Smooth Solution of the Compressible Navier–Stokes Equations in an Unbounded Domain with Inflow Boundary Condition

The barotropic compressible Navier–Stokes equations in an unbounded domain are studied. We prove the unique existence of the solution (u, p) of the system (1.1) in the Sobolev spaceH^{k + 3} × H^{k + 2}provided that the derivatives of the data of the problem are sufficiently small, wherek ≥ 0 is any integer. The proof follows from an analysis of the linearized problem, the solvability of the continuity equation, and the Schauder fixed point theory. Similar smoothness results are obtained for a linearized form of (1.1).     

Asymmetric synthesis of homo-apioneplanocin A from d-ribose

Homo-apioneplanocin A was efficiently synthesized via stereoselective hydroxymethylation, regio- and chemoselective hydroboration, and chemoselective oxidation as key steps from d-ribose.     

Transformation of highly ordered large pore silica mesophases (Fm3m, Im3m and p6mm) in a ternary triblock copolymer-butanol-water system

Exceptional control of the phase behavior of highly ordered large pore mesostructured silica (with the choice of Fm3m, Im3m or p6mm symmetry) is achieved using a triblock copolymer (EO(106)PO(70)EO(106)) and butanol at low acid concentrations.     

Controlled polymerization in mesoporous silica toward the design of organic-inorganic composite nanoporous materials

Free-radical polymerization inside mesoporous silica has been investigated in order to open a route to functional polymer-silica composite materials with well-defined mesoporosity. Various vinyl monomers, such as styrene, chloromethyl styrene, 2-hydroxyethyl methacrylate, and methacrylic acid, were polymerized after impregnation into mesoporous silicas with various structures, which were synthesized using polyalkylene oxide-type block copolymers. The location of the polymers was systematically controlled with detailed structures of the silica framework and the polymerization conditions. Particularly noteworthy is the polymer-silica composite structure obtained by in situ polymerization after the selective adsorption of monomers as a uniform film on silica walls. The analysis of XRD data and the N(2) adsorption isotherms indicates the formation of uniform polymer nanocoating. The resultant polymer-silica composite materials can easily be post-functionalized to incorporate diverse functional groups in high density, due to the open porous structure allowing facile access for the chemical reagent. The fundamental characteristics of the composite materials are substantiated by testing the biomolecule's adsorption capacity and catalytic reactivity. Depending on the structure and composition of polymers, the resultant polymer-silica composite materials exhibit notably distinct adsorption properties toward biomolecules, such as proteins. Furthermore, it is demonstrated that the nanocoatings of polymers deposited on the mesopore walls have remarkably enhanced catalytic activity and selectivity, as compared to that of bulk polymer resins. We believe that, due to facile functionalization and attractive textural properties, the mesoporous polymer-silica composite materials are very useful for applications, such as adsorption, separation, host-guest complexes, and catalysis.     

Electrostatically stabilized metal oxide particle dispersions in carbon dioxide

We report electrostatic stabilization of micrometer-sized TiO(2) particles at long range (several micrometers) in liquid and supercritical CO(2) despite the ultralow dielectric constant, as low as 1.5. The counterions were solubilized in dry reverse micelles, formed with a low-molecular weight cationic perfluoropolyether trimethylammonium acetate surfactant, to prevent ion pairing with the particle surface. Dynamic light scattering and settling velocities indicate a particle diameter of 620-740 nm. The electrophoretic mobility of -2.3 x 10(-8) m(2)/V s indicated a particle charge on the order of -1.7 x 10(-17) C, or 105 elementary negative charges per particle. The balance of particle compression by an electric field versus electrostatic repulsion generated an amorphous arrangement of particles with 5-9 mum spacing, indicating Debye lengths greater than 1 mum. Scattering patterns also indicate that chains of particles may be achieved in CO(2) by dielectrophoresis with alternating fields. The electrostatic stabilization has been achieved by solubilizing a small concentration of counterions in only a small fraction of the reverse micelles in the double layer. Whereas many low-molecular weight surfactants have been shown to form reverse micelles in CO(2), very few polymers are able to stabilize micrometer-sized colloids sterically. Thus, electrostatic stabilization has the potential to expand markedly the domain of colloid science in apolar supercritical fluids.     

Edge Singular Behavior for the Heat Equation on Polyhedral Cylinders in \boldsymbol{\mathbb{R}}^{\bf 3}

We study the Heat equation in the polyhedral cylinder with a non-convex edge. We construct the singularity functions depending on the time and edge axis, and the coefficient of the singularity, called the stress intensity distributions, and show regularity results for the solution and the coefficient. The regularity is achieved in the (not weighted) Sobolev space in the L² and L ^q spaces, respectively. An application to the finite polyhedral cylinder is described.     

Facile Fabrication of Multi‐targeted and Stable Biochemical SERS Sensors

The direct transfer of single‐crystalline Au nanowires (NWs) onto Au substrates was achieved by a simple attachment and detachment process. In the presence of a lubricant, Au NWs grown vertically on a sapphire substrate were efficiently moved to an Au substrate through van der Waals interactions. We demonstrate that the transferred Au NWs on the Au substrate can act as sensitive, reproducible, and long‐term‐stable surface‐enhanced Raman scattering (SERS) sensors by detecting human α‐thrombin as well as Pb²⁺ and Hg²⁺ ions. These three biochemically and/or environmentally important analytes were successfully detected with high sensitivity and selectivity by Au NW‐SERS sensors bound by a thrombin‐binding aptamer. Furthermore, the as‐prepared sensors remained in working order after being stored under ambient conditions at room temperature for 80 days. Because Au NWs can be routinely transferred onto Au substrates and because the resultant Au NW‐SERS sensors are highly stable and provide with high sensitivity and reproducibility of detection, these sensors hold potential for practical use in biochemical sensing.     

Effect of aspect ratio of vertically aligned copper nanowires in the presence of cellulose nanofibers on the thermal conductivity of epoxy composites

The composites comprising vertically aligned network of copper nanowires (CuNWs) in the presence of cellulose nanofibers were fabricated by using the freeze‐templating method and the effect of aspect ratio (A/R) of CuNWs on the thermal conductivity of epoxy composites was investigated. The thermal conductivity of epoxy composites increased to 0.79 W m^?1 K^?1 at 1.12 vol% of high A/R CuNWs loading, corresponding to the thermal conductivity enhancement of 365% as compared to the pure epoxy. The thermal conductivity of vertically aligned higher A/R CuNWs/epoxy, which is 38.5% and 51.9% higher than those of the lower A/R CuNWs and the randomly aligned CuNWs, respectively. The application of the epoxy composites in heat dissipation was demonstrated by the temperature changes of composites on a hot plate with the increase of heating time. These results indicate that the thermally conductive composites in this study could be applied for thermal dissipating materials in electronic devices.