Multilevel preconditioners for a quadrature Galerkin solution of a biharmonic problem

Efficient multilevel preconditioners are developed and analyzed for the quadrature finite element Galerkin approximation of the biharmonic Dirichlet problem. The quadrature scheme is formulated using the Bogner–Fox–Schmit rectangular element and the product two‐point Gaussian quadrature. The proposed additive and multiplicative preconditioners are uniformly spectrally equivalent to the operator of the quadrature scheme. The preconditioners are implemented by optimal algorithms, and they are used to accelerate convergence of the preconditioned conjugate gradient method. Numerical results are presented demonstrating efficiency of the preconditioners. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

An estimation of the measurement uncertainty for an optical emission spectrometric method

 A validation procedure based on the ISO/IEC 17025 standard was used to demonstrate the long-term stability of a calibration process and to assess the measurement uncertainty of a standard test method for optical emission vacuum spectrometric analysis of carbon and low-alloy steel (ASTM E 415–99a). The validation was used to provide documented evidence that the selected method fulfils the requirements and that the method is ”fit for purpose”. A test for drift was applied to determine statistically whether the analytical results vary systematically with time. The accuracy and traceability of the optimised method were tested by an analysis of closely matched matrix certified reference materials (CRMs). The measurement uncertainty estimations took account of the precision study, the bias and its uncertainty, and the qualification of uncertainties not considered in the overall performance studies. Received: 2 November 2002 Accepted: 2 January 2003 Acknowledgement The author expresses gratitude to Dr. Aleš Fajgelj for helpful discussions during the 3rd Central European Conference on Reference Materials and Measurements. Presented at CERMM-3, Central European Reference Materials and Measurements Conference: The function of reference materials in the measurement process, May 30–June 1, 2002, Rogaška Slatina, Slovenia Correspondence to T. Drglin     

Efficient discretization of pressure‐correction equations on non‐orthogonal grids

An alternative discretization of pressure‐correction equations within pressure‐correction schemes for the solution of the incompressible Navier–Stokes equations is introduced, which improves the convergence and robustness properties of such schemes for non‐orthogonal grids. As against standard approaches, where the non‐orthogonal terms usually are just neglected, the approach allows for a simplification of the pressure‐correction equation to correspond to 5‐point or 7‐point computational molecules in two or three dimensions, respectively, but still incorporates the effects of non‐orthogonality. As a result a wide range (including rather high values) of underrelaxation factors can be used, resulting in an increased overall performance of the underlying pressure‐correction schemes. Within this context, a second issue of the paper is the investigation of the accuracy to which the pressure‐correction equation should be solved in each pressure‐correction iteration. The scheme is investigated for standard test cases and, in order to show its applicability to practical flow problems, for a more complex configuration of a micro heat exchanger. Copyright © 2003 John Wiley & Sons, Ltd.     

Synthesis, band structure, and optical properties of Ba2ZnV2O8

A novel compound Ba₂ZnV₂O₈ has been synthesized in high temperature solution reaction and its crystal structure has been characterized by means of single crystal X-ray diffraction analysis. It crystallizes in monoclinic system and belongs to space group P2₁/c with a=7.9050(16), b=16.149(3), , β=90.49(3). It builds up from 1-D branchy chains of [ZnV₂O₈⁴⁻]_∞, and the Ba²⁺ cations are located in the space among these chains. The IR spectrum, ultraviolet-visible diffuse reflection integral spectrum and fluorescent spectra of this compound have been investigated. The calculated results of energy band structure by the density functional theory method show that the solid-state compound of Ba₂ZnV₂O₈ is an insulator with direct band gap of 3.48 eV. The calculated total and partial density of states indicate that the top valence bands are contributions from the mixings of O-2p, V-3d, and Zn-3d states and low conduction bands mostly originate from unoccupied antibonding states between the V-3d and O-2p states. The V-O bonds are mostly covalence characters and Zn-O bonds are mostly ionic interactions, and the ionic interaction strength is stronger between the Ba-O than between the Zn-O. The refractive index of n_x, n_y, and n_z is estimated to be 1.7453, 1.7469, and 1.7126, respectively, at wavelength of 1060 nm for Ba₂ZnV₂O₈ crystal.     

