IMEX Runge–Kutta schemes for reaction–diffusion equations

A fundamental research is carried out into convergence and stability properties of IMEX (implicit–explicit) Runge–Kutta schemes applied to reaction–diffusion equations. It is shown that a fully discrete scheme converges if it satisfies certain conditions using a technique of the B-convergence analysis, developed by Burrage, Hundsdorfer and Verwer in 1986. Stability of the schemes is also examined on the basis of a scalar test equation, proposed by Frank, Hundsdorfer and Verwer in 1997.     

Uniform perfectness of the limit sets of Kleinian groups

In this note, we show, in a quantitative fashion, that the limit set of a non-elementary Kleinian group is uniformly perfect if the quotient orbifold is of Lehner type, i.e., if the space of integrable holomorphic quadratic differentials on it is continuously contained in the space of (hyperbolically) bounded ones. This result covers the known case when the group is analytically finite. As applications, we present estimates of the Hausdorff dimension of the limit set and the translation lengths in the region of discontinuity for such a Kleinian group. Several examples will also be given.

     

Interfacial structure of oxidized inner pores in precursor-derived Si–C–N ceramics

Inner pore channels were commonly found in precursor-derived Si–C–N ceramics. After annealing in air at 1420 °C, their oxidation structures were investigated by analytical TEM. A carbon-rich ring was frequently observed under the silica layer inside the pore channels, which consisted of graphite-like clusters in size of 20–30 nm. Origin of such interfacial structure is due to the excessive free-carbon in the amorphous Si–C–N matrix that had survived the oxidation process. This graphitic interface could further improve the oxidation resistance of the SiO₂ over-layer. This novel interfacial structure was also found by annealing in N₂, reaffirming the effect of composition of Si–C–N matrix.     

Effect of poly(butylene succinate) crystals on spherulitic growth of poly(ethylene oxide) in binary blends of the two substances

The effects of the lamellar growth direction, extinction rings, and spherulitic boundaries of poly(butylene succinate) (PBSU) on the spherulitic growth of poly(ethylene oxide) (PEO) were investigated in miscible blends of the two crystalline polymers. In the crystallization process from a homogeneous melt, PBSU first developed volume‐filling spherulites, and then PEO spherulites nucleated and grew inside the PBSU spherulites. The lamellar growth direction of PEO was identical with that of PBSU even when the PBSU content was about 5 wt %. PEO, which intrinsically does not exhibit banded spherulites, showed apparent extinction rings inside the banded spherulites of PBSU. The growth rate of a PEO spherulite, G_PEO, was influenced not only by the blend composition and the crystallization temperature of PEO, but also by the growth direction with respect to PBSU lamellae, the boundaries of PBSU spherulites, and the crystallization temperature of PBSU, T_PBSU. The value of G_PEO first increased with decreasing T_PBSU when a PEO spherulite grew inside a single PBSU spherulite. Then, G_PEO decreased when T_PBSU was further decreased and a PEO spherulite grew through many tiny PBSU spherulites. This behavior was discussed based on the aforementioned factors affecting G_PEO. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 539–547, 2009     

Synthesis and reactions of benzopentathiepin having hydroxyl group

The synthesis of benzopentathiepin having a hydroxyl group at the neighboring position of polysulfur ring was performed by demethylation of 6-ethyl-9-methoxybenzopentathiepin with hydrogenbromide. Benzotrithiole having hydroxyl group was not isolated at all. The hydroxyl group was also alkylated with alkyl iodide in the presence of weak base.