Derivation of the k–ε model for locally homogeneous turbulence by homogenization techniques

We derive the incompressible and compressible k–ε model for locally homogeneous turbulence. The model is rigorously derived on formal mathematical grounds using the MPP modelling technique. This lets us calculate by either analytical or numerical means the closure constants of the model. To cite this article: T. Chacón Rebollo, D. Franco Coronil, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

On the direct solution of Riccati equations arising in boundary control theory

Two classes of Riccati equations arising in the boundary control of parabolic systems are studied by direct methods. The new feature with respect to previous works on this subject is the low regularity of the final data. The classes considered here generalize those of [7]and [5]on one side, and of [14]on the other one. Completely new methods are used to obtain the solution of the Riccati equations, in both cases. The central theme is the dependence of the solutions on a «symmetric» norm of the final data, yielding these new results as well as a new proof of existence for the related algebraic Riccati equation under more general assumptions. The synthesis of the associated linear-quadratic-regulator problems is easily solved using these results.     

Exploring new directions for research in problem structuring methods: on the role of cognitive style

Prior research has argued that cognitive style can have a significant impact on group decision making. In addition, several scholars have proposed that cognitive style can play a key role in the design and use of group decision support systems. However, cognitive style has not received a great deal of attention in the problem structuring methods (PSMs) community. This is surprising, given that PSMs are specifically developed to support a group in their decision making. The purpose of this paper is thus to examine the significance of cognitive style within PSMs. The paper identifies and explores the role of four different cognitive style functions in problem structuring interventions. This analysis is carried out by focusing on the different tasks embedded within a group process supported by PSMs. Implications for the research and practice of PSMs are then discussed.     

Higher order shock waves

Shock waves and the relevant Rankine-Hugoniot conditions may be inadequate even in simple cases. As an example, the electromagnetic field generated by a point charge, whose velocity jumps from0 to a constant value, not only jumps across a spherical surface expanding at light speed, but also includes a-distribution term. This suggests that the concept of higher order shock waves be introduced, the associated compatibility conditions being also deduced.

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Sommario Il concetto di onda d'urto può rivelarsi inadeguato per descrivere situazioni anche semplici. A titolo di esempio, si determina esplicitamente l'espressione del campo elettromagnetico generato da una carica puntiforme la cui velocità passa istantaneamente da0 a un valore costante. Il campo elettromagnetico non solo è discontinuo attraverso una superficie sferica che si espande alla velocità della luce, ma include anche un termine che coinvolge la distribuzione. Ciò suggerisce di definire le onde d'urto di ordine superiore, per le quali si determinano le corrispondenti condizioni di compatibilità.

     

The behaviour of alkylcobalt carbonyls under “oxo” conditions

Both normal and secondary alkylcobalt carbonyls are shown not to undergo isomerization under catalytic “oxo” conditions, and the relevance of this obervation for the mechanism of the “oxo” reaction is discussed.     

Effects of substrate relaxation in regular chemisorption. Hydrogen on graphite

Substrate relaxation is shown to play an important role in the 1 : 2 regular chemisorption of hydrogen atoms above alternate carbon atoms in a graphite monolayer. Binding energy, population analysis and electron density maps show that the direct HC bond is strengthened on relaxation.     

Oxidation of steroid α-diketones by thallium (III) acetate : Crystal and molecular structure of a spiro-cyclopentan-a,s-indaceno derivative obtained from 3,4-diketo steroids

Treatment of 2,3-diketo-cholestane (1) with thallium triacetate in acetic acid afforded mainly 3α-carbomethoxy-A-nor-5α-cholestan-2-one (2). Under similar conditions, the 3,4-diketo steroids (3 and 4) underwent extensive rearrangement affording spiro-lactones (9 and 10), in low yields. The structural assignment of the spiro-cholestane derivative was supported by crystallographic X-ray analysis. This product was the result of A and B-ring contractions followed by acid-catalysed cyclization of an unsaturated carboxy intermediate.