Explicit approximate controllability of the Schr\"odinger equation with a polarizability term

We consider a controlled Schr\"odinger equation with a dipolar and a polarizability term, used when the dipolar approximation is not valid. The control is the amplitude of the external electric field, it acts non linearly on the state. We extend in this infinite dimensional framework previous techniques used by Coron, Grigoriu, Lefter and Turinici for stabilization in finite dimension. We consider a highly oscillating control and prove the semi-global weak $H^2$ stabilization of the averaged system using a Lyapunov function introduced by Nersesyan. Then it is proved that the solutions of the Schr\"odinger equation and of the averaged equation stay close on every finite time horizon provided that the control is oscillating enough. Combining these two results, we get approximate controllability to the ground state for the polarizability system

Proceedings of the 13th annual conference of INEBRIA

CITATION: Watson, R., et al. 2016. Proceedings of the 13th annual conference of INEBRIA. Addiction Science & Clinical Practice, 11:13, doi:10.1186/s13722-016-0062-9.The original publication is available at https://ascpjournal.biomedcentral.comENGLISH SUMMARY : Meeting abstracts.https://ascpjournal.biomedcentral.com/articles/10.1186/s13722-016-0062-9Publisher's versio

Appareillage pour l'ionisation thermique des produits de pulvérisation

An apparatus is described in some details for checking a new method of solid elemental analysis. Neutral particles sputtered from a solid target by ion bombardment interact with a tungsten surface heated at very high temperature. The formed ions are then analyzed by means of a quadrupole mass spectrometer. Results for indium ionization after ion sputtering are quite similar to those precedently published where thermal atomic streams were used.Nous décrivons en détail un appareillage destiné à tester une nouvelle méthode d'analyse élémentaire des solides. Les particules arrachées sous forme neutre au cours du bombardement ionique d'une cible solide viennent interagir avec une surface de tungstène portée à très haute température. Les ions formés sont ensuite analysés dans un spectromètre de masse quadrupolaire. Les résultats ainsi obtenus pour l'ionisation de l'indium après pulvérisation sont similaires à ceux déjà publiés utilisant des jets atomiques thermiques

An infinite dimensional bifurcation problem with application to a class of functional differential equations of neutral type

In this paper we consider an infinite dimensional bifurcation equation depending on a parameter epsilon > 0. By means of the theory of condensing operators, we prove the existence of a branch of solutions, parametrized by epsilon, bifurcating from a curve of solutions of the bifurcation equation obtained for epsilon = 0. We apply this result to a specific problem, namely to the existence of periodic solutions bifurcating from the limit cycle of an autonomous functional differential equation of neutral type when it is periodically perturbed by a nonlinear perturbation term of small amplitude

Periodic bifurcation problems for fully nonlinear neutral functional differential equations via an integral operator approach: the multidimensional degeneration case

We consider a T-periodically perturbed autonomous functional differential equation of neutral type. We assume the existence of a T-periodic limit cycle x_0 for the unperturbed autonomous system. We also assume that the linearized unperturbed equation around the limit cycle has the characteristic multiplier 1 of geometric multiplicity 1 and algebraic multiplicity greater than 1. The paper deals with the existence of a branch of T-periodic solutions emanating from the limit cycle

A systematic review of alcohol screening and assessment measures for young people

CITATION: Watson, R., et al. 2016. Proceedings of the 13th annual conference of INEBRIA. Addiction Science & Clinical Practice, 11:13, doi:10.1186/s13722-016-0062-9.The original publication is available at https://ascpjournal.biomedcentral.comENGLISH SUMMARY : Meeting abstracts.https://ascpjournal.biomedcentral.com/articles/10.1186/s13722-016-0062-9Publisher's versio