Moduli Spaces of Higher Spin Curves and Integrable Hierarchies

We prove the genus zero part of the generalized Witten conjecture, relating moduli spaces of higher spin curves to Gelfand–Dickey hierarchies. That is, we show that intersection numbers on the moduli space of stable r-spin curves assemble into a generating function which yields a solution of the semiclassical limit of the KdV _r equations. We formulate axioms for a cohomology class on this moduli space which allow one to construct a cohomological field theory of rank r–1 in all genera. In genus zero it produces a Frobenius manifold which is isomorphic to the Frobenius manifold structure on the base of the versal deformation of the singularity A _r–1. We prove analogs of the puncture, dilaton, and topological recursion relations by drawing an analogy with the construction of Gromov–Witten invariants and quantum cohomology.     

Titanium Dioxide Nanoparticles Produced in Water-in-oil Emulsion

Titanium dioxide (titania) particles were prepared by a water-in-oil emulsion system, and studied for the photodecomposition property of methylene blue. Microemulsion (ME) consisted of water, cyclohexane or octane, and surfactant, such as polyoxyethylene (10) octylphenyl ether (TX-100), polyoxyethylene lauryl ether, or bis (2-ethylhexyl) sodium sulfosuccinate. Titanium tetraisopropoxide (TTIP) was dropped into the ME solution and then titania particles were formed by the hydrolysis reaction between TTIP in the organic solvent and the water in the core of ME. It was found that ME could be classified to the reversed micelle (RM) region and the swelling reversed micelle (SM) region according to the water content. The water droplets in RM were almost monodispersed, where the water content was small. On the other hand, the water droplets in SM had a size distribution, although most of the water molecules associated with surfactant molecules. The size of the particles prepared in the RM region was smaller than the ME size. In contrast, the size of the particles formed in the SM region was larger than the ME size, and coagulation of the particles was observed within a few hours. The smallest diameter of the particles was 2 nm in the system of cyclohexane with TX-100 surfactant when the molar ratio of water to surfactant was 2. Titania particles prepared in this condition were collected as amorphous powder, and converted to anatase phase at less than 500 K, which is lower than the ordinal phase transition temperature. These anatase phase titania particles only showed a significant photodecomposition of methylene blue by illumination with a Xenon lamp.     

Flow visualization of vortex structure of an excited coaxial jet

This paper describes the results of experimental and numerical studies concerning the near-field vortical structure and dynamics of a coaxial jet. The effect of excitation of annular and circular jets on the vortical structure in the inner and outer shear-layers was studied. The flow visualization and the measurements of mean and fluctuating velocities, by a hot-film probe and the particle image velocimetry (PIV) technique, were carried out in an open water tank. The results of flow visualization and numerical simulation are in good agreement. With the excitation of a half of the initial vortex frequency, it is found that the vortex-pairing event is promoted by the forced excitation and it results in the rapid expansion of the jet width and the increase of velocity fluctuation and the entrainment rate. For the velocity ratio near unity, the dominant peak frequency coincides with the initial vortex frequency, i.e., the lip wake vortex frequency, independent of the forced excitation frequency.     

Thermo-Optic Switch using Fluorinated Silicon Oxide and Organic Spin-on-Glass Films

A thermo-optic switch in a thin-film optical waveguide was investigated. Fluorinated silicon oxide (SiOF) and organic spin-on-glass (SOG) films were used as core-layer and clad-layer, respectively, in the waveguide structure. The SiOF films were formed at 23#x00B0;C by a liquid-phase deposition (LPD) technique using a supersaturated hydrofluosilicic acid (H₂SiF₆) aqueous solution. Thermal coefficients of the refractive indices for LPD-SiOF and organic SOG films formed on silicon (Si) substrates were #x2212;4.0 #x00D7; 10^#x2212;6/#x00B0;C, #x2212;60 #x00D7; 10^#x2212;6/#x00B0;C at the wavelength of 632.8 nm, respectively. A high extinction ratio of 15 dB was obtained for this switch at the applied voltage of 12.8 V.     

Suspension viscosity of colloidal crystals and liquids in exhaustively deionized aqueous suspensions coexisting with ion-exchange resins

 Viscosities of exhaustively deionized aqueous suspensions of colloidal silica spheres are measured with coexisting ion-exchange resins using an Ubbelohde-type viscometer. The reduced viscosities of small silica spheres (56.3 nm in diameter) with and without resins decrease as the sphere concentration increases. However, the former are larger than the latter especially at low sphere concentrations. The reduced viscosities of other silica spheres, 81.2, 103, 110 and 136 nm in diameter, with resins decrease as the sphere concentration increases, whereas those without resins increase especially at low sphere concentrations. The significant effect of the extent of deionization upon the viscometric properties supports the important role of the extended electrical double layers formed around the colloidal spheres. Received: 28 October 1999 Accepted: 24 December 1999     

Controlling the thermomechanical properties of biobased ABA triblock copolymers comprising polylactide (A) and poly(1,2-propylene succinate) (B) with high molecular weight

Bis-hydroxyl-terminated poly(1,2-propylene succinate) (PPS-diols) with high molecular weight (10–40 kDa) are prepared by two-step melt polycondensation of succinic acid and 1,2-propanediol with Ti(BuO)₄ as the catalyst. By using these PPS-diols as macroinitiators, the ring-opening polymerization of d - and l -lactides is readily conducted to obtain enantiomeric ABA triblock copolymers consisting of poly(l -lactide) and PPS (B) (t-l -PPS) as well as those of poly(d -lactide) and PPS (B) (t-d -PPS) which have higher PPS compositions (20–70 wt%) in addition to high molecular weight (20–80 kD). The T_g, T_m, and ΔH_m values of the t-l -PPS copolymers as well as the stereo mixtures of t-l -PPS/t-d -PPS are controlled to linearly decrease with increasing the PPS content. The copolymers also exhibit higher elastomeric properties with increasing the PPS content. The tensile properties of the copolymer films having higher PPS contents (both the single block copolymers and stereo mixtures) are comparable to those of the oil-based thermoplastic elastomers. It is therefore concluded that these block copolymers can afford thermoplastic elastomers or flexible plastic materials having a 100% biobased content.