Third power associative composition algebras

Classical composition algebras, with a unit element, are well-known and can be obtained by means of the Cayley-Dickson doubling process. If the condition on the existence of unit element is dropped, many new algebras arise. However, it is shown in this paper that if such a weak condition as the associativity of third powers of any element is imposed, only the known flexible composition algebras appear. Partially supported by the DGICYT (PS 90-0129) and by the DGA (PCB-6/91) Supported by a grant from the ‘Plan de Formación del Personal Investigador’ (DGICYT, Spain) This article was processed by the authors using the Springer-Verlag TEX P Jour1g macro package 1991.     

A numerical method for the calculation of incompressible,steady, separated flows around aerofoils

The present work deals with the numerical calculation of the incompressible turbulent flow around aerofoils. An orthogonal curvilinear grid of ‘C’ type is used for the solution of the time averaged equations and Reynolds stresses are modelled according to the κ-ε turbulence model. PISO and SIMPLE algorithms are used to solve the strongly coupled system of the derived finite volume equations and convergence is improved by applying the method of variable local underrelaxation factors. Comparisons between the calculated and measured pressure distributions are presented for NACA 0012 and NACA 4412 wing sections. The formation of separation bubbles according to calculations is also shown.     

An experimental investigation of how accurate,simply supported boundary conditions can be achieved in compression testing of panels

How accurate, simply supported boundary conditions can be obtained experimentally in the testing of rectangular panels subjected to uniaxial compression has been investigated. Experimental buckling loads are obtained using the Southwell method and are compared with theoretical predictions. Several support arrangements are examined and compared to the idealized support conditions.     

Average distribution of prime ideals in families of number fields

We view an algebraic curve over ℚ as providing a one-parameter family of number fields and obtain bounds for the average value of some standard prime ideal counting functions over these families which are better than averaging the standard estimates for these functions.      

On the macroscopic dynamics induced by a model wave-particle collision operator

The macroscopic dynamics of a kinetic equation involving a model wave-particle collision operator of plasma physics is investigated. The Chapman-Enskog asymptotics is first considered in the framework of a hydrodynamic scaling. The obtained macroscopic model still involves a kinetic variable, the particle energy in the rest frame of the fluid, but shares similarities with the compressible Navier-Stokes equation of gas dynamics. Then a diffusive scaling is examined under the hypothesis of small perturbations of a global equilibrium. In this case, the macroscopic model couples the usual incompressible Navier-Stokes with a diffusion equation for the energy distribution function of the particles, constrained by an extended version of the Boussinesq relation. In both cases, the effect of a Lorentz force term is developed, in the perspective of plasma physical modelling. Received June 16, 1997     

An experimental investigation of the influence of stiffener torsional rigidity on buckling of compression panels

The influence of torsional ridigity of the stiffeners on the buckling of reinforced aluminum-alloy panels has been investigated. Experimental results reveal that stiffener torsional rigidity must be introduced in the analysis of compressed panels, for, if the stiffener has a closed cross section, the stiffener shape may change the buckling mode shape essentially and increase the critical load considerably.José María Mínguez was Postgraduate Student in Engineering, Metallic Structures Group, University of Bath, United Kingdom     

Confined and Agitated Swirling Flows with Applications in Chemical Engineering

Turbulent, swirling flows are encountered frequently in chemical engineering practice. In this article, experiments and simulations on two classes of swirling flows, viz. agitated flows (stirred tanks), and confined swirling flows are discussed. Results of large-eddy simulations of stirred tank flow are compared with experimental data, mainly phase-resolved LDA data of the flow in the vicinity of the impeller. Next to the average velocity field, also the turbulent kinetic energy, and the anisotropy of the Reynolds stress tensor have been assessed. An important application of confined swirling flow is the cyclone separator (hydrocyclones for the separation of liquids, gas cyclones for gas-solid separation). The flow in a swirl tube geometry exhibiting many of the typical features of swirl flows (e.g. vortex breakdown) is discussed. Furthermore, a large-eddy simulation of the gas flow in a high-efficiency Stairmand cyclone separator is presented. Two examples of process modeling based on flow simulations are briefly treated: orthokinetic agglomeration of crystals in a stirred tank, and particle separation in a cyclone. This revised version was published online in July 2006 with corrections to the Cover Date.     

Observation of Diastereotopic Signals in 15N NMR Spectroscopy

The first example in the literature of a compound showing anisochronous ¹⁵N atoms resulting from diastereotopicity is described. Racemic 1,3‐dimethyl‐2‐phenyloctahydro‐1H‐benzimidazole was prepared and studied by ¹H, ¹³C and ¹⁵N NMR spectroscopy. If convenient conditions were used (monitored by theoretical calculations of ²J_N‐H spin–spin coupling constants), two ¹⁵N NMR signals were observed and corresponded to the diastereotopic atoms. GIAO/density‐functional calculations of chemical shifts were not only in good agreement with the experimental values but also served as prediction tools. This study suggests that ¹⁵N NMR spectroscopy could be used to probe chirality.     

Carboxylic‐Acid‐Passivated Metal Oxide Nanocrystals: Ligand Exchange Characteristics of a New Binding Motif

Ligand exchange is central in the processing of inorganic nanocrystals (NCs) and requires understanding of surface chemistry. Studying sterically stabilized HfO₂ and ZrO₂ NCs using ¹H solution NMR and IR spectroscopy as well as elemental analysis, this paper demonstrates the reversible exchange of initial oleic acid ligands for octylamine and self‐adsorption of oleic acid at NC surfaces. Both processes are incompatible with an X‐type binding motif of carboxylic acids as reported for sulfide and selenide NCs. We argue that this behavior stems from the dissociative adsorption of carboxylic acids at the oxide surface. Both proton and carboxylate moieties must be regarded as X‐type ligands yielding a combined X₂ binding motif that allows for self‐adsorption and exchange for L‐type ligands.