Universality and the scaling laws in the superfluid phase transition of3He-4He mixtures

From the second-sound velocityU ₂ near the superfluid transition point, the superfluid densities in³He-⁴He mixtures, _s (X) and _s (), were deduced along the paths of constant³He concentrationX and of constant chemical potential difference of³He and⁴He. The following critical exponents of _s are determined: (a) =XX for _s (X) in the(X, T) plane,(b) X for _s (X) in the(, T) plane, and(c) for _s () in the(, T) plane. It is found that and _X change by about 4–6% relative to with increasing³He concentration up toX=0.4 and by 8–10% up toX=0.53. It seems that, belowX=0.53, universality hold for . Values of have been found to be in good agreement with the critical exponent of _s in pure⁴He under constant pressure. The values of and _X forX0.53 are also found to be consistent with the scaling relations in the (,T) plane of³He-⁴He mixture.Work performed in part while at the Electrotechnical Laboratory.     

Effect of Normal-State Pseudogap on Physical Quantities in Hubbard Model for Underdoped High-T c Cuprates

We develop the strong-coupling theory of coexisting charge-density-wave (CDW) and superconductivityd-wave gaps within the framework of the FLEX (fluctuation exchange) approximation for the two-dimensional Hubbard model. For nested sections of the Fermi surface these equations reduce to the previous FLEX equations for superconductivity where the squared energy gap _s ² in the denominator of the Green's function is replaced by ( _s ² + _c ² ) (here _s is the superconductivity and _c the CDW gap). We solve these equations by taking for _c a phenomenologicald-wave gap. The resulting neutron scattering intensity, spin-lattice relaxation rate 1/T₁ , Knight shift, resistivity, and photoemission intensity are in qualitative agreement with the data on underdoped high-T_c cuprates. TheT_c for superconductivity decreases and the crossover temperature T_* for 1/T₁Tincreases with increasing gap amplitude of _c which is in qualitative agreement with the phase diagram for underdoped cuprates.     

Vanadium sesquioxide-polymer composites: the study of electrical conductivity

The electrical conductivity of V₂O₃-polymer composites were studied by examining the dependence of resistivity (conductivity) on the volume fraction of V₂O₃. The experimental data (_m versus ) were fitted (using a computer program) to the GEM equation with satisfactory accuracy. The critical volume fraction and other parameters evaluated by fitting (t, _h and _c) and calculated after fitting L and m , L _f and m _f were analysed by taking into account the geometry, orientation and arrangement of the two components. The physical meanings of L, m and t are further illustrated on the basis of their definitions.     

Second-order wave force on a large cylinder

Summary A new technique has been developed for estimating the wave loadings on large circular cylinders. The theory, mainly due to Lighthill, has been applied to the case of large cylinders. Comparison with the previously reported experimental results shows favourable agreement for the range of parameters indicated in the graphs.Notations The following symbols are used in this paper a Wave amplitude - b Radius of the cylinder - D Diameter of the cylinder - F _l Linear force - F _d Dynamic force - F _q Quadratic force - F _w Water line force - g Acceleration due to gravity - h Depth of water - H=2a Total wave height - k Wave number,k=2/L - L Wave length - n Outward normal to body surface - n _x Direction cosine between the normaln and the given force - S Body surface - t Time - T Wave period - x, y, z Cartesian coordinates - r, ,z Cylindrical coordinates - W Vertical velocity of fluid - Density of fluid - Wave frequency, =2/T - Total velocity potential - _r , _z Partial derivatives with respect tor andz, respectively - ⁽¹⁾, _l Linear theory velocity potential - ⁽²⁾, _q Second-order velocity potential - Water surface elevation or wave height - _i Linear theory wave height - _q Quadratic theory wave height With 3 Figures     

Determination of the local angular radiation coefficients in certain two-body systems

A method is shown and formulas are derived by which local angular radiation coefficients can be determined in certain two-body systems where the configuration is arbitrary but one of the bodies is either a cylinder or a rectangular plate.Notation _int radiation vector of body 1 - _E ^int intrinsic radiation intensity of body 1 - _x, _y, _z components of the geometrical radiation vector along rectangular coordinates - r₀=x²+z² shortest distance from point M(x, y, z) to linear radiator - ₀ , ₀ ^' angles subtending the two segments of the linear radiator from point M(x, y, z) on area element 2 of irradiated surface - l length of the cylinders - x, y, z space coordinates of point M Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 1080–1088, June, 1972.     

