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In view of rapid developments in iterative solvers, it is timely to re‐examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two‐field mixed formulation. The standard displacement and two‐field mixed formulations are solved using both direct and iterative approaches to assess if it is cost‐effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ‘exactly’, does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large‐scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi‐minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   
54.
The influence of magnetic fields on the energy level populations of atoms is firstly studied by analysing the Stokes profiles of Fe  i 6302.5 forming in the solar magnetized atmosphere, with the aid of a departure factor defined to evaluate the deviation from the normal Boltzmann distribution without a magnetic field. This factor is directly related to the ratio of line-source function to the continuum one. The relationship between the departure and the magnetic field reveals an effect that the magnetic field induces an exponential increase in the level population of the lower level of Fe  i 6302.5 (Landé factor   g = 2.5  ) with the field strength. This indicates that the magnetic field can cause the redistribution of populations of those levels whose Landé factors are non-zero. Therefore, this effect should be included in the calculation of the statistical equilibrium. Secondly, an experiment utilizing the Hg5461 line in the laboratory on the Earth is carried out to reveal that the exponential relation is independent of variations in temperature, and the excitation is completely magneto-induced. Finally, the exponential relation is explained by taking account of the magnetic energy in the Boltzmann distribution.  相似文献   
55.
The hydrodynamic instability, which develops on the contact surface between two fluids, has great importance in astrophysical phenomena such as the inhomogeneous density distribution following a supernova event. In this event acceleration waves pass across a material interface and initiate and enhance unstable conditions in which small perturbations grow dramatically. In the present study, an experimental technique aimed at investigating the above-mentioned hydrodynamic instability is presented. The experimental investigation is based on a shock-tube apparatus by which a shock wave is generated and initiates the instability that develops on the contact surface between two gases. The flexibility of the system enables one to vary the initial shape of the contact surface, the shock-wave Mach number, and the density ratio across the contact surface. Three selected sets of shock-tube experiments are presented in order to demonstrate the system capabilities: (1) large-initial amplitudes with low-Mach-number incident shock waves; (2) small-initial amplitudes with moderate-Mach-number incident shock waves; and (3) shock bubble interaction. In the large-amplitude experiments a reduction of the initial velocity with respect to the linear growth prediction was measured. The results were compared to those predicted by a vorticity-deposition model and to previous experiments with moderate- and high-Mach number incident shock waves that were conducted by others. In this case, a reduction of the initial velocity was noted. However, at late times the growth rate had a 1/t behavior as in the small-amplitude low-Mach number case. In the small-amplitude moderate-Mach number shock experiments a reduction from the impulsive theory was noted at the late stages. The passage of a shock wave through a spherical bubble results in the formation of a vortex ring. Simple dimensional analysis shows that the circulation depends linearly on the speed of sound of the surrounding material and on the initial bubble radius.  相似文献   
56.
Abstract— Quantifying the peak temperatures achieved during metamorphism is critical for understanding the thermal histories of ordinary chondrite parent bodies. Various geothermometers have been used to estimate equilibration temperatures for chondrites of the highest metamorphic grade (type 6), but results are inconsistent and span hundreds of degrees. Because different geothermometers and calibration models were used with different meteorites, it is unclear whether variations in peak temperatures represent actual ranges of metamorphic conditions within type 6 chondrites or differences in model calibrations. We addressed this problem by performing twopyroxene geothermometry, using QUILF95, on the same type 6 chondrites for which peak temperatures were estimated using the plagioclase geothermometer (Nakamuta and Motomura 1999). We also calculated temperatures for published pyroxene analyses from other type 6 H, L, and LL chondrites to determine the most representative peak metamorphic temperatures for ordinary chondrites. Pyroxenes record a narrow, overlapping range of temperatures in H6 (865–926 °C), L6 (812–934 °C), and LL6 (874–945 °C) chondrites. Plagioclase temperature estimates are 96–179 °C lower than pyroxenes in the same type 6 meteorites. Plagioclase estimates may not reflect peak metamorphic temperatures because chondrule glass probably recrystallized to plagioclase prior to reaching the metamorphic peak. The average temperature for H, L, and LL chondrites (~900 °C), which agrees with previously published oxygen isotope geothermometry, is at least 50 °C lower than the peak temperatures used in current asteroid thermal evolution models. This difference may require minor adjustments to thermal model calculations.  相似文献   
57.
By use of the reddening free [m 1], [c 1], and indices data inuvby photometric system for three classical cepheids whose reddening values had been determined with the aid of photometry of field stars, three intrinsic relations of [m 1]–(b–y), [c 1]–(b–y), and –(b–y) have been established. It was shown that these three relations can be used to determine the colour excesses for other classical cepheids.  相似文献   
58.
It has become clear in recent years that relativistic beaming is a good explanation for the BL Lac phenomenon. Of studies based on the relativistic beaming model of BL Lac objects, we note that the orientation of jet's axis to the line-of-sight is very small and, therefore, the observed flux emitted from a rapidly moving source is orders of magnitude higher than the flux in its rest-frame:F obs = 3 + F intr, where is the bulk relativistic Doppler factor. Then the observed apparent magnitudem v must be corrected for this effect. For our 39 samples, the corrected apparent magnitudem v corr and logZ have a good correlation.  相似文献   
59.
We have calculated the emission spectra of hydrogen and sodium atoms in the cool part of prominence models which satisfy simultaneously the constraints of radiative transfer, statistical equilibrium and charge-particle conservations.In the considered range of our model parameters, emission strengths of H and Nai D lines increase with the temperature and the total number density. Low-pressure models raise the ionization rate highly but yield very weak Nai D line intensities, since these model prominences contain small amounts of free electrons and sodium atoms which have a deep relation with the formation of sodium lines. We find that sodium D lines should be emitted in the high pressure region of prominences, and that their intensities are difficult to attain in the cool core of any model prominence with a temperature as low as 4000 K. In order to explain consistently the spectral emissions of H and Nai D lines observed in quiescent prominences, a total number density higher than 4 x 1011 cm-3 and a temperature over 5000 K are required at least in the cool part of prominences.Contributions from the Kwasan and Hida Observatories, University of Kyoto, No. 282.  相似文献   
60.
A survey of the 4(04)-3(03) and 1(01)-0(00) transitions of HOCO+ has been made toward several molecular clouds. The HOCO+ molecule was not observed in any sources except Sgr B2 and Sgr A. The 5(05)-4(04) and 4(14)-3(13) transitions were also detected toward Sgr B2. The results indicate that gas phase CO2 is not a major carbon reservoir in typical molecular clouds. In Sgr B2, the HOCO+ antenna temperature exhibits a peak approximately 2' north of the Sgr B2 central position (Sgr B2[M]) and the 4(04)-3(03) line emission is extended over a approximately 10' x 10' region. The column density of HOCO+ at the northern peak in Sgr B2 is approximately 3 x 10(14) cm-2, and the fractional abundance relative to H2 > or = 3 x 10(-10), which is about 2 orders of magnitude greater than recent predictions of quiescent cloud ion-molecule chemistry.  相似文献   
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