Enhanced accuracy by post-processing for finite element methods for hyperbolic equations

We consider the enhancement of accuracy, by means of a simple post-processing technique, for finite element approximations to transient hyperbolic equations. The post-processing is a convolution with a kernel whose support has measure of order one in the case of arbitrary unstructured meshes; if the mesh is locally translation invariant, the support of the kernel is a cube whose edges are of size of the order of only. For example, when polynomials of degree are used in the discontinuous Galerkin (DG) method, and the exact solution is globally smooth, the DG method is of order in the -norm, whereas the post-processed approximation is of order ; if the exact solution is in only, in which case no order of convergence is available for the DG method, the post-processed approximation converges with order in , where is a subdomain over which the exact solution is smooth. Numerical results displaying the sharpness of the estimates are presented.

     

Eu2+,Dy3+共掺杂硼铝锶长余辉玻璃陶瓷

首次介绍了一种新型长余辉材料:Eu^2 ,Dy^3 共掺杂硼铝锶长余辉玻璃陶瓷，该玻璃陶瓷用紫外灯、日光、荧光灯均可激发，发射黄绿色余辉，余辉的发射峰位于516nm，来自于Eu^2 的5d→^8S7/2跃迁。用12000 lx的荧光灯激发样品20分钟，停止激发后10秒时，该玻璃陶瓷的余辉亮度为3．53cd/m^2，色坐标为：x=0.2842,y=0.5772;停止激发后5小时55分钟，该玻璃陶瓷的余辉亮度为0．01cd/m^2；停止激发30小时后，余辉在黑暗中仍肉眼可见。文中对该玻璃陶瓷的相关性质进行了表征，并提出了可能的长余辉机理。     

硫和银共掺杂介孔TiO2的制备、表征及其对染料的光催化降解活性

以P123为模板,以钛酸四正丁酯、硝酸银和硫脲为原料采用模板法制备了一系列硫和银共掺杂介孔TiO₂光催化材料．利用SEM、XRD、BET和紫外-可见光谱等技术对其形貌、晶体结构及表面结构、光吸收特性等进行了表征．以甲基橙溶液的光催化降解为模型反应,考察了不同掺杂量的样品在紫外和可见光下的光催化性能．结果表明,用模板法制备的共掺杂介孔TiO₂光催化材料在紫外和可见光条件下较纯介孔TiO₂和单掺杂介孔TiO₂对甲基橙溶液具有更好的光催化降解效果, 且硫和银的掺杂量及样品焙烧温度显著影响该材料的催化性能．当硫掺杂量为2mol%和银掺杂量为1mol%,在500 oC 焙烧2 h所得光催化材料的催化性能最佳,4 h即可使甲基橙的降解率达98.8%,重复使用4次仍可使甲基橙的降解率保持在87.5%以上     

〈I〉型三角剖分下非张量积连续小波基的构造

多维非张量积小波是近年小波研究领域中的热点问题之一 ,它们与多维张量积小波相比具有更多的优势 .关于高维张量积、非张量积小波 ,目前已有一些很好的工作 (见文[2 ] [3 ] [4 ] ) ,但关于样条小波 ,还有许多问题有待于研究 .本文针对〈I〉型三角剖分下的二维线性元空间 ,讨论其具有紧支集和对称性的半正交样条小波基 .给定 x1 x2 平面上的〈I〉型三角剖分 (图 1 ( a)所示 ) ,记 j=( j1 ,j2 ) ,| j| =j1 + j2 ,πm= { 0≤ |j|≤ mCj1j2 xj11 xj22 ,Cj1,j2 是任意实数 }为次数不超过 m的代数多项式全体 .引入剖分尺度为 1的线性元空间 V0…     

谷值电流型脉冲序列控制开关变换器及其能量建模研究

脉冲序列控制是针对工作于电感电流断续导电模式的开关变换器提出的一种非线性、离散控制技术.当开关变换器工作在电感电流连续导电模式时,脉冲序列控制开关变换器存在低频振荡现象,严重影响了脉冲序列控制开关变换器的稳态及瞬态性能.针对这一问题,本文提出一种谷值电流型脉冲序列控制方法,将脉冲序列控制的应用范围从电感电流断续导电模式扩展到电感电流连续导电模式.建立了谷值电流型脉冲序列控制开关变换器的能量迭代模型,并与传统脉冲序列控制开关变换器的能量模型进行对比.结果表明谷值电流型脉冲序列控制电感电流连续导电模式开关变换器具有与传统脉冲序列控制电感电流断续导电模式开关变换器相同的能量传递模式,从而在根本上消除了传统脉冲序列控制电感电流连续导电模式变换器存在的低频振荡现象.     

