Design of an Optimal Grid for Finite Element Methods

ABSTRACT Finite element solutions of improved quality are obtained by optimizing the location of nodes of the finite element grid, while keeping the number of degrees of freedom fixed. The formulation of the grid optimization problem is based on the reduction of error associated with interpolation of the exact solution, using functions from the finite element space. Element sizes are selected as design variables: length in R1 and area in R2. Analytically derived optimality conditions are presented and an approximation to these conditions is introduced to obtain a set of operationally useful equations that can be used as guidelines for construction of improved grids. Example problems are given for illustration.     

Local forms of molecular mobility in copolymethacrylates containing side‐chain nonlinear optical chromophores

Local forms of molecular mobility of comb‐like random copolymethacrylates, containing side‐chain nonlinear optical chromophores and amyl‐ or octafluoroamyl‐groups, are studied. In the glassy state, two relaxation processes are found, which are due to reorientation of terminal polar groups (γ₂‐process) and rotation of chromophore groups about their long axes (β‐process). For octafluoroamyl‐containing copolymers, the γ₂‐process is superposition of the two molecular motions due to reorientation of terminal chromophore groups and ? CF₂H groups. The intensity and relaxation times in the range of the γ₂‐process depend on the chemical structure and concentration of chromophores in a copolymer. For the β‐process, the molecular mobility weakly depends on the chromophore structure, being mainly determined by the relative lengths of the rigid chromophore and flexible side chains. On the global spectrum of depolarization current it was observed the γ₁‐process due to reorientation of (CH₂)_n spacers between chromophore groups and copolymer backbone. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1488–1496, 2008     

Comparison of three hypothesis testing approaches for the selection of the appropriate number of clusters of variables

Within the scope of cluster analysis of variables, the selection of the appropriate number of clusters is of paramount interest. The strategy of determination of the appropriate number of clusters adopted herein is based on a hypothesis testing approach. It consists in testing whether the variation of a partition quality criterion between two consecutive partitions is far removed from the expected variation under the null-hypothesis stipulating a lack of structure. Three hypothesis testing strategies are detailed and compared in the scope of clustering of variables: Gap, Weighted Gap and a statistic associated with CLV methodology. Finally, an illustration is presented based on data from a preference study.     

Linear‐dendritic block copolymer hosts for the encapsulation of electro‐optic chromophores via H‐Bonding

Linear‐dendritic block copolymer hosts were synthesized by end‐functionalizing poly(methylmethacrylate) with dendrons that acted as hydrogen‐bonding acceptors for nonlinear optical chromophores. Second harmonic generation experiments indicate that the d₃₃ coefficients and maximum chromophore loading are increased in linear‐dendritic block copolymer hosts over comparable homopolymer hosts. Transmission electron microscopy shows 5–10 nm chromophore domains, confirming the effective spatial dispersion of the chromophores. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5017–5026, 2009     

In search for mixed transition metal/lanthanide single-molecule magnets: Synthetic routes to NiII/TbIII and NiII/DyIII clusters featuring a 2-pyridyl oximate ligand

Employing the mononuclear complex [Ni{(py)C(Me)NO}₂{(py)C(Me)NOH}] (1) as ‘ligand’ [(py)C(Me)NOH = methyl 2-pyridyl ketone oxime], the use of the ‘metal complexes as ligands’ approach has led to the synthesis of the mixed Ni^II/Ln^III complexes [NiTb{(py)C(Me)NO}₂(NO₃)₃{(py)C(Me)NOH}] (2), [Ni₂Ln₂{(py)C(Me)NO}₆(NO₃)₄] (Ln = Dy, 3; Ln = Tb, 4) and [Ni₂Tb{(py)C(Me)NO}₆](NO₃) (5). The structures of 2, 3, and 5, and the magnetic properties of 2 and 5 are briefly discussed.     

Determination of Aristocularine Enantiomers by Dispersive Liquid–Liquid Microextraction and Chiral High-performance Liquid Chromatography

Here is reported a novel analytical approach for the extractive separation and determination of enantiomeric ratios of aristocularine in bovine serum albumin. The results demonstrate suitable analytical performances. The separation was performed by chiral high-performance liquid chromatography with a 5-µm column using a mobile phase of 1:1 n-hexane:ethanol at a flow rate of 0.7?mL?min^?1 with ultraviolet–visible absorption, circular dichroism, and polarimetric detection. The enantiomers were eluted at 13.2 and 15.6?min for (+) and (?)-aristocularine, with a resolution of 1.58 and a separation factor of 1.27. The analytical parameters for the dispersive liquid–liquid microextraction were optimized; under these conditions, the extraction recoveries were from 88.6% to 93.9% for a two-step extraction. The precision, reported as the percent relative standard deviation, had values from 2.9% to 3.2% for 0.5?µg?mL^?1 of analyte for five replicate measurements using ultraviolet–visible absorption and circular dichroism detection. The limits of detection were between 0.05 and 0.08?µg?mL^?1 with enrichment ratios up to a value of 12.     

Heronapyrroles A-C: farnesylated 2-nitropyrroles from an Australian marine-derived Streptomyces sp

Chemical analysis of a marine-derived Streptomyces sp. (CMB-M0423) isolated from beach sand off Heron Island, Australia, yielded three new members of the rare pyrroloterpene biosynthetic structure class. Identified by detailed spectroscopic analysis as the first reported examples of naturally occurring 2-nitropyrroles, heronapyrroles A-C (1-3) displayed promising biological activity-with low to submicromolar IC(50) activity against Gram-positive bacteria but no cytotoxicity toward mammalian cell lines.     

Real-time increase in depth of field of an uncooled thermal camera using several phase-mask technologies

Imaging systems that combine a phase mask in the pupil and digital postprocessing may have better performance than conventional ones. We have built such a system to enhance the depth of field of an uncooled thermal camera. The phase masks are binary, their structures are optimized thanks to an image quality criterion, and they have been realized with three different technologies that give equivalent results. The deconvolution postprocessing is performed in real time with a graphics processing unit. A significant increase of the depth of field of a factor 3 has been obtained.