Indirect Methods For Determination of The Protective Effects of Coating Films on The Surface of Crystals

The extents of the protective effects of coating films on the surface of crystals were determined. Three different samples were made with different quantities of coating fluid (Sepifilm LP 010 in 10% aqueous solution). Since the atomizing rate was constant, the coating time increased in parallel with the volume of coating fluid applied. The direct measurement of film thickness and smoothness is very difficult, and therefore indirect methods were used. Dimenhydrinate was chosen as model drug; this is a heat-sensitive antihistamine with a low melting point. This temperature can be reached during the tableting process. The behaviour of samples on exposure to heat was examined by differential scanning calorimetry. The water uptakes of the samples were determined with an Enslin apparatus. Plasticity was studied with an instrumented tablet machine. These indirect methods (thermal conductivity, water uptake and plasticity measurements) revealed connections between the results of the various experiments. An overlong coating time decreased the protective effect of the coating film. This revised version was published online in August 2006 with corrections to the Cover Date.     

Convexity of Domains of Riemannian Manifolds

In this paper the problem of the geodesic connectedness and convexity ofincomplete Riemannian manifolds is analyzed. To this aim, a detailedstudy of the notion of convexity for the associated Cauchy boundary iscarried out. In particular, under widely discussed hypotheses,we prove the convexity of open domains (whose boundaries may benondifferentiable) of a complete Riemannian manifold. Variationalmethods are mainly used. Examples and applications are provided,including a result for dynamical systems on the existence oftrajectories with fixed energy.     

Time Evolution of Vibration-Induced Excited State Decay

A simple model consisting of two electronic levels and one vibrational mode (phonon) was theoretically studied. The electronic-vibrational interaction was linear in the vibrational displacement. The vibrational mode was taken in the harmonic approximation and was attached to the thermal bath formed by the ambient environment. The kinetic constants of the vibrational dissipation were of the second order in the vibrational-bath coupling and were taken in the Markovian limit. Although, depending on the parameters of the model, different curves of the non-radiative vibration-induced excited state decay were obtained, in general, three time intervals, corresponding to different physical behaviour, were found. In the short-time interval, small oscillations superimposed on the excited state decay were observed. They were determined by the vibrational frequency and influenced by electronic-vibrational coupling. In the middle-time interval, almost quasi-exponential decay was detected; its rate constant increased with stronger electronic-vibrational interaction and speed of vibrational relaxation. In the long-time interval, the decay was very slow and, under special conditions, even an asymptotic non-zero excited state population was observed. Its value increased with the strength of the off-diagonal electron-vibrational coupling. Links of the parameters of the model with quantum chemical terms were estimated.     

Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.     

Une nouvelle méthode de raffinement de maillage spatio-temporel pour l'équation des ondes

In the present Note we introduce an extension of the conservative space–time mesh refinement method presented by Fouquet et al. We also propose a post-treatment of the solution that reduces the spurious phenomena due to the non-conformity between the time meshes. A reinterpretation of the equations in terms of new unknowns leads to a new scheme with second order consistent coupling equations. Numerical experiments in 2D and a plane wave analysis for the 1D model show that the method is second order accurate for an arbitrary refinement. To cite this article: J. Rodríguez, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Remarks on exact controllability for Stokes and Navier–Stokes systems

This Note deals with the controllability of Stokes and Navier–Stokes systems with distributed controls with support in possibly small subdomains. We first present a new global Carleman inequality for the solutions to Stokes-like systems that leads to the null controllability at any time T>0. Then, we present a local result concerning exact controllability to trajectories of the Navier–Stokes system. To cite this article: E. Fernández-Cara et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Unavoidable Traces Of Set Systems

Sauer, Shelah, Vapnik and Chervonenkis proved that if a set system on n vertices contains many sets, then the set system has full trace on a large set. Although the restriction on the size of the groundset cannot be lifted, Frankl and Pach found a trace structure that is guaranteed to occur in uniform set systems even if we do not bound the size of the groundset. In this note we shall give three sequences of structures such that every set system consisting of sufficiently many sets contains at least one of these structures with many sets.