QUADRATURE METHODS FOR HIGHLY OSCILLATORY SINGULAR INTEGRALS

We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates the run-time for wave-enriched boundary integral formulations for wave scattering,and many of these exhibit singularities.We show that the asymptotic behaviour of the integral depends on the integrand and its derivatives at the singular point of the integrand,the stationary points and the endpoints of the integral.A truncated asymptotic expansion achieves an error that decays faster for increasing frequency.Based on the asymptotic analysis,a Filon-type method is constructed to approximate the integral.Unlike an asymptotic expansion,the Filon method achieves high accuracy for both small and large frequency.Complex-valued quadrature involves interpolation at the zeros of polynomials orthogonal to a complex weight function.Numerical results indicate that the complex-valued Gaussian quadrature achieves the highest accuracy when the three methods are compared.However,while it achieves higher accuracy for the same number of function evaluations,it requires signi cant additional cost of computation of orthogonal polynomials and their zeros.     

Lamb波频域逆散射全聚焦成像方法研究

Lamb波因其传播距离远、衰减小常被用于板状结构的无损检测中,在基于Lamb波损伤检测的诸多成像技术中,全聚焦方法(Total Focus Method,TFM)方法因其成像分辨率高、信噪比高而受青睐.然而Lamb波的频散效应导致时域延时量不能被准确计算,进而影响传统TFM方法对损伤定位及成像的精度;此外,既有的TFM...     

对固体圆二色光谱测试方法的再认识——兼谈“浓度效应”

对近期发展的固体圆二色(CD)光谱测试方法进行了概述、评价和比较, 着重探讨了“浓度效应”的存在使固体CD光谱失真的原因. 通过对本课题组和其他作者已报道的四种化合物的固体CD谱再测试的反思, 强调了依手性化合物的手性光谱学性质不同, 根据浓度梯度实验选择其合适测试浓度的必要性. 对固有手性的阻转异构化合物(S)-1,1'-联二萘酚(S-BINOL)进行了成膜法固体CD谱浓度梯度测试, 发现所得固体薄膜CD谱中也存在着“浓度效应”     

微波/电热板组合消解-电感耦合等离子体质谱(ICP-MS)法测定土壤中重金属元素

为提高土壤检测的重金属得率,采用了微波消解/电热板组合预处理-电感耦合等离子体质谱法(ICP-MS)测定土壤重金属含量。分析了硝酸(HNO3)、氢氟酸(HF)、高氯酸(HClO4)和盐酸(HCl)组合消解液及赶酸温度对土壤预处理影响。结果显示：在硝酸和盐酸混合消解液中,硝酸占比越高,铬(Cr)、钴(Co)、铜(Cu)、镉(Cd)得率更高;消解液体系中加入氢氟酸可使消解更加彻底,提高铬与铜的得率。最优预处理消解条件为硝酸 6ml+ 氢氟酸 2ml消解液组合进行微波消解,1ml 高氯酸于155℃电热板上赶酸。经土壤标准样品GBW07401(GSS-1)和GBW07452(GSS-23)实际应用,预处理条件优化后测试准确度和稳定性均显著提高。此外使用元素铑(Rh)作为内标物时,其方法稳定性和准确性高于内标物钪(Sc)和锗(Ge)。可为相关国家土壤重金属测定标准的修制订提供方法学参考。     

对固体圆二色光谱测试方法的再认识——兼谈“浓度效应”

对近期发展的固体圆二色(CD)光谱测试方法进行了概述、评价和比较,着重探讨了"浓度效应"的存在使固体CD光谱失真的原因.通过对本课题组和其他作者已报道的四种化合物的固体CD谱再测试的反思,强调了依手性化合物的手性光谱学性质不同,根据浓度梯度实验选择其合适测试浓度的必要性.对固有手性的阻转异构化合物(S)-1,1-联二萘酚(S-BINOL)进行了成膜法固体CD谱浓度梯度测试,发现所得固体薄膜CD谱中也存在着"浓度效应".     