Computation of particle settling speed and orientation distribution in suspensions of prolate spheroids

A numerical technique for the dynamical simulation of three-dimensional rigid particles in a Newtonian fluid is presented. The key idea is to satisfy the no-slip boundary condition on the particle surface by a localized force-density distribution in an otherwise force-free suspending fluid. The technique is used to model the sedimentation of prolate spheroids of aspect ratio b/a=5 at Reynolds number 03. For a periodic lattice of single spheroids, the ideas of Hasimoto are extended to obtain an estimate for the finite-size correction to the sedimentation velocity. For a system of several spheroids in periodic arrangement, a maximum of the settling speed is found at the effective volume fraction (b/a)²04, where is the solid-volume fraction. The occurence of a maximum of the settling speed is partially explained by the competition of two effects: (i) a change in the orientation distribution of the prolate spheroids whose major axes shift from a mostly horizontal orientation (corresponding to small sedimentation speeds) at small to a more uniform orientation at larger , and (ii) a monotonic decrease of the the settling speed with increasing solid-volume fraction similar to that predicted by the Richardson–Zaki law (1–)⁵⁵ for suspensions of spheres.     

Collective oscillations at long wavelengths in liquid4He

The recent successful calculation of the lower collective branch of the excitation spectrum in liquid ⁴ He by Sunakawaet al. contains a phenomenological parameter (k) whose relation to microscopic theory is obscure. To clarify matters, an exact identity is presented for the absorptive part of the density-density correlation function and is employed to show that Pines' zero-sound concept of the phonon in liquid ⁴ He is accurate in the limit of infinitely long wavelengths. Since the zero-sound theory can be made to produce an explicit relation between (k) and the two-particle potential in the liquid, the foundation has been laid for a microscopic expression for the excitation spectrum in the range of very low wave numbers, where the classic Feynman theory of the phonon is known to be accurate. A numerical calculation of (k) using this expression results in a theoretical excitation spectrum which is in excellent agreement with neutron scattering measurements in the regionk0.4 Å ^–1 .     

Temperature-enthalpy approach to the modelling of self-propagating combustion synthesis of materials

A new temperature-enthalpy approach has been proposed to model self-propagating combustion synthesis of advanced materials. This approach includes the effect of phase change which might take place during a combustion process. The effect of compact porosity is also modelled based on the conduction, convection and radiation in the local scale. Various parametric studies are made to analyse numerically the effects of activation energy, non-reacting phase content, porosity, Biot number, etc. The model predictions of the combustion pattern are in close agreement with those observed in experiments.Nomenclature c Concentration (wt %) - B _i Biot number =hL/k - f Fractional value - c _p Specific heat (J kg^–1 K) - h Heat-transfer coefficient (W m^–2 K) - L Height of material,m - Q Heat of reaction (J kg^–1) - H _SL ^* Latent heat of fusion (J kg^–1) - H _SE ^* Latent heat of fusion at eutectic (J kg^–1) - k Thermal conductivity (W m^–1 K) - k Equilibrium partition coefficient - Reaction kinetic function - t Time (s) - Non-dimensional time - T Temperature (K) - T ₀ Initial temperature (K) - Non-dimensional temperature - H Enthalpy (J kg^–1) - Kinetic function - Non-dimensional enthalpy - v _f Volume fraction of non-reactive phase - V Volume (m₃) - k ₀ Pre-exponential constant to reaction rate (s^–1) - z Cartesian co-ordinate - z^* Non-dimensional co-ordinate - Non-dimensional reacted fraction - Density (kg m^–3) - A non-dimensional temperature - Pore surface emissivity - Planck's constant - i Initial state - r Reacted state - l, L Liquid state - s Solid state - E Eutectic - M Melting point of pure material - P Centre of control volume - s Southern side of central volume - S Southern control volume - n Northern side of central volume - N Northern control volume - * Non-dimensional term - n New time level - o Old time level - m Iteration level     

