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).     

Inhibition of the reduction of Cr(VI) at the magnetite–water interface by calcium carbonate coatings

The effect of calcium carbonate coatings on the reduction of aqueous chromate on the magnetite(1 1 1) surface has been investigated using a combination of synchrotron based X-ray photoemission spectroscopy (PES) and X-ray absorption near edge structure (XANES) spectroscopy, along with laboratory-based powder X-ray diffraction (XRD) and scanning electron microscopy (SEM). CaCO₃ coatings (dominantly calcite with minor quantities of aragonite and vaterite) of thicknesses ranging from 10 Å to 20 m were grown on magnetite(1 1 1) surfaces by exposure to supersaturated aqueous solutions followed by evaporation of the solution—a process that mimics pore-water evaporation in vadose zones leading to the formation of caliche and calcium carbonate coatings on mineral grains. Coating thicknesses were determined from attenuation of the Fe 2p photoemission signal by the carbonate coating. For coatings less than 15 Å thick, Cr 2p photoemission and Cr L_II, L_III-edge XANES spectra show that chromate is reduced by the underlying magnetite surface; however, as the minimum coating thickness increases beyond 15 Å, the magnetite surface becomes passivated and further chromate reduction ceases. Our findings suggest that carbonate coatings on natural magnetite grains can significantly reduce or eliminate their ability to reduce Cr(VI), which is a toxic and highly mobile environmental contaminant.     

Asymmetry in the Multiprotein Systems of Molecular Biology

Signaling in living systems needs to achieve high specificity, to be reversible, and to achieve high signal to noise. Signaling mediated by multiprotein systems has evolved that avoids the requirement for high-affinity binary complexes that would be difficult to reverse and which, in the overcrowded cell, would lead to excessive noise in the system. Symmetrical structures are only occasionally formed. When they are, it is principally to colocate components, for example, the tyrosyl kinases of growth factors, where dimers form. Symmetry is, however, often broken, presumably to create more sensitivity and specificity in the signaling system by assembling other components, into higher-order multiprotein systems. The binding of a single heparin to two 1:1 FGF:FGFR complexes is an example, as is the binding of a single ligase to the Xrcc4 dimer, perhaps so creating a further DNA-binding site.     

Approximately Optimal Recovery of a Multicohort Fishery from Depleted Stocks and Excess Vessel Capacity

Journal of the Operational Research Society - The effect of current harvesting on future fish stocks is best captured with a multicohort model. In principle, numerical dynamic programming can be...     

Pullback attractors for non-autonomous 2D-Navier–Stokes equations in some unbounded domains

In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets. Finally, we prove the existence of a pullback attractor for a non-autonomous 2D Navier–Stokes model in an unbounded domain, a case in which the theory of uniform attractors does not work since the non-autonomous term is quite general. To cite this article: T. Caraballo et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Measurements and simulations of particle dispersion in a turbulent flow

A particle imaging technique has been used to collect droplet displacement statistics in a round turbulent jet of air. Droplets are injected on the jet axis, and a laser sheet and position-sensitive photomultiplier tube are used to track their radial displacement and time-of-flight. Dispersion statistics can be computed which are Lagrangian or Eulerian in nature. The experiments have been simulated numerically using a second-order closure scheme for the jet and a stochastic simulation for the particle trajectories. Results are presented for non-vaporizing droplets of sizes from 35 to 160 μm. The simulations have underscored the importance of initial conditions and early droplet displacement history on the droplet trajectory for droplets with large inertia relative to the turbulence. Estimates of initial conditions have been made and their effect on dispersion is quantified.     

The effect of buoyancy on the weight gain signal in LEC crystal growth

Crystal diameter monitoring in liquid encapsulated Czochralski (LEC) growth using the weighing method is investigated. An analytical expression for the differential weight gain signal is derived for stationary growth conditions accounting for bouyancy. For the GaAs/B₂O₃ system the buoyancy component of the signal can easily amount to 30%. The formula can be applied to determine the crystal/melt interface area, provided the radius of the part emerging from the encapsulant is known, either in advance as the seed dimension, or by separate monitoring using, e.g., conventional optical methods.     

Cyclolinear polysiloxanes. II. Crosslinking and characterization

The synthesis and characterization of two groups of novel networks prepared from cyclolinear polysiloxanes are described. The first group of networks from cyclolinear polysiloxanes (N‐CLPSs) was synthesized by the hydrosilation of vinyl‐terminated cyclolinear polyorganosiloxanes [prepared from diacetoxydiethyltetramethylcyclotetrasiloxane (D₄Et₂OAc₂) or diacetoxytriethylpentamethylcyclopentasiloxane (D₅Et₃OAc₂)] with a copolymer of dimethylsiloxane and methylhydrosiloxane as the crosslinking agent. Hydrosilation was effected with a platinum carbonyl catalyst with a cyclovinylsiloxane moderator. The second group of networks (N‐eCLPSs) was prepared similarly with extended cyclolinear polysiloxanes. The mechanical properties of the novel networks were comparable to those of polydimethylsiloxane networks (N‐PDMS). The oxygen permeabilities were similar to or slightly higher than that of N‐PDMS. The glass‐transition temperatures of D₄Et₂OAc₂‐ and D₅Et₃OAc₂‐based N‐CLPSs were ?67.8 and ?90.8 °C, respectively, whereas the incorporation of polydimethylsiloxane spacers into similar N‐eCLPSs lowered their glass‐transition temperatures to ?109.7 and ?115.0 °C. Upon heating to 800 °C in air, N‐CLPSs yielded more residue than N‐eCLPSs, which in turn yielded more residue than N‐PDMS. These results may have been due to the presence of T units in the cyclic siloxane units, which may have inhibited chain degradation or the formation of volatile products. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4053–4062, 2006