Polyoxometalate Derivatives with Multiple Organic Groups. 3. Synthesis and Structure of Bis(phenyltin) Bis(decatungstosilicate), [(PhSnOH(2))(2)(gamma-SiW(10)O(36))(2)](10)(-)

A new phenyltin tungstosilicate derivative, [(PhSnOH(2))(2)(gamma-SiW(10)O(36))(2)](10)(-) (1), has been prepared by reaction of phenyltin trichloride with K(8)[gamma-SiW(10)O(36)].xH(2)O. The new heteropolyanion was characterized by elemental analysis, infrared spectroscopy, multinuclear NMR, and X-ray crystallography. The crystals of Cs(9)H[(PhSnOH(2))(2)(gamma-SiW(10)O(36))(2)].16H(2)O (Cs salt of 1) are triclinic, space group P&onemacr;, with lattice constants a = 12.401(3) ?, b = 13.832(3) ?, c = 16.313(3) ?, alpha = 96.17(2) degrees, beta = 109.73(2) degrees, gamma = 97.13(2) degrees, V = 2579.9(10) ?, and Z = 1. Anion 1 has a structure of virtual C(2)(h)() symmetry with two phenyltin groups sandwiched between two gamma-SiW(10) groups. Such a structure is different from all previously reported polytungstates derived from [gamma-SiW(10)O(36)](8)(-) lacunary anions.     

Modelling effects of subgrid-scale mixture fraction variance in LES of a piloted diffusion flame

A posteriori analysis of the statistics of two large-eddy simulation (LES) solutions describing a piloted methane–air (Sandia D) flame is performed on a series of grids with progressively increased resolution reaching about 10.5 million cells. Chemical compositions, density and temperature fields are modelled with a steady flamelet approach and parametrised by the mixture fraction. The difference between the LES solutions arises from a different numerical treatment of the subgrid scale (SGS) mixture fraction variance – an important quantity of interest in non-premixed combustion modelling. In the first case (model I), the variance transport equation is solved directly, while in the second (model II), an equation for the square of the mixture fraction is solved, and the variance is computed from its definition. The comparison of the LES solutions is based on the convergence properties of their statistics with respect to the turbulence resolution length scale. The dependence of the LES statistics is analysed for velocity and the mixture fraction fields, and tested for convergence. For the most part, the statistics converge for the finest grids, but the variance of the mixture fraction shows some residual grid dependence in the high-gradient regions of the jet near field. The SGS variance given by model I exhibits realisability everywhere, whereas in regions of the flame model II is non-realisable, predicting negative variances. Furthermore, the LES statistics of model I exhibit superior convergence behaviour.     

Sensitised near-infrared emission from lanthanides using a covalently-attached Pt(II) fragment as an antenna group

In a series of heterodinuclear complexes in which a Pt(PPh3)2(catecholate) chromophore is covalently linked to a lanthanide tris(diketonate) unit, sensitised near-IR emission from Yb(III), Nd(III) and Er(III) occurs on excitation of the Pt(II) chromophore at 520 nm.     

Is there a unique consistent theory of quantum gravity?

Superstrings have been proposed as a quantum-theoretical framework for unifying all the fundamental forces, including gravity. We consider the question of whether there might be more general supersymmetric possibilities, based on higher extended objects such as membranes, jellies, etc. We argue that all the possible extended objects in all possible spacetime dimensions are quantummechanically inconsistent except for the 10-dimensional superstring and the 11-dimensional supermembrane. These are also the only two such theories that contain massless gravitons and, thus, that can describe gravity at low energies. It is remarkable that the range of possibilities can be narrowed down to this extent. Whether these can be further narrowed down to just one consistent theory remains open to further research.This essay received the first award from the Gravity Research Foundation for the year 1988.-Ed.     

The Re(I) coordination chemistry of a series of pyrido[2,3-b]pyrazine-derived ligands: Syntheses,characterisation and crystal structures

