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1.
We show how to construct integral results for the multi-dimensional nonlinear diffusion equation c/t=·(D(c)c) and for some generalisations of this. For appropriate boundary conditions these become integral invariants. An application of these results to determining the large-time behaviour of some radially symmetric problems is indicated.  相似文献   

2.
This paper presents experimental data on a comparative study of a dc SQUID with voltage and current bias. We introduce a cross-correlated dynamic resistance of the device defined as a ratio R dCV = VC/IV, where VC = (V/) A is the slope of the voltage-to-flux characteristics measured in the current bias mode and IV = (I/) A is the slope of the current-to-flux characteristics measured with voltage bias. It has been found that R dCV may deviate strongly from the dynamic resistance observed in the current bias mode of operation. The intrinsic energy resolution of the SQUID remains unchanged for both modes of operation, but the current noise of the voltage biased device scales with the cross-correlated dynamic resistance. In our SQUID with the loop inductance L = 105 pH, is equal to 37 h in the white noise region at a temperature of 4.2 K.  相似文献   

3.
The temperature changes as a result of rapid hydrostatic pressure applications are reported for high density polyethylene (HDPE) and low density polyethylene (LDPE) in the reference temperature range from 298 to 423 K and in the pressure range from 13.8 to 200 MN m–2. The adiabatic temperature changes were found to be a function of pressure and temperature. A curve fitting analysis showed that the empirical curve (/P) =ab(P)b–1 described the experimental thermoelastic coefficients obtained from the experiments. The data were analyzed by determining the predicted thermoelastic coefficients derived from the Thomson equation (/P) = T 0/C p. The experimental and predicted Grüneisen parameter T were also determined.  相似文献   

4.
Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic-stiffness tensor components Cu and the adiabatic bulk modulus, BS, of a ferromagnetic Heusler structure Cu41Mn20Al39 at % alloy single crystal as functions of temperature in the range 14–300 K and hydrostatic pressure up to 0.2 GPa at room temperature. At 295 K the elastic stiffnesses are: C11=133 GPa, C44=92 GPa, C (=(C11–C12)/2)=17 GPa, C12=99 GPa, CL(=C11+C44–C)=205 GPa, and BS (=C11–4C/3)=106 GPa. Cu41Mn20Al39 is a comparatively soft material elastically because its elastic properties are influenced strongly by magnetoelastic effects. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to obtain the hydrostatic-pressure derivatives of the elastic – stiffness tensor components. At 295 K (C11/P)P=0, (C44/P)P=0, (C/P)P=0, (C12/P)P=0, (CL/P)P=0, and (BS/P)P=0 are 5.0±0.1, 3.0±0.1, 1.0±0.2, 3.0±0.3, 7.7±0.4 and 3.7±0.4, respectively. Application of hydrostatic pressure does not induce acoustic-mode softening: the pressure derivatives (CIJ/P)P=0 and (BS/P)P=0 and the acoustic-mode Grüneisen parameters are positive. An interesting feature of the non-linear acoustic behaviour of this alloy is that the value obtained for (C/P)P=0, associated with the softer shear mode propagated along the [1 1 0] direction and polarized along the [1 1 0] direction, is small in comparison with those of the other shear and longitudinal modes. The Grüneisen parameter of this mode, and hence its vibrational anharmonicity, is much larger than those of the other long-wavelength acoustic phonon modes. © 1998 Kluwer Academic Publishers  相似文献   

5.
We have determined the effect of hydrostatic pressureP on the superconducting transition temperatureT c of bulk, A15 Nb3Si. For 0P20 kbar (2 GPa),T c decrease linearly with increasing pressure at a rate T c/P=–2.67×10–5 K/bar. From an estimate of T c/P obtained using recent band structure calculations for the density-of-electronic-states change as a function of lattice parameter in Nb3Si, we conclude that the pressure dependence of the electron-phonon interaction primarily determines T c/P.Work performed under the auspices of the U.S. DOE.  相似文献   

