Numerical prediction of recirculation flows with free convection encountered in gas-agitated reactors

Flows in a gas-agitated reactor have been predicted by a finite difference procedure. The free-convection phenomena in the gas-liquid mixtures have been accounted for by the calculation of a void fraction determined from the gas flow rate. Computations have been performed for two different situations: first, with the allowance of slip between gas and liquid phases, and second, without any slip. Reasonable agreement has been achieved between the measurements.     

Carbon-13 nuclear magnetic resonance spectra and conformations of cis,cis-1,5-cyclooctadiene monoepoxide and cis,syn,cis-1,5-cyclooctadiene diepoxide

The natural-abundance ¹³C NMR spectra of cis,cis-1,5-cyclooctadiene monoepoxide and cis,syn,cis-1,5-cyclooctadiene diepoxide have been investigated over the temperature range of – 10 to – 180°C. Whereas the spectra of the former showed no dynamic NMR effect, two different conformations in the ratio of 3:1 were observed at low temperatures for the latter. The free-energy barrier (ΔG^≠) for conversion of the major conformation to the minor conformation is calculated to be 5.9°0.2 kcal mol^?1 from a line-shape analysis of spectra obtained at intermediate temperatures. It is shown that cis,syn,cis-1,5-cyclooctadiene diepoxide exists in solution in chair (major) and in twist-boat (minor) conformations of slightly different energies. Interconversion paths between these conformations are discussed. The monoepoxide is suggested to have a twist-boat conformation that is rapidly pseudorotating via a boat conformation even at – 180°C.     

Radon inversion of plasma emission

An analytical inversion of plasma spectral emission using the Radon transform is discussed for a plasma with a constant coefficient of absorption and a model displaced gaussian as the spatial distribution of its coefficients of emission.     

Raman scattering study of LiKSO4—phases II and III

Detailed Raman scattering investigation of LiKSO₄ in phases II and III across the transition temperatureT _c ? 700 K is reported. Abrupt change in frequency and line width of the external and internal modes have been observed. Analysis of the results suggests lithium positional disorder and sulphate orientational disorder in the high temperature phase (II). The results also throw some light on the existence of twin domains in the crystal.     

Prolongation structure of a new integrable system

We have obtained the inverse scattering equations associated with a new pair of coupled nonlinear evolution equations in two dimensions. The spectral parameter is introduced by invoking the invariance of the equation set, and imposing those on the Lax pair.     

Polymerization of 1,2:5,6-di-O-isopropylidene-α-D-glucofuranose and 1,2-O-isopropylidene-α-D-glucofuranose

A new method for preparing D -glucose polymers is described. Isopropylidene derivatives of D -glucofuranose, particularly the 1,2-mono-O-derivative, are treated with Lewis acids, such as boron trifluoride, to eliminate acetone and produce a highly branched polymer with a molecular weight of 12,700. Approximately one isopropylidene unit remains, possibly on the potential reducing end of the glucan. Up to 95% of the polymer units are D-glucopyranoside units indicating that ring expansion occurs during the condensation.     

Generalized existence conditions for surface states of a semi-infinite Kronig–Penney crystal

A derivation of most general existence conditions for surface states of a semi-infinite Kronig–Penney crystal is reported. They reduce to Steslicka's conditions under a subsidiary restriction and also indicate that the surface-state energies may lie in the allowed bulk bands. Numerical computations supporting the qualitative conclusions are provided.