Thermal diffusivity of inhomogeneous systems

The possibility of analyzing the nonsteady temperature fields of inhomogeneous systems using the quasi-homogeneous-body model is investigated.Notation t, t_I, t_i temperature of quasi-homogeneous body inhomogeneous system, and i-th component of system - a, , c thermal diffusivity and conductivity and volume specific heat of quasi-homogeneous body - a_{i i}, c_i same quantities for the i-th component - q heat flux - S, V system surface and volume - x, y coordinates - macrodimension of system - dimensionless temperature Fo=a/² - Bi=/ Fourier and Biot numbers - N number of plates - =h/ ratio of micro- and macrodimensions - _V, volumeaveraged and mean-square error of dimensionless-temperature determination - time - m_i i-th component concentration Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 126–133, July, 1980.     

Submillimeter surface impedance and relaxation: A case study of quasi-two-dimensional YBa2Cu3Ox

Surface impedance measurements in the normal and superconducting state are an excellent method to study the conduction electron dynamics in metals. This holds especially in the relaxation range, i.e., for distances traveled in one r.f. periods= _F/(_f is the Fermi velocity) being smaller or of the order of the penetration depth and mean free pathl. For materials with _F<-10⁷ cm/sec the relaxation range is easily accessible forf>0.1 THz. Then, in the normal state, relaxation defines the surface impedance with a penetration depth approaching the London penetration depth _L, andR _0l/2 as surface resistance allowing a measure of _L and relaxation time (T, ). In the superconducting state the photon interaction scales with _F/_L=l/ ( _f is the dimension of Cooper pairs for l) and causes at low frequencies an absorption rate growing with, which is decreasing with _F/l. The rate increase proportional to turns to a decrease above 0.1 THz, being accompanied by a decrease of with frequency which is stronger for large and small _F/l. These characteristic dependences allow a measurement of material parameters, anisotropy, and dynamics of electrons. To evaluate the consequences of theâ, b, and-direction anisotropy, the integral kernels for normal and superconducting surface impedances in its nonintegrated, angle-dependent form are presented, analyzed, and compared with impedance measurements above 0.1 THz of YBa₂Cu₃O_x.     

Dependence of helium II viscosity properties on oscillation frequency

The causes of a discrepancy in the results of measurements of He II viscosity below T 1.6 k obtained with different measurement methods are investigated. It is shown that to obtain correct results in oscillation experiments, the condition _ph should obtain, where is the depth of viscous wave penetration and _ph is the phonon free path length. Results of viscosity measurements at different ratios /_ph (by a wire viscometer) are presented. It is shown that for the condition _ph, the results obtained are in good agreement with the results of Andronikashvili (in which /_ph > 100). If the mentioned relation is not satisfied, then, as the value of the ratio /_ph is decreased, the value measured for the viscosity is increasingly lower than the results of Andronikashvili.     

Specific heat near the lambda point in 4He and 3He-4He mixtures: Test of universality of the critical exponent and the amplitude ratio,and observation of the critical-tricritical crossover effect

The specific heat under saturated vapor pressure of pure ⁴He and of six ³He-⁴He mixtures up to X = 0.545 was measured in the temperature range 3 × 10^–6 <¦T-T ¦ <10^–2 K. The critical exponents and along the path = are independent of X up to X = 0.545, where (= ₃ – ₄) is the difference between chemical potentials. If we take account of higher order terms, the exponent (= ) and the amplitude ratio A /A are independent of X up to X = 0.545. The values of and A /A are –0.023 and 1.090, respectively. The critical-tricritical crossover effect was observed for X = 0.545 and the boundary of crossover region closest to the critical region was at /T = (1–2) × 10^–4, where is the distance ¦T – T ¦ along the path = . This value is in good agreement with the estimated value by Riedel et al. But, remarkably, in the case of X = 0.439 this effect was not observed.     

