Quantile-based optimization under uncertainties using adaptive Kriging surrogate models

Uncertainties are inherent to real-world systems. Taking them into account is crucial in industrial design problems and this might be achieved through reliability-based design optimization (RBDO) techniques. In this paper, we propose a quantile-based approach to solve RBDO problems. We first transform the safety constraints usually formulated as admissible probabilities of failure into constraints on quantiles of the performance criteria. In this formulation, the quantile level controls the degree of conservatism of the design. Starting with the premise that industrial applications often involve high-fidelity and time-consuming computational models, the proposed approach makes use of Kriging surrogate models (a.k.a. Gaussian process modeling). Thanks to the Kriging variance (a measure of the local accuracy of the surrogate), we derive a procedure with two stages of enrichment of the design of computer experiments (DoE) used to construct the surrogate model. The first stage globally reduces the Kriging epistemic uncertainty and adds points in the vicinity of the limit-state surfaces describing the system performance to be attained. The second stage locally checks, and if necessary, improves the accuracy of the quantiles estimated along the optimization iterations. Applications to three analytical examples and to the optimal design of a car body subsystem (minimal mass under mechanical safety constraints) show the accuracy and the remarkable efficiency brought by the proposed procedure

New Results for Light Gravitinos at Hadron Colliders - Tevatron Limits and LHC Perspectives

We derive Feynman rules for the interactions of a single gravitino with (s)quarks and gluons/gluinos from an effective supergravity Lagrangian in non-derivative form and use them to calculate the hadroproduction cross sections and decay widths of single gravitinos. We confirm the results obtained previously with a derivative Lagrangian as well as those obtained with the non-derivative Lagrangian in the high-energy limit and elaborate on the connection between gauge independence and the presence of quartic vertices. We perform extensive numerical studies of branching ratios, total cross sections, and transverse-momentum spectra at the Tevatron and the LHC. From the latest CDF monojet cross section limit, we derive a new and robust exclusion contour in the gravitino-squark/gluino mass plane, implying that gravitinos with masses below $2\cdot10^{-5}$ to $1\cdot10^{-5}$ eV are excluded for squark/gluino-masses below 200 and 500 GeV, respectively. These limits are complementary to the one obtained by the CDF collaboration, $1.1\cdot 10^{-5}$ eV, under the assumption of infinitely heavy squarks and gluinos. For the LHC, we conclude that SUSY scenarios with light gravitinos will lead to a striking monojet signal very quickly after its startup.Comment: 30 pages, 12 figures. Tevatron limit improved and unitarity limit included. Version to be published in Phys. Rev.

Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction

We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers. The problem is reformulated as a nonautonomous recurrence in a space of time-periodic functions, where the dynamics is considered along the discrete spatial coordinate. We show that small amplitude oscillations are determined by finite-dimensional nonautonomous mappings, whose dimension depends on the solutions frequency. We consider the case of two-dimensional reduced mappings, which occurs for frequencies close to the edges of the phonon band. For an homogeneous chain, the reduced map is autonomous and reversible, and bifurcations of reversible homoclinics or heteroclinic solutions are found for appropriate parameter values. These orbits correspond respectively to discrete breathers, or dark breathers superposed on a spatially extended standing wave. Breather existence is shown in some cases for any value of the coupling constant, which generalizes an existence result obtained by MacKay and Aubry at small coupling. For an inhomogeneous chain the study of the nonautonomous reduced map is in general far more involved. For the principal part of the reduced recurrence, using the assumption of weak inhomogeneity, we show that homoclinics to 0 exist when the image of the unstable manifold under a linear transformation intersects the stable manifold. This provides a geometrical understanding of tangent bifurcations of discrete breathers. The case of a mass impurity is studied in detail, and our geometrical analysis is successfully compared with direct numerical simulations

Filling bone defects with β-TCP in maxillofacial surgery: A review

Reconstruction of bone defects prior to implant placement now involves synthetic substitutes such as β-TCP because of its ability to promote bone remodeling. Its capacity to be progressively substituted by the patient\u27s bone allows to regenerate a dense bone volume. In addition, its availability in large quantities, avoiding the morbidity observed with harvesting autogenous bone, widens the operative indications. In this paper, the main indications of β-TCP in maxillofacial surgery (dentistry, parodontology and dental implant surgery) are reviewed. They include periodontal bone disease, bone disjunction, pre-implant surgery (sinus floor elevation and lateralization of the inferior alveolar nerve)

Optical Probe of Quantum Shot Noise Reduction at a Single-Atom Contact

Visible and infra-red light emitted at a Ag-Ag(111) junction has been investigated from tunneling to single atom contact conditions with a scanning tunneling microscope. The light intensity varies in a highly nonlinear fashion with the conductance of the junction and exhibits a minimum at conductances close to the conductance quantum. The data are interpreted in terms of current noise at optical frequencies, which is characteristic of partially open transport channels

Reply to "Comment on `Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined' ''

In his Comment [see preceding Comment, Phys. Rev. A 82, 037601 (2010)] on the paper by Roux [Phys. Rev. A 79, 021608(R) (2009)], Rigol argued that the energy distribution after a quench is not related to standard statistical ensembles and cannot explain thermalization. The latter is proposed to stem from what he calls the eigenstate thermalization hypothesis and which boils down to the fact that simple observables are expected to be smooth functions of the energy. In this Reply, we show that there is no contradiction or confusion between the observations and discussions of Roux and the expected thermalization scenario discussed by Rigol. In addition, we emphasize a few other important aspects, in particular the definition of temperature and the equivalence of ensemble, which are much more difficult to show numerically even though we believe they are essential to the discussion of thermalization. These remarks could be of interest to people interested in the interpretation of the data obtained on finite-size systems.Comment: 3 page

Latéralisation du nerf alvéolaire inférieur (NAI) à visée préimplantaire

International audienceLe déplacement du nerf alvéolaire inférieur (NAI) est une alternative opératoire encore peu eff ectuée dans l’arsenal des protocoles visant à permettre la pose d’im-plants en territoire mandibulaire postérieur. Cette réticence repose sur la crainte d’altérations neurosensorielles et une méconnaissance de la technique opératoire. L’analyse critique de ces éléments montre néanmoins que le déplacement du NAI eff ectué après une étude clinique rigoureuse et un protocole opératoire strict est une technique fi able permettant d’obtenir un territoire osseux conséquent libéré du passage de la gaine nerveuse. La technique de latéralisation et de postériorisation du NAI montre l’intérêt à long terme de ce type de chirurgie préimplantaire