Viscous coupling of shear-free turbulence across nearly flat fluid interfaces

The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs.

Stereochemically non-rigid helical mercury(II) complexes

Reactions of the 1: 2 condensate (L) of benzil dihydrazone and 2-acetylpyridine with Hg(ClO4)(2) center dot xH(2)O and HgI2 yield yellow [HgL2](ClO4)(2) (1) and HgLI2 (2), respectively. Homoleptic 1 is a 8-coordinate double helical complex with a Hg(II)N-8 core crystallising in the space group Pbca with cell dimensions: a = 16.2250(3), b = 20.9563(7), c = 31.9886(11) angstrom. Complex 2 is a 4-coordinate single helical complex having a Hg(II)N2I2 core crystallising in the space group P2(1)/n with cell dimensions a = 9.8011(3), b = 17.6736(6), c = 16.7123(6) angstrom and b = 95.760(3). In complex 1, the N-donor ligand L uses all of its binding sites to act as tetradentate. On the other hand, it acts as a bidentate N-donor ligand in 2 giving rise to a dangling part. From variable temperature H-1 NMR studies both the complexes are found to be stereochemically non-rigid in solution. In the case of 2, the solution process involves wrapping up of the dangling part of L around the metal. (C) 2008 Elsevier B.V. All rights reserved.

Reducing implicit prejudice by blurring intergroup boundaries

In two experiments we examined whether and when blurring intergroup boundaries reduces implicit prejudice. In Experiment 1 we observed that when participants first completed a task in which they generated characteristics that overlapped between an ingroup and an outgroup they showed less implicit bias as measured by an Implicit Association Test. In Experiment 2 we found that the effectiveness of blurring intergroup boundaries for reducing implicit bias was moderated by pretask levels of ingroup identification. We discuss these findings in the context of extending differentiation-based interventions for reducing explicit bias to the domain of implicit attitudes.

Planning rigid body motions using elastic curves

This paper tackles the problem of computing smooth, optimal trajectories on the Euclidean group of motions SE(3). The problem is formulated as an optimal control problem where the cost function to be minimized is equal to the integral of the classical curvature squared. This problem is analogous to the elastic problem from differential geometry and thus the resulting rigid body motions will trace elastic curves. An application of the Maximum Principle to this optimal control problem shifts the emphasis to the language of symplectic geometry and to the associated Hamiltonian formalism. This results in a system of first order differential equations that yield coordinate free necessary conditions for optimality for these curves. From these necessary conditions we identify an integrable case and these particular set of curves are solved analytically. These analytic solutions provide interpolating curves between an initial given position and orientation and a desired position and orientation that would be useful in motion planning for systems such as robotic manipulators and autonomous-oriented vehicles.

Dimetallic complexes of macrocycles with two rigid dibenzofuran units as receptors for detection of anionic substrates

The hexaazamacrocycles [28](DBF)2N6 {cyclo[bis(4,6-dimethyldibenzo[b,d]furaniminoethyleneiminoethylene]} and [32](DBF)2N6 {cyclo[bis(4,6-dimethyldibenzo[b,d]furaniminopropyleneiminopropylene]} form stable dinuclear copper(II) complexes suitable to behave as receptors for several anionic substrates. These two receptors were used to study the binding interactions with several substrates, such as imidazole (Him) and some carboxylates [benzoate (bz−), oxalate (ox2−), malonate (mal2−), phthalate (ph2−), isophthalate (iph2−), and terephthalate (tph2−)] by spectrophotometric titrations and EPR spectroscopy in MeOH (or H2O):DMSO (1:1 v/v) solution. The largest association constant was found for ox2− with Cu2[32](DBF)2N64+, whereas for the aromatic dicarboxylate anions the binding constants follow the trend ph2− > iph2− > tph2−, i.e. decrease with the increase of the distance of the two binding sites of the substrate. On the other hand, the large blue shift of 68 nm observed by addition of Him to Cu2[32](DBF)2N64+ points out for the formation of the bridged CuimCu cascade complex, indicating this receptor as a potential sensor for the detection and determination of imidazole in solution. The X-band EPR spectra of the Cu2[28](DBF)2N64+ and Cu2[32](DBF)2N6]4+ complexes and the cascade complexes with the substrates, performed in H2O:DMSO (1:1 v/v) at 5 to 15 K, showed that the CuCu distance is slightly larger than the one found in crystal state and that this distance increases when the substrate is accommodated between the two copper centres. The crystal structure of [Cu2[28](DBF)2N6(ph)2]·CH3OH was determined by X-ray diffraction and revealed the two copper centres bridged by two ph2− anions at a Cu···Cu distance of 5.419(1) Å. Each copper centre is surrounded by three carboxylate oxygen atoms from two phthalate anions and three contiguous nitrogen atoms of the macrocycle in a pseudo octahedral coordination environment.