Reaction of 2,3-diaminopyridine with one equivalent of a functionalised vicinal diketone, in ethanol, yields a series of ligands based upon the pyrido[2,3-b]pyrazine core. The ligands were characterised by ¹H, ¹³C–{¹H} NMR, MS and UV–Vis spectroscopy. Reaction of the ligands with one equivalent of {ReBr(CO)₅} gave a series of Re-Lⁿ complexes based upon the general formula fac-{ReBr(CO)₃(L)} (where L = pyrido[2,3-b]pyrazine-derived ligands, L¹–L⁶). Solution IR studies confirmed the retention of the facially capped, tri-carbonyl coordination geometry at rhenium, and ¹H NMR studies confirmed coordination of the ligand to Re(I). EI HR MS data were obtained for each complex confirming the proposed formulation and stoichiometry. Single crystal X-ray structures were obtained for three of the complexes (Re-L¹, Re-L², Re-L⁶), with each demonstrating that the ligands coordinate to Re(I) in a bidentate manner, via a four-membered chelate ring, which was unsymmetrical in the former two cases. The electronic absorption spectra of the complexes showed absorption into the visible region ca. 375–500 nm, (the complexes are orange-red in appearance). Following irradiation at 350–450 nm, the complexes display a solid-state broad emission peaking between 600–700 nm. The complexes were not sufficiently luminescent in solution to allow further investigation into the origin of this emission band, although with reference to related 1,8-naphthyridine complexes of Re(I) it is likely to incorporate significant ³MLCT character.     

Synthesis and photophysical properties of kinetically stable complexes containing a lanthanide ion and a transition metal antenna group

A series of bimetallic complexes has been prepared in which an octadentate DOTA-monoamide pocket containing a bound lanthanide ion is linked covalently to a Re(I) or Ru(II) bipyridyl unit via an alkyl spacer group. The transition metal chromophores incorporated in this way act as effective sensitisers for lanthanide-centred luminescence. The rate and efficiency of energy transfer are dependent upon the nature of the spacer group, and upon the nature of the lanthanide acceptor. For the RuNd diad, there is a long rise-time associated with the energy-transfer step, such that energy transfer is rate determining in H(2)O, but not in D(2)O. The results also lead us to suggest that energy transfer may precede formation of the (3)M((Ru/Re))L((bpy))CT state and may be a competitive deactivation pathway for the precursor state ((1)M((Ru/Re))L((bpy))CT).     

Critical gravity in four dimensions

We study four-dimensional gravity theories that are rendered renormalizable by the inclusion of curvature-squared terms to the usual Einstein action with a cosmological constant. By choosing the parameters appropriately, the massive scalar mode can be eliminated and the massive spin-2 mode can become massless. This "critical" theory may be viewed as a four-dimensional analogue of chiral topologically massive gravity, or of critical "new massive gravity" with a cosmological constant, in three dimensions. We find that the on-shell energy for the remaining massless gravitons vanishes. There are also logarithmic spin-2 modes, which have positive energy. The mass and entropy of standard Schwarzschild-type black holes vanish. The critical theory might provide a consistent toy model for quantum gravity in four dimensions.     

Intercalation-induced changes in DNA supercoiling observed in real-time by atomic force microscopy

Atomic force microscopy (AFM) has been employed to observe in real-time and in an aqueous environment the process of ethidium bromide induced supercoiling in individual DNA plasmid molecules. Image data reveal both the onset and the progressive presence of plectonemic DNA supercoiling. In addition, significant molecular motion of the surface adsorbed DNA is observed. These data illustrate the potential of AFM in the time-resolved study of biomolecular processes, and hence, provide new insights into biomolecular structure and function.     

On the singularity of Green's tensor for a perfectly conducting semi-infinite cone

This paper is intended to clarify a misunderstanding concerningthe source singularity of the electric Green's tensor for aperfectly conducting semi-infinite cone of circular cross-section.Tai's series expansion of the Green's tensor is known to lacka singular term at the source region. Jones has reconstructedthe solution to this problem and has pointed out the differencebetween his result and that of Tai. The aim of our paper isto demonstrate that, although Jones's closed-form solution iscorrect, there is a mistake in his comparison with Tai's seriessolution. We conclude that one of the two additional singularterms that Jones claims as missing from Tai's formula must beomitted. Besides, we compare Jones's closed-form solution withSmyshlyaev's solution to the very same problem. We concludethat the magnetic field expressions given by Jones and Smyshlyaevcoincide, but a singular term is missing from Smyshlyaev's expressionfor the electric field.     

An acoustic/viscous splitting technique for computational aeroacoustics

A new technique for the numerical analysis of aerodynamic noise generation is developed. The approach involves first solving for the time-dependent incompressible flow for the given geometry. A hydrodynamic density correction to the constant incompressible density is then calculated from knowledge of the incompressible pressure fluctuations. The compressible flow solution is finally obtained by considering perturbations about the corrected incompressible flow. This fully nonlinear technique, which is tailored to extract the relevant acoustic fluctuations, appears to be an efficient approach to the numerical analysis of aerodynamic noise generation, particularly in viscous flows. Applications of this technique to some classical acoustic problems of interest, including some with moderately high subsonic Mach numbers, are presented to validate the approach. The technique is then applied to a fully viscous problem where sound is generated by the flow dynamics.