Environmental crazing in a glassy polymer: the role of solvent absorption

According to a recent theory of Andrews and Bevan, the work of solvent craze formation, ₀ is governed by the cavitation properties of a solvated zone of polymer at the craze tip. In particular, the shear yield stress of this zone and its temperature dependence dictate the variation of ₀ with temperature. In order to investigate this matter further, samples of poly-methylmethacrylate were swollen to equilibrium in a variety of alcohols at different temperatures, and the equilibrium polymer fraction ₂ determined as a function of temperature and solvent. The variation of yield stress with ₂, solvent and temperature was also investigated, and the glass transition temperatures determined as functions of ₂ and solvent.The temperature at which the equilibrium swelling was just sufficient to depress the polymerT _g to a co-incident value was found to correspond closely to the characteristic temperature, identified by Andrews and Bevan, at which the temperature dependence of ₀ changes abruptly. This is shown to be in complete accord with the cavitation theory referred to.     

Analysis of the formation and removal of gas bubbles in rotationally moulded thermoplastics

The presence of internal bubbles is a characteristic feature of thermoplastic products manufactured by rotational moulding. The bubbles in the mouldings are generally undesirable since they reduce strength and stiffness and impair the appearance of the product if they occur at the surface. The bubbles form as a result of powder particles coalescing during the heating stage of the process and they subsequently decrease in size as a function of time and temperature. This paper presents a semi-empirical model to predict the bubble size which is likely to occur under any specified processing conditions.Nomenclature r ₀ Initial radius of bubble at time t = 0 (mm) - r Radius of bubble at any time t (mm) - Distance from the centre of the bubble at time t (mm) - x Neck radius of two spheres (mm) - Surface tension (Ncm^–1) - P pressure inside the bubble (Ncm^–2) - Viscosity at time t (Nsm^–2) - ₀ Initial viscosity (Nsm^–2) - t Time - K Experimental constant - Apparent relaxation constant - Q Quantity of oxygen in the bubble (cm³) - Diameter of the bubble (mm) - ₀ Initial diameter of the bubble (mm) - _p Density of the polymer - _b Density of the bubble - u Terminal velocity of the bubble - g Acceleration due to gravity - J Solute flux - c Concentration of dissolved oxygen in the glass at a distance from the centre of the bubble at time t - c ₀ Constant concentration maintained at the surface of bubble in equilibrium with oxygen gas at 1 atm inside the bubble - Diffusion coefficient - c _s Concentration of solute in the sphere - c _i Concentration of solute in the solution at the sphere-solution interface - c Solute concentration at a large distance from the sphere     

Spin-lattice relaxation in gadolinium-doped calcium tungstate

The spin-lattice relaxation of the S-state ion Gd³⁺ in a calcium tungstate host lattice has been examined at 37.5 GHz over the temperature range 1.5 to 30 K. The gadolinium concentrations in the doped single crystals used were about 50 ppm. Single exponential recovery was observed and the spin-lattice relaxation time (T ₁) varied from about 14 msec at 1.5 K to 0.03 msec at 30 K, measured with =90° and =8°. It was found that T ₁ varied with temperature (T) as T ₁ T ^–1 below 8 K and as T ₁ T ^–3 between 8 and 30 K. The experimental data was fitted by the expressions T ₁ ^–1 =35 T+0.5 T ³ and T ₁ ^–1 =35T+0.1 T ^3.6 for crystals of nominal gadolinium concentrations 0.005 wt % and 0.05 wt % respectively. The difference between the observed dependence and the T ^–5 variation predicted in the Raman region for an S-state ion in a perfect lattice is attributed to defects. Measurements in the -plane at 4.2 K showed that T ₁ was anisotropic with a maximum value at =25° about three times greater than the minimum value obtained at =55°. The angular positions at which these features occur show a remarkable coincidence with the acoustic axes of symmetry of the crystal, which have recently been determined by ultrasonic methods.     

