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.     

Thermal activation and reaction of allyl alcohol on Ni(100)

The thermal chemistry of allyl alcohol (CH₂CHCH₂OH) on a Ni(100) single-crystal surface was studied by the temperature programmed desorption (TPD) and the X-ray photoelectron spectroscopy (XPS). The allyl alcohol adsorbs molecularly on the metal surface at 100 K. Intact molecular desorption from the surface occurs at temperatures around 180 K, but some molecules exhibit chemical reactivity on the surface: activation of the OH, CC, and CO bonds produces η¹(O)-allyloxy CH₂CHCH₂O_(a), η²(C, C) allyl alcohol (C_(a)H₂C_(a)HCH₂OH), and η³(C, C, O)-alkoxide (C_(a)H₂C_(a)CH₂ O_(a)) intermediates. Further thermal activation of allyl alcohol on the surface yields propylene (CH₂CHCH₃), 1-propanol (CH₃CH₂CH₂OH), propanal (CH₃CH₂CHO), and combustion and dehydrogenation products (H₂O, H₂, and CO). Propylene desorbs from the surface at temperatures of around 270 K. Hydrogenation to the η³(C, C, O)-alkoxide intermediate leads to the production of propanal which desorbs from the surface around 320 K, while hydrogenation of the η²(C, C) allyl alcohol intermediate produces 1-propanol, which desorbs at around 310 K. The co-adsorption of hydrogen atoms on the surface enhances the formation of the saturated alcohol, while co-adsorption of oxygen enhances the formation of both the saturated alcohol and the saturated aldehydes.     

Quantum entanglement and quantum phase transitions in frustrated Majumdar-Ghosh model

By using the density matrix renormalization group technique, the quantum phase transitions in the frustrated Majumdar-Ghosh model are investigated. The behaviors of the conventional order parameter and the quantum entanglement entropy are analyzed in detail. The order parameter is found to peak at J₂∼0.58, but not at the Majumdar-Ghosh point (J₂=0.5). Although, the quantum entanglements calculated with different subsystems display dissimilarly, the extremes of their first derivatives approach to the same critical point. By finite size scaling, this quantum critical point J^C₂ converges to around 0.301 in the thermodynamic limit, which is consistent with those predicted previously by some authors (Tonegawa and Harada, 1987 [6]; Kuboki and Fukuyama, 1987 [7]; Chitra et al., 1995 [9]). Across the J^C₂, the system undergoes a quantum phase transition from a gapless spin-fluid phase to a gapped dimerized phase.     

Third-order nonlinear optical studies of new anthraquinone derivatives

Four new donor-acceptor-donor anthraquinone derivatives were synthesized and characterized by UV, IR, ¹H NMR and elemental analysis. Their off-resonant third-order nonlinear optical properties were measured using femtosecond laser and degenerate four-wave mixing technique. The third-order nonlinear optical susceptibilities χ⁽³⁾ were 3.36-3.76 × 10⁻¹³ esu. The nonlinear refractive indexes n₂ were 6.19-6.91 × 10⁻¹² esu. The second-order hyperpolarizabilities γ of the molecules were 3.36-3.76 × 10⁻³¹ esu. The response times were 101-115 fs. The results show that these compounds have potential nonlinear optical applications.     

Temperature dependence of magnetic properties and change of specific heat in perovskite ErCrO3 chromites

