Product Integration Rules at Clenshaw-Curtis and Related Points: A Robust Implementation

Product integration rules generalizing the Fej?r, Clenshaw-Curtis,and Filippi quadrature rules respectively are derived for integralswith trigonometric and hyperbolic weight factors. The Chebyshevmoments of the weight functions are found to be given by well-conditionedexpressions, in terms of hypergeometric functions ₀F₁. An a priori error estimator is discussed which is shown bothto avoid wasteful invocation of the integration rule and toincrease significantly the robustness of the automatic quadratureprocedure. Then, specializing to extended Clenshaw-Curtis (ECC) rules,three types of a posteriori error estimates are considered andthe existence of a great risk of their failure is demonstratedby large scale validation tests. An empirical error estimator,superseding them for slowly varying integrands, is found toresult in a spectacular increase in the output reliability. Finally, enhancements in the control of the interval subdivisionstrategy aiming at increasing code robustness is discussed.Comparison with the code DQAWO of QUADPACK, with about a hundredthousand solved integrals, is illustrative of the increasedrobustness and error estimate reliability of our computer codeimplementation of the ECC rules.     

Charge-transfer photochemistry of bis(diethyl-diselenocarbamato)copper(II)

The photochemical reactions of bis(diethyl-diselenocarbamato)copper(II), Cu(Et2dsc)2, complex have been studied in toluene, CH2Cl2, CHCl3 and chloroalkane/EtOH mixed solvents. Charge-transfer irradiation induces intramolecular oxidation of the ligand and reduction of copper(II) to copper(I) as evidenced by EPR and UV-Vis spectra of the complex as well as quantum yield results. When photolysis is carried out in CHCl3 or CH2Cl2 or in the solvent mixture CHCl3/EtOH resp. CH2Cl2/EtOH of lower than 1:1 EtOH content, the primary photoproduct CuI(Et2dsc) is further oxidised in a dark reaction with the chloroalkane producing the corresponding paramagnetic mixed-ligand CuII(Et2dsc)Cl complex in equilibrium with its chloride-bridged and EPR silent, dimeric form Cu2(Et2dsc)2Cl2. At low concentration of EtOH the equilibrium is shifted to the dimeric form whereas at higher than 1:1 EtOH content in the mixed solvent CHCl3/EtOH it is shifted to CuII(Et2dsc)Cl. A reaction mechanism is proposed and the role of ethanol is discussed.     

Thermodynamic Complexation of Dopamine with Zinc(II) in Media with Different Dielectric Constants

The complexation of zinc(II) with dopamine has been investigated by spectrophotometric measurements in mixed solvent system at an ionic strength of 0.2 mol•dm－3 sodium chloride, employed at at (15±0.1), (25±0.1), (35±0.1) ℃ at inin a pH range of ca. 6 to ca. 7 with a high ratio of ligand to metal. The effect of solvent systems on protonation and complexation are was was discussed. Linear relationships are werewere observed by plotting lg K versus 1/D, where K and D show stability and dielectric constants, respectively.     

Liquid-crystalline bisadducts of [60]fullerene

A second-generation cyanobiphenyl-based dendrimer was used as a liquid-crystalline promoter to synthesize mesomorphic bisadducts of [60]fullerene. Liquid-crystalline trans-2, trans-3, and equatorial bisadducts were obtained by condensation of the liquid-crystalline promoter, which carries a carboxylic acid function, with the corresponding bisaminofullerene derivatives. A monoadduct of fullerene was also prepared for comparative purposes. All the compounds gave rise to smectic A phases. An additional mesophase, which could not be identified, was observed for the trans-2 derivative. The supramolecular organization of the monoadduct derivative is governed by steric constraints. Indeed, for efficient space filling, adequacy between the cross-sectional areas of fullerene (approximately 100 A(2)) and of the mesogenic groups (approximately 22-25 A(2) per mesogenic group) is required. As a consequence, the monoadduct forms a bilayered smectic A phase. The supramolecular organization of the bisadducts is essentially governed by the nature and structure of the mesogenic groups and dendritic core. Therefore, the bisadducts form monolayered smectic A phases. The title compounds are promising supramolecular materials as they combine the self-organizing behavior of liquid crystals with the properties of fullerene.     

