An $L^{\infty}$ Second Order Cartesian Method for 3D Anisotropic Interface Problems

A second order accurate method in the infinity norm is proposed for general three dimensional anisotropic elliptic interface problems in which the solution and its derivatives, the coefficients, and source terms all can have finite jumps across one or several arbitrary smooth interfaces. The method is based on the 2D finite element-finite difference (FE-FD) method but with substantial differences in method derivation, implementation, and convergence analysis. One of challenges is to derive 3D interface relations since there is no invariance anymore under coordinate system transforms for the partial differential equations and the jump conditions. A finite element discretization whose coefficient matrix is a symmetric semi-positive definite is used away from the interface; and the maximum preserving finite difference discretization whose coefficient matrix part is an M-matrix is constructed at irregular elements where the interface cuts through. We aim to get a sharp interface method that can have second order accuracy in the point-wise norm. We show the convergence analysis by splitting errors into several parts. Nontrivial numerical examples are presented to confirm the convergence analysis.     

Co-Production of Dimethyl Carbonate,Dimethoxymethane and Dimethyl Ether from Methanol: Process Design and Exergy Analysis

Dimethyl carbonate is an important green chemical that has been widely used in the chemical industry. In the production of dimethyl carbonate, methanol oxidative carbonylation has been studied, but the conversion ratio of dimethyl carbonate using this method is too low, and the subsequent separation requires a large amount of energy due to methanol and dimethyl carbonate being azeotrope. In this paper, the strategy of “reaction instead of separation” is proposed. Based on this strategy, a novel process is developed to combine the production of DMC with that of dimethoxymethane (DMM) and dimethyl ether (DME). The co-production process was simulated using Aspen Plus software, and the product purity was up to 99.9%. The exergy analysis of the co-production process and the existing process was carried out. The exergy destruction and exergy efficiency were compared with those of the existing production processes. The results show that the exergy destruction of the co-production process is about 276% less than that of the single-production processes, and the exergy efficiencies in the developed co-production process are significantly improved. The utility loads of the co-production process are significantly lower than that of the single-production process. The developed co-production process increases the methanol conversion ratio to 95%, with a reduced energy requirement. It is proved that the developed co-production process can provide an advantageous option over the existing processes with improved energy efficiency and material savings. The strategy of “reaction instead of separation” is feasible. A new strategy is proposed for azeotrope separation.     

植物叶片可见与近红外光谱反射率数据库的建立与主成分分析

可见与近红外波段光谱反射率数据库是颜色科学与技术和遥感目标地物分类识别领域等研究与应用的基础数据。主成分分析(PCA)在光谱数据分析、光谱重建、高光谱数据降维以及遥感图像分类等方面有广泛应用。测量并建立了云南公园常见绿化植物柳树、樟、红花檵木、蓝花楹等48种植物150条叶片从可见光到近红外波段光谱反射率数据库,波长范围400～1 000 nm、间隔4 nm。并且分别对可见与可见到近红外两种波段范围进行PCA研究。结果表明：不同植物叶片按照红、绿、黄相同色相的光谱反射率曲线基本相似;但对于同一种植物,在可见光波段400～700 nm,因为体内叶绿素、叶黄素、叶红素和花青苷含量的不同,光谱反射率曲线有较大的差异;在近红外波段700～1 000 nm,所有植物叶片光谱反射率仅仅是大小不同,而同一植物光谱反射率基本不随波长变化。PCA分析表明：在可见光和可见与近红外波段前三个主成分的累积贡献率分别达到98.62%和94.97%。数据库及其PCA分析结果将为自然物体光谱重建、多光谱成像技术和遥感目标地物分类识别等领域应用提供支撑。     

