Momentum and heat transfer over a continuous moving surface in a non-Darcian fluid

The momentum and heat transfer characteristics associated with the boundary layer on a continuous moving flat surface in a non-Darcian fluid have been investigated exploiting a local similarity solution procedure. The full boundary layer equations, which describe the effects of convective inertia, solid boundary, and porous inertia in addition to the Darcy flow resistance, were solved using novel transformed variables, deduced from a scale analysis on the momentum and energy conservation equations. Details are provided for the effects of convective inertia and porous inertia on the velocity and temperature profiles. The resulting friction and heat transfer characteristics are found to be substantially different from those of forces convection over a stationary flat plate. Furthermore, useful asymptotic expressions for the local Nusselt number are presented in consideration of possible physical limiting conditions.     

Buoyancy-induced flow of non-Newtonian fluids over a non-isothermal body of arbitrary shape in a fluid-saturated porous medium

The buoyancy-induced flows of non-Newtonian fluids over non-isothermal bodies of arbitrary shape within saturated porous media have been treated using the boundary layer approximations and the power-law model to characterize the non-Newtonian fluid behavior. Upon introducing a general similarity transformation which considers both the geometrical effect and the wall temperature effect on the development of the boundary layer length scale, the governing equations for a non-isothermal body of arbitrary shape have been reduced to those for a vertical flat plate. The transformed equations reveal that a plane or axisymmetric body of arbitrary shape possesses its corresponding family of the wall temperature distributions which permit similarity solutions. Numerical integrations were carried out using the Runge-Kutta-Gill method, and the results of the heat transfer function were presented once for all plane and axisymmetric bodies. As illustrations, local wall heat flux distributions were discussed for wedges, cones, spheres, circular cylinders and other geometries. Furthermore, an approximate formula based on the Karman-Pohlhausen integral relation has been presented for speedy and sufficiently accurate estimation of heat transfer rates.     

Free convection in a saturated porous medium beyond the similarity solution

The non-similar problems associated with a non-isothermal vertical flat plate embedded in a fluid-saturated porous medium were considered to assess the performances of the two distinctive boundary layer solution methods, namely, the local similarity solution and the integral method. The results generated from these two approximate solution methods are compared against the results from a two-point finite difference and those based on a Merk-type series expansion. Comparison of the results reveals that both integral and local similarity methods perform excellently. Especially, the accuracy acquired by the local similarity solution is so high that the difference between the results from the local similarity solution and those from the two-point finite difference and local non-similarity solution methods is hardly discernible for the case of monotonic increasing wall temperature.     

In Situ Transmission Electron Microscopy Observation of Melted Germanium Encapsulated in Multilayer Graphene

Germanene is a two-dimensional germanium (Ge) analogous of graphene, and its unique topological properties are expected to make it a material for next-generation electronics. However, no germanene electronic devices have yet been reported. One of the reasons for this is that germanene is easily oxidized in air due to its lack of chemical stability. Therefore, growing germanene at solid interfaces where it is not oxidized is one of the key steps for realizing electronic devices based on germanene. In this study, the behavior of Ge at the solid interface at high temperatures is observed by transmission electron microscopy (TEM). To achieve such in situ heating TEM observation, this work fabricates a graphene/Ge/graphene encapsulated structure. In situ heating TEM experiments reveal that Ge like droplets move and coalesce with other Ge droplets, indicating that Ge remains as a liquid phase between graphene layers at temperatures higher than the Ge melting point. It is also observed that Ge droplets incorporate the surrounding amorphous Ge as Ge nuclei, thereby increasing its size (domain growth). These results indicate that Ge crystals can be grown at the interface of van der Waals materials, which will be important for future germanene growth at solid interfaces.     

