Segregation of Carbon Paste in a Smelting Electrode

Requests for reprints to A. C. Fowler An industrial problem concerning segregation in carbon pasteis described. Billets of paste, which are a mixture of cokeand pitch, are fed into a steel tube in a furnace, and the tubeis lowered at a rate of about 0.75 m day^–1. In the tube,the pitch is defonnable, and the paste is essentially a veryviscous two-phase participate medium. The grain size distributionis essentially bimodal, consisting of coarse ({small tilde}10mm) particles in a distribution of finer (100 µm) particles.Segregation occurs near the walls of the tube, leading to alower content of coarse particles; such segregation is unwanted,and so the length of this segregated region is required to beminimized. It is suggested that segregation is due to the stiffnessof the coarse particulate mixture, which is less able to deformthan the pitch/fines mixture. Consequently, the length of thesegregated region is controlled by the coarse mixture viscosity,and an expression is derived for the segregation length.     

Geometry,strength of binding and Br2 charge redistribution in the complex OC ··· Br2 determined by rotational spectroscopy

The ground-state rotational spectra of the six isotopomers ¹⁶O¹²C ··· ⁷⁹Br⁷⁹Br, ¹⁶O¹²C ··· ⁸¹Br⁷⁹Br, ¹⁶O¹²C ··· ⁸¹Br⁸¹Br, ¹⁶O¹²C ··· ⁷⁹Br⁸¹Br, ¹⁶O¹³C ··· ⁷⁹Br⁷⁹Br, ¹⁶O¹³C ··· ⁸¹Br⁷⁹Br, were observed by pulsed-nozzle, Fourier-transform microwave spectroscopy. The spectroscopic constants B _O, D _J, χ _aa (Br_i), χ _aa (Br_o), M_bb (Br_i) and M _bb (Br_o), where i = inner and o = outer, were determined for each isotopomer. The complex is linear, with the weak bond between the C atom of CO and Br_i. The rotational constants were used to determine the distance r(C ··· Br_i) = 3.1058Å and to show that the Br—Br bond lengthens by ～0.005–0.01Å on complex formation. The intermolecular stretching force constant kσ = 5.0 Nm^?1 was obtained from D_J and the Br nuclear quadrupole coupling constants were interpreted to reveal that a fraction δ = 0.02 of an electronic charge is transferred from Br_i to Br_o when Br₂ is subsumed into the complex. Properties of the two series OC ··· XY and H₃N ··· XY, where XY = C1₂, Br₂ and BrC1, are compared.     

Linear and Non-linear Stability of Heat Exchangers

The hydrodynamical problem of one-dimensional flow with a uniformheat input resulting in a change of phase is considered. Equationsof mass, momentum, energy and state representing the dynamicbehaviour of such a system are reduced to two coupled equationsfor the density p(x, t) and the inlet velocity U(t) on the assumptionthat the pressure drop applied between the inlet and the outletis "small". A linear stability analysis is carried out whichleads to the problem of computing the zeros of a complicatedanalytic function. A non-linear analysis is applied to the caseof weak instability to find the evolution of the slowly varyingamplitude of a small oscillation: in certain circumstances,a "burst" occurs, and in such cases no such small oscillationcan exist.     

Electric and magnetic properties of hexaethynylbenzene

Coupled Hartree—Fock theory is used to compute the magnetizability and nuclear shielding tensors of hexaethynylbenzene (HEB), and to map the electron current density induced by an external magnetic field. The electric quadrupole moment and polarizability are also computed, and compared with those of benzene and ethyne. The calculations of magnetic properties demonstrate the clear superiority of distributed-origin methods over the conventional common-origin method in which a single fixed origin of vector potential is used. It is shown that the CTOCD-PZ2 formulation provides an efficient and accurate method for the magnetic properties. The current-density maps of HEB show the characteristic π ring current associated with the delocalization of π electrons around the central ring of carbons and local circulations in the ethynyl groups. There is no evidence of a significant induced current linking the ethynyl groups, either through space or through bond. The experimental shielding constants of HEB are well reproduced by the CTOCD-PZ2 calculations, and an analysis of the computed shielding tensors is used to provide a detailed interpretation of the NMR spectrum.     

