Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design

We describe an elementary algorithm to build convex inner approximations of nonconvex sets. Both input and output sets are basic semialgebraic sets given as lists of defining multivariate polynomials. Even though no optimality guarantees can be given (e.g. in terms of volume maximization for bounded sets), the algorithm is designed to preserve convex boundaries as much as possible, while removing regions with concave boundaries. In particular, the algorithm leaves invariant a given convex set. The algorithm is based on Gloptipoly 3, a public-domain Matlab package solving nonconvex polynomial optimization problems with the help of convex semidefinite programming (optimization over linear matrix inequalities, or LMIs). We illustrate how the algorithm can be used to design fixed-order controllers for linear systems, following a polynomial approach

Etablissement d'un Plan de Prévention des Risques liés à la présence d'anciennes carrières souterraines. Principes d'une analyse par configurations types

International audienceThe north-western districts of Aix-en-Provence (South-East of France) are partly undermined by very old underground abandoned gypsum mines whose localization and extension are no more precisely known. A geotechnical hazard prevention study was prescribed in order to control the urbanization of the studied zone and to manage the potential risks related to the existing frame. INERIS developped a method based on the analysis of representative configurations allowing to define within the whole studied zone (more than thousand hectares) a limited number of representative configurations within which mechanisms of evolution and surface instability phénomena are nearly similar. Hence, seven representative configurations have been identified. A specifical hazard assessment method has then been applied to each configuration in order to grade the different hazard levels. Lastly, the principle adopted to transcribe the hazard mapping in term of lawful prescriptions is presented.Les quartiers nord-ouest de la commune d'Aix-en-Provence (sud-est de la France) sont en partie sous-minés par de très anciennes carrières souterraines de gypse dont, pour la plupart, on ne connaît plus exactement ni la localisation ni l'extension. Un Plan de Prévention des Risques naturels prévisibles (PPR) a été prescrit pour maîtriser l'urbanisation des zones concernées et gérer les risques liés au bâti existant. Pour mener à bien l'établissement de ce PPR, l'INERIS a développé une technique d'analyse par types de configurations permettant de regrouper l'ensemble du secteur d'étude (plus d'un millier d'hectares) en un nombre limité d'environnements représentatifs soumis à des mécanismes d'évolution et des manifestations d'instabilités de surface sensiblement identiques. Sept configurations types ont ainsi pu être identifiées. Chacune a été soumise à une méthode de hiérarchisation de l'aléa spécifiquement adaptée au cas d'Aix-en-Provence. Enfin, le principe adopté pour transcrire la cartographie de l'aléa en terme de zonage réglementaire est présenté

Impact of climate change on the stability of underground shallow cavities. The case of a tragedy in France in relation with the Seine flooding in 1910

International audienceThe present paper deals with climate change impact on stability of underground cavities due to its indirect effect on ground water levels. In France, several back-analyses have confirmed that variations of underground water tables play a key role in the genesis of surface disorders above shallow mine workings. The paper presents the forecast impacts of climate change on the behaviour of underground water tables as well as the consequences of those variations on the stability of disused underground cavities. A particular collapse that affected the Paris Basin during a major flood of the Seine River, one century ago (January 1910), with dramatic consequences, illustrates the importance of water variation impacts on the rock mass behaviour. The high sensitivity of the extracted material (very pure chalk) to water as well as the dynamics of the mine flooding process are described. The most realistic mechanisms and scenario enabling to explain massive failure of the underground workings are then discussed

The French experience of post-mining management

International audienceThe proposed paper presents the French mining historical context that lead to the present situation. Recent evolutions of the French mining legal scope specifically dedicated to post mining management are explained and the systematic prevention policy adopted in France is described, including the major tools used to assure the post mining risks prevention and management process. Finally, some information concerning a first assessment of work progress and experience feedback of the last decade is synthesised.L'article présente sommairement le contexte historique minier qui a conduit à la situation actuelle. Les récentes évolutions du Code Minier concernant la gestion de l'après-mine sont ensuite expliquées et la politique de prévention systématique des risques adoptée en France est décrite, en s'appuyant notamment sur les principaux outils de prévention et de gestion des risques récemment développés. Pour finir, un état des lieux de l'avancement des travaux et du retour d'expérience acquis durant les dix dernières années est proposé

Adsorption behavior of conjugated {C}3-oligomers on Si(100) and HOPG surfaces

A pi-conjugated {C}3h-oligomer involving three dithienylethylene branches bridged at the meta positions of a central benzenic core has been synthesized and deposited either on the Si(100) surface or on the HOPG surface. On the silicon surface, scanning tunneling microscopy allows the observation of isolated molecules. Conversely, by substituting the thiophene rings of the oligomers with alkyl chains, a spontaneous ordered film is observed on the HOPG surface. As the interaction of the oligomers is different with both surfaces, the utility of the Si(100) surface to characterize individual oligomers prior to their use into a 2D layer is discussed