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.     

Cooperative,Reversible Self‐Assembly of Covalently Pre‐Linked Proteins into Giant Fibrous Structures

We demonstrate a simple bioconjugate polymer system that undergoes reversible self‐assembling into extended fibrous structures, reminiscent of those observed in living systems. It is comprised of green fluorescent protein (GFP) molecules linked into linear oligomeric strands through click step growth polymerization with dialkyne poly(ethylene oxide) (PEO). Confocal microscopy, atomic force microscopy, and dynamic light scattering revealed that such strands form high persistence length fibers, with lengths reaching tens of micrometers, and uniform, sub‐100 nm widths. We ascribe this remarkable and robust form of self‐assembly to the cooperativity arising from the known tendency of GFP molecules to dimerize through localized hydrophobic patches and from their covalent pre‐linking with flexible PEO. Dissipative particle dynamics simulations of a coarse‐grained model of the system revealed its tendency to form elongated fibrous aggregates, suggesting the general nature of this mode of self‐assembly.     

Disc-shaped triphenylenes in a smectic organisation

A layered phase (SmA) was observed in a novel linked disc-rod mesogen, containing a triphenylene mesogen and attached to three cyanobiphenyl moieties.     

Theory of the Greenspan viscometer

We present a detailed acoustic model of the Greenspan acoustic viscometer, a practical instrument for accurately measuring the viscosity eta of gases. As conceived by Greenspan, the viscometer is a Helmholtz resonator composed of two chambers coupled by a duct of radius rd. In the lowest order, eta=pi f rho(rd/Q)2, where f and Q are the frequency and quality factor of the isolated Greenspan mode, and rho is the gas density. In this level of approximation, the viscosity can be determined by measuring the duct radius and frequency response of the resonator. In the full acoustic model of the resonator, the duct is represented by a T-equivalent circuit, the chambers as lumped impedances, and the effects of the diverging fields at the duct ends by lumped end impedances with inertial and resistive components. The model accounts for contributions to 1/Q from thermal dissipation (primarily localized in the chambers) and from a capillary used for filling and evacuating the resonator. A robust, prototype instrument is being used for measuring the viscosity of reactive gases used in semiconductor processing. For well-characterized surrogate gases, the prototype viscometer generated values of eta that were within +/-0.8% of published reference values throughout the pressure range 0.2-3.2 MPa. Remarkably, we achieved this level of agreement by only slight adjustment of the numerically calculated inertial and resistive end effect parameters to improve the agreement with helium reference values. No other parameters were adjusted.     

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.     

Experimental and kinetic modeling study of tetralin: A naphtheno-aromatic fuel for gasoline,jet and diesel surrogates

Distillate fuels contain significant proportions of naphtheno-aromatic components and tetralin is a suitable surrogate component to represent this molecular moiety. The presence of aromatic and naphthyl rings makes kinetic modeling of tetralin very challenging. Primary radicals formed during the oxidation of tetralin can be aryl, benzylic or paraffinic in nature. Using available information on reaction paths and rate constants of naphthenes and alkyl-aromatics, a kinetic model of tetralin has been developed in the current study with emphasis on low-temperature chemistry and high-pressure conditions. Due to the lack of high-level quantum chemical calculations on reaction pathways of tetralin, analogous rates from ab-initio studies on benzylic and paraffinic radicals have been adopted here. Some modifications to the reaction rate rules are incorporated to account for the unique characteristics of tetralin's molecular structure. Important reaction channels have been identified using reaction path and brute force sensitivity analyses. In order to investigate the model performance at low temperatures, new experiments are carried out in a rapid compression machine on blends of tetralin and 3-methylpentane. Blending of low-reactivity tetralin with a high-reactivity alkane allowed the investigation of tetralin ignition at very low temperatures (665 – 856 K). The kinetic model developed in the current study is found to predict the current experiments and literature data adequately. The new model will aid in high-fidelity surrogate predictions at engine-relevant conditions.     

Computer simulation of crystallization kinetics and morphology in fiber-reinforced thermoplastic composites. II. Three-dimensional case

A three-dimensional computer simulation has been used to predict crystallization kinetics and crystalline morphology in composite materials that are based on crystallizable thermoplastics. Reinforcing fibers in three-dimensional simulations show similar behavior to those in two-dimensional simulations; fibers suppress crystallization relative to an unreinforced polymer since they constrain spherulitic growth by an impingement mechanism, and also enhance crystallization by providing added surface nucleation sites. The effects of varying controlling parameters on crystallization kinetics and morphology are qualitatively the same as those observed in the two-dimensional case. The relative bulk and fiber nucleation denisities, in addition to the fiber volume fraction, fiber diameter, and spherulitic growth rate control the crystallization kinetics and crystalline morphology that develop in reinforced thermoplastic composites. It is more difficult to achieve the transcrystalline morphology in slices of three-dimensional composites than it is in two-dimensional composites because nuclei in 3-D systems are not constrained to positions in or near a 2-D plane. © 1993 John Wiley & Sons, Inc.     

The Van der Waals interaction between an atom and a solid

Measurements of the scattering of neutral atoms by metal cylinders have indicated a serious discrepancy between theory and experiment for the strength of the long-range Van der Waals interaction. To clarify the content of the theory, we present here a formal analysis of the Van der Waals interaction between an atom and a solid, based on the approach of McLachlan. A key quantity in the theory is the response of the solid to an external, time-dependent dipole. This response is amenable to classical analysis, and we calculate it for a variety of model systems. When the solid may be treated as a continuum with a flat surface, the concept of surface impedance allows a convenient parameterization and we may incorporate thereby magnetic effects, non-local dielectric response, and the influence of finite layers in the solid. We also study the modifications induced by a rough surface, finding the average change in the coupling strength in the presence of weak roughness.     

Theory of the effect of heat currents on the velocity of second sound in liquid helium

An explanation of the decrease of the velocity of second sound due to heat currents in liquid helium is given. The explanation is based on Hall and Vinen's theory of the interaction of second sound with vortex lines. The predictions are in reasonable agreement with experiment.