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.     

An angle resolved electron-ion recoil vector correlation study of alternate ion dissociation channels in A CF3I+

Electron-ion recoil vector correlations are examined for the ionization and subsequent dissociation of A state CF3I+. The magnitude of the electron and fragment ion recoil vectors permits the energetics of two alternative decays to I+ and CF3+ to be compared, while differences between the angular correlations are interpreted as molecule-frame photoelectron angular distributions which, in the I+ channel, are smeared by molecular rotation between ionization and dissociation. Quantitative estimates of sub-ps I+ decay lifetimes are extracted, indicating very different decay rates for the alternative dissociation channels. Surprisingly, the ka1 and ke photoelectron continua exchange polarization dependence in the I+ channel correlations and vibronic interactions are postulated in explanation. This can also rationalize the non-adiabatic A CF3I+-->I+ decay mechanism and the branching competition between the CF3+ and I+ channels.     

An Unprecedented (1infinity)

A chain of vertex-linked "bare" nido-Ge(9)(2-) clusters (shown in the picture) is featured by the novel polymeric Zintl anion formed from the binary alloy "KGe(4)", ethylenediamine, and [18]crown-6. The polymerization of nido-Ge(9)(4-) clusters is counterintuitive to known two-electron oxidation behavior of nido clusters and the existence of the isolated closo-Ge(9)(2-) ion. The novel semiconducting cluster "wire" establishes direct structural and mechanistic links between molecular Zintl cluster ions with the extended structures of Zintl phases and elemental nanophase materials.     

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.     

An engineering approach to blade designs for low to medium pressure rise rotor-only axial fans

Low to medium pressure rise axial fan equipment of the arbitrary vortex flow rotor-only type is widely used in industrial and commercial applications, with many of the installations and rotor designs being far from optimum. Complex computational methods exist for analyzing flows in, for example, high-speed axial flow compressors with multistage blade rows; however, the designers and manufacturers of low-speed, general-purpose axial flow fan equipment have been reluctant to embrace this technology. A simpler yet reliable design technique is presented that allows this category of ducted axial fan rotors, in the presence of swirl-free inlet flow, to be designed to achieve a specified duty with sufficient accuracy for engineering purposes. Practical blade design recommendations and limits, similar to those that exist for free vortex flow axial rotors, have been established for the arbitrary vortex flow rotor-only case.

The technique employs a straightforward engineering approach to arbitrary vortex flow axial fan rotor design, and the equation set can be solved by using relatively simple numerical methods. Estimates of pressure rise and shaft power characteristics for a proposed fan/rotor design can be computed and the design loop iterated until an acceptable set of blade parameters is identified. It is also possible to analyze the performance of an existing axial fan installation as a prelude to the design of a more efficient and effective replacement rotor.

Experimental data used in validating the design and analysis techniques are also presented. These data include comprehensive Cobra pressure probe surveys of local flow parameters downstream of three different low boss ratio, low solidity, arbitrary vortex flow rotors (all with circular arc camber line type blades) as well as fan performance characteristics for one of the experimental rotors configured as a direct-exhaust fan unit. Installation-dependent factors such as direct-exhaust losses and tip clearance effects are also examined. The analytical technique is shown to provide acceptable estimates of fan/rotor pressure rise performance and shaft power characteristics over a moderately wide range of blade angles and operating conditions.     

A high resolution visible spectrum of iridium monophosphide

Laser induced fluorescence spectra of iridium monophosphide, IrP, have been obtained at low and high resolution in the blue region of the visible spectrum. Two electronic transitions were observed with origins near 459.6 and 471.9 nm. Three vibronic bands in each of these transitions have been observed at high resolution allowing for full characterization of the states. A J-independent doubling of the rotational lines has been ascribed to nuclear electric quadrupole coupling in the ground state. Multireference configuration interaction (MRCI) calculations have been performed in order to confirm the nature of the ground state and aid in the assignment of the excited states. The two observed transitions have been assigned as the [21.7]¹Σ⁺-X¹Σ⁺ and the [21.2] ³Σ⁺-X¹Σ⁺ electronic systems based on comparison with the theoretical calculations. The v + 2 level of each of these electronic transitions was found to be heavily perturbed and a successful deperturbation analysis was performed allowing for a complete global fit of the data.     

Long holographic lifetimes in bacteriorhodopsin films

The D85N genetic variant of bacteriorhodopsin (BR) displays a nearly permanent lifetime of the photochromic P(490) state. We present pump-probe measurements that demonstrate this behavior. However, diffraction efficiency measurements made from holograms recorded in a hydrated D85N film show markedly different decay behavior, suggesting that a molecular diffusion process is occurring in the film. Holograms recorded with different grating frequencies display correspondingly different decay times, thus supporting this hypothesis. A thin D85N film was fabricated that was chemically cross linked, resulting in the elimination of diffusion of BR molecules within the polymer matrix. This film exhibits a grating lifetime of the order of weeks or more, thus permitting the long-term holographic storage of information.