The homogeneous projective transformation of general quadratic matrix equations

^** Email: vassilios.tsachouridis{at}ieee.org^*** Email: basil.kouvaritakis{at}eng.ox.ac.uk Algebraic quadratic equations are a special case of a singlegeneralized algebraic quadratic matrix equation (GQME). Hence,the importance of that equation in science and engineering isevident. This paper focus on the study of solutions of thatGQME and a unified framework for the characterization and identificationof solutions at infinity and of finite solutions of generalquadratic algebraic matrix equations is presented. The analysisis based on the concept of homogeneous projective transformationfor general polynomial systems (Morgan, 1986). In addition,a numerical error analysis for the computed solutions is providedfor the assessment of numerical accuracy, stability and conditioningof the computed solutions. The proposed framework is independentof any numerical method and therefore it can be used along withvarious possible numerical methods for the GQME solution, especiallymatrix flow-based algorithms (Chu, 1994) (e.g. continuation/homotopy,Morgan, 1989).     

Determination of trace elements in a human serum reference material by inductively coupled plasma mass spectrometry

A method was developed for the determination of Fe, Co, Cu, Zn, Rb, Mo and Cs in human serum by ICP-MS. Sample preparation was kept as limited as possible: Serum samples were diluted with nitric acid and indium was added as internal standard. The results for Fe, Co, Cu, and Zn were corrected for interferences from polyatomic ions using a suitable blank solution. No interferences occur for the considered isotopes of Rb, Mo, and Cs. A second-generation human serum reference material was analyzed, in order to test the accuracy and precision of the analytical procedure. The results obtained are in good agreement with the certified values.Presented in part at the 1989 European Winter Conference on Plasma Spectrochemistry, Reutte, AustriaResearch Director of the National Fund for Scientific Research (Belgium)     

激光跟瞄仿真系统及两种跟瞄方法

基于OpenGL和大气传输光学分析的3维全数字仿真是激光跟瞄系统的重要研究手段。为提高跟踪和瞄准精度,从激光跟瞄仿真系统整体出发,研究了目标成像中的投影变换、成像与跟踪的关系、高精度跟踪现有算法的控制过程仿真等内容,并提出了基于大视口、目标大气传输图像序列的跟瞄仿真技术。说明了仿真系统中跟瞄精度分析的特点。就某仿真场景,设计了"头部顶点"和"两点提取"两种跟瞄方法,在不同大气湍流条件下得到了它们的跟瞄精度,说明应用该激光跟瞄仿真系统,能够预先设计、测试和验证一些跟瞄方法,帮助进行算法分析和改进,从而提高工作效率和节约成本。     

目标表面发射率对红外热像仪测温精度的影响

介绍了红外热像仪测温原理,分析了影响红外热像仪测温精度的因素,计算了不同表面发射率下红外热像仪的测温误差曲线。理论分析表明,目标表面发射率越高,红外热像仪测温精度越高。实验改变表面发射率的设置,计算了不同表面发射率对应的总辐射亮度,得到TP8型长波红外热像仪能够精确测温时,目标表面发射率必须大于0.5的结果。最后,对表面发射率分别为0.96、0.93和0.3的3种材料进行实际测温,结果表明,材料表面发射率较高时,红外热像仪具有较好的测温精度。     

地基多孔径成像系统验证实验设计

基于工程实践中高分辨率目标成像技术的需求,讨论了光学合成孔径成像技术的成像原理以及在提高成像分辨率方面的优越性,阐述了国内外在相关领域取得的科研成果及存在的技术难点。在现有加工工艺及装调检测条件下,设计了基于两个子望远镜的合成孔径成像实验。以斐索型多孔径望远镜为研究对象,从几何光学理论出发,讨论了地基斐索型合成孔径成像系统实验的可行性。分析实验中关键组件的调整精度,提出了合成孔径成像系统精确成像的方案。实验中设计了分辨率±0.03mm的微调机构来保证系统获得清晰的像,并使用分辨率达到0.05μm的压电直线精密驱动器来保证两束光相位同步。分析结果表明,本文设计的地基多孔径成像系统实验切实可行,可得到合成孔径成像系统分辨率的确切值,为进一步研究合成孔径成像系统奠定了基础。     

Finite‐difference approximation for the u(k)‐derivative with O(hM−k+1) accuracy: An analytical expression

An approximation of function u(x) as a Taylor series expansion about a point x₀ at M points x_i, ～ i = 1,2,…,M is used where x_i are arbitrary‐spaced. This approximation is a linear system for the derivatives u^(k) with an arbitrary accuracy. An analytical expression for the inverse matrix A ^?1 where A = [A_ik] = (x_i ? x₀)^k is found. A finite‐difference approximation of derivatives u^(k) of a given function u(x) at point x₀ is derived in terms of the values u(x_i). © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

不可压磁流体力学方程组的高精度数值解法

为数值求解低雷诺数下不可压流体在电磁场作用下的流动,提出一种四阶紧致差分方法.由二维原始变量的MHD方程组出发,推导出具有较少未知量的电流密度-涡量-流函数形式MHD方程组.建立了求解二维非定常不可压MHD方程组的电流密度-涡量-流函数形式的四阶精度紧致差分格式.为验证本文提出的高精度紧致差分方法的精确性和可靠性,对有...     

A high-order discontinuous Galerkin method for wave propagation through coupled elastic–acoustic media

We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic–acoustic media. A velocity–strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic–acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic–acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.     

Effect of instrumental particle sizing resolution on the modelling of aerosol radiative parameters

A more realistic estimation of the scattering and hemispheric backscattering coefficients, σ_sp and σ_bsp, and their respective optical cross section, C_sca and C_bk, of aerosol particles is presented on the basis of the exact resolution of the width of the size bins of the particle counter instruments when size distribution measurements are used, and, with the exact optical detector instruments ability. The scattering and hemispheric backscattering cross sections, C_sca and C_bk, of the particles are averaged over the full size bins of the particle counter instrument, while these quantities are usually estimated only on the value of the mean geometric diameter of each size bin. Six instruments, the APS, ASASP-X, DMPS, FSSP-100, ELPI, and SMPS frequently used in particle size distribution measurements are reviewed, for spherical sea-salt particles at a wavelength λ=0.55 μm. The comparison using the conventional geometric mean diameter versus the use of the full size bin leads to large amount of errors for the optical cross section with non-negligible effects on their respective optical coefficients. The maximal accuracy expected for these optical quantities depend on the particle diameter as well as on the channel width of the instruments, and are also function of the angular detector probe used to measure them.