The symmetric eigenvalue complementarity problem

In this paper the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed. It is shown that the symmetric (EiCP) is equivalent to finding an equilibrium solution of a differentiable optimization problem in a compact set. A necessary and sufficient condition for solvability is obtained which, when verified, gives a convenient starting point for any gradient-ascent local optimization method to converge to a solution of the (EiCP). It is further shown that similar results apply to the Symmetric Generalized Eigenvalue Complementarity Problem (GEiCP). Computational tests show that these reformulations improve the speed and robustness of the solution methods.

     

Cu(II)-catalyzed enantioselective aldol condensation between malonic acid hemithioesters and aldehydes

A mild, decarboxylative, aldol-type addition of malonic acid hemithioesters to aldehydes has been shown to occur with up to 39% enantioselectivity when the reaction was carried out in the presence of catalytic amounts of a Cu(II) salt, an enantiopure, tartaric acid-derived bis-benzimidazole and an achiral base.     

Convergence of the parabolic Ginzburg–Landau equation to motion by mean curvature

We present some new results for the asymptotic behavior of the complex parabolic Ginzburg–Landau equation. In particular, we establish that, as the parameter ε tends to 0, vorticity evolves according to motion by mean curvature in Brakke's weak formulation. The only assumption we make is a natural energy bound on the initial data. In some cases, we also prove convergence to enhanced motion in the sense of Ilmanen. To cite this article: F. Bethuel et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Effect of the particle size distribution on the low shear viscosity of high‐solid‐content latexes

The production of high‐solid‐content, low‐viscosity latexes is an active field in both industry and academia. The viscosity of polymer dispersions has a clear dependence on the particle size distribution (PSD). An example is the rule of thumb that a bimodal PSD enables the reduction of the viscosity with respect to monomodal systems. Despite important progress in theoretical work, not much has been done to quantitatively predict the low shear viscosity of aqueous polymer dispersions as a function of the complex PSD. In this work, the capability of a low‐shear‐viscosity equation to quantitatively account for the influence of both the PSD and the physicochemical characteristics of the dispersions is experimentally assessed. An analysis, consistent with theoretical concepts, of the data with semiempirical correlations is proposed. Next, with values of the parameters of the viscosity equation obtained experimentally, the effect of a latex with a 70% solid content on the low shear viscosity is examined. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3936–3946, 2004     

Dynamics of multiple degree Ginzburg–Landau vortices

For the two-dimensional complex parabolic Ginzburg–Landau equation we prove that, asymptotically, vortices evolve according to a simple ordinary differential equation, which is a gradient flow of the Kirchhoff–Onsager functional. This convergence holds except for a finite number of times, corresponding to vortex collisions and splittings, which we describe carefully. The only assumption is a natural energy bound on the initial data. To cite this article: F. Bethuel et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Large number hypothesis

Dirac's large number hypothesis (LNH) and the Whitrow-Randall-Sciama relation are related to some cosmological models. The LNH and Whitrow-Randall-Sciama relations are neither equivalent nor consistent in general relativity, but they may both be valid in the Brans-Dicke theory and in another theory considered in this paper.     

A tentative approach to the direct simulation of drag reduction by polymers

An efficient technique for drag reduction uses dilute solutions of a few p.p.m. of polymers. A possible reduction in drag of up to 80% is achieved. Several experimental observations have been made which tend to indicate that the polymers modify the turbulence structures within the buffer layer. Flow visualisations have shown that the changes consist of a weakening of the strength of the streamwise vortices. Existing literature reveals no attempts of numerical simulation of this phenomenon. In this paper an approach is pursued by using a constitutive equation which relates the elongation viscosity to the local properties of the flow. According to this model this viscosity is large in zones where the amount of strain rate is greater than the amount of vorticity, and is zero when the vorticity exceeds the strain rate. Simulations have been performed in a “minimal channel” to give good resolution with a limited number of grid points. The accuracy of the method is tested by comparison with the results of other techniques. For simulations with polymers, quantitative comparisons cannot be made, but the results reproduce the qualitative outputs of the experiments. The mean streamwise velocity is modified in the buffer layer; the peak of the streamwise turbulent intensity, in wall units, increases and its maximum moves far from the wall; and the vertical turbulent intensity is largely reduced in the wall region. An interesting outcome from both the simulation and the experiments is that the strength of the longitudinal vortices is reduced when the polymers are present.