Vibrational properties of wood along the grain

The dynamic Young's modulus (E_L) and loss tangent (tan _L ) along the grain, dynamic shear modulus (G_L) and loss tangent (tan _S) in the vertical section, and density () of a hundred spruce wood specimens used for the soundboards of musical instruments were determined. The relative acoustic conversion efficiency ( ) and a ratio reflecting the anisotropy of wood (, (E_L/G_L)(tan _S/tan _L)) were defined in order to evaluate the acoustic quality of wood along the grain. There was a positive correlation between and , and the variation in was larger than that in . It seemed logical to evaluate the acoustic quality of spruce wood by a measure of . By using a cell wall model, those acoustic factors were expressed with the physical properties of the cell wall constituents. This model predicted that the essential requirement for an excellent soundboard is smaller fibril angle of the cell wall, which yields higher and higher . On the other hand, the effects of chemical treatments on the and of wood were clarified experimentally and analyzed theoretically. It was suggested that the and of wood cannot be improved at the same time by chemical treatment.     

Heat transfer in a “pseudoturbulent” bed of dispersed material

A two-phase model is proposed for the steady heat exchange between a surface and a pseudoturbulent bed of dispersed material. Expressions are obtained for the temperature fields of the gaseous and solid phases.Notation _g effective thermal conductivity of gaseous phase - _s effective thermal conductivity of the mixed solid phase - porosity - _m molecular thermal conductivity - d particle diameter - temperature of dispersed bed at a large distance from heat source - , g gas temperature - _p particle temperature - _w wall temperature - x current coordinate in the direction perpendicular to the wall - l bed thickness - q heat flux - coefficient of heat exchange between wall and pseudoturbulent bed of dispersed material - ^* coefficient of interphase heat exchange - _g=_g/_w dimensionless gas temperature - _p = _p/_w dimensionless particle temperature - Y = x/d dimensionless coordinate - L =l/d dimensionless bed thickness - A_h dimensionless coefficient of interphase heat exchange - Nu_g = d/_s Nusselt number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 465–469, September, 1981.     

The thermal conductivity and Lorenz function of the tin-lead alloy system Sn x Pb1 − x (x = 0.85, 0.7 0.5 0.3)

The thermal conductivity and electrical resistivity of the tin-lead alloy system Sn _x Pb_{1 – x} (x = 0.85, 0.7 0.5 0.3) were measured in the temperature range 7–300 K. The thermal conductivity was analyzed at temperature T 20K, assuming 1//T+Tⁿ, where , , and n are constants. The analysis shows that n < 2, and not n 2, which would be expected for a normal pure metal. The electrical resistivities could be represented by a T ⁵ relation for temperatures up to about 60 K. The characteristic temperature _R appears to decrease with increasing weight percent of lead. The total Lorenz functions were high, indicating the presence of phonon conductivity. The phonon conductivity _g appears to vary with T, and can be represented by _g=a/Tⁿ (a > 0) and n2.Work supported by the Universiti Sains Malaysia.     

Nonlinear viscoelasticity and relaxation phenomena of polymer solids

Summary The specific Helmholtz free energy of nonlinear viscoelastic isotropic polymer solids is assumed to be a separable, symmetric function along three orthogonal principal strain directions, i.e.=( ₁,q _n ⁽¹⁾)+( ₂,q _n ⁽²⁾)+( ₃,q _n ⁽³⁾), where the _r (r=1, 2, 3) are three principal stretch ratios and theq _n ( ^r ) are a set of internal state variables. It is shown that, by using this postulated form of the free energy function, one can readily characterize the mechanical response of viscoelastic polymer solids.

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Nichtlineare Viskoelastizität und Relaxationserscheinungen in festen Polymeren

Zusammenfassung Die spezifische Helmholtzsche freie Energie nichtlinear-viskoelastischer, isotroper, fester Polymere wird als separable, symmetrische Funktion der Form=( ₁,q _n ⁽¹⁾)+( ₂,q _n ⁽²⁾)+( ₃,q _n ⁽³⁾) angenommen mit den drei Hauptdehnungsverhältnissen _r (r=1, 2, 3) und inneren Zustandsvariablenq _n ( ^r ). Es wird gezeigt, daß dann das mechanische Verhalten der viskoelastischen festen Polymere schnell charakterisiert werden kann.

