamic free convection of an electrically conducting fluid in a two-dimensional rectangular enclosure in which two side walls are maintained at uniform heat flux condition. The horizontal top and bottom walls are thermally insulated. A finite difference scheme comprising of modified ADI (Alternating Direction Implicit) method and SOR (Successive-Over-Relaxation) method is used to solve the governing equations. Computations are carried out over a wide range of Grashof number, Gr and Hartmann number, Ha for an enclosure of aspect ratio 1 and 2. The influences of these parameters on the flow pattern and the associated heat transfer characteristics are discussed. Numerical results show that with the application of an external magnetic field, the temperature and velocity fields are significantly modified. When the Grashof number is low and Hartmann number is high, the central streamlines are elongated and the isotherms are almost parallel representing a conduction state. For sufficiently large magnetic field strength the convection is suppressed for all values of Gr. The average Nusselt number decreases with an increase of Hartmann number and hence a magnetic field can be used as an effective mechanism to control the convection in an enclosure.List of symbols Ar aspect ratio,H/L - B ₀ induction magnetic field - H ₀ magnetic field,H ₀=B ₀/ _m - g gravitational acceleration - Gr Grashof number,gq(L/k)L ³/v ² - H height of the enclosure - Ha Hartmann number, - k thermal conductivity - Nu local Nusselt number - average Nusselt number - p pressure - Pr Prandtl number, / - q heat flux - t time - T dimensionless temperature, (–₀)/q(L/k) - u vertical velocity - U dimensionless vertical velocity,uL/ - v horizontal velocity - V dimensionless horizontal velocity,vL/ - x vertical coordinate - X dimensionless vertical coordinate,x/L - y horizontal coordinate - Y dimensionless horizontal coordinate,y/L - thermal diffusivity - thermal expansion coefficient - temperature - ₀ reference temperature - density - kinematic viscosity - viscosity - _m magnetic permeability - electrical conductivity - stream function - dimensionless stream function, / - dimensionless time,t/L ² - vorticity - dimensionless vorticity, L ²/ - X grid spacing inX-direction - Y grid spacing inY-direction - time increment - ² Laplacian operator     

Interplay of Nuclear Magnetism and Superconductivity

The ratio of nuclear saturation magnetization and superconducting critical field, ₀ M _sat / B _S0*, classifies the strength of mutual influence of nuclear magnetism and superconductivity. In order to investigate the interplay of both phenomena for the three distinct cases 1, 1, and 1 we have measured the ac susceptibility of Al, of the intermetallic compound AuIn ₂ , and of the metal hydride TiH _2.07 at ultralow temperatures, 17 K T 1 K, as function of static field 0 B 15 mT. For Al, the interplay enables an absolute measurement of the nuclear magnetization. For AuIn ₂ , we get a steep decrease of B _S (T) and a broadening of the superconducting transition in its nuclear ferromagnetic phase. Surprisingly, the nuclear ferromagnetic state coexists with type-I superconductivity in AuIn ₂. The metal hydride TiH _2.07 , which is under present investigation, is a good candidate to show reentrant superconductivity.     

Temperature dependence of electrical resistivity of deformed and undeformed V-rich V3Si single crystals

The electrical resistivity (T) of V-rich V₃Si single crystals (T _c-11.4 K) was measured from 4.2 to 300 K along the directions of [1 0 0] and [1 1 1] before and after plastic deformation at 1573 K. Anisotropy of (T) was observed although V₃Si has the cubic A15 structure. Plastic deformation does not affect the normal-state (T) behaviour but changes the normal-superconducting transition width T_c. At low temperatures (T _c<T 40 K), (T) varies approximately as T ⁿ where n-2.5 and this behaviour does not contradict the (0)- phase-diagram plot proposed by Gurvitch, where is the electron-phonon coupling constant and (0) is the residual resistivity.     

The Interplay of Electronic and Nuclear Magnetism in PtFe x at Milli-, Micro-, and Nanokelvin Temperatures

We have measured ac susceptibility, nuclear magnetic resonance, and nuclear heat capacity of two PtFe _x samples with concentrations of magnetic impurities x = 11 ppm and 41 ppm at magnetic fields (0 ± 0.05) mTB248 mT. The susceptibility data have been measured at temperatures of 0.3 KT100 mK, no hint for nuclear magnetic ordering could be detected to a temperature of 0.3 K. The nuclear heat capacity data taken at 1.4 KT10 mK show enhanced values which scale with x at low polarization. This effect is described by a model assuming an internal magnetic field caused by the impurities. No indication for nuclear magnetic ordering could be detected to 1.4 K. The nuclear magnetic resonance experiments have been performed on these samples at 0.8 KT0.5 mK and 2.5 mTB22.8 mT as well as on three other samples with x = 5, 10, 31 ppm in a different setup at 40 KT0.5 mK and at 5.4 mTB200 mT. Spin-lattice and effective spin-spin relaxation times ₁and ₂ ^* of ¹⁹⁵ Pt strongly depend on x and on the external magnetic field. No temperature dependence of ₁and ₂ ^* could be detected and the NMR data, too, give no hint for nuclear magnetic ordering to 0.8 K.     

Phase transformations in permanent-mould-cast aluminium bronze

The phases obtained in aluminium bronze (Cu-10Al-4Fe) cast into a permanent mould were investigated. The parameters examined were the pre-heating temperature of the mould and the graphite coating thickness. The phases and ₂ were detected as well as the metastable phases and . The intermetallics of the system Fe-Al were obtained in various stoichiometric compositions. The different cooling rates of the casting resulted in two mechanisms of transformation to grains out of the unstable phase, one being nucleation and growth producing needle-shaped grains, the other exhibiting a massive transformation to spherical grains. These two mechanisms determine the changes in the size of the a grains as result of changes in the cooling rate in its various ranges.     

