Mathematical studies of the solution of Burgers' equations by Adomian decomposition method

In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi-analytic solution. In the best cases, when a closed-form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers.     

An analytical approach to global optimization

Global optimization problems with a few variables and constraints arise in numerous applications but are seldom solved exactly. Most often only a local optimum is found, or if a global optimum is detected no proof is provided that it is one. We study here the extent to which such global optimization problems can be solved exactly using analytical methods. To this effect, we propose a series of tests, similar to those of combinatorial optimization, organized in a branch-and-bound framework. The first complete solution of two difficult test problems illustrates the efficiency of the resulting algorithm. Computational experience with the programbagop, which uses the computer algebra systemmacsyma, is reported on. Many test problems from the compendiums of Hock and Schittkowski and others sources have been solved.The research of the first and the third authors has been supported by AFOSR grants #0271 and #0066 to Rutgers University. Research of the second author has been supported by NSERC grant #GP0036426 and FCAR grants #89EQ4144 and #90NC0305.     

Dielectric Barrier Discharge in Analytical Spectrometry

Abstract

Dielectric barrier discharge is a nonequilibrium plasma, and its industrial application has been on a large scale. Similarly, its prominent features of high dissociation ability at low working temperature and low power consumption, simple and adjustable configuration, ambient working conditions, and long lifetime are favorable for developing a wide array of analytical devices as well. This review addresses the basics of dielectric barrier discharge and emphasizes their analytical applications in analytical atomic spectrometry, chemiluminescence, gas chromatographic detectors, ion source for mass spectrometry, and ion mobility spectrometry with 103 references.     

Solution of the skin effect problem with an arbitrary coefficient of specular reflection

An analytical solution of the skin effect problem in a metal with specular-diffuse boundary conditions is obtained. A new analytical method is developed that makes it possible to obtain a solution up to an arbitrary degree of accuracy. The method is based on the idea of representing not only the boundary condition on the field in the form of a source (which is conventional) but also the boundary condition on the distribution function. The solution is obtained in the form of a von Neumann series.     

临近空间单粒子串扰的解析模型

随着尺寸不断缩减, 串扰对单粒子效应的影响越来越重要. 为了量化串扰效应对单粒子瞬态(SET)的影响, 基于SET等效电路和互连线的6 结点模型, 利用所定义的导纳的四种规则, 简化计算, 推导了单粒子串扰(SEC)的解析模型. 通过求导和泰勒公式, 导出了串扰电压峰值的表达式. 仿真结果显示, 该解析模型与SPICE电路的一致性较好, 平均相对误差为2.51%, 最大误差为5.11%.     

Challenges and Opportunities of Implementing Data Fusion in Process Analytical Technology—A Review

The release of the FDA’s guidance on Process Analytical Technology has motivated and supported the pharmaceutical industry to deliver consistent quality medicine by acquiring a deeper understanding of the product performance and process interplay. The technical opportunities to reach this high-level control have considerably evolved since 2004 due to the development of advanced analytical sensors and chemometric tools. However, their transfer to the highly regulated pharmaceutical sector has been limited. To this respect, data fusion strategies have been extensively applied in different sectors, such as food or chemical, to provide a more robust performance of the analytical platforms. This survey evaluates the challenges and opportunities of implementing data fusion within the PAT concept by identifying transfer opportunities from other sectors. Special attention is given to the data types available from pharmaceutical manufacturing and their compatibility with data fusion strategies. Furthermore, the integration into Pharma 4.0 is discussed.     

An Integrated Microfluidic Probe for Mass Spectrometry Imaging of Biological Samples**

Ambient ionization based on liquid extraction is widely used in mass spectrometry imaging (MSI) of molecules in biological samples. The development of nanospray desorption electrospray ionization (nano-DESI) has enabled the robust imaging of tissue sections with high spatial resolution. However, the fabrication of the nano-DESI probe is challenging, which limits its dissemination to the broader scientific community. Herein, we describe the design and performance of an integrated microfluidic probe (iMFP) for nano-DESI MSI. The glass iMFP, fabricated using photolithography, wet etching, and polishing, shows comparable performance to the capillary-based nano-DESI MSI in terms of stability and sensitivity; a spatial resolution of better than 25 μm was obtained in these first proof-of-principle experiments. The iMFP is easy to operate and align in front of a mass spectrometer, which will facilitate broader use of liquid-extraction-based MSI in biological research, drug discovery, and clinical studies.     

Maintaining the predictive abilities of multivariate calibration models by spectral space transformation

In quantitative on-line/in-line monitoring of chemical and bio-chemical processes using spectroscopic instruments, multivariate calibration models are indispensable for the extraction of chemical information from complex spectroscopic measurements. The development of reliable multivariate calibration models is generally time-consuming and costly. Therefore, once a reliable multivariate calibration model is established, it is expected to be used for an extended period. However, any change in the instrumental response or variations in the measurement conditions can render a multivariate calibration model invalid. In this contribution, a new method, spectral space transformation (SST), has been developed to maintain the predictive abilities of multivariate calibration models when the spectrometer or measurement conditions are altered. SST tries to eliminate the spectral differences induced by the changes in instruments or measurement conditions through the transformation between two spectral spaces spanned by the corresponding spectra of a subset of standardization samples measured on two instruments or under two sets of experimental conditions. The performance of the method has been tested on two data sets comprising NIR and MIR spectra. The experimental results show that SST can achieve satisfactory analyte predictions from spectroscopic measurements subject to spectrometer/probe alteration, when only a few standardization samples are used. Compared with the existing popular methods designed for the same purpose, i.e. global PLS, univariate slope and bias correction (SBC) and piecewise direct standardization (PDS), SST has the advantages of implementation simplicity, wider applicability and better performance in terms of predictive accuracy.