Selective sorption of iodide onto organo-MnO2 film and its electrochemical desorption and detection

This paper reports an electrochemically grown film consisting of layered MnO₂ intercalated with hexadecylpyridinium cations (HDPy⁺), which can selectively sorb and detect iodide anions in aqueous solution amperometrically. Sorption of iodide by the HDPy/MnO₂ film did not occur via ion exchange, but through hydrophobic interactions between the interlayer organic phase of the film and iodide ions in solution. The sorption rate increased with the deposited amount of MnO₂. During the sorption process, the interlayer spaces expanded, and new diffraction peaks appeared that were attributed to the incorporated species. Anodic polarization of the iodide-sorbed HDPy/MnO₂ film led to electron transfer from the incorporated iodide to the underlying substrate through the MnO₂ sheets. The oxidized iodide was expelled from the film as molecular I₂, while the expanded interlayer spaces were restored to their original state. Thus, the MnO₂ layers and the incorporated HDPy can synergistically sorb/desorb iodide anions, resulting in a unique “self-cleaning” function that can operate electrochemically. This property allowed amperometric detection of iodide at a concentration as low as 0.0186 μM, which was below the detection limits reported for previous iodide sensors.     

Quaternary ammonium salt-catalyzed carboxylative cyclization of propargylic amines with CO2

By employing quaternary ammonium salts as catalysts, the carboxylative cyclization of the propargylic amines with CO₂ proceeded to afford the corresponding 2-oxazolidinones. In particular, tetra-n-butylammonium fluoride was the most effective catalyst for the reaction, providing a 2-oxazolidinone derivative in a maximum chemical yield of 99%. From a screening of the structure of a catalyst, it was found that both a quaternary ammonium cation and a basicity of the counter anion were essential to catalyze the carboxylative cyclization of the propargylic amines with CO₂.     

Extraction of weak transition strengths via the (3He, t) reaction at 420 MeV

Differential cross sections for transitions of known weak strength were measured with the (3He, t) reaction at 420 MeV on targets of 12C, 13C, 18O, 26Mg, 58Ni, 60Ni, 90Zr, 118Sn, 120Sn, and 208Pb. Using these data, it is shown that the proportionalities between strengths and cross sections for this probe follow simple trends as a function of mass number. These trends can be used to confidently determine Gamow-Teller strength distributions in nuclei for which the proportionality cannot be calibrated via beta-decay strengths. Although theoretical calculations in the distorted-wave Born approximation overestimate the data, they allow one to understand the main experimental features and to predict deviations from the simple trends observed in some of the transitions.     

Some remarks on the odd hadwiger’s conjecture

We say that H has an odd complete minor of order at least l if there are l vertex disjoint trees in H such that every two of them are joined by an edge, and in addition, all the vertices of trees are two-colored in such a way that the edges within the trees are bichromatic, but the edges between trees are monochromatic. Gerards and Seymour conjectured that if a graph has no odd complete minor of order l, then it is (l ? 1)-colorable. This is substantially stronger than the well-known conjecture of Hadwiger. Recently, Geelen et al. proved that there exists a constant c such that any graph with no odd K _k -minor is ck√logk-colorable. However, it is not known if there exists an absolute constant c such that any graph with no odd K _k -minor is ck-colorable. Motivated by these facts, in this paper, we shall first prove that, for any k, there exists a constant f(k) such that every (496k + 13)-connected graph with at least f(k) vertices has either an odd complete minor of size at least k or a vertex set X of order at most 8k such that G–X is bipartite. Since any bipartite graph does not contain an odd complete minor of size at least three, the second condition is necessary. This is an analogous result of Böhme et al. We also prove that every graph G on n vertices has an odd complete minor of size at least n/2α(G) ? 1, where α(G) denotes the independence number of G. This is an analogous result of Duchet and Meyniel. We obtain a better result for the case α(G)= 3.     

Four-wave parametric oscillation in sodium vapor by electromagnetically induced diffraction

We have observed a novel type of parametric oscillation in sodium atomic vapor where four off-axis signal waves simultaneously build up under resonant and counterpropagating pump beams with elliptical beam profiles. The four waves, two of them Stokes shifted and the other two anti-Stokes shifted, have similar output powers of up to 10 mW with a conversion efficiency of 30% and are parametrically coupled by electromagnetically induced diffraction.