Classification of BPS instantons in N=4 D=4 supergravity

This talk is based on the recent work in collaboration with M. Azreg-A\"{\i}nou and G. Cl\'ement devoted to extremal instantons in the one-vector truncation of the Euclidean $\mathcal{N}=4,\, D=4$ theory. Extremal solutions satisfying the no-force condition can be associated with null geodesic curves in the homogeneous target space of the three-dimensional sigma model arising in toroidal reduction of the four-dimensional theory. Here we (preliminarily) discuss the case of two vector fields sufficient to find all relevant metrics in the full $\mathcal{N}=4,\, D=4$ theory. Classification of instanton solutions is given along the following lines. The first is their possible asymptotic structure: asymptotically locally flat (ALF), asymptotically locally Euclidean (ALE) and ALF or ALE with the dilaton growing at infinity. The second is the algebraic characterization of matrix generators according to their rank and the nature of the charge vectors in an associated Lorentzian space. Finally, solutions are distinguished by the number of independent harmonic functions with unequal charges (up to four).Comment: Submitted to Proceedings of "Quantum Theory and Symmetries" (QTS-7), Prague, August 7-13, 201

Consistent local projection stabilized finite element methods

This work establishes a formal derivation of local projection stabilized methods as a result of an enriched Petrov-Galerkin strategy for the Stokes problem. Both velocity and pressure finite element spaces are enhanced with solutions of residual-based local problems, and then the static condensation procedure is applied to derive new methods. The approach keeps degrees of freedom unchanged while gives rise to new stable and consistent methods for continuous and discontinuous approximation spaces for the pressure. The resulting methods do not need the use of a macro-element grid structure and are parameter-free. The numerical analysis is carried out showing optimal convergence in natural norms, and moreover, two ways of rendering the velocity field locally mass conservative are proposed. Some numerics validate the theoretical results

A symmetric nodal conservative finite element method for the Darcy equation

This work introduces and analyzes novel stable Petrov-Galerkin EnrichedMethods (PGEM) for the Darcy problem based on the simplest but unstable continuous P1/P0 pair. Stability is recovered inside a Petrov-Galerkin framework where element-wise dependent residual functions, named multi-scale functions, enrich both velocity and pressure trial spaces. Unlike the velocity test space that is augmented with bubble-like functions, multi-scale functions correct edge residuals as well. The multi-scale functions turn out to be the well-known lowest order Raviart-Thomas basis functions for the velocity and discontinuous quadratics polynomial functions for the pressure. The enrichment strategy suggests the way to recover the local mass conservation property for nodal-based interpolation spaces. We prove that the method and its symmetric version are well-posed and achieve optimal error estimates in natural norms. Numerical validations confirm claimed theoretical results

Santé mentale et asile : quelle réalité locale ?

Problématique : En Suisse, la situation des requérants d'asile est réglementée depuis 1999 par la Loi sur l'Asile (LAsi) qui leur donnait droit jusqu'en 2008 à une aide sociale, que leur demande soit acceptée, refusée ou que les autorités responsables n'entrent pas en matière. Depuis janvier 2008, tout requérant d'asile ne recevant pas de réponse positive perd cette aide sociale au profit d'une aide dite « d'urgence », impliquant un durcissement des conditions de vie. Depuis lors, un Groupe de Travail « Critères de vulnérabilité » (GT-Vulnérabilité) se charge, sur mandat de l'Etablissement Vaudois d'Accueil des Migrants (EVAM), d'évaluer la situation de certaines personnes percevant l'aide d'urgence sur la base de rapports médicaux et psychiatriques. Il détermine premièrement si la personne doit être considérée comme « vulnérable » pour raison de santé et pose ensuite un préavis médical quant à la possibilité d'amélioration des conditions d'hébergement. Les personnes reconnues comme particulièrement vulnérables sont soumises à un régime différent, impliquant des avantages spécifiés dans l'aide d'urgence. Objectifs : Décrire l'état de santé physique mais surtout mental des personnes percevant l'Aide d'urgence, pour lesquelles une demande a été effectuée auprès de ce groupe et identifier des facteurs associés à cet état de santé. Présenter comment le système de soins organise sa prise en charge et explorer les implications sur la pratique médicale. Méthodologie : Revue exhaustive de la littérature afin de mieux comprendre le contexte social, le cadre légal et les questions éthiques qu'ils impliquent. A partir des dossiers traités par le GT- Vulnérabilité, établissement d'une base de données regroupant des informations d'ordre démographique, médical et anamnestique et analyse descriptive univariée. Résultats: De janvier 2008 à avril 2011, le GT-Vulnérabilité a traité 411 demandes. Parmi les personnes concernées, 52% viennent d'Afrique et sont principalement sans famille. Le GT- Vulnérabilité a pu rendre une décision dans 79% des cas, donnant un préavis en faveur du requérant d'asile pour 82% d'entre eux. On retrouve plus fréquemment une réponse positive lorsqu'il s'agit d'une femme, ou d'une personne avec sa famille. L'étude des dossiers contenant un rapport de généraliste, a montré la présence d'au moins deux diagnostics somatiques chez 42% des personnes, concernant notamment les maladies infectieuses et parasitaires et des atteintes du système nerveux. On retrouve au moins un trouble psychiatrique dans 74% des cas. Il s'agit en particulier de troubles de l'humeur unipolaires et de syndromes de stress post-traumatiques. Les rapports psychiatriques ont également permis d'identifier l'existence de traumatismes chez 81% des personnes, associés surtout à la guerre, à des maltraitance et violences, dans le pays d'origine, mais aussi en Suisse. Conclusion : La situation médicale des requérants d'asile soumis au régime de l'aide d'urgence est préoccupante. Elle met le système de santé et ses divers protagonistes face à des questionnements et des enjeux d'ordre éthique et demande une nécessaire réflexion en termes de santé publique et de politique sanitaire