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This represents the results of one phase of research being carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract NAS 7-100, sponsored by the National Aeronautics and Space Administration.     

On the analysis of tunneling data for A15 superconductors

We examine the applicability of the standard McMillan inversion of Eliashberg's equations for superconductors with a nonconstant electronic density of statesN(). We do this usign simple models forN() and a realistically shapedN() taken from recent band structure work for Nb₃Sn. It turns out that peak structure inN() near _F may lead to gross errors in the derived Eliashberg function ²F() when the energy dependence ofN() is omitted in the inversion procedure. For Nb₃Sn, this leads to a 40% overestimate of when ²F() is evaluated via the standard McMillan program.     

Effect of phase fluctuations upon penetration depth

The temperature dependence of the static penetration (T) has been used as a guide to the nature of the superconducting state in high-T _c materials. It has been argued that an algebraic temperature dependence in the ratio (T)/(0) [(T) — (0)]/(0) at low temperature is evidence for d-wave pairing. This paper examines the effect of superconducting phase fluctuations upon (T) and finds an algebraic dependence over a broad range of temperature.     

Zero-point motion and superfluid helium

We propose that He II exhibits macroscopic [ _P /N O(1)] quantum zero-point motion in momentum space, i.e., that a nonzero root-mean-square superfluid velocity exists even in an equilibrium superfluid system at rest. At absolute zero, using coherent states, we relate the uncertainty _P /N in the total momentumP (per particle) to the long-range-order (LRO) part of the phase gradient correlation function, which is proposed as an order parameter. The local equilibrium equation for the superfluid velocity potential derived by Biswas and Rama Rao yields, in the strict equilibrium limit, the equation determining this order parameter in terms of fluctuation correlations that remain to be determined. The order parameter is interaction dependent, nonzero atT=0 if (0)–₀V₀>0, and can vanish at some transition temperatureT when fluctuation terms become comparable to theT=0 value. (HereV _{0 0}, and (0) are the uniform parts of the potential, density, and chemical potential with shifted zero of energy, respectively.) A characteristic length (T), diverging atT=T , appears naturally, with its defining relation reducing to a macroscopic uncertainty relation ( _P /N)(0)=/2 atT=0. With certain assumptions it is shown that atT=0, LRO in the phase gradient correlation function is incompatible with off-diagonal long-range order (ODLRO) in the (r)(r) correlation function, and with nonzero condensate function.     

Antiplane strain problem of diamond inclusion

In this paper, the singular stress fields created by an antiplane deformation at an inclusion corner are studied. It is shown that these singular stress fields can be separated into two independent types: a symmetric type with the stress singularity of 1/ ^1–1 and a skew-symmetric type with the stress singularity of 1/ ^1–2. These two types of the singular stress field can not occur simultaneously at the corner. If G ₂<G ₁, there exists only the singularity of the skew-symmetric type, and if G ₂>G ₁, there exists only the singularity of the symmetric type. A general expression of stress fields in the vicinity of the corner is presented. In the expression the singular stress fields for the symmetric type and the skew-symmetric type are defined in terms of the constants K _III, ₁ and K _III, ₂, respectively. K _III, ₂ and K _III, ₂ have to be determined from the complete boundary conditions of the given problem. For the problem of an infinite plate containing a diamond inclusion and subjected to a uniform longitudinal shear stress at infinity, the values of K _III, ₁ and K _III, ₂ are obtained by body force method. In the body force method, the investigated stresses are simulated by the superposition of the fundamental stress fields due to point forces. In order to obtain accurate solutions, the basic density functions of the distributed point forces are used, so that the stress singularities at the corner tip can be simulated by the point forces.     