Hydraulic characteristics and vapor content in a channel with boiling of a liquid underheated up to the saturation temperature

A method is proposed for calculating the hydraulic characteristic and vapor content in a channel with underheated boiling.Notation H heated length of channel - d_t thermal diameter - d_h hydraulic diameter - _t thermal perimeter - _h hydraulic perimeter - s through cross section - N power of channel - q heat flux - G weight flow rate - W velocity - coefficient of heat transfer - t, T temperatures - t temperature difference - i enthalpy - P pressure - P pressure drop - x weight vapor content - volumetric vapor content - C_p heat capacity - r heat of vaporization - coefficient of thermal conductivity - coefficient of surface tension - liquid density - vapor density - g acceleration of gravity - _o coefficient of friction of liquid against the channel wall - shear stress - density of two-phase medium averaged over a channel cross section - dynamic viscosity Indices s on saturation line - en at channel entrance - l liquid - v vapor - w wall Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 784–792, November, 1979.     

Equations of generalized thermoelasticity of a Cosserat medium in stresses

Thermoelasticity equations in stresses are derived in this paper for a Cosserat medium taking into account the finiteness of the heat propagation velocity. A theorem is proved on the uniqueness of the solution for one of the obtained systems of such equations.Notation u displacement vector - small rotation vector - absolute temperature - ₀ initial temperature of the medium - relative deviation of the temperature from the initial value - , , , , , ,, m constants characterizing the mechanical or thermophysical properties of the medium - density - I dynamic characteristic of the medium reaction during rotation - k heat conduction coefficient - ₀ a constant characterizing the velocity of heat propagation - X external volume force vector - Y external volume moment vector - w density of the heat liberation sources distributed in the medium - E unit tensor - T force stress tensor - M moment stress tensor - nonsymmetric strain tensor - bending-torsion tensor - s entropy referred to unit volume - V volume occupied by the body - surface bounding the body - (T)_ki, (M)_ki components of the tensorsT andM - q thermal flux vector Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 482–488, March, 1981.     

High-frequency dielectric properties of Mg-Al-Si,Ca-Al-Si and Y-Al-Si oxynitride glasses

Recently developed coaxial line techniques [1] have been used to determine, at room temperature, the values of the real () and imaginary (') parts of the dielectric constants for some Mg-Al-Si, Ca-Al-Si and Y-Al-Si oxynitride glasses over the frequency range 500 MHz to 5 GHz. The frequency dependencies of and ' are consistent with the universal law of dielectric response in that (-_t8)^(n–1) and '^(n–1) for all glass compositions; the high experimental value of the exponent (n=1.0±0.1) suggests the limiting form of lattice loss [2] situation. In this frequency range, as previously reported [3] at longer wavelengths, the addition of nitrogen increases the dielectric constant, (); in both the oxide and oxynitride glasses is also influenced by the cation, being increased with cation type in the order magnesium, yttrium, calcium as at lower frequencies.     

Measurements of the dynamic input impedance of a dc SQUID

The impedance of a circuit coupled magnetically via a mutual inductanceM _i to a dc SQUID of geometric inductanceL is modified by the dynamic input impedance of the SQUID, which can be characterized by the flux-to-current transfer functionJ J/;J is the current circulating in the SQUID loop and is the flux applied to the loop. At the same time, the SQUID is modified by the presence of the input circuit: in the lumped circuit approximation, one expects its inductance to be reduced toL ^r=(1– _e ² )L, where _e is an effective coupling coefficient. Calculations of J using an analog simulator are described and presented in the form of a dynamic inductance and a dynamic resistance versus bias currentI and . Experimental measurements of and were made on a planar, thin-film SQUID tightly coupled to a spiral input coil that was connected in series with a capacitorC _i to form a resonant circuit. Thus,J was determined from the change in the resonant freqency and quality factor of this circuit as a function ofI and . At low bias currents (low Josephson frequencies) the measured values of were in reasonable agreement with values simulated for the reduced SQUID, while at higher bias currents (higher Josephson frequencies) the measured values were in better agreement with values simulated for the unscreened SQUID. Similar conclusions were reached in the comparison of the experimental and simulated values of the flux-to-voltage transfer functionV . The reduction in the screening at the higher Josephson frequencies is believed to result from the parasitic capacitanceC _p between the SQUID and the input coil. In contrast to the behavior of the input inductance, the change in the input resistance R _i could not be explained in terms of the dynamic impedance of the SQUID reflected into the input circuit. Instead, R _i was dominated by capacitive feedback between the output of the SQUID and the input circuit viaC _p . The experimental values of R _i were satisfactorily explained by a simplified model that predicts R _i –M _iV ^r (C _p /C _i ).     

The age hardening effect in Ti-6 Al-4 V due to ω and α precipitation in the β grains

The structure at room temperature of a quenched TA6V titanium alloy has been investigated. This structure is + or + according to the treatment temperature; it is always metastable. During ageing the grains decomposed by the reaction + + +; this decomposition was accompanied by a large increase of the 0.2% yield stress. No structural modification was observed in. The and phase of TA6V were separately investigated in the form of single-phase alloys. The hardness of was insensitive to ageing, while was considerably hardened by and; we deduced that the strengthening of the minor phase during ageing is mainly responsible for the hardening of TA6V.