6.
Shallow cavity flows driven by horizontal temperature gradients are analysed over a range of Rayleigh numbersR and Prandtl numbers , whereR is comparable in size to the aspect ratioL(1). Eigenvalue calculations show the existence of a critical Prandtl number R > R c (), below which the parallel core-flow structure is destroyed for Rayleigh numbersR>R c(). For other Rayleigh numbers and Prandtl numbers the horizontal scale of influence of the end walls of the cavity is determined.  相似文献   

7.
The thermal pressure coefficient (p/T) v has been measured for ethanenitrile from 299 to 364 K, for propanenitrile from 295 to 377 K, and for butanenitrile from 297 to 398 K. The results are discussed in terms of the diminishing role of polarity in the alkanenitrile series and of a corresponding-states approach using gas-liquid critical properties as reduction factors. Although (p/T) v varies unevenly with chain length, the reduced quantity shows a more regular behavior similar to that of the related quantity the cohesive energy density.  相似文献   

8.
Differences in the lattice constants of Mo-100 and Mo-92 have been measured by x-ray diffraction, in order to search directly for the volume effect of isotopes in a superconductor. No significant difference in the lattice constanta(Mo-100)–a(Mo-92) could be detected at 290 K, while the differences –0.0014±0.0008 and –0.0029±0.0009 Å were detected at 85.3 and 4.31 K, respectively. These values, and their temperature dependence, are considered to be theoretically reasonable. The exponent in the isotope effect defined by TcM- is represented thermodynamically by =–( lnT c / lnM)–( lnT c / lnV)(d lnV/d lnM). From the results, d lnV/d lnM is found to be –0.033±0.009 at 4.31 K. Then, the second term representing the isotopic volume effect is estimated to be about 0.09, with lnT c / lnV2.81. The observed value of is 0.33, so that the contribution of the second term, 0.09, is 27% of the value of . It becomes quite clear that the isotopic volume effect in superconducting Mo should not be neglected.  相似文献   

9.
We have measured the length change due to the transition from the super-conducting to the normal state in pure In and Sn and in In-Sn alloys. The measurements were made on single-crystal specimens. The alloys had Sn content ranging from zero to 12 at %. Crystals parallel and perpendicular to the tetragonal axis were grown at each alloy content. We find that the relative length changes l/l are very sensitive to alloy content. From l/l we have calculated the stress derivatives H c/ and T c / and we find that T c / changes from +59 to –92 mK/bar for stress along the tetragonal axis, and from –9 to 46 mK/kbar for stress perpendicular to the tetragonal axis. We suggest that these large changes are due to Fermi surface topology changes upon increasing the Sn content in In.  相似文献   

10.
Measurements of the pressure coefficient (P/T),x are reported for a 3 He- 4 He mixture with a mole fractionX=0.805 of 3 He in the neighborhood of the liquid-vapor critical point. These include data on 16 isochores taken over the density interval–0.50.5 and over the temperature range–0.1 t0.1, where =(– c )/ c andt=(T-T c )/T c ,with c andT c ,respectively, the critical density and temperature of the mixture. From the discontinuity of (P/T),x at the boundary between the two-phase and the one-phase regions we determine the dew-bubble curve nearT c with better precision than was done in recentPVT experiments. From the extrapolation of data not approachingT c closer than1 mK, (P/T),x along the critical isochore appears to be discontinuous atT c ,while for the isochore / c 0.92, (P/T),x is continuous across the dew curve. It is found that this latter isochore cuts the dew curve at its highest temperature. These observations are discussed in terms of general thermodynamic arguments and theoretical predictions of the asymptotic behavior. We calculate (P/T),x from the scaling equation of state proposed by Leung and Griffiths for 3 He- 4 He mixtures, using their numerical parameters. In spite of some systematic deviations, especially in the two-phase region, there is in general good agreement with experimental results. In particular, the shape of the measured dew-bubble curve and the apparent discontinuity of (P/T),x along the critical isochore show excellent agreement with theory.Work supported by a grant from the National Science Foundation. A report of this work has been presented at the Washington Meeting of the APS [Bull. Am. Phys. Soc. 20, 618 (1975)].  相似文献   

