Topologically Irreducible Representations and Radicals in Banach Algebras

It is shown that the topologically irreducible representationsof a normed algebra define a certain topological radical inthe same way that the strictly irreducible representations definethe Jacobson radical and that this radical can be strictly smallerthan the Jacobson radical. An abstract theory of ‘topologicalradicals’ in topological algebras is developed and usedto relate this radical to the Baer radical (prime radical).The relations with topologically transitive representationsand standard representations in the sense of Meyer are alsoexplored. 1991 Mathematics Subject Classification: 46H15, 46H25,16Nxx.     

Anisotropic Organised Eddy Simulation for the prediction of non-equilibrium turbulent flows around bodies

The unsteady turbulent flow around bodies at high Reynolds number is predicted by an anisotropic eddy-viscosity model in the context of the Organised Eddy Simulation (OES). A tensorial eddy-viscosity concept is developed to reinforce turbulent stress anisotropy, that is a crucial characteristic of non-equilibrium turbulence in the near-region. The theoretical aspects of the modelling are investigated by means of a phase-averaged PIV in the flow around a circular cylinder at Reynolds number 1.4×10⁵. A pronounced stress–strain misalignment is quantified in the near-wake region of the detached flow, that is well captured by a tensorial eddy-viscosity concept. This is achieved by modelling the turbulence stress anisotropy tensor by its projection onto the principal matrices of the strain-rate tensor. Additional transport equations for the projection coefficients are derived from a second-order moment closure scheme. The modification of the turbulence length scale yielded by OES is used in the Detached Eddy Simulation hybrid approach. The detached turbulent flows around a NACA0012 airfoil (2-D) and a circular cylinder (3-D) are studied at Reynolds numbers 10⁵ and 1.4×10⁵, respectively. The results compared to experimental ones emphasise the predictive capabilities of the OES approach concerning the flow physics capture for turbulent unsteady flows around bodies at high Reynolds numbers.     

Études numérique et expérimentale de la cinétique de refroidissement d'un disque de polymère: Application aux cables

A numerical study of polymer cooling has been done taking into account the variations of all parameters with temperature, as well as the crystallization heat. The case of a radial temperature distribution (disc or sphere) was considered. The results of the calculation were compared with those of some experiments performed on a disc of low density polyethylene. The results indicate that the parameters have effects upon the creation of voids in the material. Despite different boundary conditions in the calculation compared with the experiments, agreement is reasonable demonstrating the validity of the numerical treatment. This analysis can be extended to a two-component model (case of the cooling of a coaxial cable).     

Two Useful Photolabile Surfaces for Solid-Phase Synthesis

o-Nitrobenzyl-based photolabile surfaces 3 and 4 have been synthesized from 2-phenylcyclohexanone and aminopropylsiloxane-grafted controlled pore glass. The procedures are simple and inexpensive and generate materials whose minimally functionalized reactive chromophore should tolerate a range of subsequent chemistries. Time- and solvent-dependent analysis of photodegradation demonstrates a performance comparable to related photolabile systems.