On finite element approximation and stabilization methods for compressible viscous flows

This work is devoted to the numerical solution of the Navier–Stokes equations for compressible viscous fluids. Finite element approximations and stabilization techniques are addressed. We present methods to implement discontinuous approximations for the pressure and the density. An upwinding methodology is being investigated which combines the ideas behind the stream line Petrov–Galerkin method and the flux limiter methods aiming to introduce numerical diffusion only where it is necessary.     

Classical solutions to a quadratically nonlinear gauge theory

We present some classical solutions to a gauge theory based on quadratically nonlinear Lie algebras without a central term. We observe that instanton-like and meron-like solutions force the internal fields to behave like solitons.     

Developing a risk-assesment methodology in the U.K.defence industry

As a leading defence equipment company, the Dynamics Divisionof British Aerospace Defence Company (BAeDef(DD)) has experiencedthe worst effects of post-Coldwar defence cuts, a global recession,and a determination by the U.K. Government to achieve greatervalue for money in defence procurement. The major tenet of thisnew approach to defence prwurement was 'eyes on, hands off',promoting a shift of the management of project risks from theMinistry of Defence (MOD) to industry. Initial industry reactionwas sceptical but bxame increasingly compliant as tenderingrequirements included visibility of contractors' risk assessment.This paper describes the risk-assessment methodology createdby BAeDef(DD) to meet these changed conditions. The human and organizational aspects of these developments onrisk have helped create a pro-active risk-management cultureat BAeDef(DD). Continuous assessment of project risks providesthe impetus for wider thinking beyond risk-taking or risk-aversionpreferences, leading to greater realism in planning. Decisionsto implement risk resolution measures require competence incost-benefit analysis. The conditions to foster this new behaviourare better-informed senior management, with the rejection ofbad news eliminated at all levels, and the laying of a pathto becoming a learning company.     

The star chromatic number of a graph

We study a generalization of the notion of the chromatic number of a graph in which the colors assigned to adjacent vertices are required to be, in a certain sense, far apart. © 1993 John Wiley & Sons, Inc.     

Aqueous solution and solid state interactions of lanthanide ions with a methacrylic ester polymer bearing pendant 15‐crown‐5 moieties

The interaction between trivalent lanthanide ions and poly(1,4,7,10,13‐pentaoxacyclopentadecan‐2‐yl‐methyl methacrylate), PCR5, in aqueous solution and in the solid state have been studied. In aqueous solution, evidence of a weak interaction between the lanthanides and PCR5 comes from the small red shift of the Ce(III) emission spectra and the slight broadening of the Gd(III) EPR spectra. From the Tb(III) lifetimes in the presence of H₂O and D₂O the loss of one or two water coordinated molecules is confirmed when Tb(III) is bound to PCR5. An association constant of the order of 200 M^?1 was obtained for a 1:1 (lanthanide:15‐crown‐5) complex from the shift of the polymer NMR signals induced by Tb(III). A similar association constant is obtained from the differences of the molar conductivity of Ce(III) solution at various concentrations in presence and absence of PCR5. When Tb(III) is adsorbed on PCR5 membranes, lifetime experiments in H₂O and D₂O confirm the loss of 5 or 6 water coordinated molecules indicating that in solid state the lanthanide(III)‐PCR5 interaction is stronger than in solution. The adsorption of Ce(III) in PCR5 membranes shows a Langmuir type isotherm, from which an equilibrium constant of 39 M^?1 has been calculated. SEM shows that the membrane morphology is not much affected by lanthanide adsorption. Support for lanthanide ion–crown interactions comes from ab initio calculations on 15‐crown‐5/La(III) complex. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1788–1799, 2007     

A hyperbolic three-phase flow model

We introduce a hyperbolic entropy-consistent model to describe three-phase flows, which ensures that void fractions, mass fractions and pressures remain positive through single waves occurring in the one dimensional solution of the Riemann problem. To cite this article: J.-M. Hérard, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Latin Squares without Orthogonal Mates

In 1779 Euler proved that for every even n there exists a latin square of order n that has no orthogonal mate, and in 1944 Mann proved that for every n of the form 4k + 1, k ≥ 1, there exists a latin square of order n that has no orthogonal mate. Except for the two smallest cases, n = 3 and n = 7, it is not known whether a latin square of order n = 4k + 3 with no orthogonal mate exists or not. We complete the determination of all n for which there exists a mate-less latin square of order n by proving that, with the exception of n = 3, for all n = 4k + 3 there exists a latin square of order n with no orthogonal mate. We will also show how the methods used in this paper can be applied more generally by deriving several earlier non-orthogonality results.     

Infrared Features of Unquenched Lattice Landau Gauge QCD

The running coupling and the Kugo-Ojima parameter of unquenched lattice Landau gauge are simulated and compared with the continuum theory. Although the running coupling measured by the ghost and gluon dressing function is infrared suppressed, the running coupling has a maximum of α₀ ∼ 2 − 2.5 at around q = 0.5 GeV irrespective of the fermion actions (Wilson fermions and Kogut-Susskind (KS) fermions). The Kugo-Ojima parameter c which saturated to about 0.8 in quenched simulations becomes consistent with 1 in the MILC configurations produced with the use of the Asqtad action, after averaging the dependence on polarization directions caused by the asymmetry of the lattice. The presence of the correction factor 1 + c ₁/q ² in the running coupling depends on the lattice size and the sea quark mass. In the large lattice size and small sea quark mass, c ₁ is confirmed of the order of a few GeV. The MILC configuration of a = 0.09 fm suggests also the presence of dimension-4 condensates with a sign opposite to the dimension-2 condensates. The gluon propagator, the ghost propagator, and the running coupling are compared with recent pQCD results including an anomalous dimension of fields up to the four-loop level.     

Effect of oxygen exposure on the magnetic properties of ultrathin Co/Ge(1 1 1) films

Influences of oxygen exposure on the magnetic properties of Co/Ge(1 1 1) ultrathin films have been investigated by surface magneto-optic Kerr effect technique. As the oxygen exposure increases on Co/Ge(1 1 1) films, their magnetic properties could be modified. As an example for 15 ML Co/Ge(1 1 1) films, the coercivity increases from 730 to 920 Oe and the remanence Kerr intensity is reduced for 500 Langmuir (L) of oxygen exposure. Corresponding compositions analyzed by Auger electron spectroscopy measurement shows that the amount of oxygen on the surface layers increases with increasing the oxygen exposure time. Oxygen distributes on the topmost layers of the film. The adsorbed oxygen influences the electronic density of states of Co and results in the changes of the magnetic properties. Besides, the appearance of O/Co/Ge interface could modify the stress anisotropy, and as a result the coercivity of ultrathin Co/Ge(1 1 1) film is enhanced.     

The Influence of Variable Convective Velocities on Longitudinal Diffusion

Solutions are presented for the impulsively started uniformstream and simple shear flows past a point source of momentum,which can be interpreted to describe the position and the widthof the front which transmits the knowledge of the singularitythrough a slightly viscous fluid. These understandings are thengeneralized to show that the front always moves with velocityslower than that of a (strictly monotonic) convective velocity,and also that its width always grows faster than with simplediffusion. Finally, a remarkably simple, exact expression is given forvorticity due to a simple shear flow past a point vortex.