11.
When a heat flux is switched on across a fluid binary mixture, steady state conditions for the temperature and mass concentration gradients T and c are reached via a diffusive transient process described by a series of terms modes involving characteristic times n . These are determined by static and transport properties of the mixture, and by the boundary conditions. We present a complete mathematical solution for the relaxation process in a binary normal liquid layer of heightd and infinite diameter, and discuss in particular the role of the parameterA=k T 2 (/c) T,P /TC P,c coupling the mass and thermal diffusion. Herek T is the thermal diffusion ratio, (/c) T,P –1 is the concentration susceptibility, is the chemical potential difference between the components, andC P,c is the specific heat. We present examples of special situations found in relaxation experiments. WhenA is small, the observable times (T) and (c) for temperature and concentration equilibration are different, but they tend to the same value asA increases. We present experimental results on four examples of liquid helium of different3He mole fractionX, and discuss these results on the basis of the preceding analysis. In the simple case for pure3He (i.e., in the absence of mass diffusion) we find the observed (T) to be in good agreement with that calculated from the thermal diffusivity. For all the investigated3He-4He mixtures, we observe (c) and (T) to be different whenA is small, a situation occurring at high enough temperatures. AsA increases with decreasingT, they become equal, as predicted. For the mixtures with mole fractionsX(3He)=0.510 and 0.603, we derive the mass diffusionD from the analysis of (c) and demonstrate that it diverges strongly with an exponent of about 1/3 in the critical region near the superfluid transition. As the tricritical point (T t,X t) is approached for the mixtureX=X t0.675,D tends to zero with an exponent of roughly 0.4. These results are consistent with predictions and also with theD derived from sound attenuation data. We discuss the difficulties of the analysis in the regime close toT andT t, with special emphasis on the situation created by the onset of a superfluid film along the wall of the cell forX=0.603 and 0.675.Work supported by grants from the National Science Foundation and the Research Corporation and by an A. P. Sloan fellowship to one of the authors (RPB).  相似文献   

12.
We present steady-state measurements of the thermal diffusion ratiok T and of the heat conductivity for three dilute mixtures of3He in4He with concentrations 9×10–3X(3He)5×10–2 at saturated vapor pressure in the normal phase close to the superfluid transition. The data are compared with predictions by Dohm and Folk from the renormalization group (RG) theory. From auxiliary determinations of thermodynamic derivatives for these mixtures, we obtain the separation factor =–(k T /T)×(/X) T,P /(/T) X,P above T over the range wherek T is positive. Here is the mass density. From the transients of X(t) as a function of time, we obtain an estimation for the mass diffusion coefficientD and compare the results with predictions by Dohm and Folk and with results from other experiments.  相似文献   

13.
Experimental data on the thermal conductivity of five liquid n-alkanes-hexane, heptane, octane, decane, and dodecane-are presented in the temperature range from 283 to 373 K at pressures up to 250 MPa or the freezing pressures. The measurements were performed on an absolute basis by an automated transient hot-wire apparatus. The uncertainty of the reported data is estimated to be within ±1%. The thermal conductivity of each alkane decreases almost linearly with rising temperature at a constant pressure and increases with increasing pressure at a constant temperature. Both the temperature coefficient of the thermal conductivity ¦(/T) p¦ and the pressure coefficient (/P) T decrease with increasing carbon number of alkanes. The experimental results were correlated with temperature and pressure by a similar expression to the Tait equation. It is also found that both the dense hard-sphere model presented by Menashe et al. and the modified significant structure theory proposed by Prabhuram and Saksena provide good representations of the present experimental results.  相似文献   

