THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Normal coordinate ab initio force relaxation

A procedure for optimization of molecular geometries is presented, combining ab initio calculations with vibrational molecular data from spectroscopy or empirical force fields. Theoretical cartesian forces are transformed to vibrational normal coordinate forces from which geometry increments are calculated. Test results indicate that the method saves considerable effort compared to other optimization schemes.     

Some reactions of tetrafluoroethylene oligomers

As part of a programme to prepare and evaluate a series of perfluoro- chemicals for use as inert fluids, the fluorinations of some tetrafluoroethylene oligomers over cobalt (III) fluoride have been studied.Fluorination of perfluoro-3,4-dimethylhex-3-ene (tetramer) and perfluoro-4-ethyl-3,4-dimethylhex-2-ene (pentamer) over CoF₃ at 230°C and l45°C respectively afforded the corresponding saturated fluorocarbons however, at 250°C, pentamer gave predominantly the saturated tetramer. The thermal behaviour of these saturated fluorocarbons alone and in the presence of bromine and toluene has been studied.Pyrolysis of pentamer over glass beads at 500°C gave perfluoro-1,2,3- trimethylcyclobutene and isomers of perfluoro-2,3-dimethylpenta-1,3- diene. Under similar conditions perfluoro-2-(1-ethyl-1-methylpropyl). 3-methylpent-1-ene (hexamer) gave perfluoro-1-methyl-2-(1-methyl- propyl)-cyclobut-1-ene and perfluoro-2-methyl-3-(1-methylpropyl)-buta- 1,3-diene.These reactions and the structural elucidation of the products will be discussed.     

Synthesis and anticholinesterase activity of some new fluorogenic analogues of organophosphorus nerve agents

Eighteen new fluorogenic analogues of organophosphorus nerve agents were synthesised and characterised. They included analogues of tabun, sarin, cyclosarin, soman, VX, and Russian VX, with the 7-oxy-4-methylcoumarin or 7-oxy-4-(trifluoromethyl)coumarin leaving group. These analogues inhibited acetylcholinesterase (AChE) effectively in vitro and therefore have potential as tools for the identification of novel organophosphatases in biological systems. Analogues of VX and Russian VX with the 7-amino-4-methylcoumarin group, although poor AChE inhibitors, may have utility for screening enzyme libraries for phosphoramidases capable of cleaving P-N bonds.     

Ab initio studies of structural features not easily amenable to experiment: the molecular structures of some hydrogenfluoride clusters

The completely relaxed ab initio structures of some forms of H₂F₂ and H₃F₃ reflect the cooperative nature of hydrogen bonding and can be used to estimate the order of magnitude of the variations in local geometry which are neglected when interactive potentials for HF in clusters or in the liquid state are evaluated with constrained geometries.