A formal construction of a divergence-free basis in the nonconforming virtual element method for the Stokes problem

Numerical Algorithms - We develop a formal construction of a pointwise divergence-free basis in the nonconforming virtual element method of arbitrary order for the Stokes problem introduced in Zhao...     

Key Role of a-Top CO on Terrace Sites of Metallic Pd Clusters for CO Oxidation

Pd-based catalysts are the most widely used for CO oxidation because of their outstanding catalytic activity and thermal stability. However, fundamental understanding of the detailed catalytic processes occurring on Pd-based catalysts under realistic conditions is still lacking. In this study, we investigated CO oxidation on metallic Pd clusters supported on Al₂O₃ and SiO₂. High-angle annular dark-field scanning transmission electron microscopy revealed the formation of similar-sized Pd clusters on Al₂O₃ and SiO₂. In contrast, CO chemisorption analysis indicated a gradual change in the dispersion of Pd (from 0.79 to 0.2) on Pd/Al₂O₃ and a marginal change in the dispersion (from 0.4 to 0.24) on Pd/SiO₂ as the Pd loading increased from 0.27 to 5.5 wt %; these changes were attributed to differences in the metal-support interactions. Diffuse reflectance infrared Fourier-transform spectroscopy revealed that fewer a-top CO species were present in Pd supported on Al₂O₃ than those in Pd supported on SiO₂, which is related to the morphological differences in the metallic Pd clusters on these two supports. Despite the different dispersion profiles and surface characteristics of Pd, O₂ titration demonstrated that linearly bound CO (with an infrared signal at 2090 cm⁻¹) reacted first with oxygen in the case of CO-saturated Pd on Al₂O₃ and SiO₂, which suggests that a-top CO on the terrace site plays an important role in CO oxidation. The experimental observations were corroborated by periodic density functional calculations, which confirmed that CO oxidation on the (111) terrace sites is most plausible, both kinetically and thermodynamically, compared to that on the edge or corner sites. This study will deepen the fundamental understanding of the effect of Pd clusters on CO oxidation under reaction conditions.     

On translation lengths of Anosov maps on the curve graph of the torus

Geometriae Dedicata - We show that an Anosov map has a geodesic axis on the curve graph of the torus. The direct corollary of our result is the stable translation length of an Anosov map on the...     

All-solid-state carbonate-selective electrode based on a molecular tweezer-type neutral carrier with solvent-soluble conducting polymer solid contact

Carbonate-selective membranes were prepared by incorporating a molecular tweezer-type carbonate-selective neutral carrier [N,N-dioctyl-3alpha,12alpha-bis(4-trifluoroacetylbenzyloxy)-5beta-cholan-24-amide] into a room temperature vulcanizing-type silicone rubber (3140 RTV-SR) matrix, and deposited on the planar-type electrodes (Pt containing Ag/AgCl electrodes formed on a ceramic plate) with and without an intermediary conducting polymer layer. Two types of solvent-soluble conducting polymers [poly(1-hexyl-3,4-dimethyl-2,5-pyrrolylene) or poly(3-octylthiophene-2,5-diyl)] have been examined as the solid contact material. Potentiometric properties of the resultant all-solid-state electrodes were evaluated in terms of their carbonate selectivity, response slope, potential stability and reproducibility. The sensitivity and carbonate selectivity of the SR membrane-based all-solid-state electrodes with conducting polymer solid contact were comparable to those of conventional electrodes. Experimental results also showed that the intermediary conducting polymer layer used in the all-solid-state electrodes greatly reduces the interference from dissolved oxygen.     

Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems

We construct and analyze a mixed finite volume method on quadrilateral grids for elliptic problems written as a system of two first order PDEs in the state variable (e.g., pressure) and its flux (e.g., Darcy velocity). An important point is that no staggered grids or covolumes are used to stabilize the system. Only a single primary grid system is adopted, and the degrees of freedom are imposed on the interfaces. The approximate flux is sought in the lowest-order Raviart-Thomas space and the pressure field in the rotated- nonconforming space. Furthermore, we demonstrate that the present finite volume method can be interpreted as a rotated- nonconforming finite element method for the pressure with a simple local recovery of flux. Numerical results are presented for a variety of problems which confirm the usefulness and effectiveness of the method.

     

Synthesis of 2,3-disubstituted benzofurans on solid-support

A library of 2,3-disubstituted benzofuran scaffold was developed by using intramolecular Wittig olefination and Friedel-Crafts acylation.     

Reinvestigation of Ge4Se9 based on single‐crystal data

Tetra­germanium nona­selenide, Ge₄Se₉, adopts a two‐dimensional layered structure. The layer is made up of infinite chains of corner‐sharing GeSe₄ tetra­hedra and the chains are connected via the Ge₂Se₇ unit to form the two‐dimensional layer. These layers are stacked to form the three‐dimensional structure with a van der Waals gap. A previous structure report on Ge₄Se₉ based on powder diffraction data [Fjellvåg, Kongshaug & Stølen (2001). J. Chem. Soc. Dalton Trans. pp. 1043–1045] is comparable with our results except for the absolute structure determination.     

Gas permeability and n‐butane solubility of poly(1‐trimethylgermyl‐1‐propyne)

The gas permeability and n‐butane solubility in glassy poly(1‐trimethylgermyl‐1‐propyne) (PTMGP) are reported. As synthesized, the PTMGP product contains two fractions: (1) one that is insoluble in toluene and soluble only in carbon disulfide (the toluene‐insoluble polymer) and (2) one that is soluble in both toluene and carbon disulfide (the toluene‐soluble polymer). In as‐cast films, the gas permeability and n‐butane solubility are higher in films prepared from the toluene‐soluble polymer (particularly in those films cast from toluene) than in films prepared from the toluene‐insoluble polymer and increase to a maximum in both fractions after methanol conditioning. For example, in as‐cast films prepared from carbon disulfide, the oxygen permeability at 35 °C is 330 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐soluble polymer and 73 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐insoluble polymer. After these films are conditioned in methanol, the oxygen permeability increases to 5200 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐soluble polymer and 6200 × 10^?10 cm³ (STP) cm/(cm² s cmHg) for the toluene‐insoluble polymer. The rankings of the fractional free volume and nonequilibrium excess free volume in the various PTMGP films are consistent with the measured gas permeability and n‐butane solubility values. Methanol conditioning increases gas permeability and n‐butane solubility of as‐cast PTMGP films, regardless of the polymer fraction type and casting solvent used, and minimizes the permeability and solubility differences between the various films (i.e., the permeability and solubility values of all conditioned PTMGP films are similar). © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2228–2236, 2002     

Comparison of V‐cycle multigrid method for cell‐centered finite difference on triangular meshes

We consider a multigrid algorithm (MG) for the cell centered finite difference scheme (CCFD) on general triangular meshes using a new prolongation operator. This prolongation is designed to solve the diffusion equation with strongly discontinuous coefficient as well as with smooth one. We compare our new prolongation with the natural injection and the weighted operator in Kwak, Kwon, and Lee ( 8 ) and the behaviors of these three prolongation are discussed. Numerical experiments show that (i) for smooth problems, the multigrid with our new prolongation is fastest, the next is the weighted prolongation, and the third is the natural injection; and (ii) for nonsmooth problems, our new prolongation is again fastest, the next is the natural injection, and the third is the weighted prolongation. In conclusion, our new prolongation works better than the natural injection and the weighted operator for both smooth and nonsmooth problems. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006