Large deviations principle for the cubic NLS equation

In this paper, we present a probabilistic study of rare phenomena of the cubic nonlinear Schrödinger equation on the torus in a weakly nonlinear setting. This equation has been used as a model to numerically study the formation of rogue waves in deep sea. Our results are twofold: first, we introduce a notion of criticality and prove a Large Deviations Principle (LDP) for the subcritical and critical cases. Second, we study the most likely initial conditions that lead to the formation of a rogue wave, from a theoretical and numerical point of view. Finally, we propose several open questions for future research.     

Thermodynamic aspects of the adsorption of hexametaphosphate on kaolinite

The adsorption of hexametaphosphate ion, an important deflocculant used in the ceramic industry, from aqueous solutions onto kaolinite has been studied at different temperatures. The adsorption isotherm follows the Langmuir model: the thermodynamic parameters DeltaG(ads)(0), DeltaH(ads)(0), and DeltaS(ads)(0) were calculated and found to be consistent with an interaction model involving the formation of an inner-sphere complex between HMP and aluminol groups. Also, the dependence of the adsorption behavior on the kaolinite volume fraction has been studied and discussed in term of association processes between the clay particles.     

Nonconventional synthesis and characterization of ultrahigh-molar-mass polyacrylamides

In spite of the significant progresses in the field of replaceable sieving matrices for separating DNA in capillary electrophoresis (CE), an intense research activity is still going on to improve the separation of large size DNA sequencing fragments. There are evidences, both from experimental and theoretical sides that the resolution of these fragments, at the single base, requires the use of sieving matrices comprised of long chain linear polymers. In the separation of DNA fragments by CE are of upmost importance: (i) the complete solubility of the polymer, (ii) the linearity of the chain, (iii) the achievement of ultrahigh viscosity in dilute solutions. The aim of this work is the synthesis of ultrahigh-molecular-weight polymers which possess the three requirements mentioned above by employing a nonconventional method. We demonstrate that the sieving performance of polyacrylamide is directly correlated to its intrinsic viscosity.     

Randomization and the Gross–Pitaevskii Hierarchy

Archive for Rational Mechanics and Analysis - We study the Gross–Pitaevskii hierarchy on the spatial domain $${mathbb{T}^3}$$ . By using an appropriate randomization of the Fourier...     

On the uniqueness of solutions to the periodic 3D Gross–Pitaevskii hierarchy

In this paper, we present a uniqueness result for solutions to the Gross–Pitaevskii hierarchy on the three-dimensional torus, under the assumption of an a priori spacetime bound. We show that this a priori bound is satisfied for factorized solutions to the hierarchy which come from solutions of the nonlinear Schrödinger equation. In this way, we obtain a periodic analogue of the uniqueness result on R³${\mathbb{R}}^3$ previously proved by Klainerman and Machedon [75], except that, in the periodic setting, we need to assume additional regularity. In particular, we need to work in the Sobolev class H^α$H^{\alpha }$ for α>1$\alpha >1$. By constructing a specific counterexample, we show that, on T³${\mathbb{T}}^3$, the existing techniques from the work of Klainerman and Machedon approach do not apply in the endpoint case α=1$\alpha =1$. This is in contrast to the known results in the non-periodic setting, where these techniques are known to hold for all α?1$\alpha ?1$. In our analysis, we give a detailed study of the crucial spacetime estimate associated to the free evolution operator. In this step of the proof, our methods rely on lattice point counting techniques based on the concept of the determinant of a lattice. This method allows us to obtain improved bounds on the number of lattice points which lie in the intersection of a plane and a set of radius R, depending on the number-theoretic properties of the normal vector to the plane. We are hence able to obtain a sharp range of admissible Sobolev exponents for which the spacetime estimate holds.     

Medium-range order in phospho-silicate bioactive glasses: Insights from MAS-NMR spectra,chemical durability experiments and molecular dynamics simulations

The medium-range order of phospho-silicate bioactive glasses (with compositions (2 ? p)SiO₂ · 1Na₂O · 1.1CaO · pP₂O₅, in which p = 0.10, 0.20, 0.26) has been studied by means of a combined-experimental (MAS-NMR, chemical durability measurements) and computational (classical molecular dynamics (MD)) approach. The structural model obtained by MD is showed to be helpful in the interpretation of the NMR spectra. A small amount of Si–O–P link units has been detected in glasses with low P₂O₅-content, but at high P₂O₅ concentration the percentage of Si–O–P bridges becomes important. However, Qⁿ distributions show that the HP5 (p = 0.20) glass structure is less polymerized with respect to the H (p = 0.10) and HP6.5 (p = 0.26) glasses. These results provide useful explanation of the behavior of these glasses in water and highlight the influence of the medium-range order on a very important property of potential bioactive glasses such as the chemical durability.     

Local smoothing effects for the water-wave problem with surface tension

The water-wave problem with a one-dimensional free surface of infinite depth is considered, based on the formulation as a second-order nonlinear dispersive equation. The local smoothing effects are established under the influence of surface tension, stating that on average in time solutions acquire locally 1/4 derivative of smoothness as compared to the initial state. The analysis combines energy methods with techniques of Fourier integral operators. To cite this article: H. Christianson et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).