A fractional differential equation for a MEMS viscometer used in the oil industry

A mathematical model is developed for a micro-electro-mechanical system (MEMS) instrument that has been designed primarily to measure the viscosity of fluids that are encountered during oil well exploration. It is shown that, in one mode of operation, the displacement of the device satisfies a fractional differential equation (FDE). The theory of FDEs is used to solve the governing equation in closed form and numerical solutions are also determined using a simple but efficient central difference scheme. It is shown how knowledge of the exact and numerical solutions enables the design of the device to be optimised. It is also shown that the numerical scheme may be extended to encompass the case of a nonlinear spring, where the resulting FDE is nonlinear.     

Teaching scenario planning: Lessons from practice in academe and business

In this paper, we engage with O’Brien’s [O’Brien, F.A., 2004. Scenario planning – lessons for practice from teaching and learning. European Journal of Operational Research 152, 709–722] identification of both pitfalls in teaching scenario planning and proposed remedies for these. We consider these remedies in relation to our own experience – based on our practice in both the academic and business arenas – and we highlight further pitfalls and proposed remedies. Finally, we propose the use of “hard” multi-attribute decision analysis as a complement to “soft” scenario planning, in order to allow a more formal method of strategy evaluation against a range of constructed scenarios, This approach is intended to remedy biases that are associated with holistic evaluations – such as lexicographic ranking – where undue attention is paid to particular strategic objectives at the expense of others. From this discussion, we seek to contribute to cumulative refinement of the scenario process.     

The photophysics of some intramolecular ternary complexes formed between aryl and amino groups

The fluorescence properties of (3)–(6) in solvents of varying polarity have been examined and the conclusion reached that in non-polar solvents they exhibit fluorescence (low quantum yield) from an intramolecular ternary complex. In polar solvents very little fluorescence is observable. Although each compound exhibits extensive intramolecular fluorescence quenching, the quantum yield of localised triplet naphthalene in non-polar solvents remains relatively high indicating that intersystem crossing occurs in the non-relaxed exciplex.     

Shear field modification of strongly flocculated suspensions — Aggregate morphology

Rheological and microscopical studies have been made to elucidate the effects of shear fields on the morphology of concentrated, aggregated model colloids. The models employed are well-characterised, predominantly chargestabilised polymer latices, coagulated by the addition of excess electrolyte. Continuous shear rheological and viscoelastic measurements indicate a very significant decrease in shear yield stress, apparent viscosity and shear modulus following prolonged shearing.Electron microscopy reveals the source of these changes. Freshly coagulated suspensions form networks that are porous, strong and qualitatively similar to simulated structures for diffusion limited aggregation. Following protracted shearing, the network structure is rearranged to yield discrete, tightly packed aggregates with a characteristic size, which is principally a function of the primary particle size.     

Interaction of nitrogen oxides with sublimed layers of (meso-tetraphenylporphyrinato)cobalt(II); IR evidence of oxo-transfer from (nitro)porphyrinatocobalt(III) to free nitric oxide

Interaction of a low-pressure NO2 with sublimed layers of (meso-tetraphenylporphyrinato)cobalt(II) (Co(TPP)) leads to formation of 5-coordinate nitro complex Co(III)(TPP)(NO2). Upon exposure of these layers to pyridine vapors, the fast reaction with formation of 6-coordinate nitro-pyridine porphyrins (Py)Co(III)(TPP)(NO2) occurs. By means of IR spectroscopy and use of nitrogen oxide isotopomers, it is shown that an oxo-transfer reaction occurs from 5-coordinate species to free nitric oxide (NO) while the 6-coordinate complex is rather inert. It is also demonstrated that the stepwise addition of low-pressure NO2 to nitrosyl complex Co(TPP)(NO) leads to formation of the nitro complex most likely by an exchange reaction.     

Valency-bond studies of some conjugated hydrocarbons—I Penny-dirac bond orders; general theory and applications to 1,3-butadiene and fulvene

The Penney-Dirac calculation of bond orders in conjugated hydrocarbons is reconsidered, and a method of computing them, which does not involve perturbation theory, is developed. This method is general, in that it permits the exchange and Coulomb integrals for the various bonds to have values appropriate to their lengths, and not necessarily all equal. Detailed application to 1,3-butadiene and fulvene leads to results in close correspondence with molecular-orbital calculations.