In this paper, the temperature dependence of magnetic properties and specific heat are systematically investigated for perovskite ErCrO₃ chromites. The results show that there exists a strong temperature dependence of magnetic ordering and phase coexistence in the region of low temperature. Specifically, ErCrO₃ possesses the long-range antiferromagnetic ordering and the appearance of weak ferromagnetism, occurring at T _N =133 K. In the range of higher temperature, above 133.0 K, the reciprocal of magnetic susceptibility χ ⁻¹ behaves linearly, indicating a typical Curie–Weiss behavior fitted. The effective magnetic moment μ _eff=10.57μ _B and asymptotic paramagnetic Curie temperature T _cw=−30 K, which suggests the predominance of antiferromagnetic interactions in ErCrO₃ chromites. Around T _SR≈22 K, ErCrO₃ undergoes a spin reorientation from \varGamma ₄(G_x,A_y,F_z;F^R_z)\varGamma _{4}(G_{x},A_{y},F_{z};F^{R}_{z}) to \varGamma ₁(A_x,G_y,C_z;C^R_z)\varGamma _{1}(A_{x},G_{y},C_{z};C^{R}_{z}) or Γ ₁(0). Also, the stability of the ferromagnetic Γ ₄ phase increases with increasing applied field. Furthermore, the ac susceptibilities exhibit frequency-independent anomalies near 133 K and the coexistence of the magnetic configuration \varGamma ₂(F_x,G_y,C_z;F^R_x,C^R_y)\varGamma _{2}(F_{x},G_{y},C_{z};F^{R}_{x},C^{R}_{y}) and Γ ₄. Combining the magnetic properties and the specific-heat measurements, this current magnetization can be interpreted from the interaction between C ^r3+–Cr³⁺, Cr³⁺–Er³⁺ and Er³⁺–Er³⁺.     

Non-collinear efficient continuous optical frequency doubling in periodically poled lithium niobate

Non-collinear continuous frequency doubling with relatively high conversion efficiency is demonstrated in periodically-poled lithium niobate. It is shown that about 80% of the total second harmonic energy can be collected to one output channel by tuning incident angle. The fractional phase-matching condition is introduced to interpret the phenomenon. These results make it possible for direct power applications of continuous frequency doubling over the broad spectral range from the visible to the infrared without temperature or angle tuning.     

Spatio-temporal expression of a novel neuron-derived neurotrophic factor (NDNF) in mouse brains during development

Background  

Neuron-derived neurotrophic factor (NDNF) is evolutionarily well conserved, being present in invertebrate animals such as the nematode, Caenorhabditis elegans, as well as in the fruit fly, Drosophila melanogaster. Multiple cysteines are conserved between species and secondary structure prediction shows that NDNF is mainly composed of beta-strands. In this study, we aimed to investigate the function of NDNF.     

密度泛函理论计算内掺氢分子富勒烯H2@C60及其二聚体的几何结构和电子结构

采用密度泛函理论中的广义梯度近似(generalized gradient approximation, 简称GGA),对内掺氢分子富勒烯H2@C60及其二聚体的几何结构和电子结构进行了计算研究.发现无论是在H2@C60单体,还是在其二聚体中,氢倾向以分子形式存在于碳笼中心处,且在室温下氢分子可以做自由旋转.电子结构分析表明,氢分子掺入到C60和C120中,仅对距离费米能级以下-8eV至-5eV能级处有一定的贡献,其他能级的分布和能隙几乎没有变化.     

基片温度对SiNx薄膜结晶状态及机械性能的影响

利用微波电子回旋共振增强磁控反应溅射法在不同基片温度下制备无氢SiNx薄膜.通过傅里叶变换红外光谱、透射电子显微镜、台阶仪、纳米硬度仪等表征技术,研究了基片温度对SiNx薄膜结晶状态、晶粒尺寸、晶体取向等结晶性能以及薄膜的生长速率、硬度等机械性能的影响,并探讨了薄膜结晶性能与机械性能之间的关系.研究结果表明,在基片温度低于300℃时制备的SiNx薄膜以非晶状态存在,硬度值仅为18 GPa左右;基片温度在320-620℃范围内,SiNx薄膜中出现纳米晶粒,且晶粒尺寸随沉积温度的增加而增加,在沉积温度为620℃时达到最大,为20±1.5 nm;当沉积温度为700℃时,SiN<,x>薄膜的晶粒尺寸突然减小,但由于此时晶粒密度为最大,因此薄膜硬度达到最大值(36.7 GPa).