Evidence of Raleigh-Hertz surface waves and shear stiffness anomaly in granular media

Due to the non-linearity of Hertzian contacts, the speed of sound in granular matter increases with pressure. Under gravity, the non-linear elastic description predicts that acoustic propagation is only possible through surface modes, called Rayleigh-Hertz modes and guided by the index gradient. Here we directly evidence these modes in a controlled laboratory experiment and use them to probe the elastic properties of a granular packing under vanishing confining pressure. The shape and the dispersion relation of both transverse and sagittal modes are compared to the prediction of non-linear elasticity that includes finite size effects. This allows to test the existence of a shear stiffness anomaly close to the jamming transition.Comment: 4 pages 4 figure

Topologically massive gravito-electrodynamics: exact solutions

We construct two classes of exact solutions to the field equations of topologically massive electrodynamics coupled to topologically massive gravity in 2 + 1 dimensions. The self-dual stationary solutions of the first class are horizonless, asymptotic to the extreme BTZ black-hole metric, and regular for a suitable parameter domain. The diagonal solutions of the second class, which exist if the two Chern-Simons coupling constants exactly balance, include anisotropic cosmologies and static solutions with a pointlike horizon.Comment: 15 pages, LaTeX, no figure

Gravitating Chern-Simons vortices

The construction of self-dual vortex solutions to the Chern-Simons-Higgs model (with a suitable eighth-order potential) coupled to Einstein gravity in (2 + 1) dimensions is reconsidered. We show that the self-duality condition may be derived from the sole assumption $g_{00} = 1$. Next, we derive a family of exact, doubly self-dual vortex solutions, which interpolate between the symmetrical and asymmetrical vacua. The corresponding spacetimes have two regions at spatial infinity. The eighth-order Higgs potential is positive definite, and closed timelike curves are absent, if the gravitational constant is chosen to be negative.Comment: 11 pages, LaTe

From the stress response function (back) to the sandpile `dip'

We relate the pressure `dip' observed at the bottom of a sandpile prepared by successive avalanches to the stress profile obtained on sheared granular layers in response to a localized vertical overload. We show that, within a simple anisotropic elastic analysis, the skewness and the tilt of the response profile caused by shearing provide a qualitative agreement with the sandpile dip effect. We conclude that the texture anisotropy produced by the avalanches is in essence similar to that induced by a simple shearing -- albeit tilted by the angle of repose of the pile. This work also shows that this response function technique could be very well adapted to probe the texture of static granular packing.Comment: 8 pages, 8 figures, accepted version to appear in Eur. Phys. J.

Stress response function of a granular layer: quantitative comparison between experiments and isotropic elasticity

We measured the vertical pressure response function of a layer of sand submitted to a localized normal force at its surface. We found that this response profile depends on the way the layer has been prepared: all profiles show a single centered peak whose width scales with the thickness of the layer, but a dense packing gives a wider peak than a loose one. We calculate the prediction of isotropic elastic theory in presence of a bottom boundary and compare it to the data. We found that the theory gives the right scaling and the correct qualitative shape, but fails to really fit the data.Comment: 22 pages, 9 figures, submitted to Euro. Phys. J.

Density modulations in an elongated Bose-Einstein condensate released from a disordered potential

We observe large density modulations in time-of-flight images of elongated Bose-Einstein condensates, initially confined in a harmonic trap and in the presence of weak disorder. The development of these modulations during the time-of-flight and their dependence with the disorder are investigated. We render an account of this effect using numerical and analytical calculations. We conclude that the observed large density modulations originate from the weak initial density modulations induced by the disorder, and not from initial phase fluctuations (thermal or quantum).Comment: Published version; 4+ pages; 4 figure