On the internal stepsize of an extrapolation algorithm for IVP in ODE

We propose an extrapolation algorithm for initial value problems in ordinary differential equations. In the algorithm, an appropriately chosen stepsizeH is divided into smaller stepsizes by a sequence and a new stopping rule is proposed. The sequences applied to the algorithm are Romberg {2,4,8,16,32,...}, Bulirsch {2,4,6,8,16...} and Harmonic {2,4,6,8,10,12,...} types. The proposed algorithm is compared numerically with the algorithm introduced by Stoer. In view of the accuracy of numerical solutions, the relatively small number of calculations, the stability and reliability of the algorithm, we found that the algorithm with the Romberg sequence is the best.     

Preparation and lithium doping of gallium oxynitride by ammonia nitridation via a citrate precursor route

Gallium oxynitride, isostructural to hexagonal gallium nitride (h-GaN), was obtained by ammonia nitridation of a precursor prepared from the addition of citric acid to an aqueous solution of gallium nitrate. Gallium oxynitride produced at 750 °C had a small amount of gallium vacancies, and was formulated as (Ga_0.89□_0.11) (N_0.66O_0.34) where the symbol □ stands for gallium vacancy. Both the gallium vacancies and oxygen substituted for nitrogen were randomly distributed within the structure. The amount of vacancies decreased with nitridation temperatures in the range of 750-850 °C. Approximately, 10 at% Li⁺ was doped into the gallium oxynitride, using a similar preparation with the additional presence of lithium nitrate, resulted in the random substitution of Ga³⁺ in an atomic ratio of Li/Ga<1 at 750 °C. Oxygen was codoped with lithium and substituted nitrogen in the wurtzite-type crystal lattice. These substitutions reduced the electrical conductivity in the gallium oxynitride semiconductor. A new oxynitride, Li₂Ga₃NO₄, was also obtained with Li₂CN₂ impurity using similar preparations from a mixture of Li/Ga?1. The crystal structure was isostructural with h-GaN, and was refined as P6₃mc with a=0.31674(1) nm, and c=0.50854(2) nm. The Ga and Li occupancies at the 2b site were refined to be 0.6085 and 0.3915, respectively, assuming that the other 2b site was randomly occupied with 1/5O and 4/5N. When the new compound was washed for over 1 min for the removal of Li₂CN₂ impurities, it was decomposed to a mixture of α-GaOOH and α-LiGaO₂. The as-prepared product with Li/Ga=1 showed the highest intensity in yellow luminescence among the products under excitation at 254 nm.     

Temperature dependence of ion and water transport in perfluorinated ionomer membranes for fuel cells

To clarify the mechanisms of transport of ions and water molecules in perfluorosulfonated ionomer membranes for fuel cells, the temperature dependence of their transport behaviors was investigated in detail. Two types of Flemion membranes having different equivalent weight values (EW) were utilized along with Nafion 117 as the perfluorinated ionomer membranes, and H-, Li-, and Na-form samples were prepared for each membrane by immersion in 0.03 M HCl, LiCl, and NaCl aqueous solutions, respectively. The ionic conductivity, water self-diffusion coefficient (D(H)(2)(O)), and DSC were measured in the fully hydrated state as a function of temperature. The ionic conductivity of the membranes was reflected by the cation transport through the intermediary of water. Clearly, H(+) transports by the Grotthuss (hopping) mechanism, and Li(+) and Na(+) transport by the vehicle mechanism. The differences of the ion transport mechanisms were observed in the activation energies through the Arrhenius plots. The D(H)(2)(O) in the membranes exhibited a tendency similar to the ionic conductivity for the cation species and the EW value. However, no remarkable difference of D(H)(2)(O) between H- and the other cation-form membranes was observed as compared with the ionic conductivity. It indicates that water in each membrane diffuses almost in a similar way; however, H(+) transports by the Grotthuss mechanism so that conductivity of H(+) is much higher than that of the other cations. Moreover, the D(H)(2)(O) and DSC curves showed that a part of water in the membranes freezes around -20 degrees C, but the nonfreezing water remains and diffuses below that temperature. This fact suggests that completely free water (bulk water) does not exist in the membranes, and water weakly interacting with the cation species and the sulfonic acid groups in secondary and higher hydration shells freezes around -20 degrees C, while strongly binding water in primary hydration shells does not freeze. The ratio of freezing and nonfreezing water was estimated from the DSC curves. The D(H)(2)(O) in the membranes was found to be influenced by the ratio of freezing and nonfreezing water. DFT calculation of the interaction (solvation) energy between the cation species and water molecules suggested that the water content and the ratio of freezing and nonfreezing water depend strongly on the cation species penetrated into the membrane.     

