An adaptation of the lattice gas to the water problem. II. Second-order approximation

The adaptation of the lattice-gas model to embody features possessed by water is further explored. On the basis of Martin's functional derivative formulation of Ising problems, a perturbation scheme is developed which allows calculation of the free energy to any desired order in the interaction potential at fixed density. The free energy correct to second order in the interaction strength is utilized here for calculation of other thermodynamic properties of the model. With reasonable choices of values of the interaction parameters these thermodynamic properties of the model can be brought into agreement with those of real water.     

Homographic solutions of the n-body problem in E4

We prove the existence of many homographic solutions of the n-body problem in E⁴ by topological methods. Homographic solutions are associated with relative equilibria. Homothetic solutions always give rise to central configurations. In Euclidean space E⁴ central configurations are a proper subset of the relative equilibria for any n ? 3 and for any (m_i)?R₊ⁿ. We compare the existence and classification of homographic solutions of the n-body problem in E³ with the Newtonian potential and that of homographic solutions of the n-body problem in E⁴. Classifying relative equilibria leads to classifying homographic solutions.     

The reaction of O(1D) with CH4

The room-temperature photolysis of N₂O (10–100 torr) at 2139 Å to produce O(¹D) has been studied in the presence of CH₄ (10–891 torr). The reactions of O(¹D) with CH₄ were found to be The method of chemical difference was used to measure the rate constant ratio k₄/(k₂ + k₃), where reactions (2) and (3) are The CH₃ radicals produced in reaction (4) react with the O₂ and NO produced in reactions (2) and (3). Thus, near the endpoint of the internal titration, ?{C₂H₆} gives an accurate measure of k₄/(k₂ + k₃). For the translationally energetic O(¹D) atoms produced in the photolysis, k₄/(k₂ + k₃) = 2.28 ± 0.20. However, if He is added to remove the excess translational energy, then k₄/(k₂ + k₃) drops to 1.35 ± 0.3.     

Nonrelativistic dyon-dyon scattering

The nonrelativistic problem of the scattering of two dyons (including the case of electron scattering by magnetic monopoles) is systematically studied, both classically and quantum mechanically, with a view toward the discrimination between various combinations of electric and magnetic charges. We analyze the classical cross section with particular attention to the interesting phenomena which occur for large angle scattering, the “rainbows” and “glory,” where the cross section becomes infinite. Quantum mechanically, we find that these infinities do not occur and that, when the partial wave scattering amplitude is summed, a very elaborate structure emerges for the cross section, which depends sensitively upon the electric and magnetic charges of the particles, as well as on their relative speed. We further discuss a large modification, leading to spin flip and nonflip amplitudes, due to the dipole moments of the particles. Numerical results are presented for a variety of values of these parameters. In principle, these results could be used to distinguish the δ-ray distributions produced by the various species of electrically and magnetically charged particles. Quite apart from the experimental implications of our numerical results, we have made a number of theoretical improvements and extensions. Numbered among these are the consideration of dyons and particles having dipole moments, and the explicit demonstration, based on the methods of angular momentum, that the differential cross section is independent of the choice of singularity line.     

Total synthesis of (+)-13-deoxytedanolide

A total synthesis of 13-deoxytedanolide is described. The synthesis features a highly stereoselective fragment assembly aldol reaction of methyl ketone 4 and aldehyde 5 to establish the complete carbon skeleton of the natural product in the form of aldol 15. The facile formation of the remarkably unreactive hemiketal 16 thwarted attempts to elaborate 15 to tedanolide. However, deoxygenation of the C(13)-hydroxyl of 16 provided the 13-deoxy hemiketal 17 that was smoothly elaborated to 13-deoxytedanolide.     

H2 formation in the reaction of O(1D) with CH4

The reaction of O(¹D) with CH₄ was studied to determine the efficiency of H₂ production in a direct process, and it was found to be 0.11 ± 0.02. Thus the two channels which account for all of the reaction between O(¹D) and CH₄ in the gas phase are      

Characterization of polymeric dielectric insulation by thermomechanical analysis

Use of a thermomechanical analyzer, TMA, affords a rapid, precise method for determining linear expansion coefficients and linear expansivities of cross-linked polymeric insulation material. Completed cable samples were dissassembled and insulation specimens were cut longitudinally and examined with repeated temperature cycling: ethylene—propylene copolymer rubbers and filled and unfilled crosslinked polyethylenes. The TMA results indicated that all specimes were oriented, likely incurred from extrusion processing. The facility of TMA for investigating potential anisotropic behavior from prior orientation is illustrated by examples of TMA measurements on radial specimens, similarly free of mechanical constraints.     

Luminescence of Mn ions in ordered and disordered LiAl5O8

The phosphorescence and excitation spectra of Mn ions in the ordered and disordered phases of LiAl₅O₈ have been measured. In both phases Mn²⁺ ions substitute for Al³⁺ ions in two different tetrahedral sites of the LiAl₅O₈ lattice. In both sites in the ordered phase, sharp zero-phonon transitions have been observed in the low temperature phosphorescence and excitation spectra - these transitions were considerably broadened in the disordered phase due to crystal field inhomogeneity in that phase. The deviation from neutrality caused by the Mn²⁺ ions in the ordered phase is largely compensated by Mn⁴⁺ ions occupying octahedral Al³⁺ sites. On disordering, a large proportion of Mn⁴⁺ is reduced to Mn²⁺, while the remainder takes up a site with a higher proportion of Li⁺ ions as next nearest neighbours. This leads to an increase in the ionicity of the Mn⁴⁺ site in the disordered phase and hence to a larger value of the Racah parameter B.