Models of environmental effects on anion polarizability

This paper deals with three different approaches to the representation of environmental effects on anion polarizability in cubic crystals of the stoichiometry MX, where M is an alkali metal and X is a halogen. Ab initio embedded cluster calculations of the variation in anion polarizability with pressure in a fixed crystal type are presented and compared with experiment. The results are then used in a scaled ab initio model used to predict further values for the pressure dependence of the in-crystal anion polarizability. This scaled model is compared with a fully empirical ‘universal’ model due to Batana et al. based on polarizability change with ionic radius [1997, Molec. Phys., 92, 1029]. The assumptions of the two models differ substantially and the central purpose of this paper is to contrast these differences and highlight their consequences for prediction. Although the empirical model typically overestimates the experimental pressure derivatives, and the ab initio calculations somewhat underestimate them, it is shown that the assumption of incompressible cations in the scaled ab initio-derived model has a firmer physical basis than the empirical picture in which all ions are compressible.     

Anisotropie dipole polarizabilities and quadrupole moments of open-shell atoms and ions: O,F, S,Cl, Se,Br and isoelectronic systems

Quadrupole moment and dipole polarizability tensor components are calculated at the correlated complete-active-space self-consistent-field (CASSCF) and complete-active-space perturbation-theory (CASPT) levels for ²P states of O^?, F, Ne⁺, Na²⁺, S^?, Cl, Ar⁺, 98, K²⁺ , Se^?, Br, Kr⁺, Rb²⁺ and ³P, ¹D, ¹S states of O^?, F⁺, Ne²⁺, Na³⁺, S, Cl⁺, Ar²⁺, K³⁺, Se, Br⁺, Kr²⁺, Rb³⁺. Relativistic corrections are included perturbatively for the 34- and 35-electron systems.     

An Asymptotic Analysis of the Delayed Logistic Equation when the Delay is Large

We show how to construct an asymptotic solution to the delayedlogistic equation = y(1–y₁), corresponding to the asymptoticlimit . The results of the analysis are compared with a numericalcomputation, and found to be comparatively accurate for >2. Since the approach adopted is novel, we comment on some featureswhich may be relevant in other problems.     

Cation polarization and the crystal structure of SnO

Tin(II) oxide has an unusual crystal structure (litharge) which exhibits numerous ‘non-ionic’ features, such as nearest neighbour ions of like charge and a large lattice energy compared with other oxides of similar cation radius. It is shown that a generic ionic interaction model for oxides, with an ab initio based representation of such many-body effects as ionic polarization and the compression of the oxide ion by its environment, predicts litharge as the lowest energy structure. Cation polarization is found to play the dominant role.     

A transferable representation of the induced multipoles in ionic crystals

Electronic structure calculations of the induced dipole and quadrupole moments on a fluoride ion at low symmetry sites in a model crystalline environments are described. The results are used to characterize the short range contributions to the induced multipoles on the F^? ion that arise from overlap between the wavefunctions of the ions. These are represented by general functions of the positions of the surrounding ions, suitable for use in a computationally tractable simulation model. The present calculations are designed to test the transferability to other classes of materials of this representation which, to date, largely has been deduced from calculations on distorted alkali halide crystals. First, the induced multipoles in mixed crystals of the alkali halides are considered, in order to check that they are predicted reliably by combining the representations deduced for the corresponding pure materials. Second, polarization effects in the alkaline earth fluorides MgF₂, and CaF₂, in a locally distorted fluorite crystal structure are examined. It is found that the material-specific parameters in the representation are related through simple functions of the ionic radii. This relationship holds between MgF₂, and CaF₂, in the fluorite structure, but also extends to the alkali fluorides previously studied. In order to illustrate the significance of polarization effects, the polarization model for CaF₂ is combined with an ab initio pair potential for the repulsion and dispersion interactions and used in a molecular dynamics simulation. Inclusion of the polarization term improves greatly the calculated phonon frequencies in the crystal.