A synthetic iron phosphate mineral, spheniscidite, [NH4]+[Fe2(OH)(H2O)(PO4)2]?H2O, exhibiting reversible dehydration

Spheniscidite, a synthetic iron phosphate mineral has been synthesized by hydrothermal methods. The material is isotypic with another iron phosphate mineral, leucophosphite. Spheniscidite crystallizes in the monoclinic spacegroupP2₁/n. (a=9·845(1),b=9·771(3),c=9·897(1),β=102·9°,V=928·5(1),Z=4,M=372·2,d _calc=2·02 g cm⁻³ andR=0·02). The structure consists of a network of FeO₆ octahedra vertex-linked with PO₄ tetrahedra forming 8-membered one-dimensional channels in which the NH₄ ⁺ ions and H₂O molecules are located. The material exhibits reversible dehydration and good adsorption behaviour. Magnetic susceptibility measurements indicate that the solid orders antiferromagnetically.     

Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by “turns,” which are equivalence classes of directed great circle arcs on the unit sphere S ², in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group SU(1, 1)=Sp(2, R)=SL(2, R), the double cover of SO(2, 1). The present work develops a theory of turns for SL(2, C), the double and universal cover of SO(3, 1) and SO(3, C), rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation. PACS numbers: 02.20.-a     

On the interaction between retailers inventory policies and manufacturer trade deals in response to supply-uncertainty occurrences

This paper models a retailer’s response to temporary manufacturer’s trade deals characterized by a time interval of random length and of uncertain duration. Uncertainty is handled primarily through the establishment of a reordering point, which serves as a trigger mechanism for new special orders. The timing at which this point is activated becomes another decision variable to be determined optimally. The model generates relatively easy-to-implement ordering policies, applicable to any probability distribution.     

Resonant amplification of the magnetoelectric effect in ferrite-piezoelectric composites

The magnetoelectric effect in ferrite-piezoelectric composites is considered. A theory of the magnetoelectric effect in the electromechanical-resonance region for disk-shaped samples is presented. The magnetooptical coefficient is calculated for longitudinal and transverse orientations of electric and magnetic fields. It is shown that the effect increases by a few orders of magnitude at the electromechanical-resonance frequency. The frequency dependence of the effect is experimentally studied for a ferrite-nickel spinel-PZT composite. A resonant increase in the effect is observed (in agreement with the theory); the highest value of the magnetoelectric coefficient was 15 V/(cm Oe).     

Bisectors of linearly separable sets

A bisector of two sets is the set of points equidistant form them. Bisectors arise naturally in several areas of computational geometry. We show that bisectors of weakly linearly separable sets inE ^d have many properties of interest. Among these, the bisector of a restricted class of linearly separated sets is a homeomorphic image of the linear separator. We also give necessary and sufficient conditions for the existence of a particular continuous map from (a portion of) any linear separator to the bisector.     

Segmented multigrid domain decomposition procedure for incompressible viscous flows

The application of grid stretching or grid adaptation is generally required in order to optimize the distribution of nodal points for fluid-dynamic simulation. This is necessitated by the presence of disjoint high gradient zones, that represent boundary or free shear layers, reversed flow or vortical flow regions, triple deck structures, etc. A domain decomposition method can be used in conjunction with an adaptive multigrid algorithm to provide an effective methodology for the development of optimal grids. In the present study, the Navier-Stokes (NS) equations are approximated with a reduced Navier-Stokes (RNS) system, that represents the lowest-order terms in an asymptotic Re expansion. This system allows for simplified boundary conditions, more generality in the location of the outflow boundary, and ensures mass conservation in all subdomain grid interfaces, as well as at the outflow boundary. The higher-order (NS) diffusion terms are included through a deferred corrector, in selected subdomains, when necessary. Adaptivity in the direction of refinement is achieved by grid splitting or domain decomposition in each level of the multigrid procedure. Normalized truncation error estimates of key derivatives are used to determine the boundaries of these subdomains. The refinement is optimized in two co-ordinate directions independently. Multidirectional adaptivity eliminates the need for grid stretching so that uniform grids are specified in each subdomain. The overall grid consists of multiple domains with different meshes and is, therefore, heavily graded. Results and computational efficiency are discussed for the laminar flow over a finite length plate and for the laminar internal flow in a backward-facing step channel.     

Superconducting transition temperature for semimetals like bismuth

The superconducting transition temperatureT _c for semimetals like bismuth has been calculated as a function of the densityn _c of the electron and hole charge carriers. A simplified two-band model for describing the longitudinal dielectric function for such a system has been used in our model calculation. We find that the attractive interaction responsible for the instability of the normal ground state comes not only from the exchange of lattice phonons, but also from the electronhole sound mode, provided the ratio of the averaged hole to electron mass,m _h /m _e ≠ 1. We have compared our theoretical values ofT _c (n _c ) with experimental results for bismuth under hydrostatic pressure, and find reasonable agreement ifm _h /m _e is assumed to have a value which is only slightly larger than that at atmospheric pressures. A linear variation of the negative band gap as a function of pressure has been assumed for the sake of this comparison.     

Quantitative 15N NMR spectroscopy

Line intensities in ¹⁵N NMR spectra are strongly influenced by spin-lattice and spin–spin relaxation times, relaxation mechanisms and experimental conditions. Special care has to be taken in using ¹⁵N spectra for quantitative purposes. Quantitative aspects are discussed for the ¹⁵N NMR of molecules with different nitrogen functional groups and also mixtures of nitrogen-containing compounds. It is shown that, in general, quantitative data are obtainable from integration of ¹⁵N lines in proton decoupled ¹⁵N NMR spectra using NOE suppression. Addition of paramagnetic relaxation reagents (PARR) under controlled conditions is frequently needed to accomplish the experiment within reasonable time limits.