Rapid formation of diphenylmethyl ethers and thioethers using microwave irradiation and protic ionic liquids

Using microwave irradiation and protic ionic liquids (pIL) as co-solvent and catalyst for the synthesis of several diphenylmethyl ethers was achieved. The desired ethers were isolated simply by filtration through a silica plug to remove the pIL and proceeded in high yields (60–98%). These reactions were extremely rapid (10–30 min) and occurred under mild conditions (80 °C). This protocol was also successfully applied to the synthesis of thioethers.     

The Radiation-Induced Copolymerization of Methyl Methacrylate with Di- and Trimethacrylates

The rates and gel formation of the radiation-induced co-polymerization of a number of dimethacrylates and trimethylol propane trimethacrylate with methyl methacrylate has been studied in detail. The rates were found to be linked to the nature and amount of gel formed rather than to differences in the reactivities of the monomers.     

Experimental results on aerofoil manipulators at high subsonic speeds

An extensive series of measurements of the boundary layer development and drag downstream of aerofoil manipulators have been made in the high speed tunnels at Cambridge. This work forms part of a combined study with the University of Poitiers into the possible drag reducing properties of manipulators and was supported by Airbus Industrie. Overall the test results showed that the reduction in turbulent skin-friction downstream of the device did not compensate for the drag of the device itself in any of the cases studied, thus no overall drag saving was possible although in certain cases the overall drag penaly was small. This finding suggests that such devices may have a use in regions where a local reduction in skin-friction (and hence possible heat transfer) is needed and a low level of loss can be accepted. However, the actual drag reduction obtained was found to be extremely sensitive to changes in the aerofoil shape and incidence.     

Generating the Acyclic Orientations of a Graph

The acyclic orientations of a graph are related to its chromatic polynomial, to its reliability, and to certain hyperplane arrangements. In this paper, an algorithm for listing the acyclic orientations of a graph is presented. The algorithm is shown to requireO(n) time per acyclic orientation generated. This is the most efficient algorithm known for generating acyclic orientations.     

Application of holographic interferometry for evaluation of 3D Navier-Stokes calculations

Holographic interferometry is a non-intrusive optical measuring technique which can potentially capture instantaneous information about a complete three-dimensional flow field onto a single holographic image. However subsequently extracting the flow data so that it can be used to validate CFD results, is for most practical wind tunnel applications not yet possible.An approach applied in this paper, is to compare experimental interferograms with equivalent images obtained by post-processing the CFD solution. We have investigated transonic flow in a wind tunnel environment and computationally reconstructed both 2D image-plane interferograms and full 3D holographic interferograms. These comparisons have subsequently helped us to evaluate and improve our 3D Reynolds Averaged Navier-Stokes calculations.The main part of this study was conducted by the authors at Cambridge University Engineering Department where the work was funded by RAE Farnborough under contract 2029/233 XR Aero and monitored by Dr. B. Williams and Dr. P. Smith     

A gauge symmetric band model of the Woodward–Hoffmann rules

The Woodward–Hoffmann (WH ) Rules for the prediction of relative rates and stereochemistry of concerted reactions are based on considerations of the orbital symmetry of the reactants and products. Literally hundreds of reactions have been successfully categorized by these remarkably simple-appearing Rules. This paper develops a one-dimensional band model of these Rules. By explicit inclusion of the effects of an electromagnetic field in a standard gauge-invariant fashion, it can be shown that at certain levels of field strength the model suggests that the Rules may be reversed. This is because the Rules appear in the model as a consequence of a centrifugal angular momentum barrier that can be shifted by an electromagnetic field. This barrier could account for “aromatic” stabilization. As an additional effect, the model predicts flux-dependent oscillations and persistent currents for “aromatic” molecules due to the Aharonov–Bohm effect. The possible health effects of electromagnetic fields are speculated. The likelihood of experimental observations to verify the applicability of the model is discussed.     

Muon hyperfine fields in iron and its dilute alloys

The temperature dependence (240 to 633 K) of the interstitial magnetic field, B_μ, as determined by the rotation of the spin of the μ⁺, has been measured for dilute polycrystalline iron alloys with Mo, Ti and Nb additions. In all cases the behaviours differ from one another and from the Fe(A1) alloys previously studied. B_μ, which is negative with respect to the magnetization, is increased in magnitude by A1 and Mo, and decreased greatly by Ti. The addition of Nb creates a two- phase alloy from which we can assess the role of heterogeneity and/or strain on B_μ in iron. If the temperature dependence of the hyperfine field B_hf extracted from B_μ for Fe(Mo) alloys is interpreted on the model previously used to discuss the Fe(A1) data, we would conclude that the muon is attracted to the Mo atom while repelled by the A1 atoms as the temperature decreases. Measurements giving room temperature values of B_μ for iron alloys with Mn, Cr, V and W taken after annealing above the recrystallization temperature are also reported.     

Axisymmetric bodies of minimum drag in hypersonic flow

The problem of determining the longitudinal contour of a slender, axisymmetric body in hypersonic flow which has minimum drag is considered. The pressure distribution is assumed to be Newtonian, while the skin-friction distribution is for laminar flow and depends on body geometry. This investigation is conducted with the method of steepest descent, whose feasiblity is demonstrated by solving minimum drag problems having known analytical solutions.     

A unified theory of turbulent flow

Summary A general theory of turbulent flow is applied to incompressible plane Couette flow. It is found that a unique formulation is not obtained because of a singularity in the equations and problems relating to the boundary conditions. Solutions are obtained for several different assumptions. The characteristic feature is a square root velocity profile for high Reynolds numbers. The logarithmic law is obtained as a divergent approximation. There are discrepancies in the available experimental data; one set agreeing with the square root form, and a second set with the logarithmic form.