The first quaternary lanthanide(III) nitride iodides: NaM4N2I7 (M=La-Nd)

In attempts to synthesize lanthanide(III) nitride iodides with the formula M₂NI₃ (M=La-Nd), moisture-sensitive single crystals of the first quaternary sodium lanthanide(III) nitride iodides NaM₄N₂I₇ (orthorhombic, Pna2₁; Z=4; a=1391-1401, b=1086-1094, c=1186-1211 pm) could be obtained. The dominating structural features are chains of trans-edge linked [NM₄]⁹⁺ tetrahedra, which run parallel to the polar 2₁-axis [001]. Between the chains, direct bonding via special iodide anions generates cages, in which isolated [NaI₆]^5- octahedra are embedded. The IR spectrum of NaLa₄N₂I₇ recorded from 100 to 1000 cm^-1 shows main bands at υ=337, 373 and 489 cm^-1. With decreasing radii of the lanthanide trications these bands, which can be assigned as an influence of the vibrations of the condensed [NM₄]⁹⁺ tetrahedra, are shifted toward higher frequencies for the NaM₄N₂I₇ series (M=La-Nd), following the lanthanide contraction.     

A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS

In this paper, a reactive dynamic user equilibrium model is extended to simulate two groups of pedestrians traveling on crossing paths in a continuous walking facility. Each group makes path choices to minimize the travel cost to its destination in a reactive manner based on instantaneous information. The model consists of a conservation law equation coupled with an Eikonal-type equation for each group. The velocity-density relationship of pedestrian movement is obtained via an experimental method. The model is solved using a finite volume method for the conservation law equation and a fast-marching method for the Eikonal-type equation on unstructured grids. The numerical results verify the rationality of the model and the validity of the numerical method. Based on this continuum model, a number of results, e.g., the formation of strips or moving clusters composed of pedestrians walking to the same destination, are also observed.     

Stability results for the heat equation backward in time

For the heat equation backward in time

     

Magic of centroids

In this paper, we show some properties of centroids of geometric figures, such as triangles, quadrilaterals and tetrahedra. In particular, we will prove the properties by means of geometric transformations and by introducing extensions of triangles and quadrilaterals, i.e. by adding one, two or three new vertices to the figure. The study of these properties can be used, with profit, in a classroom activity supported by a dynamic geometry system.     

Molecular surface generation using marching tetrahedra

A method is presented to generate and triangulate molecular surfaces rapidly. It is based on the ‘marching tetrahedra’ approach. The method is fast, simple and easy to implement. Our approach is not analytical in nature. Hence no special treatment is required for complications with singularity, degeneracy, or with self-intersecting re-entrant surfaces. A quick test for determining the solvent accessibility of a point in space forms an important part of the method. This test has potential use outside of the surface generation algorithm such as in molecular field analysis where the solvent accessibility of a point needs to be determined. The triangulated surface generated is suitable for molecular graphics display as well as boundary element continuum dielectric calculations. © 1998, Government of Canada. Exclusive worldwide publication rights in the article have been transferred to John Wiley & Sons, Inc. in perpetuity. J Comput Chem 19: 1268–1277, 1998     

时间推进方法在叶轮机械内部流场计算中的进展

时间推进方法目前广泛应用于叶轮机械内部流场的计算,这种方法可以划分成显式时间推进方法和隐式时间推进方法．本文简要介绍了时间推进方法用于叶轮机械内部流场计算的起源及这种方法的优点和缺点,重点记述了国内外叶轮机界应用显式时间推进方法和隐式时间推进方法计算叶轮机内部流场的最新进展,并简要介绍世界上一些著名的研究机构开发的时间推进方法计算程序所采用的数值计算方法      

用粘性体力方法计算轴流叶轮机械内部流场

阐述了一种用于叶轮机械内部三维粘性流场计算程序。该程序以有限体积显式时间推进方法为基础,用Baldwin-Lomax模型模拟湍流流动,用局部时间步长和多重网格方法提高计算效率。使用上述方法计算了NASA 37^#跨音速压气机转子流场,并与实验结果进行了比较,从而证明文中提出的方法能够快速、准确地模拟轴流叶轮机械内部复杂三维流场,该方法具有较强的工程实用意义。     

Designing Silicates as Deep‐UV Nonlinear Optical (NLO) Materials using Edge‐Sharing Tetrahedra

Discovering new deep‐ultraviolet (DUV) nonlinear optical (NLO) materials is currently a great challenge. The reported DUV NLO materials are almost exclusively borates or phosphates. Silicates—the largest constituent of the earth's crust—are excluded owing to their weak second harmonic generation (SHG) response. We report a silicate, Li₂BaSiO₄, with edge‐sharing LiO₄–SiO₄ tetrahedra that achieves the balance between a short UV absorption edge, below 190 nm, and a large SHG response, 2.8×KDP. The SHG intensity is the largest for silicates without second‐order Jahn–Teller cations, and exceeds that of non‐isomorphic Li₂SrSiO₄ by more than an order of magnitude. As such Li₂BaSiO₄ may be seen as a promising DUV‐UV NLO material. This research indicates that edge‐sharing tetrahedra is a new design parameter for discovering new DUV NLO materials.