Optical thermophysical characteristics of the condensed phase of combustion products and heatproof materials

An unconventional unit for experimentally studying the optical thermophysical properties of materials over a wide temperature range is described. Results are presented of studying the temperature function and dispersion of the absorption index for the condensed phase of the combustion products of a metalbearing fuel and of the emittance of fiber fireproof materials.Notation K spectral absorption coefficient - D spectral transmission coefficient - spectral absorption index - wavelength - d sample thickness - d_s surface layer thickness - I spectral intensity of radiation - , spectral and total emittances Kirov Polytechnical Institute. Kazan Chemical Engineering Institute, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 3, pp. 330–336. March, 1993     

Thermal conductivity of hydrocarbons in the naphthene group under high pressures

The thermal conductivity of hydrocarbons in the naphthene group has been experimentally determined. An equation is now proposed for calculating the thermal conductivity over the given temperature and pressure ranges.Notation thermal conductivity - ₂₀ and ₃₀ values of the thermal conductivity at 20 and 30°C, respectively - t₀,P₀ thermal conductivity at t₀, p₀ - _t p thermal conductivity at temperature t and under pressure P - change in thermal conductivity - P pressure - P_melt melting pressure - P₀ atmospheric pressure - t₀ 20°C temperature - T, t temperature - T_cr critical temperature - temperature coefficient of thermal conductivity - ₂₀ temperature coefficient of density - density - ₂₀ density at 20°C - _cr critical density - M molar mass - =T/T_cr referred temperature - v specific volume - v₀ specific volume at 20°C - v change in specific volume - _{3 0} a coefficient - B (t) a function of the temperature - S a quadratic functional - W_i, weight of the i-th experimental point - _i error of the i-th experimental value of thermal conductivity - B _{y, =0.6} value of B (t) at T = 0.6T_cr - B = B (t)/B_{, =0.6} referred value of coefficient B (t) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 491–499, September, 1981.     

Effect of the LIII Absorption Edge of Uranium on Chemical Shifts of the Lβ1 Line of Uranium in UO2+x

The effect of intraatomic absorption of the L₁ X-ray emission line of uranium was studied. To eliminate the effect of the L _{I I I} absorption edge on the chemical shift () of the L₁ line, the dependence of L₁ on the oxygen index x in oxide systems of variable composition UO_{2 + x} was determined indirectly. It was shown that, in the absence of the effect of the L _{I I I} absorption edge, the dependence of L₁ on x is ordinary and, as in the case of other hard emission lines of the uranium L series, can be described by a second-order polynomial. The abnormal dependence of L₁ on x is explained.     

Bounding-surface plasticity: Stress space versus strain space

Summary A bounding-surface plasticity model is formulated in stress space in a general enough manner to accommodate a considerable range of hardening mechanisms. Conditions are then established under which this formulation can be made equivalent to its strain-space analogue. Special cases of the hardening law are discussed next, followed by a new criterion to ensure nesting. Finally, correlations with experimental data are investigated.Notation (a) centre of the stress-space (strain-space) loading surface; i.e., backstress (backstrain) - ^* (a ^*) centre of the stress-space (strain-space) bounding surface - (a ) target toward which the centre of the stress-space (strain-space) loading surface moves under purely image-point hardening - (b) parameter to describe how close the loading surface is to nesting with the bounding surface in stress (strain) space; see (H10) - (c) elastic compliance (stiffness) tensor - (d) parameter to describe how close the stress (strain) lies to its image point on the bounding surface; see (H10) - (D) generalised plastic modulus (plastic compliance); see (1) - function expressing the dependence of the generalised plastic modulus on (plastic complianceD ond) - ^* (D ^*) analogue to (D) for the bounding surface - function expressing the dependence of ^* on (D ^* ond) - () strain (stress) - ' (') deviatoric strain (stress) - ^P ( ^R ) plastic strain (stress relaxation); see Fig. 1 - () image point on the bounding surface corresponding to the current strain (stress) - _iso (f _iso) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change of radius; i.e., fraction of isotropic hardening in the stress-space theory - _kin (f _kin) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change in the backstress (backstrain); i.e., fraction of kinematic hardening in the stress-space theory - _nor (f _nor) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - _ima (f _ima) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - function relating _iso to , , and (f _iso tob,d, andl) - function relating _kin to , , and (f _kin onb,d, andl) - function relating _nor to , , and (f _nor onb,d, andl) - function relating _ima to , , and (f _ima onb,d, andl) - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change of radius - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change in the centre - function relating _iso ^* to (f _iso ^* tod) - function relating _kin ^* to (f _kin ^* tod) - (l) parameter to describe the full extent of plastic loading up to the present, giving the arc length of plastic strain (stress relaxation) trajectory; see (H10) - function relating the direction for image-point translation of the loading surface to various other tensorial directions associated with the current state; see (H5). With 6 Figures     