国产滤纸室温燐光背景的考察和降低背景方法的研究

固体基质室温燐光法(SS-RTP)的检出限依赖于固体基质的RTP背景的高低。本文考察了七种国产滤纸在重原子存在时和不存在时的RTP背景。研究了各种降低滤纸背景的处理方法。研究结果表明,采用NaOH、β-环糊精、EDTA、乙醇和丙酮浸泡或煮沸滤纸,都能不同程度的降低滤纸背景,最大降低率为88％。KI、NaAc、Pb(Ac)_2、TlNO_3和Cscl等重原子可使滤纸背景有较大幅度的增强,而经处理的滤纸,RTP背景较未处理滤纸背景降低一倍以上,最大可降低94.5％。用NaOH溶液处理滤纸,不仅能有效地降低背景,而且能提高分析物的RTP信号。研究表明纤维素伴生物质——木素,可能是产生燐光背景的杂质之一。     

Synthesis of Ultra-Fine Columbite Powder MgNb2O6 by the Polymerized Complex Method

Pure MgNb₂O₆ powders with high specific surface area and high crystallinity have been successfully synthesized by the Polymerized Complex (PC) Method. A solution of water, citric acid, ethylene glycol and niobium and magnesium ions, was polymerized at 130°C by the water elimination and was calcined at 400°C for 2 h. The precursor formed was calcined at temperatures from 700°C to 1000°C in air to obtain the columbite phase. Thermal analysis, Raman spectroscopy, x-ray diffraction, adsorption/desorption hysteresis and scanning electron microscopy were used to investigate the polymer decomposition and the columbite phase evolution. No evidence for phase separation of crystalline MgCO₃ and Nb₂O₅ in Raman spectra and x-ray diffraction pattern as distinct intermediates were found, and the MgNb₂O₆ probably is formed through a single-step decomposition of oxycarbonate intermediate, as other double oxide synthesized by the PC Method, as indicated by the thermal decomposition of the precursor.     

改进力法计算的研究

针对传统力法的缺点, 利用VBA进行了Excel电子表格的编制, 对传统力法 进行了改进. 在保持传统力法的基本原理和计算过程的基础上, 解决了力法计算繁琐的问题, 提高了计算速度和学习效率, 增强了结构力学课程与实际的联系, 对工科课程的教学具有一 定的指导意义.     

Dynamics of two elliptical particles sedimentation in a vertical channel: chaotic state

The LB-DF/FD method derived from the Lattice Boltzmann Method and direct forcing/fictitious domain method is used to numerically investigate the dynamics and interaction of two elliptical particles settling in an infinitely long channel. One particle (EP0) is initially kept horizontal (major axis perpendicular to sedimentation) for all simulations while the other's (EP1) orientation is varied. It is found that if EP1strays away from horizontality, the particles undergo transitions from a steady state to reach a chaotic state. Furthermore, there are two distinct chaotic states for the particle motion when EP1 orientation is varied, in which a turning point is observed to distinguish the two states.     

解非定常不可压缩N-S方程的迭代压力Poisson方程法

１．引 言 数值求解不可压缩流体流动问题可以采用原始变量的方程作为控制方程,也可以用涡量一流函数方程作为控制方程．直接求解原始变量的不可压缩 Ｎａｖｉｅｒ—Ｓｔｏｋｅｓ方程存在一个主要困难：速度向量在每一时刻都必须满足零散度约束条件,即不可压缩性连续方程．用涡量一流函数方程求解时,连续方程自动满足,所以不存在约束条件的问题,但涡量的边界条件比较难处理,且不易应用于三维问题和带有自由表面或其它流体交界面的问题． 解决上述速度向量必须满足零散度约束条件的困难的方法有：人工压缩法［３,１７］;压力Ｐｏｉｓ…