基于Rietveld精修方法解析Bi2O3的原子热振动

三氧化二铋(Bi₂O₃)是氧离子导电体,为了获得它的原子热振动各向同性温度因子,对该粉末晶体进行X射线衍射实验,建立了晶体结构模型,利用Rietveld 精修方法的RIETAN-2000 程序对所得实验结果进行了晶体结构精修,通过最大熵方法(MEM)解析得到了粉末晶体的等高电子密度分布三维(3D) 和二维(2D)可视化图谱。结果表明,各原子Bi₍₁₎、Bi₍₂₎、O₍₁₎、O₍₂₎和O₍₃₎的原子热振动各向同性温度因子分别为0.004 938 nm²、0.004 174 nm²、0.007 344 nm²、0.007 462 nm²、和0.007 857 nm²,等高电子密度分布的可视化,进一步验证了晶体结构模型和原子位置的准确性,这些参数对研究晶体材料的热性质具有一定参考意义。     

基于改进格林元的压裂水平井动态分析方法

以建立高效的动态分析方法为出发点，以边单元作为求解点，改进传统的格林元方法，减少未知数和求解矩阵维度；并提出基于改进格林元的加密网格加密方法，保证考虑复杂裂缝网络的压裂水平井动态模拟的早期精度.退化模型与半解析解、数值模拟结果进行对比，验证本文基于加密网格的改进格林元方法的准确性和动态分析的高效性.最后进行动态响应的敏感性分析，结果表明：①格林元方法是一种高精度的动态模拟方法，将求解节点设置在网格的边上可以提高压裂水平井动态模拟的速度；②改进格林元方法的加密基于叠加原理，不需要通过插值近似，其求解精度高.在相同加密网格条件下，基于本文改进格林元方法的加密效果比有限差分加密效果更佳；③复杂裂缝导流能力、改造区渗透率提高倍数、改造区大小等参数对压裂水平井动态特征影响较大，在动态分析和参数反演时，应着重考虑这些因素的影响.     

An investigation of the electron density of a Jahn–Teller‐distorted CrII cation: the crystal structure and charge density of hexakis(acetonitrile‐κN)chromium(II) bis(tetraphenylborate) acetonitrile disolvate

In the crystal structure of the title homoleptic Cr^II complex, [Cr(CH₃CN)₆](C₂₄H₂₀B)₂·CH₃CN, the [Cr(CH₃CN)₆]²⁺ cation is a high‐spin d⁴ complex with strong static, rather than dynamic, Jahn–Teller distortion. The electron density of the cation was determined by single‐crystal X‐ray refinements using aspherical structure factors from wavefunction calculations. The detailed picture of the electronic density allowed us to assess the extent and directionality of the Jahn–Teller distortion of the Cr^II cation away from idealized octahedral symmetry. The topological analysis of the aspherical d‐electron density about the Cr^II cation showed that there are significant valence charge concentrations along the axial Cr—N axes. Likewise, there were significant valence charge depletions about the Cr^II cation along the equatorial Cr—N bonds. These charge concentrations are in accordance with a Jahn–Teller‐distorted six‐coordinate complex.     

Inversion twinning in a second polymorph of the hydrochloride salt of the recreational drug ethylone

A second polymorph of the hydrochloride salt of the recreational drug ethylone, C₁₂H₁₆NO₃⁺·Cl⁻, is reported [systematic name: (±)‐2‐ethylammonio‐1‐(3,4‐methylenedioxyphenyl)propane‐1‐one chloride]. This polymorph, denoted form (A), appears in crystallizations performed above 308 K. The originally reported form (B) [Wood et al. (2015). Acta Cryst. C 71 , 32–38] crystallizes preferentially at room temperature. The conformations of the cations in the two forms differ by a 180° rotation about the C—C bond linking the side chain to the aromatic ring. Hydrogen bonding links the cations and anions in both forms into similar extended chains in which any one chain contains only a single enantiomer of the chiral cation, but the packing of the ions is different. In form (A), the aromatic rings of adjacent chains interleave, but pack equally well if neighbouring chains contain the same or opposite enantiomorph of the cation. The consequence of this is then near perfect inversion twinning in the structure. In form (B), neighbouring chains are always inverted, leading to a centrosymmetric space group. The question as to why the polymorphs crystallize at slightly different temperatures has been examined by density functional theory (DFT) and lattice energy calculations and a consideration of packing compactness. The free energy (ΔG) of the crystal lattice for polymorph (A) lies some 52 kJ mol⁻¹ above that of polymorph (B).     

Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games

We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of all satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. While the proposed algorithm guarantees progress and soundness in every iteration, it is computationally demanding. We offer an alternative, more efficient solution for the reachability properties that decomposes the problem into a series of smaller problems of the same type. All algorithms are demonstrated on an illustrative case study.     

Improving the Accuracy of Small-Molecule Crystal Structures Solved from Powder X-Ray Diffraction Data by Using External Sources

Structural analysis using powder X-ray diffraction data has overcome many obstacles and nowadays is readily applicable for structural analysis of all types of compounds and materials. Being less straightforward than single crystal diffraction, it requires significant users’ input and consequently, implementation of standardized tools to assess the accuracy of crystal structures. This article discusses potential errors in crystal structure solution and refinement of small-molecule structures obtained from PXRD data. Moreover, it proposes how accuracy of these structures can be improved by using high-quality PXRD data, complementary external analytical techniques, knowledge stored in crystal structure databases, as well as an approach to search the parameter space to avoid local minima in testing different sets of geometry restraints.     

薄板弯曲问题的P型杂交解析有限元方法

本文采用两套变量构造有限元试函数空间，在单元内部要求试函数精确满足平衡微分方程，在单元边界上对位移和转角分别用Ｐｅａｎｏ升阶函数插值，然后利用广义变分原理建立了一种薄板弯曲问题的Ｐ型杂交解析有限方法，与常规有限元法相比，该方法不心进行过细的网格剖分，通过增加单元插值多项式的阶数Ｐ来提高精度，此外，该方法还具有积分计算只需在单元边界上进行、单元钢度矩阵和载荷向量具有嵌入结构、协调程度可以自动控制等优     

自适应网格加密和多重网格求解严重病态方程

本文探讨用自适应网格加密技术结合多重网格法求解由有限元离散导致的病态方程。计算结果表明；自适应多重网格有限元法是求解严重病态方程珠有效方法。     

An adaptive multilevel wavelet framework for scale‐selective WENO reconstruction schemes

We put forth a dynamic computing framework for scale‐selective adaptation of weighted essential nonoscillatory (WENO) schemes for the simulation of hyperbolic conservation laws exhibiting strong discontinuities. A multilevel wavelet‐based multiresolution procedure, embedded in a conservative finite volume formulation, is used for a twofold purpose. (i) a dynamic grid adaptation of the solution field for redistributing grid points optimally (in some sense) according to the underlying flow structures, and (ii) a dynamic minimization of the in built artificial dissipation of WENO schemes. Taking advantage of the structure detection properties of this multiresolution algorithm, the nonlinear weights of the conventional WENO implementation are selectively modified to ensure lower dissipation in smoother areas. This modification is implemented through a linear transition from the fifth‐order upwind stencil at the coarsest regions of the adaptive grid to a fully nonlinear fifth‐order WENO scheme at areas of high irregularity. Therefore, our computing algorithm consists of a dynamic grid adaptation strategy, a scale‐selective state reconstruction, a conservative flux calculation, and a total variation diminishing Runge‐Kutta scheme for time advancement. Results are presented for canonical examples drawn from the inviscid Burgers, shallow water, Euler, and magnetohydrodynamic equations. Our findings represent a novel direction for providing a scale‐selective dissipation process without a compromise on shock capturing behavior for conservation laws, which would be a strong contender for dynamic implicit large eddy simulation approaches.