Temperature dependence of the experimental penetration depth of superconducting thin films

Experimental magnetic field penetration depths (t, d, H) of the stable and superheated Meissner state were calculated as a function of temperature for various applied magnetic fields and various film thicknesses for two cases: (1) (t)/d and (2) 2(t)/d ( is the Ginzburg-Landau penetration depth,d is the film thickness, is the GL parameter). The results of the first case should be a useful tool for obtaining (0) of amorphous superconducting thin films.¹ This work was supported in part by NSF Grant No. INT 8006927.     

Mutual friction and vortex motion near the superfluid transition

The mutual friction parametersB and B for a moving vortex are calculated near the superfluid transition. They are proportional to the kinetic coefficient associated with the order parameter and, asT , diverge as (T – T)^–1/3, in agreement with experiment. The nonlinear couplings between the order parameter and the entropym, both the reversible one and the one in the free energy, are found to be crucial in the mutual friction near the point. These couplings were neglected in a previous paper by the author. First, the reversible coupling in the dynamic equations makes the chemical potential deviation long-ranged and causes the dissipation to take place only near the vortex core. Second,B can diverge asT T only in the presence of the coupling of the formm||² in the free energy. Thus theE model of Halperin et al., where the latter coupling is absent, cannot explain the critical anomaly ofB. The helical mode of a single vertex line is also investigated and its dispersion relation is found to be quite different from that at low temperatures. This mode has the same time scale as that of the second-sound mode when the wave vectors are of the order of the inverse correlation length, thus obeying the usual dynamic scaling law. The time correlation functions of the displacement fluctuations of a vortex line are also obtained. The force acting on a moving vortex is calculated and is found to be equal to the classical Magnus force.     

Gneralized McMillan tunneling model of the superconducting proximity effect. Specific heat jump

The reduced specific heat jumps for the superconducting (S) side and the normal (N) side of a strongly coupled N-S composite have been calculated by using the generalized McMillan tunneling model of the superconducting proximity effect. Both cases _N = 0 and _N 0 (where _N is the BCS interaction constant) have been studied. The results obtained by using the generalized model are significantly different from the ones given by the McMillan tunneling model.Work supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada.     

The anomalous thermal boundary resistance in superfluid4He near Tλ

The anomalous thermal boundary resistance R of superfluid⁴He near the lambda point T was studied in a cell with parallel copper faces and with various fluid layer thicknesses. The study was made as a function of the heat current Q and reduced temperature (T — T)/T = . In all cases, R tends to a maximum value R_itmax at T = T. This value is independent of Q, and is reproducible for various experiments. This contrasts with the regular boundary resistance which can vary considerably between successive experiments. Near T, the limiting slope dR/d¦¦ is found to be proportional to Q^–1, and this leads to a scaled representation of the data. This analysis is extended to data of similar experiments with gold plated copper surfaces by Duncan and Ahlers and by Zhong et al. The measurements of R over the whole range of¦¦ where it is observable are discussed and compared with previous experiments.