Physalis method for heterogeneous mixtures of dielectrics and conductors: Accurately simulating one million particles using a PC

Prosperetti’s seminal Physalis method, an Immersed Boundary/spectral method, had been used extensively to investigate fluid flows with suspended solid particles. Its underlying idea of creating a cage and using a spectral general analytical solution around a discontinuity in a surrounding field as a computational mechanism to enable the accommodation of physical and geometric discontinuities is a general concept, and can be applied to other problems of importance to physics, mechanics, and chemistry. In this paper we provide a foundation for the application of this approach to the determination of the distribution of electric charge in heterogeneous mixtures of dielectrics and conductors. The proposed Physalis method is remarkably accurate and efficient. In the method, a spectral analytical solution is used to tackle the discontinuity and thus the discontinuous boundary conditions at the interface of two media are satisfied exactly. Owing to the hybrid finite difference and spectral schemes, the method is spectrally accurate if the modes are not sufficiently resolved, while higher than second-order accurate if the modes are sufficiently resolved, for the solved potential field. Because of the features of the analytical solutions, the derivative quantities of importance, such as electric field, charge distribution, and force, have the same order of accuracy as the solved potential field during postprocessing. This is an important advantage of the Physalis method over other numerical methods involving interpolation, differentiation, and integration during postprocessing, which may significantly degrade the accuracy of the derivative quantities of importance. The analytical solutions enable the user to use relatively few mesh points to accurately represent the regions of discontinuity. In addition, the spectral convergence and a linear relationship between the cost of computer memory/computation and particle numbers results in a very efficient method. In the present paper, the accuracy of the method is numerically investigated by example computations using one dielectric particle, one isolated conductor particle, one conductor particle connected to an external source with imposed voltage, and two conductor/dielectric particles with strong interactions. The efficiency of the method is demonstrated with one million particles, which suggests that the method can be used for many important engineering applications of broad interest.     

二重数值积分公式的高精度对偶公式及其应用

给出了计算二重积分的Simpson公式与两点高斯公式的对偶公式的构造过程,得到与之对应的高精度对偶修正解,提高了二重数值积分公式的计算精度,同时给出了二重积分的一种估值方法.最后,应用于几个典型的数值算例,计算结果表明：对偶修正解比对应的数值积分公式及其对偶公式的解有更高的计算精度和更快的收敛速度.     

一种新的自动聚焦算法的研究

聚焦评价函数和极点搜索策略是自动聚焦的重要模块,直接影响聚焦的效果.为同时满足自动聚焦速度和精度上的要求,提出了一种新的自动聚焦算法.该算法综合了快速改进的灰度差分法和高精度小波变换法的优点,根据各阶段聚焦评价函数的梯度选择合适的评价函数和镜头移动步长,并且实现了从大步长快速粗扫到小步长精确细调的过渡.实验表明,与传统...     

标准镜的高精度柔性支撑镜框的优化设计

为了实现干涉仪标准镜中光学元件的高精度定位,设计了一种柔性支撑镜框,研究了该结构的力学模型、结构参数、定位精度和透镜变形。首先,根据材料力学原理将柔性镜框等效为一个弹簧系统;根据力学方程和几何关系,建立了透镜中心位置与柔性结构的挠度之间的二元方程。然后,分析了安装位置、温度、结构参数对透镜位置以及作用力的影响。最后,应用有限元仿真分析了所设计结构的力学性能,并进行对比验证。结果表明,数值仿真分析的结果与有限元仿真结果基本相同,柔性镜框的柔性结构厚度最优值为1.5 mm。该设计方案完全满足干涉仪标准镜对镜框在定位精度、稳定性方面的要求。     

仪器定量分析中几个问题的探讨

详细介绍了分析方法的评价指标,包括检出限、测定限、灵敏度、精密度、准确度、动态范围和线性范围、抗干扰能力等,单因素优化方法与加标回收实验评定测定结果准确度的可靠性,并就分析工作中遇到的一些实际问题进行了讨论.     