Radiation-induced emission from golden hamster embryo cells

Emission from high-energy-electron-irradiated golden hamster embryo (GHE) cells has been studied over the temperature range 12–300 K both by a one-shot-single-photon-counting method and by photocurrent measurements with an oscilloscope. Emission from the irradiated phosphate buffered saline (PBS) also has been studied. The emission spectra from PBS at 12 and 77 K show a maximum around 330 and 380 nm, respectively, which are the same spectra as those from irradiated pure H₂O. The emission from irradiated GHE consists of the new band at 480 nm in addition to the emission from H₂O. The 480 nm emission is observed at the temperature range of 12–300 K, though the emission at 300 K is much lower than that at low temperature. The 480 nm emission is ascribed to the transition from excited organic substances in GHE cells. The intensity of 480 nm emission at 300 K increases linearly with increasing irradiation-dose in the range of 11–600 Gy.     

Mechanism of the CO oxidation reaction on O-precovered Pt(111) surfaces studied with near-edge x-ray absorption fine structure spectroscopy

The mechanism of CO oxidation reaction on oxygen-precovered Pt(111) surfaces has been studied by using time-resolved near-edge x-ray absorption fine structure spectroscopy. The whole reaction process is composed of two distinct paths: (1) a reaction of isolated oxygen atoms with adsorbed CO, and (2) a reaction of island-periphery oxygen atoms after the CO saturation. CO coadsorption plays a role to induce the dynamic change in spatial distribution of O atoms, which switches over the two reaction paths. These mechanisms were confirmed by kinetic Monte Carlo simulations. The effect of coadsorbed water in the reaction mechanism was also examined.     

A twin optically-pumped far-infrared CH3OH laser for plasma diagnostics

A twin optically-pumped far-infrared CH₃OH laser has been constructed for use in plasma diagnostics. The antisymmetric doublet due to the Raman-type resonant two-photon transition is reproducibly observed at 118.8 m. With the 118.8-m line, it is obtained from the frequency separation of the anti-symmetric doublet that CH₃OH absorption line center is 16±1 MHz higher than the pump 9.7-m P(36) CO₂ laser line center. It is shown that the Raman-type resonant two-photon transition is useful in order to get several-MHz phase modulation for the far-infrared laser interferometer. Some preliminary performances of this twin laser for the modulated interferometer are described.This work was carried out under the collaborating research program at the Institute of Plasma Physics, Nagoya University, Nagoya 464, Japan.     

Study of adsorption of methylene blue and new methylene blue in liquid-solid interface by slab optical waveguide spectroscopy

A slab optical waveguide (SOWG) has been used for study of adsorption of both methylene blue (MB) and new methylene blue (NMB) in liquid–solid interface. Adsorption characteristics of MB and NMB on both bare SOWG and silanized SOWG by octadecyltrichlorosilane (ODS) were compared. Effect of pH on adsorption on MB and NMB was investigated. Binding rate constant analysis showed that both MB and NMB on bare SOWG demonstrates larger association constants than those on ODS-SOWG. Interactions of MB and NMB on bare SOWG and ODS-SOWG were analyzed by molecular mechanics calculation method. The binding energy change was in the following order: E_NMB–bare > E_MB–bare > E_NMB–ODS > E_MB–ODS.     

Geometrical Evolution and Formation of the Photoproduct in the Cycloreversion Reaction of a Diarylethene Derivative Probed by Vibrational Spectroscopy

The geometrical evolution of the reactant and formation of the photoproduct in the cycloreversion reaction of a diarylethene derivative were probed using time-resolved absorption spectroscopies in the visible to near-infrared and mid-infrared regions. The time-domain vibrational data in the visible region show that the initially formed Franck-Condon state is geometrically relaxed into the minimum in the excited state potential energy surface, concomitantly with the low-frequency coherent vibrations. Theoretical calculations indicate that the nuclear displacement in this coherent vibration is nearly parallel to that in the geometrical relaxation. Time-resolved mid-infrared spectroscopy directly detected the formation of the open-ring isomer with the same time constant as the decrease of the closed-ring isomer in the excited state minimum. This observation reveals that no detectable intermediate, in which the population is accumulated, is present between the excited closed-ring isomer and the open-ring isomer in the ground state.