A model study for the steady state error of numerical approximations of inviscid flow equations on Cartesian grid

The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. In this paper we consider the influence of the refined interfaces on the steady state errors for second‐order three‐point difference approximations of flow equations. Since the various characteristic components of the Euler equations should behave similarly on such grids with regard to refinement‐induced errors, it is sufficient enough to conduct the analysis on a scalar model problem. The error we consider is a global error, different to local truncation error, and reflects the interaction between multiple interfaces. The steady state error will be compared to the errors on smooth refinement grids and on uniform grids. The conclusion seems to support the numerical findings of Yamaleev and Carpenter (J. Comput. Phys. 2002; 181: 280–316) that refinement does not necessarily reduce the numerical error. Copyright © 2005 John Wiley & Sons, Ltd.     

The epitaxial growth of gaas using alkylarsine: Part 2. molecular orbital calculation

Semi-empirical molecular orbital calculations were carried out for the compounds (C₂H₅)₃As, (C₂H₅)₃Ga and RAsH₂ (R = C₂H₅, i-C₃H₇, i-C₄H₉, and t-C₄H₉) by using the CNDO/2-U program, and their capability of β-elimination reaction is compared on the basis of the torsion energy to the transition state, electrostatic interactions and orbital overlapping between the central atom and the β-hydrogen, and bond order of the metal-carbon, and carbon-hydrogen bond. In the comparison of (C₂H₅)₃As with (C₂H₅)₃Ga, we found that the β-elimination of (C₂H₅)₃As could hardly be expected to take place in the thermal decomposition. The capability of β-elimination would be smaller in C₂H₅AsH₂ than that in (C₂H₅)₃As. Moreover when the ethyl group is replaced by a t-butyl group in RAsH₂, the β-elimination reaction appears to become more difficult and a large possibility for a radical process is suggested.     

On the excitation of a closely spaced array by a line source

An infinite row of periodically spaced, identical rigid circularcylinders is excited by an acoustic line source which is parallelto the generators of the cylinders. A method for calculatingthe scattered field accurately and efficiently is presented.When the cylinders are sufficiently close together, Rayleigh–Blochsurface waves that propagate energy to infinity along the arrayare excited. An expression is derived which enables the amplitudesof these surface waves to be computed without requiring thesolution to the full scattering problem.     

Theoretical and numerical analysis on multispectral bioluminescence tomography

Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions.     

Temperature‐modulated differential scanning calorimetry studies on the origin of double melting peaks in isothermally melt‐crystallized poly(L‐lactic acid)

In this work, the melting behaviors of nonisothermally and isothermally melt‐crystallized poly(L ‐lactic acid) (PLLA) from the melt were investigated with differential scanning calorimetry (DSC) and temperature‐modulated differential scanning calorimetry (TMDSC). The isothermal melt crystallizations of PLLA at a temperature in the range of 100–110 °C for 120 min or at 110 °C for a time in the range of 10–180 min appeared to exhibit double melting peaks in the DSC heating curves of 10 °C/min. TMDSC analysis revealed that the melting–recrystallization mechanism dominated the formation of the double melting peaks in PLLA samples following melt crystallizations at 110 °C for a shorter time (≤30 min) or at a lower temperature (100, 103, or 105 °C) for 120 min, whereas the double lamellar thickness model dominated the formation of the double melting peaks in those PLLA samples crystallized at a higher temperature (108 or 110 °C) for 120 min or at 110 °C for a longer time (≥45 min). © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 466–474, 2007     

儿童的铅中毒问题──Ⅱ．彩色油墨中铅的测定

用能量色散Ｘ射线荧光分析法测定了某厂生产的４４种彩色油墨纸中的铅含量．结果发现，除５种油墨外，其它３９种彩色油墨纸中的铅含量均比对照纸中高９倍以上，其中桔黄色、桔红色树脂胶版油墨高５００倍以上，棕色树脂胶版油墨高３７９倍，深黄色和柠檬黄色树脂铅印油墨分别高１７０和１１３倍．这表明，彩色油墨印刷品可能是儿童慢性铅中毒的重要污染源．     

