On the birth of stall cells on airfoils

Critical point theory asserts that two-dimensional topologies are defined as degeneracies and any three-dimensional disturbance of a two-dimensional flow will lead to a new three-dimensional flowfield topology, regardless of the disturbance amplitude. Here, the topology of the composite flowfields reconstructed by linear superposition of the two-dimensional flow around a stalled airfoil and the leading stationary three-dimensional global eigenmode has been studied. In the conditions monitored the two-dimensional flow is steady and laminar and is separated over a fraction of the suction side, while the amplitudes considered in the linear superposition are small enough for the linearization assumption to be valid. The multiple topological bifurcations resulting have been analysed in detail; the surface streamlines generated by the leading stationary global mode of the separated flow have been found to be strongly reminiscent of the characteristic stall cells, observed experimentally on airfoils just beyond stall in both laminar and turbulent flow.     

A density version of the Halpern–Läuchli theorem

We prove a density version of the Halpern–Läuchli Theorem. This settles in the affirmative a conjecture of R. Laver.     

Low‐frequency scattering by a penetrable body with an eccentric soft or hard core

A plane wave is scattered by an acoustically soft or hard sphere, covered by a penetrable non‐concentric spherical lossless shell that disturbs the propagation of the incident wave field. The dimensions of the coated sphere are much smaller than the wavelength of the incident field. Low‐frequency theory reduces this scattering problem to a sequence of potential problems, which can be solved iteratively. Exactly one bispherical coordinate system exists that fits the given geometry of the obstacle. For the case of a soft and hard core, the exact low‐frequency coefficients of the zeroth and the first‐order for the near field as well as the first‐ and second‐order coefficients for the normalized scattering amplitude are obtained and the cross sections are calculated. Discussion of the results and their physical meaning is included. Copyright © 2009 John Wiley & Sons, Ltd.     

Coordination-driven self assembly of a brilliantly fluorescent rhomboid cavitand composed of bodipy-dye subunits

The two sp(3) hybridized fluorine atoms of a Bodipy dye have been synthetically replaced with the linear donor ligand 4-ethynylpyridine (-C≡C-Py) to form a rigid and highly symmetrical 109.5° building block in which the fluorophore subunit is vertically aligned to the plane formed by the -C≡C-Py donors. Upon reaction of the above tecton with a 90° organoplatinum acceptor unit, an intensely fluorescent rhomboid cavitand was manifested in solution. In contrast to the vast majority of coordination-driven self-assembled chromophoric systems, the present one fully conserves the excellent photophysical properties of the parent Bodipy dye. These unique features of the present metallosupramolecular entity constitute a fascinating metal-to-ligand self-assembled prototype for building compact and intensely luminescent materials with host-guest capabilities.     

Solution of the second order linear differential equation

An integro-iteration method is applied to solve the second order linear differential equation. Although the procedure is quite elementary it produces the general solution in form of a simple series which can be made to converge absolutely, at least in the region of interest. Particular solutions with given initial or boundary values can be readily obtained from the general solution.     

Fundamental Solutions of Linear Differential Equations in the Sense of Mnemofunctions

In this paper we discuss the definition and construction of the fundamental solution of a linear differential equation with constant coefficients in the algebra of mnemofunctions. This algebra contains the tempered distributions. We also present some examples including a physical illustration of our results for the equation u = .     

Magnetism of cyano-bridged hetero-one-dimensional Ln3+-M3+ complexes (Ln3+ = Sm,Gd, Yb; M3+ = FeLS,Co)

The reaction of Ln(NO(3))(3).aq with K(3)[Fe(CN)(6)] or K(3)[Co(CN)(6)] and 2,2'-bipyridine in water led to five one-dimensional complexes: trans-[M(CN)(4)(mu-CN)(2)Ln(H(2)O)(4) (bpy)](n)().XnH(2)O.1.5nbpy (M = Fe(3+) or Co(3+); Ln = Sm(3+), Gd(3+), or Yb(3+); X = 4 or 5). The structures for [Fe(3)(+)-Sm(3+)] (1), [Fe(3)(+)-Gd(3+)] (2), [Fe(3)(+)-Yb(3+)] (3), [Co(3)(+)-Gd(3+)] (4), and [Co(3)(+)-Yb(3+)] (5) have been solved; they crystallize in the triclinic space P1 and are isomorphous. The [Fe(3+)-Sm(3+)] complex is a ferrimagnet, its magnetic studies suggesting the onset of weak ferromagnetic 3-D ordering at 3.5 K. The [Fe(3+)-Gd(3+)] interaction is weakly antiferromagnetic. The isotropic nature of Gd(3+) allowed us to evaluate the exchange interaction (J = 0.77 cm(-)(1)).     

New polyimide-polyaniline hollow fibers: Synthesis, characterization and behavior in gas separation

New polyimide-polyaniline hollow fibers were produced by dissolution of the polymers in NMP and dry/wet spinning of the resulting solution in a non-solvent (H₂O). The morphology and thermal properties of the fibers, were examined by means of SEM and TGA, and FTIR spectroscopy was used for the study of their chemical structure. Permeability and selectivity measurements in different gases (He, H₂, CH₄, CO₂, O₂ and N₂) were performed in order to evaluate the performance of the membrane in gas separation applications. The results indicate that the novel membrane is a well structured hollow fiber, thermally stable up to 500°. The introduction of polyaniline into the polyimide matrix, results in a great enhancement in fiber permeability (60-600 times) possibly due to increase of the total free volume due to the introduction of shorter polyaniline molecules in the matrix, allowing larger quantities of gases to pass through the composite membrane. Perm-selectivity ratios for the composite membranes H₂/CH₄, He/N₂, H₂/N₂ and H₂/CO₂ were found lower by a factor of 6.4, 8.9, 7.7 and 1.47, respectively, compared to membranes produced using only polyimide. The opposite effect was observed for CH₄/CO₂ and N₂/CO₂ perm-selectivity ratios that showed an increase by a factor of 3.52 and 5.2, respectively. The ratio CH₄/CO₂ is of particular interest for natural gas purification purposes.     

Characterization of the transport properties of membranes of uncertain macroscopic structural homogeneity

The present paper confirms and extends previous applications of an original method of time-lag analysis to (concentration-independent) gas permeation through porous pellets produced by uniaxial compaction of fine graphite powder. It is shown that this approach to the study of membrane permeability enables one to (i) detect unambiguously a macroscopic structural inhomogeneity affecting transport across the membrane (often present as an unsuspected artifact of the membrane fabrication process); (ii) determine appropriate average values of the resulting space-dependent diffusion, D(x), and sorption, S(x), coefficients (without recourse to equililibrium sorption measurements); (iii) secure substantial information about the functional form, as well as the degree, of variability of D(x) and S(x); and ultimately (iv) link this information to the underlying membrane structural inhomogeneity. In the present context, the salient underlying structural feature is nonuniform porosity across the membrane, represented by (x), and the link between D(x), S(x) and (x) is provided by the simple dual-mode (intrapore gas-phase + adsorbed-phase) model of sorption and transport in porous media. The effect of increasing overall pellet porosity (_obs) by reducing applied compacting pressure, was specifically studied and found to entail marked enhancement of the degree of structural inhomogeneity without material changes in the functional form of D(x), S(x) and hence of (x). The conclusions drawn from time-lag analysis were shown to be consistent with the observed behavior of apparent diffusion coefficients derived from transient-state sorption or permeation measurements and with the results of dual-mode steady-state permeation analysis. The latter results showed additionally that, for a more complete interpretation of observed transport behavior, the variability across the pellet of the orientation of graphite particles should also be taken into account.