Rigid ferrocenophane and its metal complexes with transition and alkaline-earth metal ions

The rigid [6]ferrocenophane, L-1, was synthesised by condensation of 1,1'-ferrocene dicarbaldehyde with trans-1,2-diaminocyclohexane in high dilution at r.t. followed by reduction. When other experimental conditions were employed, the [6,6,6]ferrocenephane (L-2) was also obtained. Both compounds were characterised by single crystal X-ray crystallography. The protonation of L-1 and its metal complexation were evaluated by the effect on the electron-transfer process of the ferrocene (fc) unit of L-1 using cyclic voltammetry (CV) and square wave voltammetry (SWV) in anhydrous CH3CN solution and in 0.1 M (Bu4NPF6)-Bu-n as the supporting electrolyte. The electrochemical process of L-1 between 300 and 900 mV is complicated by amine oxidation. On the other hand, an anodic shift from the fc/fc(+) wave of L-1 of 249, 225, 81 and 61 mV was observed by formation of Zn2+, Ni2+, Pd2+ and Cu2+ complexes, respectively. Whereas Mg2+ and Ca2+ only have with L-1 weak interactions and they promote the acid-base equilibrium of L-1. This reveals that L-1 is an interesting molecular redox sensor for detection of Zn2+ and Ni2+, although the kinetics of the Zn2+ complex formation is much faster than that of the Ni2+ one. The X-ray crystal structure of [(PdLCl2)-Cl-1] was determined and showed a square-planar environment with Pd(II) and Fe(II) centres separated by 3.781(1) angstrom. The experimental anodic shifts were elucidated by DFT calculations on the [(MLCl2)-Cl-1] series and they are related to the nature of the HOMO of these complexes and a four-electron, two-orbital interaction.

Peptidomimetic design of unusual turns by incorporating flexible and rigid omega-amino acids simultaneously

The tripeptides Boc-Gly-Aib-m-ABA-OMe (I), Boc-beta Ala-Aib-m-ABA-OMe (II) and Boc-gamma Abu-Aib-rn-ABA-OMe (III) (Aib: alpha-aminoisobutyric acid, beta Ala: beta-alanine, gamma Abu: gamma-aminobutyric acid, m-ABA: meta-aminobenzoic acid) with homologated amino acids at the N-terminus, the rigid gamma-amino acid m-ABA at the C-terminus and the helicogenic Aib at the central position have been chosen to create unusual turns. Single crystal X-ray diffraction studies, solvent dependent NMR titrations and 2D NMR analysis reveal that peptides II and III adopt unusual turns of 11- and 12-membered rings stabilized by modified 4 -> 1 type intramolecular hydrogen bonds. Solution phase studies indicate that peptide I exists in the beta-turn conformation stabilized by 10-membered intramolecular hydrogen bonding.

Marks, spaces and boundaries

Dictionary compilers and designers use punctuation to structure and clarify entries and to encode information. Dictionaries with a relatively simple structure can have simple typography, and simple punctuation; as dictionaries grew more complex, and encountered the space constraints of the printed page, complex encoding systems were developed, using punctuation and symbols. Two recent trends have emerged in dictionary design: to eliminate punctuation, and sometimes to use a larger number of fonts, so that the boundaries between elements are indicated by font change, not punctuation.