异质传感器数据的最优线性融合

研究了异质传感器对参数矢量进行的测量，测量数据基于线性均方估计的最优融合算法。提出和证明了异质传感器数据的最优线性融合定理，并得出“精度再差的传感器参与数据融合后都有利于提高系统的测量精度”这一结论。     

基于非同步替代光谱定标的地表下垫面影响分析

对760nm附近的氧气吸收带,选用植被、枯萎植被、人工地物、沙地和雪地五种典型地表类型,基于模拟数据进行非同步替代光谱定标方法的误差分析,比较不同地表类型得到的光谱定标准确度,为高光谱成像仪的非同步替代光谱定标提供定标图像选择策略.结果表明:运用两种光谱匹配方法——光谱角度匹配和欧氏距离法得到的定标误差基本一致;730~800nm的地表反射率曲线标准差在0.05nm以内时,定标误差集中在±0.5nm范围内;人工地物类型中个别地物如橄榄绿光泽涂料和植被大面积覆盖的图像数据不适合用于非同步替代光谱定标.     

钝头机体用FADS-α的求解算法及精度研究

针对钝头机体用嵌入式大气数据传感（flush air data sensing,FADS）系统的4类攻角求解算法及算法的求解精度进行研究.针对典型的15°钝头体外形,在Mach数Ma=2.04,3.02,5.01,攻角α=-5°~30°,侧滑角β=0°的条件下,首先基于势流理论及修正的Newton流理论建立了钝头机体用FADS系统的理论模型,并给出了典型的测压孔配置方案;然后采用经典三点式及改进三点式算法、基于线性理论的五孔探针算法、基于非线性理论的五点拟合算法、基于神经网络建模的方法及基于压力模型的加权最小二乘迭代算法,分别建立了FADS-α的4类求解算法;最后对钝头机体用FADS-α的算法求解精度进行了系统对比及论证.研究结果表明,三点式算法、改进三点式算法与加权最小二乘迭代算法精度相当,都可以比较准确地预测攻角;神经网络算法精度较好,但算法涉及的经验参数较多,且需要大批量数据集的训练及验证;拟合算法优劣明显,基于线性理论的五孔探针算法精度在小攻角时与上述几种算法精度相当,但随攻角增大（大于10°）精度下降显著;而基于非线性理论的拟合算法精度较好,但拟合过程复杂繁琐.对钝头机体用FADS-α的算法精度而言,三点式算法、改进三点式算法及加权最小二乘迭代算法是较好的计算方法.      

Ultra high performance liquid chromatography with ion‐trap TOF‐MS for the fast characterization of flavonoids in Citrus bergamia juice

We have developed a fast ultra HPLC with ion‐trap TOF‐MS method for the analysis of flavonoids in Citrus bergamia juice. With respect to the typical methods for the analysis of these matrices based on conventional HPLC techniques, a tenfold faster separation was attained. The use of a core–shell particle column ensured high resolution within the fast analysis time of only 5 min. Unambiguous determination of flavonoid identity was obtained by the employment of a hybrid ion‐trap TOF mass spectrometer with high mass accuracy (average error 1.69 ppm). The system showed good retention time and peak area repeatability, with maximum RSD% values of 0.36 and 3.86, respectively, as well as good linearity (R² ≥ 0.99). Our results show that ultra HPLC can be a useful tool for ultra fast qualitative/quantitative analysis of flavonoid compounds in citrus fruit juices.     

High‐order finite difference schemes for incompressible flows

This paper presents a new high‐order approach to the numerical solution of the incompressible Stokes and Navier–Stokes equations. The class of schemes developed is based upon a velocity–pressure–pressure gradient formulation, which allows: (i) high‐order finite difference stencils to be applied on non‐staggered grids; (ii) high‐order pressure gradient approximations to be made using standard Padé schemes, and (iii) a variety of boundary conditions to be incorporated in a natural manner. Results are presented in detail for a selection of two‐dimensional steady‐state test problems, using the fourth‐order scheme to demonstrate the accuracy and the robustness of the proposed methods. Furthermore, extensions to higher orders and time‐dependent problems are illustrated, whereas the extension to three‐dimensional problems is also discussed. Copyright © 2010 John Wiley & Sons, Ltd.