Lattice Boltzmann simulation of natural convection in nanofluid-filled 2D long enclosures at presence of magnetic field

In this paper, the effects of a magnetic field on natural convection flow in filled long enclosures with Cu/water nanofluid have been analyzed by lattice Boltzmann method. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 10³–10⁵, the volumetric fraction of nanoparticles between 0 and 6 %, the aspect ratio of the enclosure between A = 0.5 and 2. The Hartmann number has been varied from Ha = 0 to 90 with interval 30 while the magnetic field is considered at inclination angles of θ = 0°, 30°, 60° and 90°. Results show that the heat transfer decreases by the increment of Hartmann number for various Rayleigh numbers and the aspect ratios. Heat transfer decreases with the growth of the aspect ratio but this growth causes the effect of the nanoparticles to increase. The magnetic field augments the effect of the nanoparticles at high Rayleigh numbers (Ra = 10⁵). The effect of the nanoparticles rises for high Hartmann numbers when the aspect ratio increases. The rise in the magnetic field inclination improves heat transfer at aspect ratio of A = 0.5.     

Effect of solvent and remote ligand substituents on the photochemical behaviour of copper(II) dithiocarbamates and dithiophosphates

The photochemical properties of bis(dithiocarbamato)Cu^II, Cu(R¹dtc)₂, and bis(dithiophosphato)Cu^II, Cu(R₂ ²dtp)₂, complexes with different remote ligand substituents (R¹ = piperidine, morpholine, pyrrolidine and 4-phenylpiperazine; R² = Me, Et and i-Pr) have been studied in chloromethanes (CCl₄, CHCl₃, CH₂Cl₂), chloromethanes/EtOH and PhMe. The monomeric species Cu^II(R¹dtc)Cl and its chloride-bridged dimeric form Cu₂(R¹dtc)₂Cl₂ were subsequently obtained during Cu(R¹dtc)₂ photolysis in chloromethane/EtOH mixtures and the steady-state concentration of Cu₂(R¹dtc)₂Cl₂ was found to depend on the EtOH content in the mixed solvents as well as on the nature of R¹ and the oxidising ability of the chloromethane. The appearance of the mixed-ligand complex Cu^II(R₂ ²dtp)Cl has been observed as an intermediate photoproduct after longer u.v.-irradiation of Cu(R₂ ²dtp)₂ in chloromethanes/EtOH.     

Diffraction under total internal reflection for micro-fluidic analysis

This work presents the principles of a novel micro-optical system for micro- and nano-fluidic analysis. It is based on diffraction, occurring in total internal reflection conditions. The developed detector is integrated in an autonomous micro-fluidic device, produced by a unique combination of different techniques for micro- and nano-structuring and micro-machining. The micro-fluidic sensor is examined both experimentally and theoretically with respect to the parameters of the light and the diffraction grating. The most beneficial configurations with respect to maximum sensitivity towards the fluidic optical constants are discussed. Optical experiments show sensitivity of 5×10^-4 to the fluidic refractive index and of 3.5×10⁶ m^-1 to the absorption coefficient. Envisioned applications of the integrated micro-sensor are concentration and composition analysis, environmental protection control, medical, biological and chemical diagnostics, and so on. PACS 07.07.Df; 81.16.-c; 78.20.Ci; 81.70.Jb     

Clay-fulleropyrrolidine nanocomposites

In this work, we describe the insertion of a water-soluble bisadduct fulleropyrrolidine derivative into the interlayer space of three layered smectite clays. The composites were characterized by a combination of powder X-ray diffraction, transmission electron microscopy, X-ray photoemission and FTIR spectroscopies, and laser flash photolysis measurements. The experiments, complemented by computer simulations, give insight into the formation process, structural details, and properties of the fullerene/clay nanocomposites. The reported composite materials constitute a new hybrid system, where C(60) differs from its crystals or its solutions, and open new perspectives for the design and construction of novel C(60)-based organic/clay hybrid materials.