Infrared and Raman spectral interpretations of the ferroelectric phases of NaH3(SeO3)2 and NaD3(SeO3)2

The infrared and Raman spectra of NaH₃(SeO₃)₂ and NaD₃(SeO₃)₂ have been recorded from 24 to 300°K. The interpretation, assignments, and analysis of the spectral studies are presented on the paraelectric α phase (proton disordered), ferroelectric β phase (proton ordered) and ferroelectric γ phase (proton ordered). A discussion of a newly proposed proton-triggered phase transition mechanism and a possible origin of the hydrogen-bonded OH stretching region of KH₂PO₄-type ferroelectrics is given.     

The stannylation of carbonyl-stabilised phosphorus ylids,and tin-assisted elimination reactions

The interaction of organotin halides with lithium salts of mono-substituted phosphorus ylids and also with disubstituted ylids is described.     

Synthesis,spectroscopic studies,and x-ray crystallographic analysis of the organotin carbohydrate: 1,2∶3,4-di-O-isopropylidene-6-O-triphenylstannylmethyl-α-D-galactopyranose

The title organotin carbohydrate, C₃₁H₃₆O₆Sn, has been synthesized and its molecular structure has been determined in solution and in the solid state. NMR, infrared, mass and X-ray crystallographic techniques were used. The chiral molecules crystallize in the monoclinic space group P2₁ withZ=2. The triphenyltin and carbohydrate moieties are linked by a trans methylene-oxygen-methylene arrangement. The pyranosyl ring adopts a twist-boat conformation and the isopropylidene rings adopt different (half-chair and envelope) forms. Solution and solid-state conformations are similar as only three ¹³C shift values are greater than 2ppm; the ¹¹⁹Sn value is 12 ppm.     

Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions

The ground state energy of an atom of nuclear chargeZe in a magnetic fieldB is exactly evaluated to leading order asZ in the following three regions:BZ ^4/3,BZ ^4/3 andZ ^4/3BZ³. In each case this is accomplished by a modified Thomas-Fermi (TF) type theory. We also analyze these TF theories in detail, one of their consequences being the nonintuitive fact that atoms are spherical (to leading order) despite the leading order change in energy due to theB field. This paper complements and completes our earlier analysis [1], which was primarily devoted to the regionsBZ ³ andBZ³ in which a semiclassical TF analysis is numerically and conceptually wrong. There are two main mathematical results in this paper, needed for the proof of the exactitude of the TF theories. One is a generalization of the Lieb-Thirring inequality for sums of eigenvalues to include magnetic fields. The second is a semiclassical asymptotic formula for sums of eigenvalues that isuniform in the fieldB.Work partially supported by U.S. National Science Foundation grant PHY90-19433 A02Work partially supported by U.S. National Science Foundation grant DMS 92-03829Work partially supported by the Heraeus Stiftung and the Research Fund of the University of Iceland.     

Statevector reduction in discrete time: A random walk in Hilbert space

A simple model is presented in which the statevector evolves every seconds in one of two ways, according to a particular probability rule. It is shown that this random walk in Hilbert space results in reduction of the statevector. It is also shown how the continuous spontaneous localization (CSL) theory of statevector reduction is achieved as a limiting case of this model, exactly as Brownian motion is a limiting case of ordinary random walk. Finally, a slightly different but completely equivalent form of the CSL equations suggested by the simple model given here is discussed.     

Jupiter's Great Red Spot and zonal winds as a self-consistent,one-layer,quasigeostrophic flow

We present the point of view that both the vortices and the east-west zonal winds of Jupiter are confined to the planet's shallow weather layer and that their dynamics is completely described by the weakly dissipated, weakly forced quasigeostrophic (QG) equation. The weather layer is the region just below the tropopause and contains the visible clouds. The forcing mimics the overshoot of fluid from an underlying convection zone. The late-time solutions of the weakly forced and dissipated QG equations appear to be a small subset of the unforced and undissipated equations and are robust attractors. We illustrate QG vortex dynamics and attempt to explain the important features of Jupiter's Great Red Spot and other vortices: their shapes, locations with respect to the extrema of the east-west winds, stagnation points, numbers as a function of latitude, mergers, break-ups, cloud morphologies, internal distributions of vorticity, and signs of rotation with respect to both the planet's rotation and the shear of their surrounding east-west winds. Initial-value calculations in which the weather layer starts at rest produce oscillatory east-west winds. Like the Jovian winds, the winds are east-west asymmetric and have Karman vortex streets located only at the west-going jets. From numerical calculations we present an empirically derived energy criterion that determines whether QG vortices survive in oscillatory zonal flows with nonzero potential vorticity gradients. We show that a recent proof that claims that all QG vortices decay when embedded in oscillatory zonal flows is too restrictive in its assumptions. We show that the asymmetries in the cloud morphologies and numbers of cyclones and anticyclones can be accounted for by a QG model of the Jovian atmosphere, and we compare the QG model with competing models.     

Nonresonant third-order susceptibility measurements in the nematic liquid crystal K18

We have observed a large nonresonant third-order nonlinear susceptibility, X ⁽³⁾ (-; , 0, 0) in the isotropic phase of a nematic liquid crystal 4-n-hexyl-4-cyanobiphenyl (K18). The highest value of X ⁽³⁾ obtained at 632.8 nm is 1.16274×10^-18 m²V^-2 corresponding to a temperature 29.3°C. The observed second-order pretransitional temperature T ^* from our measurements is 1.2°C below the first-order nematic to isotropic transition temperature. The dependence of the Kerr constant on (T-T ^*)^-1 is found to be in good agreement with the predictions of the Landau-de Gennes model.     

X-ray and molecular mechanics studies on the sesquiterpene lactone eupatocunin-o-bromobenzoate — An unusual case of disorder involving atropisomerism

The molecular structure of the cytotoxic sesquiterpene lactone eupatocunin has been determined by X-ray crystallographic analysis of theo-bromobenzoate derivative. Two structural isomers, arising from hindered rotation, are present within the single crystal. The molecules are disordered (ratio 0.750.25) with the bromine atom occupying alternate ortho positions on the aromatic ring. Molecular mechanics has been used to examine the energies of molecular conformation by torsion angle variation.