Flow visualization glass-ceramic: Preliminary experimental and modelling results

A glass-ceramic material was developed to act as a flow visualization material. Preliminary experiments indicate that aperiodic, thermally induced, convective flows can be sustained at normal processing conditions. These flows and the stress and temperature gradients induced are most likely responsible for the anomalous behaviour seen in these materials and the difficulties encountered in their development and in their production on industrial and experimental scales. A simple model describing the dynamics of variable-viscosity fluids was developed and was shown to be in qualitative agreement with more sophisticated models as well as with experimental results. The model was shown to simulate the dependence of the critical Rayleigh number for the onset of convection on the viscous properties of the fluid at low T, and also to simulate quenching behaviour when the temperature differences were high.Nomenclature C _p Heat capacity - D, E, F Expansion coefficients - H Height of the roll cell - Pr Prandtl number - R _a Rayleigh number - R _c Critical Rayleigh number for the onset of convection in a constant-viscosity fluid - S Dimensionless stream function - T Temperature - T _m Mean temperature - T ₀ Bottom surface temperature - T _r Reference temperature - a Aspect ratio of cell - g Acceleration due to gravity - k Thermal conductivity - k ₁ Function related to ²v/T ² - k ₂ Function related to ⁴v/T ⁴ - r Rayleigh number ratioR _a/R _c - t Time - w Dimensionless vertical coordinate - w _m Mean cell height - x Horizontal coordinate - y Dimensionless horizontal coordinate - z Vertical coordinate - , Constants - _t Thermal expansion coefficient - Constant in viscosity function - T Temperature difference between top and bottom surfaces - _i Viscosity coefficients - Kinematic viscosity - _m Mean kinematic viscosity - Dimensionless kinematic viscosity - Thermal diffusivity - Non-linear temperature function - Dimensionless non-linear temperature function - _o - Stream function - Dimensionless time - Eigenvalues     

The Superconductive Critical Magnetic Field of Beryllium

We have measured the temperature dependence of the superconductive critical magnetic field of three samples of beryllium from three different sources. The irregular geometric shape of one sample prevented a complete analysis of the data, but the data for the other two samples were well represented by the BCS model of superconductivity. The values of T _c and H _c (0) are found to be sample dependent. For the purest sample studied, T _c =24.34±0.02 mK, H _c (0)=107.7±0.2 T and (/V)=32.9±0.3 J/cm³ K². By a very small extrapolation of the data as a function of purity, it is inferred that the critical parameters for pure Be are: T _c =24.38±0.02 mK, H _c (0)=107.9 T±0.2 T and (/V)=33.0±0.3 J/cm³ K².     

Disappearance of Bose-Glass Behavior in Transport Properties of YBa2Cu3O y Films with Columnar Defects

The glass transitions of the vortex system in Au-ion irradiated YBa₂Cu₃O _y films have been studied by the measurements of transport properties as a function of magnetic field B and angle of B to the direction of columnar defects. At =0°, we find an anomalous upturn behavior of the glass transition line B _g(T) at BB /3, where B is the matching field. In B>B /3, the dependence of glass transition temperature T _g reveals cusplike behavior with a peak at =0°, which is consistent with the Bose glass theory. In B<B /3, on the other hand, T _g is almost independent of , suggesting the system undergoes the vortex glass transition induced by the inherent point-like defects.     

The influence of neutron irradiation on the thermal conductivity of aluminum in the range 5–50 K

Measurements of thermal conductivity of 6N to 3N pure aluminum in the temperature range 5–50 K subjected to fast neutron irradiation, with exposures of 10¹³ and 10¹⁶ n · cm^–2, are reported. The thermal conductivity maximum was found to shift towards higher temperatures with an increase in the fast neutron irradiation exposure. At high temperatures, a departure from Wilson's theory was observed, which may be attributed to the existence of additional electron scattering mechanisms. An increase in both ideal and residual thermal resistivity components with an increase in the radiation exposure was noted.Nomenclature I ₅ (/t) Debye integral of the fifth order - –m slope of the straight line that crosses maximum thermal conductivity values - n exponent in ideal thermal resistivity component - T _m temperature corresponding to maximum thermal conductivity - W _e total electronic thermal resistivity - W _i ideal thermal resistivity - W ₀ residual thermal resistivity - ideal thermal resistivity coefficient in Eq. (4) - ideal thermal resistivity coefficient in Eq. (1) - constant related to the ideal part of thermal resistivity in Eq. (2) - () ideal thermal resistivity coefficient depending on irradiation exposure - () residual thermal resistivity coefficient depending on irradiation exposure - thermal conductivity - _m maximum thermal conductivity - Debye characteristic temperature - irradiation exposure     