Transient free‐surface flow of a viscoelastic fluid in a narrow channel

The interplay between inertia and elasticity is examined for transient free‐surface flow inside a narrow channel. The lubrication theory is extended for the flow of viscoelastic fluids of the Oldroyd‐B type (consisting of a Newtonian solvent and a polymeric solute). While the general formulation accounts for non‐linearities stemming from inertia effects in the momentum conservation equation, and the upper‐convected terms in the constitutive equation, only the front movement contributes to non‐linear coupling for a flow inside a straight channel. In this case, it is possible to implement a spectral representation in the depthwise direction for the velocity and stress. The evolution of the flow field is obtained locally, but the front movement is captured only in the mean sense. The influence of inertia, elasticity and viscosity ratio is examined for pressure‐induced flow. The front appears to progress monotonically with time. However, the velocity and stress exhibit typically a strong overshoot upon inception, accompanied by a plug‐flow behaviour in the channel core. The flow intensity eventually diminishes with time, tending asymptotically to Poiseuille conditions. For highly elastic liquids the front movement becomes oscillatory, experiencing strong deceleration periodically. A multiple‐scale solution is obtained for fluids with no inertia and small elasticity. Comparison with the exact (numerical) solution indicates a wide range of validity for the analytical result. Copyright © 2004 John Wiley & Sons, Ltd.     

Precise synthesis of porphyrin array scaffolding polyisocyanides

Aryl isocyanides bearing free‐base and metallo‐porphyrins were prepared and polymerized with a Pd–Pt μ‐ethynediyl complex as the initiator to give polymers with narrow polydispersity indices. The molecular weights of the resulting polymers were precisely controlled by the initial feed ratio of the porphyrin monomer to the initiator. The UV–VIS spectra suggested that the porphyrin pendants are regularly arranged to form stacked columns. Metallo‐porphyrin polymers were also prepared by reacting free‐base porphyrin polymers with metal salts. The successive reactions of free‐base and zinc‐porphyrin monomers resulted in the formation of diblock polymers. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 585–595, 2006     

Chiral discrimination of a helically organized crown ether array parallel to the helix axis of polyisocyanate

The asymmetric polymerization of 4′‐isocyanatobenzo‐18‐crown‐6 with the lithium amide of (S)‐(2‐methoxymethyl)pyrrolidine successfully proceeded to afford end‐functionalized poly(4′‐isocyanatobenzo‐18‐crown‐6) with (S)‐(2‐methoxymethyl)pyrrolidine (polymer 2 ). In the circular dichroism (CD) spectrum of 2 , a clear positive Cotton effect was observed in the range of 240–350 nm corresponding to the absorption of the polymer backbone, indicating that 2 partially formed a one‐handed helical structure, which was preserved by the chirality of (S)‐(2‐methoxymethyl)pyrrolidine bonding to the terminal end in 2 . In the titration experiments for the CD intensity of 2 in the presence of D ‐ and L ‐Phe·HClO₄ (where Phe is phenylalanine), a small but remarkable difference was observed in the amount of the chiral guest needed for saturation of the CD intensity and in the saturated CD intensity, indicating that the extremely stable, one‐handed helical part should exist in the main chain of 2 , which was not inverted even when the unfavorable chiral guest for the predominant helical sense, L ‐Phe·HClO₄, was added. In addition, helical polymer 2 exhibited a chiral discrimination ability toward racemic guests; that is, the guests were extracted from the aqueous phase into the organic phase with enantiomeric excess. The driving force of the chiral discrimination ability of 2 should certainly be attributed to the one‐handed helical structure in 2 . © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 325–334, 2006     

Reconstruction of an acoustically sound-soft obstacle from one incident field and the far-field pattern

The problem considered is that of determining the shape of aplane acoustically sound-soft obstacle from the knowledge ofthe far-field pattern for one time-harmonic incident field.An iterative procedure is proposed based on two boundary integralsrepresenting the incident field and the far-field pattern, respectively.Numerical examples are included which show that the proceduregives accurate numerical approximations in relatively few iterations.