Geometric conservation law and applications to high-order finite difference schemes with stationary grids

The geometric conservation law (GCL) includes the volume conservation law (VCL) and the surface conservation law (SCL). Though the VCL is widely discussed for time-depending grids, in the cases of stationary grids the SCL also works as a very important role for high-order accurate numerical simulations. The SCL is usually not satisfied on discretized grid meshes because of discretization errors, and the violation of the SCL can lead to numerical instabilities especially when high-order schemes are applied. In order to fulfill the SCL in high-order finite difference schemes, a conservative metric method (CMM) is presented. This method is achieved by computing grid metric derivatives through a conservative form with the same scheme applied for fluxes. The CMM is proven to be a sufficient condition for the SCL, and can ensure the SCL for interior schemes as well as boundary and near boundary schemes. Though the first-level difference operators δ₃ have no effects on the SCL, no extra errors can be introduced as δ₃ = δ₂. The generally used high-order finite difference schemes are categorized as central schemes (CS) and upwind schemes (UPW) based on the difference operator δ₁ which are used to solve the governing equations. The CMM can be applied to CS and is difficult to be satisfied by UPW. Thus, it is critical to select the difference operator δ₁ to reduce the SCL-related errors. Numerical tests based on WCNS-E-5 show that the SCL plays a very important role in ensuring free-stream conservation, suppressing numerical oscillations, and enhancing the robustness of the high-order scheme in complex grids.     

Theoretical studies of the optical and EPR spectra for Fe ion in the MF3:Fe (M=Al, Ga) systems

By analyzing the EPR spectra of Fe³⁺ ion in the fluorinde glasses, the local lattice structures around impurity Fe³⁺ ion in MF₃:Fe³⁺ (M=Al, Ga) systems have been studied by means of diagonalizing the complete energy matrices of the electron-electron repulsion, the ligand-field and the spin-orbit coupling for a d⁵ configuration ion in a trigonal ligand-field. Both the second-order and fourth-order EPR parameters D and (a−F) are taken simultaneously in the structural investigation. The results indicate that the local lattice structure around octahedral Fe³⁺ center has an expansion distortion for Fe³⁺ in MF₃:Fe³⁺ (M=Al, Ga). The expansion distortion may be ascribed to the fact that the radius of Fe³⁺ ion is larger than that of Al³⁺ ion and Ga³⁺ ion, and the Fe³⁺ ion will push the fluoride ligands upwards and downwards, respectively. The local lattice structure parameters R=1.927 A, θ=55.538° for Fe³⁺ in AlF₃:Fe³⁺ and R=1.931 A, θ=56.09° for Fe³⁺ in GaF₃:Fe³⁺ are determined, respectively, and the EPR spectra of the MF₃:Fe³⁺ (M=Al, Ga) systems are satisfactorily explained.     

A pigment (CuS) identified by micro‐Raman spectroscopy on a Chinese funerary lacquer ware of West Han Dynasty

A blue pigment was identified by micro‐Raman spectroscopy, X‐ray fluorescence spectroscopy (XRF), scanning electron microscopy (SEM)/energy dispersive X‐ray (EDX) and X‐ray diffraction (XRD). The test sample, a funerary lacquer tray, belongs to West Han Dynasty (206 BC–AD 8) of China and was decorated with faint blue patterns. The result from Raman spectroscopy showed that the faint blue is covellite (CuS) due to the presence of a characteristic peak at 474.5 cm⁻¹, which further was confirmed by XRF, SEM–EDX and XRD. This research indicated that CuS had been used as a blue pigment to decorate lacquer wares from the West Han Dynasty in China. Copyright © 2009 John Wiley & Sons, Ltd.     

“烧蚀模式”激光推进技术及其应用研究

随着激光技术的发展,激光推进技术越来越受到关注.“烧蚀模式”激光推进是激光推进技术中一个重要的研究领域.本文在介绍了“烧蚀模式”激光推进的原理、研究现状和几个亟待解决的热点研究问题的基础上,对激光推进的进一步应用进行了探索与研究.     

光纤型宽带可调连续波差频产生中红外激光器转换效率的研究

以掺镱光纤激光器为抽运源、掺铒光纤激光器后接掺铒光纤放大器为信号源,利用周期极化掺镁铌酸锂晶体,研究了全光纤化差频产生中红外激光器的转换效率特性。结果表明,抽运光和信号光偏振态影响差频产生过程的转换效率,利用偏振控制器,可将抽运光和信号光偏振方向调节到与晶体光轴方向平行,以获得高的转换效率。抽运光和信号光的光束质量既影响差频产生过程的转换效率,又决定晶体纵向位置的容限,当聚焦系统由自聚焦透镜和焦距100mm平凸透镜组成时,相对转换效率达0.717mW-2,晶体纵向位置容限为44mm。此外,差频光在3126.36~3529.6nm范围内调谐时,转换效率基本保持不变。     

Double-stranded helical lanthanide(III) supramolecular networks with rigid diimine ligands: Synthesis, structure, and physical properties

Two lanthanide coordination complexes [Nd(NO₃)₃(CH₃OH)₂(4,4′-bipy)₂] (1) (4,4′-bipy=4,4′-bipyridine) and [4,4′-Hbipy][La(NO₃)₄(H₂O)₂(4,4′-bipy)] (2), with a salt of cationic diprotonated 4,4′-bipy, [2(4,4′-H₂bipy)][4(NO₃)] (3), have been identified and isolated from a methanol solution of Ln(NO₃)₃·6H₂O, 4,4′-bipyridine and pyrazine in 1:2:1 ratio. Their structures have been determined by single-crystal X-ray diffraction analyses, which reveal that 1 has an interesting three-dimensional supramolecular architecture containing 2₁ double-stranded helical chains through hydrogen bonding and π–π interactions, while 2 and 3 have well defined infinite chiral 3D open networks that undergo self-interpenetration. The electrospray ionization mass spectra (ESI-MS) indicate that the covalent complex has higher stability than the electrostatic bonding one. ESI-MS/MS of these ions reveal that the Ln–O bond forms a stronger coordinated bonding than that of Ln–N system and the nitrate anion remains bound to the lanthanide centers after complete dissociation in methanol solution.     

Density and momentum dependence of the coupling strengths for scalar and vector fields

The collision term has been deduced based on the effective Lagrangian in addition to the mean-field. We propose the momentum- and density-dependent coupling strengths for scalar and vector fields. The saturation properties of nuclear matter, the experimental data of the energy-dependent optical potential and the mean free path in the nuclei can be reproduced simultaneously. The in-mediumn–n cross section has also been calculated for different densities and energies, our results are consistent with Dirac-Brueckner-Hartree-Fock calculations.Supported by National Natural Science Foundation of China