多分散Au-Ag合金纳米球的光谱消光法反演

贵金属纳米颗粒具有局域表面等离子体共振特性而引起了广泛的关注,其中Au-Ag合金纳米颗粒具有良好的结构稳定性、光热性能以及潜在的抗癌功效而得到普遍研究。在众多应用中的特性与其粒径和浓度密切相关,然而目前常用的电子显微镜观察法和动态光散射法不能同时获得粒径和浓度信息,因此采取有效手段测量颗粒粒径和浓度信息至关重要。基于光谱消光法,利用非负的Tikhonov正则化方法解决反演问题,并根据Mie理论计算消光矩阵。针对噪声问题,采取两种情况研究多分散Au-Ag合金纳米球粒径分布与浓度的反演问题。未添加噪声情况下,颗粒系Ⅰ的反演相对误差小于颗粒系Ⅱ,在波长范围300～500 nm之间的反演相对误差最小,对应平均粒径、粒径标准差和颗粒数浓度的反演相对误差分别为0%,-0.03%和0%。添加随机噪声情况下,将0.5%和1.0%的随机噪声添加进颗粒系Ⅰ中的消光谱,经过数据比较发现在波长范围200～600 nm之间的反演相对误差最小。当添加0.5%的随机噪声时,粒径分布、粒径标准差和颗粒数浓度的变化范围分别为79.76～80.15 nm, 5.60～6.61 nm和0.995 8×1010～1.005 9×1010个·cm-3;当添加1.0%的随机噪声时,粒径分布、粒径标准差和颗粒数浓度的变化范围分别为78.87～80.27 nm, 5.36～9.00 nm和0.992 4×1010～1.027 7×1010个·cm-3。反演结果随着随机噪声的增大,变化范围也明显增大即反演相对误差增大,并且每次添加相同随机噪声后的反演结果不同。为了减少随机噪声导致的不稳定性,对100次反演结果进行平均得到平均粒径、粒径标准差和颗粒数浓度。当随机噪声从0.5%增大至1.0%时,其反演结果的相对误差均增大,但是反演得到的粒径分布、粒径标准差和颗粒数浓度相对误差均小于6%,这说明通过反演算法得到的反演结果具有较好的稳定性。研究表明,光谱消光法为反演多分散Au-Ag合金纳米球粒径分布与浓度提供了一种简单、快速的表征手段,也对研究非球形纳米颗粒有启示作用。     

主成分分析排序和模糊线性判别分析的生菜近红外光谱分类

贮存时间是影响生菜品质的一项重要因素,传统的贮存时间鉴别方法主要依靠人工经验,但是这种方法的准确率和可信度并不高。研究的目标是建立一种基于模糊识别的模型进行生菜光谱分析以实现生菜贮存时间的鉴别,并与其他鉴别方法作比较。为此,在当地超市购买60份新鲜生菜样品,存放于冰箱中待用。首先,通过AntarisⅡ近红外光谱检测仪采集生菜样品的近红外光谱数据,每隔12小时检测一次,每个样本检测重复三次,并取三次平均值作为实验数据。其次,利用多元散射校正(MSC)减少近红外光谱中的冗余信息。为了进一步去除近红外光谱中的无用信息以及简化随后的数据分类过程,分别运用主成分分析(PCA)和排序主成分分析(PCA Sort)。其中,PCA Sort通过改进对主成分的排序方法能提高分类准确率,同时便于模糊线性鉴别分析(FLDA)进一步提取特征。PCA和PCA Sort的计算仅运用了前15个主成分(能充分反映光谱的主要信息)。最后,利用模糊线性鉴别分析算法(FLDA)和K近邻算法(KNN)进一步分类所得的低维数据。基于PCA和KNN算法的模型鉴别准确率达到43%,而基于PCA, FLDA和KNN算法的模型鉴别准确...     

Simulation of high fluence fast neutron damage with heavy ion bombardment

316 stainless steel has been irradiated with 5 MeV Cu ions to a fluence of 2 × 10¹⁶ ions/cm² at 500°C. Transmission electron microscopy of this sample reveals that 6 × 10¹⁵ voids/cm² of average diameter equal to 180 Å were produced. A method for correlating the fluence of ions with equivalent neutron fluences is described. This method predicts that the Cu bombardment in this study should produce a microstructure similar to that found in steel irradiated with 2–5 × 11²² neutrons/cm². A comparison of the ion produced voids with those found after previous neutron irradiation experiments confirms this prediction.     