Rheological properties of aqueous silicon nitride suspensions

The effect of surface modification of Si₃N₄ particle on the colloidal behavior and the rheological properties of aqueous Si₃N₄ suspensions under steady and oscillatory conditions are investigated in detail. Due to the decrease of the oxidizing level, the isoelectric point (IEP) of the modified particle shifts to basic region gently. Attempts have been made to apply rheological models to the suspensions with various solid volume fraction (). For the as-received suspensions, the Sisco model provides the best fit in the range of 0.30 while the Casson model in 0.35 0.45. The shear behavior of modified suspensions fits to Sisco model in the range of 0.40 and Casson model in 0.45 0.54. The rheological behavior of modified suspensions is improved efficiently. The critical strain decreases and the linear viscoelastic regime narrows continuously with increasing solid concentration. For the modified suspensions, the linear viscoelastic regime broadens and the corresponding elastic modulus decreases sharply. With increasing solid concentration, the characteristic frequency shifts toward lower frequencies and the suspension transforms from more viscous to more elastic.     

Electron Mobility Maximum in Near-Critical Argon Gas

Measurements of the drift mobility of excess electrons in dense argon gas in proximity of the critical point of the liquid–vapor transition are reported. The density and electric field dependence of at two temperatures fairly close to the critical point, namely T=162.30 K (T/T _c1.08) and T=152.15 K (T/T _c1.01) (T _c=150.7 K) in a density range (0.5N14) atoms·nm^–3 (0.06N/N _c1.73), encompassing the critical region of Ar (N _c=8.08 atoms·nm^–3), are investigated. At the lower temperature a maximum of the zero-field density-normalized mobility ₀ N was observed at the same density as observed in the liquid. A density-modified kinetic model describes well all features of in the gas phase, even at densities comparable to those of the liquid. It is argued that the electron scattering processes in the liquid phase can be described in terms of kinetic theory rather than in terms of the usual deformation potential model.     

Two-dimensional pressure-temperature phase diagram and latent heats of neon adsorbed on exfoliated graphite

A two-dimensional pressure-temperature phase diagram was constructed for neon adsorbed on exfoliated graphite using the heat capacity data obtained in our laboratory for this system. The two-dimensional pressures at the triple and critical points were found to be _t=64×10^–6 N/m and _c=128×10^–6 N/m, respectively. From Clapeyron's equation and assuming an ideal behavior for the two-dimensional gas phase, the latent heat of sublimation was calculated as a function of temperature. The latent heat of vaporization was also calculated at the triple point and consequently the latent heat of fusion was found. The following values were obtained at the triple point:l _s/k=86 K,l _v/k=24 K, andl _f/k=62 K.     

Measuring Turbidity in a Near-Critical, Liquid–Liquid System: A Precise, Automated Experiment

A ground based (1g) experiment is in progress that measures the turbidity of the density-matched, binary fluid mixture methanol–cyclohexane extremely close to its liquid–liquid critical point. By covering the range of reduced temperatures t (T–T _c)/T _c from 10^–8 to 10^–2, the turbidity measurements should allow the Green–Fisher critical exponent to be determined. This paper reports measurements showing ±0.1 % precision of the transmitted and reference intensities, and ±4K temperature control near the critical temperature of 320 K. Preliminary turbidity data show a nonzero consistent with theoretical predictions. No experiment has precisely determined a value of the critical exponent , yet its value is significant to theorists in critical phenomena. Relatively simple critical phenomena, as in the liquid–liquid system studied here, serve as model systems for more complex behavior near a critical point.