Two-Grid Finite Element Method with Crank-Nicolson Fully Discrete Scheme for the Time-Dependent Schrödinger Equation

In this paper, we study the Crank-Nicolson Galerkin finite element method and construct a two-grid algorithm for the general two-dimensional time-dependent Schrödinger equation. Firstly, we analyze the superconvergence error estimate of the finite element solution in $H^1$ norm by use of the elliptic projection operator. Secondly, we propose a fully discrete two-grid finite element algorithm with Crank-Nicolson scheme in time. With this method, the solution of the Schrödinger equation on a fine grid is reduced to the solution of original problem on a much coarser grid together with the solution of two Poisson equations on the fine grid. Finally, we also derive error estimates of the two-grid finite element solution with the exact solution in $H^1$ norm. It is shown that the solution of two-grid algorithm can achieve asymptotically optimal accuracy as long as mesh sizes satisfy $H = \mathcal{O}(h^{\frac{1}{2}})$.     

Cos-7细胞胞内pH的31 P核磁共振测定

生物细胞内pH的测定对于细胞内代谢、游离离子及离子通道的研究有重要的意义,而且一些酶的活性也与细胞内pH密切相关。猴的肾细胞cos-7细胞常用于外源基因的转染表达,研究这一细胞株细胞内的pH,可为基因转染提供可靠的依据。本文采用^31P核磁共振对cos-7细胞胞内的pH进行了分析测定。     

地震作用下高拱坝损伤开裂分析

采用应变率相关的砼非线性损伤模型模拟拱坝横缝,研究了砼非线性本构情况下整体拱坝与考虑分缝拱坝的应力响应和损伤开裂的特点与差别。对实际拱坝的地震响应分析表明,基于非线性砼模型的整体拱坝动力响应模型可以基本反映拱坝的实际应力分布情况。     

接触爆炸荷载作用下溢流坝的抗爆性能

以黄登重力坝的溢流坝为研究背景,考虑混凝土的高应变率效应,运用Lagrange-Euler耦合算法建立大坝-库水-空气-炸药全耦合数值模型,研究溢流坝在接触爆炸荷载作用下的抗爆性能。分析满库与空库时溢流坝在爆炸冲击波作用下的动力响应及损伤程度,并进一步研究满库时大坝在不同炸点的水下接触爆炸荷载作用下的动力响应及损伤分布。研究结果表明,满库时水下爆炸比空库时爆炸的动力响应及损伤程度大得多;溢流坝的抗爆薄弱部位主要集中在溢流道顶部及坝体上游折坡处。研究溢流坝的抗爆性能时应重点研究满库时水下爆炸对大坝的破坏特性。     

Al-DLC薄膜结构及其在水介质下摩擦学性能研究

采用磁控溅射技术,以Al为溅射靶材,甲烷为溅射气体,在不同射频功率下制备了一系列Al含量不同的类金刚石碳基薄膜(AL-DLC).分析了Al含量对薄膜成分、结构及机械性能的影响,并探讨了其在空气和水介质下的摩擦磨损行为.结果表明:Al掺杂使得薄膜中sp~3-C的生长受到抑制,sp~2-C增加,表面吸附水分子能力变强,在水介质摩擦过程中的剪切阻力变小,从而使得摩擦磨损减小.通过调整射频功率可以对薄膜中Al含量进行调控,在最优Al含量时,Al-DLC在空气和水介质中均具有优异的摩擦学性能.     

Superconvergence analysis of bi-<Emphasis Type="Italic">k</Emphasis>-degree rectangular elements for two-dimensional time-dependent Schrödinger equation

Superconvergence has been studied for long, and many different numerical methods have been analyzed. This paper is concerned with the problem of superconvergence for a two-dimensional time-dependent linear Schrödinger equation with the finite element method. The error estimate and superconvergence property with order O(h^k+1) in the H¹ norm are given by using the elliptic projection operator in the semi-discrete scheme. The global superconvergence is derived by the interpolation post-processing technique. The superconvergence result with order O(h^k+1 + τ²) in the H¹ norm can be obtained in the Crank-Nicolson fully discrete scheme.     