Enantiomerentrennung und chiroptische Eigenschaften eines 2,3-Dihydrobilatriens-abc

The enantiomers of the 2,3-dihydrobilatriene-abc1 have been separated by recycling chromatography on triacetylcellulose. Comparison of their chiroptical properties with those of amino acid substituted analogues, like3, reveals the chirality of center 3 to be of minor influence on the values. Stabilization of a definite helical conformation of these pigments seems to depend on this influence together with an appropriate dipole-dipole interaction.

     

Polymeric pH indicators immobilized PVA membranes for optical sensors of high basicity based on a kinetic process

Two kinds of polymeric pH indicators PPF (phenolphthalein-formaldehyde product) and CPF (o-cresolphthalein-formaldehyde product) immobilized cross-linked poly(vinyl alcohol) membranes (PPF-PVA and CPF-PVA) for optical intermittent determination of high basicity ([OH⁻] = 1-8 M) based on a kinetic process were developed. In our previous work, we had demonstrated that PPF-PVA and CPF-PVA could perform the determination of high pH values from pH 10.0 to 14.0. Here the discoloring kinetic behaviors of PPF-PVA and CPF-PVA were compared with those of free phenolphthalein, o-cresolphthalein and thymolphthalein. Experimental results and theoretical analysis indicated that the response behaviors of the optodes’ membranes in concentrated NaOH solutions were diffusion-independent and still complied with the pseudo-first-order kinetics. In addition, two data analysis methods for determination were presented. One was directly based on the reduced absorbance; the other was based on the discoloring kinetic constant. It was found that the latter could perform a rapid (60 s) and reliable (relative standard deviation: 2.6%) determination for high basicity. These kinds of optodes can be used repeatedly when they are immersed in low-pH solutions to regain the protonated form after each determination.     

Optical spectra of Yb and Yb–Nd interaction in Cs2NaNd0,4Yb0,6Cl6

Interaction between octahedrally coordinated Nd³⁺ and Yd³⁺ in Cs₂NaNd_0,4Yb_0,6Cl₆ reduces the Nd³⁺ luminescence lifetime by roughly two orders of magnitude with respect to that found in Cs₂NaNdCl_{6– · –} Analysis of low temperature absorption and emission spectra reveals that the nonradiative Nd³⁺–Yb³⁺ energy transfer has to be assisted by lattice phonon emission, nevertheless the rate of the transfer is high in the 4–300 K temperature region and attains 5.8×10⁵s^-1 at room temperature. A phase transition of Cs₂NaNd_0,4Yb_0,6Cl₆ between 12 and 13 K is evidenced by abrupt change of both the spectra and lifetimes of Yb³⁺. Reduction of Yb³⁺ lifetime from 5.3 ms to 150 μs is at the transition from low symmetry phase to high symmetry phase is supposed to be associated with a three ion interaction which occurs in ordered lattice and disappears in low temperature disordered structure.     

Hapten immobilization for antibody sensing using a dynamic modification protocol

Optical fiber (OF) sensors are often limited by the immobilization technique used to associate a specific sensing ligand with the OF surface. This is particularly true when the ligand is biologically active as, for example, in the case of immobilized haptens or antibodies. The dynamic modification protocol is a regenerable and experimentally simple way to immobilize a variety of sensing molecules on an OF surface. Furthermore, the protocol is immune to hydrolysis and not limited by diffusion through a membrane or sol–gel. In this publication the approach is extended by immobilizing the hydrophobic hapten (octadecyl 6-(2,4 dinitrophenyl)aminohexanoic acid) as a means to prepare an OF sensor for antibodies specific for 2,4 dinitrophenyl (DNP). The LOD for anti-DNP is 0.5 nanomolar and the K_apparent is 1.0±0.2×10⁶. Nonspecific antibody adsorption is problematic in this sensing approach and was found to limit the quantitative capabilities of the sensor. However, time discrimination can be used to allow the nonspecific antibody to desorb prior to measurement thus minimizing the influence of nonspecific binding on sensor performance.     

能动抛光磨盘的变形实验研究

 能动抛光磨盘实时产生不同的表面变形，在对大口径非球面光学元件进行精磨和抛光时实现与工件表面良好的大尺寸吻合，可以消除传统光学加工采用小尺寸磨头时带来的高频残余误差并提高加工效率。以加工直径1.3m左右，F/2的抛物面光学元件为例，对能动磨盘在不同离轴度时能够产生的变形进行了计算和实验。结果表明，能动磨盘能够以较高精度产生旋转对称或非对称的抛物面形状。对能动磨盘产生变形后的残余误差进行了分析。