Bashar Albaalbaki  Roger E. Khayat 《国际流体数值方法杂志》2012,69(11):1762-1785

A comparison among three weakly nonlinear approaches for thermo‐gravitational instability in a Newtonian fluid layer heated from below is presented. First, the dynamical systems describing the time evolution of the problem from different weakly nonlinear approaches, namely, the Lorenz model, the amplitude equations and the perturbation expansion approaches are obtained. Next, the steady states and their stability, as well as the transient behaviour are obtained from each dynamical system. The similarity and difference among the three models are emphasized. The role of each of the nondimensional groups, the Rayleigh number and the Prandtl number is compared for the three models. The different approaches lead to similar behaviours when the Rayleigh number is just above its critical value and Prandtl number is high. However, only the dynamical system obtained from the amplitude equations is able to reflect the role of the Prandtl number. On the other hand, the amplitude equations and perturbation expansion techniques are not suitable for predicting the uniform oscillatory behaviour observed frequently in Rayleigh–Bénard convection. The novelty of the current work lies in studying the critical differences in the findings of the three popular approaches to investigate weakly nonlinear thermal convection for the first time. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

    

Cristóbal E. Castro  Eleuterio F. Toro 《国际流体数值方法杂志》2014,75(7):467-486

We present a Roe‐type weak formulation Riemann solver where the average coefficient matrix is computed numerically. The novelty of this approach is that it is general enough that can be applied to any hyperbolic system while retaining the accuracy of the original Roe solver. We show applications to the compressible Euler equations with general equation of state. An alternative version of the method uses directly the eigenvectors in the averaging process, simplifying the algorithm. These new solvers are applied in conservative and path‐conservative schemes with high‐order accuracy and on unstructured meshes. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

    

M. Lucht  M. Lerche  H.‐C. Wille  Yu. V. Shvyd'ko  H. D. Rüter  E. Gerdau  P. Becker 《Journal of Applied Crystallography》2003,36(4):1075-1081

The lattice parameters of α‐Al₂O₃ have been measured in a temperature range from 4.5 to 250 K with a relative accuracy of better than 6 × 10⁻⁶. The experimental method uses Bragg backscattering and the recently proposed Mössbauer wavelength standard, i.e. the wavelength λ_M = 86.025474 (16) pm of the nuclear resonance radiation of ⁵⁷Fe (Shvyd'ko et al., 2000), which has previously been applied successfully to measure the lattice parameters of α‐Al₂O₃ at temperatures between 286 and 374 K (Shvyd'ko et al., 2002). The experimental data in the range from 4.5 to 374 K are consistent with the Debye model of thermal expansion. At 4.5 K, the thermal expansion coefficient is as low as 1.2 (9) × 10⁻¹⁰ K⁻¹ in the a direction.  相似文献   

    

I. G. Wood  K. S. Knight  G. D. Price  J. A. Stuart 《Journal of Applied Crystallography》2002,35(3):291-295

The structure of KMgF₃ has been determined by high‐resolution neutron powder diffraction at 4.2 K, room temperature and at 10 K intervals from 373 K to 1223 K. The material remains cubic at all temperatures. The average volumetric coefficient of thermal expansion in the range 373–1223 K was found to be 7.11 (3) × 10⁻⁵ K⁻¹. For temperatures between 4.2 and 1223 K, a second‐order Grüneisen approximation to the zero‐pressure equation of state, with the internal energy calculated via a Debye model, was found to fit well, with the following parameters: θ_D = 536 (9) K, V_o = 62.876 (6) ų, = 6.5 (1) and (V_oK_o/γ′) = 3.40 (2) × 10⁻¹⁸ J, where θ_D is the Debye temperature, V_o is the volume at T = 0, is the first derivative with respect to pressure of the incompressibility (K_o) and γ′ is a Grüneisen parameter. The atomic displacement parameters were found to increase smoothly with T and could be fitted using Debye models with θ_D in the range 305–581 K. At 1223 K, the displacement of the F ions was found to be much less anisotropic than that in NaMgF₃ at this temperature.  相似文献   

    

Y.Z. He  Y.G. Zhao  M.H. Zhu  X.P. Zhang  B.S. Cao 《Crystal Research and Technology》2002,37(12):1280-1284