Tuning the Electron Localization of Gold Enables the Control of Nitrogen‐to‐Ammonia Fixation

The (photo)electrochemical N₂ reduction reaction (NRR) provides a favorable avenue for the production of NH₃ using renewable energy in mild operating conditions. Understanding and building an efficient catalyst with high NH₃ selectivity represents an area of intense interest for the early stages of development for NRR. Herein, we introduce a CoO_x layer to tune the local electronic structure of Au nanoparticles with positive valence sites for boosting conversion of N₂ to NH₃. The catalysts, possessing high average oxidation states (ca. 40 %), achieve a high NH₃ yield rate of 15.1 μg cm^?2 h^?1 and a good faradic efficiency of 19 % at ?0.5 V versus reversible hydrogen electrode. Experimental results and simulations reveal that the ability to tune the oxidation state of Au enables the control of N₂ adsorption and the concomitant energy barrier of NRR. Altering the Au oxidation state provides a unique strategy for control of NRR in the production of valuable NH₃.     

Mo-doped V<Subscript>2</Subscript>O<Subscript>5</Subscript> hierarchical nanorod/nanoparticle core/shell porous microspheres with improved performance for cathode of lithium-ion battery

Mo-doped V₂O₅ hierarchical nanorod/nanoparticle core/shell porous microspheres (MVHPMs) were prepared via a simple hydrothermal approach using ammonium metavanadate and ammonium molybdate as precursors followed by a thermal annealing process. The samples were characterized by XRD, SEM, TEM, EDS, and XPS carefully; it confirmed that porous microspheres with uniform Mo doping in the V₂O₅ matrix were obtained, and it contains an inner core self-assembled with 1D nanorods and outer shell consisting of nanoparticles. A plausible growth mechanism of Mo-doped V₂O₅ (Mo-V₂O₅) porous microspheres is suggested. The unique microstructure made the Mo-V₂O₅ hierarchical microspheres a good cathode material for Li-ion battery. The results indicate the synthesized Mo-V₂O₅ hierarchical microspheres exhibit well-improved electrochemical performance compared to the undoped samples. It delivers a high initial reversible capacity of 282 mAh g^?1 at 0.2 C, 208 mAh g^?1 at 2 C, and 111 mAh g^?1 at 10 C, and it also exhibits good cycling stabilities; a capacity of 144 mAh g^?1 is obtained after 200 cycles at 6 C with a capacity retention of >?82%, which is much high than that of pure V₂O₅ (95 mAh g^?1 with a capacity retention of 72%).

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Graphical Abstract Mo-doped V₂O₅ hierarchical porous microspheres with improved LIB performance

     

8—21节点块体精化不协调元

本文基于文（２）提出的精化直接刚度法的变分原理，构造了８－２１节点元的精化不协调位移模式，并装入ＳＡＰ５程序中，该单元能通过分片试验数据结果表明：采用精化直接刚度法，可以有效地改装单元特性，使新单元在具原单元的简单、高效、可靠性好的同时，在精度，适应性等方面有大幅度的提高。     

锯切花岗石过程中金刚石节块磨损特征及影响因素分析

在已有的节块磨损规律的基础上，对锯切花岗石过程中的金刚石及其固位载体－粘合剂的磨损规律进行了研究。通过实验，跟踪观察了不同金刚石节块在各种加工条件下的磨损状态。结果表明；金刚石的工作状态与节块的使用性能有良好的对应关系，金刚石的微破碎和完善晶型比例越高节块耐磨性越好；宏观破碎和脱落比例越高节块耐磨性越差。金刚石的粒度，含量，品级，粘合剂和金刚石的匹配以及锯切用量组合等均明显影响锯切效果。