非参数回归函数估计的渐近正态性

本文研究了独立或相依样本时非参数回归函数的Ｎａｄａｒａｙａ-Ｗａｔｓｏｎ估计，在简洁合理的条件下，证明了估计量的渐近正态性．获得的结论可在时间序列分析中得到应用．     

Effect of incommensurate potential on the resonant tunneling through Majorana bound states on the topological superconductor chains

We study the transport through the Kitaev chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of e ² / h, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate potential suppresses the current at finite voltage bias, and then narrows the linear response regime of the I-V curve which exhibits two plateaus corresponding to the superconducting gap and the band edge, respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value 2g _s + 2Δ with Δ the p-wave pairing amplitude and g _s the hopping between neighbor sites, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage also causes an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose I-V curve exhibits an exponential shape.     

关于一阶剪切板的Kármán型精化理论

依据Mindlin_Reissner理论 ,着重研究一阶剪切板的K rm n型精化理论 ,并推导出仅以挠度和应力函数为未知变量的广义K rm n型大挠度方程 ,适用于复合材料上复合构造剪切板的非线性分析·　在当前板的精化理论中 ,消去的两个转角以隐含形式作用于板的整体变形·　这一工程理论适用于各种计及横向剪切复合材料板、正交各向异性中厚板和夹层板等的线性和非线性分析·　容易发现 ,针对具体的工程应用 ,由该方程可直接获得相应的退化形式 ,并且与文献所载的一致·     

A facile method for the synthesis of large‐size Ag nanoparticles as efficient SERS substrates

Silver nanoparticles (Ag NPs) enjoy a reputation as an ultrasensitive substrate for surface‐enhanced Raman spectroscopy (SERS). However, large‐scale synthesis of Ag NPs in a controlled manner is a challenging task for a long period of time. Here, we reported a simple seed‐mediated method to synthesize Ag NPs with controllable sizes from 50 to 300 nm, which were characterized by scanning electron microscopy (SEM) and UV–Vis spectroscopy. SERS spectra of Rhodamine 6G (R6G) from the as‐prepared Ag NPs substrates indicate that the enhancement capability of Ag NPs varies with different excitation wavelengths. The Ag NPs with average sizes of ~150, ~175, and ~225 nm show the highest SERS activities for 532, 633, and 785‐nm excitation, respectively. Significantly, 150‐nm Ag NPs exhibit an enhancement factor exceeding 10⁸ for pyridine (Py) molecules in electrochemical SERS (EC‐SERS) measurements. Furthermore, finite‐difference time‐domain (FDTD) calculation is employed to explain the size‐dependent SERS activity. Finally, the potential of the as‐prepared SERS substrates is demonstrated with the detection of malachite green. Copyright © 2016 John Wiley & Sons, Ltd.     

超高碰撞能23.84 kJ/mol下反应F+D2→DF+D的交叉分子束研究

本文搭建了一套新的实验设备,首次将氢原子里德堡态标记的飞行时间谱技术与激光爆破束源技术相结合,进行超高碰撞能下化学反应的动力学研究. 初步进行了F+D₂→DF+D在超高碰撞能23.84 kJ/mol下的实验研究. 在研究中应用了两种类型束源：一类是通过激光爆破过程产生的高能F原子束源,另一类是通过液氮冷却脉冲阀而产生的D₂束源. 实验中探测了反应产物振动态分辨的微分散射截面. 结果显示,大部分反应产物DF主要呈现侧向和后向散射分布,而产物DF(v''=4)则主要分布在前向. 对前向散射产物DF(v''=4)的动力学来源进行了讨论.