A facile method to control the contracting rate of the thermal expansible bars for pulling crystal is first suggested. The thermal expansible bars, set in a modified Dewar flask whose vacuum degree is controlled, are heated to designed temperature and then switch off the power to let it cool down at a desired rate, which depends largely on the changeable vacuum degree. This new approach is expected to completely eliminate the effects, which possibly reduces the smooth extent of thermal expansion, caused by the minor temperature fluctuations during crystal growth process and to realize the utmost smooth and slow pulling rate. It is expected to install this apparatus in optical floating zone furnace, instead of traditional motor, to grow peritectic crystal, such as crystal Bi‐2223, since for the peritectic reaction, in principle, the extremely slow growing rate is considerably essential.  相似文献   

    

N. K. Mukhopadhyay  E. A. Lord 《Acta Crystallographica. Section A, Foundations and Advances》2002,58(5):424-428

The least path criterion or least path length in the context of redundant basis vector systems is discussed and a mathematical proof is presented of the uniqueness of indices obtained by applying the least path criterion. Though the method has greater generality, this paper concentrates on the two‐dimensional decagonal lattice. The order of redundancy is also discussed; this will help eventually to correlate with other redundant but desirable indexing sets.  相似文献   

    

V. Kumar  B.S.R. Sastry 《Crystal Research and Technology》2001,36(6):565-569

The linear thermal expansion coefficient of tetrahedrally coordinated A^IIB^VIand A^IIIB^Vsemiconductors has been calculated using plasmon energy data. A simple relation between the bond length and plasm on energy has been derived. The calculated values of thermal expansion coefficient and bond length have been compared with the experimental values and the values reported by differentworkers. An excellent experiment has been obtained between them.  相似文献   

    

Wesley M. Dose  Scott W. Donne 《Journal of Applied Crystallography》2013,46(5):1283-1288

High‐temperature in situ X‐ray diffraction is used to determine the thermal expansion behaviour of manganese dioxide in air at temperatures between 298 and 673 K, the range accessible prior to material decomposition. Two manganese dioxide samples of different origins are investigated to observe the effect of synthesis conditions and resultant material properties on the thermal response. β‐MnO₂ prepared by a chemical pathway is found to expand linearly over the temperature window with thermal expansion coefficients (in units of K⁻¹) of α_a = 9.3 (4) × 10⁻⁶, α_c = 7.0 (2) × 10⁻⁶ and β = 25.6 (8) × 10⁻⁶. Conversely, the thermal expansion of heat‐treated electrolytic manganese dioxide is disjointed about 473 K in the a direction and for the overall unit‐cell volume, and about 523 K in the c direction. Coefficients are therefore given (in units of K⁻¹) as α_a = 23 (4) × 10⁻⁶ (298–473 K), 10 (3) × 10⁻⁶ (473–673 K); α_c = 0.2 (9) × 10⁻⁶ (298–523 K), 10 (1) × 10⁻⁶ (523–673 K); and β = 49 (9) × 10⁻⁶ (298–473 K), 26 (5) × 10⁻⁶ (473–673 K).  相似文献   

    

Andrew Sazonov  Vladimir Hutanu  Martin Meven  Gernot Heger  Thomas Hansen  Anatoliy Senyshyn 《Journal of Applied Crystallography》2010,43(4):720-728

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M. Alvaro  R. J. Angel  C. Marciano  S. Milani  L. Scandolo  M. L. Mazzucchelli  G. Zaffiro  G. Rustioni  M. Briccola  M. C. Domeneghetti  F. Nestola 《Journal of Applied Crystallography》2015,48(4):1192-1200

A new micro‐furnace equipped with an H‐shaped resistance heater has been developed to conduct in situ single‐crystal X‐ray diffraction experiments at high temperature. The compact design of the furnace does not restrict access to reciprocal space out to 2θ = 60°. Therefore, unit‐cell parameters and intensity data can be determined to a resolution of 0.71 Å with Mo radiation. The combined use of mineral phases with well characterized lattice expansion (e.g. pure Si and SiO₂ quartz) and a small‐diameter (0.025 mm) K‐type thermocouple allowed accurate temperature calibration from room temperature to about 1273 K and consequent evaluation of thermal gradients and stability. The new furnace design allows temperatures up to about 1273 K to be reached with a thermal stability better than ±5 K even at the highest temperatures. Measurements of the lattice thermal expansion of pure silicon (Si), pure synthetic grossular garnet (Ca₃Al₂Si₃O₁₂) and quartz (SiO₂) are presented to demonstrate the performance of the device. Its main advantages and limitations and important considerations for using it to perform high‐temperature diffraction measurements are discussed.  相似文献