Optical Analysis of Er3+:Boro-Fluoro-Phosphate Glasses

This paper deals with the preparation and optical analysis of Er³⁺ (0.2 mol%) boro-fluoro-phosphate glasses in the following glass compositions:

• Series A: 69.8 B₂O₃–10 P₂O₅–10(ZnO/CdO/TeO₂)–10 AlF₃

• Series B: 69.8 B₂O₃–10 P₂O₅–10(ZnO/CdO/TeO₂)–10 LiF

Measured Vis-NIR absorption spectra of Er³⁺:boro-fluoro-phosphate glasses have revealed nine absorption bands at 377 nm, 405 nm, 450 nm, 486 nm, 519 nm, 543 nm, 649 nm, 973 nm and 1529 nm, which correspond with the transitions of ⁴I_15/2 → ⁴G_11/2, (²G_9/2,⁴H_9/2), ⁴F_5/2, ⁴F_7/2, ²H_11/2, ⁴S_3/2, ⁴F_9/2, ⁴I_11/2, and ⁴I_13/2, respectively. With an excitation at λ _exci = 375 nm, a bright green emission (⁴S_3/2 → ⁴I_15/2) at 547 nm has been observed from these erbium glasses. Judd–Ofelt characteristic intensity Ω_λ (λ = 2, 4, 6) parameters are obtained from the absorption spectra, and these results were used to compute the radiative properties of Er³⁺:boro-fluoro-phosphate glasses. The NIR emission (⁴I_13/2 → ⁴I_15/2) at 1547 nm from these glasses was measured with an Ar⁺ laser (514.5 nm) as an excitation source.     

Determination of Chloride Content in Different Types of Cement Using Laser-Induced Breakdown Spectroscopy

The characterization and accurate determination of the chloride content in cement/concrete is very important for the assessment of the durability and safety of a concrete structure. The available analytical techniques are relatively expensive and time consuming. In this study, a laser-induced breakdown spectroscopy (LIBS) system was used for determination of elemental composition in three different types of cement samples. The plasma was generated by focusing a pulsed Nd: YAG laser at 1064 nm on the cement samples. The concentrations of different elements of significance for structural stability in cement samples were determined. The evaluation of the potential and the capabilities of LIBS as a rapid tool for characterization of cement samples is discussed. The optimum LIBS setup and experimental conditions to detect and measure chloride in building materials are reported. The LIBS results were compared with the results obtained using a standard analytical technique such as inductively coupled plasma emission spectroscopy (ICP–ES). The limits of detection were determined, and calibration curves were measured. The results of this investigation indicate the reliability of LIBS to characterize different cement samples and to assess the chloride content in these cements.     

How many maxima can there be?

Let C be a planar region. Choose n points p₁,,p_nI.I.D. from the uniform distribution over C. Let M^C_n be the number of these points that are maximal. If C is convex it is known that either E(M^C_n)=Θ(√n)> or E(M^C_n)=O(log n). In this paper we will show that, for general C, there is very little that can be said, a-priori, about E(M^C_n). More specifically we will show that if g is a member of a large class of functions then there is always a region C such that E(M^C_n)=Θ(g(n)). This class contains, for example, all monotically increasing functions of the form g(n)= nln^βn, where 0<<1 and β0. This class also contains nondecreasing functions like g(n)=ln^*n. The results in this paper remain valid in higher dimensions.     

Equality and inequality constrained optimization algorithms with convergent stepsizes

In this paper, we consider two algorithms for nonlinear equality and inequality constrained optimization. Both algorithms utilize stepsize strategies based on differentiable penalty functions and quadratic programming subproblems. The essential difference between the algorithms is in the stepsize strategies used. The objective function in the quadratic subproblem includes a linear term that is dependent on the penalty functions. The quadratic objective function utilizes an approximate Hessian of the Lagrangian augmented by the penalty functions. In this approximation, it is possible to ignore the second-derivative terms arising from the constraints in the penalty functions.The penalty parameter is determined using a strategy, slightly different for each algorithm, that ensures boundedness as well as a descent property. In particular, the boundedness follows as the strategy is always satisfied for finite values of the parameter.These properties are utilized to establish global convergence and the condition under which unit stepsizes are achieved. There is also a compatibility between the quadratic objective function and the stepsize strategy to ensure the consistency of the properties for unit steps and subsequent convergence rates.This research was funded by SERC and ESRC research contracts. The author is grateful to Professors Laurence Dixon and David Mayne for their comments. The numerical results in the paper were obtained using a program written by Mr. Robin Becker.