14.
An investigation is reported of the 75 at% nickel section of the Ni-Cr-Al-Ru system at 1523 and 1273 K. Constitutional data obtained by electron probe microanalysis, X-ray diffraction and microscopical examination are presented as partial isothermal sections. At 1523 K, the major part of the section consists of phase, while the aluminium-rich region contains a and+ region; the extent of the solid solution of chromium and ruthenium in totals ~ 4 at%. The ruthenium-rich corner of the section shows a two-phase region consisting of + ruthenium-rich solid solution. At 1273 K the,+ and + ruthenium regions increase in extent. The/ mismatch values in the equilibrated alloys studied lie in the range ~ –0.08 to –0.39%. Constitutional features of as-cast alloys are also reported.  相似文献   

15.
The interaction between a dislocation and the impurity in KCl: Mg2+ (0.035 mol% in the melt) was investigated at 77–178 K with respect to the two models: one is the Fleischer's model and the other the Fleischer's model taking account of the Friedel relation. The latter is termed the F-F. The dependence of strain-rate sensitivity due to the impurities on temperature for the specimen was appropriate to the Fleischer's model than the F-F. Furthermore, the activation enthalpy, H, for the Fleischer's model appeared to be nearly proportional to the temperature in comparison with the F-F. The Friedel relation between effective stress and average length of the dislocation segments is exact for most weak obstacles to dislocation motion. However, above-mentioned results mean that the Friedel relation is not suitable for the interaction between a dislocation and the impurity in the specimen. Then, the value of H(T c) at the Fleischer's model was found to be 0.61 eV. H(T c) corresponds to the activation enthalpy for overcoming of the strain field around the impurity by a dislocation at 0 K. In addition, the Gibbs free energy, G 0, concerning the dislocation motion was determined to be between 0.42 and 0.48 eV on the basis of the following equation ln / = G 0/(kTp0)1 – (T/T c)1/2 –1(T/T c)1/2 + ln 0/where k is the Boltzmann's constant, T the temperature, T c the critical temperature at which the effective stress due to the impurities is zero, p0 the effective shear stress without thermal activation, and 0 the frequency factor.  相似文献   

16.
We report high-resolution measurements of the pressure coefficient (P/T) for3He in both the one-phase and two-phase regions close to the critical point. These include data on 40 isochores over the intervals–0.1t+0.1 and–0.2+0.2, wheret=(T–T c )/T c and =(– c )/ c . We have determined the discontinuity (P/T) of (P/T) between the one-phase and the two-phase regions along the coexistence curve as a function of . The asymptotic behavior of (1/) (P/T) versus near the critical point gives a power law with an exponent (+–1)–1=1.39±0.02 for0.010.2 or–1×10 –2t10 –6 , from which we deduce =1.14±0.01, using =0.361 determined from the shape of the coexistence curve. An analysis of the discontinuity (P/T) with a correction-to-scaling term gives =1.17±0.02. The quoted errors are fromstatistics alone. Furthermore, we combine our data with heat capacity results by Brown and Meyer to calculate (/T) c as a function oft. In the two-phase region the slope (2/T 2)c is different from that in the one-phase region. These findings are discussed in the light of the predictions from simple scaling and more refined theories and model calculations. For the isochores 0 we form a scaling plot to test whether the data follow simple scaling, which assumes antisymmetry of – ( c ,t) as a function of on both sides of the critical isochore. We find that indeed this plot shows that the assumption of simple scaling holds reasonably well for our data over the ranget0.1. A fit of our data to the linear model approximation is obtained for0.10 andt0.02, giving a value of =1.16±0.02. Beyond this range, deviations between the fit and the data are greater than the experimental scatter. Finally we discuss the (P/T) data analysis for 4 He by Kierstead. A power law plot of (1/) P/T) versus belowT c leads to =1.13±0.10. An analysis with a correction-to-scaling term gives =1.06±0.02. In contrast to 3 He, the slopes (2/T 2)c above and belowT c are only marginally different.Work supported by a grant from the National Science Foundation.  相似文献   

