The reactions of trifluoromethyl and trichloromethyl radicals with conjugated and methylene-interrupted dienes and enynes

The photochemical addition of CF₃I to buta-1,3-diene and vinylacetylene in the gas phase gave 1,4-adducts as the main products. In gas phase reactions only products derived from hydrogen abstraction were detected in the CF₃I/penta-1,3-diene system, but the 1,4-adducts again predominated in the liquid phase. CCl₃Br similarly gave a mixture of 1,2- and 1,4-adducts, the latter predominating, on photochemical reaction with penta-1,3-diene. The 1,2-adduct was the main product from the CCl₃Br/pent-1-en-4-yn reaction, but some hydrogen abstraction was observed. The preference shown by conjugated dienes to give 1,4-adducts in the $\text{trans}$- configuration is interpreted in terms of steric factors and the propensity of dienes to adopt the $\text{s}$-$\text{trans}$ conformation.     

The quadruply bondedbis-carboxylatescis-Re2(μ-O2CCH3)2X4L2 (X = halide;L = neutral donor) as synthons in dirhenium chemistry

The reactions of the quadruply bonded dirhenium(III) carboxylatescis-Re₂(-O₂CR)₂X₄L₂ (X=CI or Br; L=a monodentate donor) with monodentate, bidentate, and tridentate phosphine donors result in several types of redox behavior, usually involving partial or complete reductive decarboxylation of the dirhenium unit. Examples of dirhenium(VI, II), dirhenium(IV, II), dirhenium(III, II), and dirhenium(II, II) complexes, in which Re-Re bond orders of 4, 3.5, 3, l, or zero are encountered, have been isolated and repre-sentative examples structurally characterized. The course of these reactions is dependent upon the nature of the phosphine. The scope of this remarkably rich chemistry is discussed.     

Solvothermal synthesis of cerium oxides

A review of the various hydrothermal and solvothermal methods that have been used for the preparation of cerium oxides is presented. Much work has focussed on the preparation of cerium dioxide (ceria) and its doped analogues because of their extensive applications in catalysis, solid-oxide fuel cells and other technologies. It is shown how the solvothermal method offers a number of distinct advantages in the one-step formation of ceria materials, including control of crystal form and morphology in the nanometre regime from spherical and cubic particles to anisotropic polyhedra and rods. The use of solution additives allows surface capping either preventing aggregation of particles or permitting their assembly into complex hierarchical structures. In terms of doping, the solvothermal synthesis method allows access to phases not possible using high temperatures synthesis, including ceria doped by transition-metal ions. These synthetic advantages all allow fine-tuning of the properties of ceria for practical applications. Finally, some recent work that has focussed on the synthesis of complex mixed-oxide phases containing cerium, both in the +3 and the +4 oxidation state, is presented: this illustrates the potential of solvothermal synthesis in the discovery of new materials.     

Reduced order modelling for unsteady fluid flow using proper orthogonal decomposition and radial basis functions

A technique is presented for interpolating unsteady solutions to parameterised fluid flow problems, using a combination of proper orthogonal decomposition and radial basis functions. The technique is validated by considering simulations involving three dimensional unsteady compressible inviscid flow over an oscillating ONERA M6 wing. It is demonstrated that the approach can result in a large reduction in the cpu time required to find solutions at new parameter values, without a significant loss in accuracy.     

Shrinking the period lengths of continued fractions while still capturing convergents

Here we prove that every real quadratic irrational α can be expressed as a periodic non-simple continued fraction having period length one. Moreover, we show that the sequence of rational numbers generated by successive truncations of this expansion is a sequence of convergents of α. We close with an application relating the structure of a quadratic α to its conjugate.     

Bernoulli excitation and detection of gas bubbles.

A simple method is proposed for detecting and sizing bubbles in pipeline fluid flow. This is based on changing the pressure of the fluid, which in turn excites volume oscillations in the bubble. If the change in pressure is of sufficient brevity and magnitude, the transient distortion results in excitation of the bubble into radiative oscillation at its natural frequency. In a moving fluid, the Bernoulli equation predicts that such a pressure change can be achieved through a suitable gradient in the flow velocity. In the experiments described here, this is achieved by altering the cross-sectional area of the pipe in which the fluid is flowing. We demonstrate the efficacy of this excitation method and, by detecting the radiated sound using a nearby hydrophone, determine the size of individual bubbles from their characteristic oscillation frequency.