Stokes问题低阶非协调混合元的改进加罚算法(英文)

通过对由经典加罚算法得到的两个解进行线性组合,研究Stokes方程低阶非协调混合元的改进加罚算法.该方法利用较大的罚参数能得到同使用较小参数的经典加罚方法一样的收敛阶.此外,基于单元的特性和插值后处理技巧,得到一些超收敛结果,从而改进以往的文献结果.     

非线性Sine-Gordon方程Hermite型有限元新的超收敛分析及外推

在半离散格式下讨论了一类非线性Sine-Gordon方程的Hermite型矩形元逼近.利用该元的高精度分析和对时间t的导数转移技巧,得到了H1模意义下O(h2)阶的最优误差估计和O(h3)阶的超逼近性.进一步地,通过运用插值后处理方法,给出了超收敛结果.与此同时,借助于构造一个新的外推格式,导出了与线性情形相同的O(h4)阶外推解.     

Incident laser modulation of a repaired damage site with a rim in fused silica rear subsurface

Local CO2 laser treatment has proved to be an effective method to prevent the 351-nm laser-induced damage sites in a fused silica surface from exponentially growing, which is responsible for limiting the lifetime of optics in high fluence laser systems. However, the CO2 laser induced ablation crater is often surrounded by a raised rim at the edge, which can also result in the intensification of transmitted ultraviolet light that may damage the downstream optics. In this work, the three-dimensional finite-difference time-domain method is developed to simulate the distribution of electrical field intensity in the vicinity of the CO2 laser mitigated damage site located in the exit subsurface of fused silica. The simulated results show that the repaired damage sites with raised rims cause more notable modulation to the incident laser than those without rims. Specifically, we present a theoretical model of using dimpled patterning to control the rim structure around the edge of repaired damage sites to avoid damage to downstream optics. The calculated results accord well with previous experimental results and the underlying physical mechanism is analysed in detail.     

Fabrication processing effects on the microstructure and morphology of erbium film

The effect of substrate temperature on the microstructure and the morphology of erbium film are systematically investigated using X-ray diffraction (XRD) and scanning electron microscopy (SEM). All the erbium films are grown by electron-beam vapor deposition (EBVD). A novel preparation method for observing the cross-section morphology of the erbium film is developed. The films deposited at 200°C have (002) preferred orientation, and the films deposited at 450°C have a mixed (100) and (101) texture, due to the different growth mechanisms of surface energy minimization and recrystallization, respectively. The peak positions and the full widths at half maximum (FWHMs) of erbium diffraction lines (100), (002), and (101) shift towards higher angles and decrease with the increasing substrate temperature in a largely uniform manner, respectively. Also, the lattice constants decrease with increasing temperature. The transition in the film stresses can be used to interpret the changes in peak positions, FWHMs, and lattice constants. The stress is compressive for the as-growth films, and is counteracted by the tensile stress formed during the process of temperature cooling to room temperature. The tensile stress mainly originates from the difference in the coefficients of thermal expansion of the substrate-film couple.     

Rear-surface light intensification caused by a Hertzian-conical crack in 355-nm silica optics

Theoretical studies show that a Hertzian-conical crack can be considered to be composed of double cone faces for simplicity. In the present study, the three-dimensional finite-difference time-domain method is employed to quantify the electric-field distribution within the subsurface in the presence of such a defect under normal incidence irradiation. Both impurities (inside the crack) and the chemical etching have been investigated. The results show that the maximum electric field amplitude |E| max is 9.57374 V/m when the relative dielectric constant of transparent impurity equals 8.5. And the near-field modulation will be improved if the crack is filled with the remainder polishing powders or water vapor/drops. Meanwhile, the laser-induced initial damage moves to the glass-air surface. In the etched section, the magnitude of intensification is strongly dependent on the inclination angle θ. There will be a highest modulation when θ is around π/6, and the maximum value of |E| max is 18.57314 V/m. When θ ranges from π/8 to π/4, the light intensity enhancement factor can easily be larger than 100, and the modulation follows a decreasing trend. On the other hand, the modulation curves become smooth when θ > π/4 or θ < π/8.     

Photonic approach to microwave frequency measurement with extended range based on phase modulation

We propose and demonstrate a photonic approach to instantaneous frequency measurement with an extended range based on phase modulation.In the measurement system,two optical wavelengths and two dispersion fiber segments are used to construct the frequency-dependent amplitude comparison functions(ACFs).Several ACFs can be utilized jointly to determine the microwave frequency without ambiguities beyond a monotonic region of the lone conventional ACF.The measurable range of microwave frequency can be extended and the accuracy can be improved by selecting an ACF with a large slope.The experimental results show that the errors are limited within ±140 MHz of a frequency measuremental range from 8 to 20 GHz.     

诱导公式的推广与逆用

高中数学诱导公式这一章节,学生要达到的要求是能既快又准地使用诱导公式,可实际情况却非如此.学生学习诱导公式的困难有两点:一是诱导公式多,记不住,运算过程中容易出错;二是不能有效地逆用诱导公式.下面就这两点给出详细的介绍.一、诱导公式的推广书上对诱导公式运用的思想:任意负角的三角函数→任意正角的三角函数→[0,2π)的三角函数→[0,π/2]的三角函数,按     

非线性无约束优化问题的滤子填充函数算法

提出了一个求解无约束非线性规划问题的无参数填充函数,并分析了其性质.同时引进了滤子技术,在此基础上设计了无参数滤子填充函数算法,数值实验证明该算法是有效的.     

氢氧化钾法与硫酸法制备硫酸铝钾的区别探讨

研究了氢氧化钾和硫酸溶解铝箔制备十二水合硫酸铝钾的区别,通过返滴定法测定制备过程中各阶段的铝含量,深入分析了实验过程中的相关物料守恒,发现氢氧化钾法在铝箔溶解阶段由于副反应形成Al(OH)3沉淀,导致最终产率很低,进行搅拌及降低体系浓度可很大程度上提高产率,不过仍低于硫酸法。此外,硫酸法在实验操作上也相对更简捷。因此推荐学生使用硫酸法来制备十二水合硫酸铝钾。     

微波消解–分光光度法测定陶瓷原料中二氧化钛

采用微波消解–二安替比林甲烷分光光度法测定陶瓷原料中二氧化钛的含量。探讨了样品消解用酸的种类、检测波长、显色时间和显色剂用量对测定结果的影响。试验结果表明,以HNO_3–HF–H_2O_2溶解样品,395 nm为检测波长,显色20 min,显色液用量为12 m L时测试结果满意。测定钛的线性范围为0~2.0μg/m L,线性相关系数r~2=0.999 5,方法检出限为0.56μg/g。用该法对4种标准物质进行分析验证,测定结果与推荐值相符,测定结果的相对标准偏差为0.64%~2.28%(n=6),加标回收率为95.3%~104%。用该方法和国标方法对乐山和眉山地区陶瓷原料样品进行分析比对,经t检验证明,两种方法测定结果无显著性差异。该方法快速、准确,适合陶瓷原料中二氧化钛的检测。