17.
When helium is confined to a uniform small dimension L, its behavior is modified due to the limitation of the growth of the correlation length. This has been explored for planar confinement over a wide range of L. Less is known about confined mixtures, especially in the case of the specific heat. Here two principal effects come into play: the magnitude of the correlation length increases, and the measured heat capacity Cpx must be converted to Cp, where = 3 4 , before finite-size scaling predictions can be verified. The increase in makes a given confinement L look smaller as the concentration x is increased. This, as well as changes of L itself, can be used to test predictions of correlation-length scaling. We report measurements of the specific heat of confined mixtures and compare with the well established scaling for the pure system.  相似文献   

18.
19.
Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of aluminum nitride (AlN) ceramic samples as functions of temperature in the range 100–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. Aluminum nitride is an elastically stiff but light ceramic: at 295 K, the longitudinal stiffness (C L), shear stiffness (), adiabatic bulk modulus (B S), Young's modulus (E) and Poisson's ratio () are 373 GPa, 130 GPa, 200 GPa, 320 GPa and 0.234, respectively. The temperature dependences of C L and B S show normal behaviour and can be approximated by the conventional model for vibrational anharmonicity. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to determine the hydrostatic-pressure derivatives of elastic stiffnesses and the acoustic-mode Grüneisen parameters. The values determined at 295 K for the hydrostatic-pressure derivatives (C L/P) P=0, (/P) P=0 and (B S/P) P=0 are 4.7 ± 0.1, 0.22 ± 0.03 and 4.4 ± 0.15, respectively. The adiabatic bulk modulus B S and its hydrostatic-pressure derivative (B S/P) P=0 are in good agreement with the results of recent high pressure X-ray diffraction measurements and theoretical calculations. The longitudinal (L), shear (S), and mean (el) acoustic-mode Grüneisen parameters of AlN are positive: the zone-centre acoustic phonons stiffen under pressure. The shear S (=0.006) is much smaller than the longitudinal L (=1.09) accounting for the low thermal Gr¨neisen parameter th (=0.65) obtained for this ceramic: since the acoustic Debye temperature D (=980 ± 5 K) is so high, the shear modes play an important role in acoustic phonon population at room temperature. Hence knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic AlN.  相似文献   

20.
Pulse-echo overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of ceramic transition-metal carbides TiC and TaC as functions of temperature in the range 135–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. The carbon concentration of each ceramic has been determined using an oxidation method: the carbon-to-metal atomic ratios are both 0.98. In general, the values determined for the adiabatic bulk modulus (B S), shear stiffness (), Young's modulus (E), Poisson's ratio () and acoustic Debye temperature (D) for the TiC and TaC ceramics agree well with the experimental values determined previously. The temperature dependences of the longitudinal stiffness (C L) and shear stiffness measured for both ceramics show normal behaviour and can be approximated by a conventional model for vibrational anharmonicity. Both the bulk and Young's moduli of the ceramics increase with decreasing temperature and do not show any unusual effects. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to determine the hydrostatic pressure derivatives of elastic stiffnesses and the acoustic-mode Grüneisen parameters. The values determined at 295 K for the hydrostatic pressure derivatives (C L/P)P = 0, (/P)P = 0 and (B S/P)P = 0 for TiC and TaC ceramics are positive and typical for a stiff solid. The adiabatic bulk modulus B S and its hydrostatic pressure derivative (B S/P)P = 0 of TiC are in good agreement with the results of recent high pressure X-ray diffraction measurements and theoretical calculations. The longitudinal (L), shear (S) and mean (el) acoustic-mode Grüneisen parameters of TiC and TaC ceramics are positive: the zone-centre acoustic phonons stiffen under pressure. The shear S is much smaller than the longitudinal L. The relatively larger values estimated for the thermal Grüneisen parameter th in comparison to el for the TiC and TaC ceramics indicate that the optical phonons have larger Grüneisen parameters. Hence knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic TiC and TaC.  相似文献   

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