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The Coefficient Problem and Multifractality of Whole-Plane SLE & LLE
No full textInternational audienceKarl Löwner (later known as Charles Loewner) introduced his famous differential equation in 1923 to solve the Bieberbach conjecture for series expansion coefficients of univalent analytic functions at level n = 3. His method was revived in 1999 by Oded Schramm when he introduced the Stochastic Loewner Evolution (SLE), a conformally invariant process which made it possible to prove many predictions from conformal field theory for critical planar models in statistical mechanics. The aim of this paper is to revisit the Bieberbach conjecture in the framework of SLE processes and, more generally, Lévy processes. The study of their unbounded whole-plane versions leads to a discrete series of exact results for the expectations of coefficients and their variances, and, more generally, for the derivative moments of some prescribed order p. These results are generalized to the “oddified” or m-fold conformal maps of whole-plane SLEs or Lévy–Loewner Evolutions. We also study the (average) integral means multifractal spectra of these unbounded whole-plane SLE curves. We prove the existence of a phase transition at a moment order p = p *(κ) > 0, at which one goes from the bulk SLE κ average integral means spectrum, as predicted by the first author (Duplantier Phys. Rev. Lett. 84:1363–1367, 2000) and established by Beliaev and Smirnov (Commun Math Phys 290:577–595, 2009) and valid for p ≤ p *(κ), to a new integral means spectrum for p ≥ p *(κ), as conjectured in part by Loutsenko (J Phys A Math Gen 45(26):265001, 2012). The latter spectrum is, furthermore, shown to be intimately related, via the associated packing spectrum, to the radial SLE derivative exponents obtained by Lawler, Schramm and Werner (Acta Math 187(2):237–273, 2001), and to the local SLE tip multifractal exponents obtained from quantum gravity by the first author (Duplantier Proc. Sympos. Pure Math. 72(2):365–482, 2004). This is generalized to the integral means spectrum of the m-fold transform of the unbounded whole-plane SLE map. A succinct, preliminary, version of this study first appeared in Duplantier et al. (Coefficient estimates for whole-plane SLE processes, Hal-00609774, 2011)
Empirical φ∗-Divergence Minimizers for Hadamard Differentiable Functionals
No full textInternational audienceWe study some extensions of the empirical likelihood method, when the Kullback distance is replaced by some general convex divergence or φ-discrepancy. We show that this generalized empirical likelihood method is asymptotically valid for general Hadamard differentiable functionals
When and where are Mediterranean heavy rain events sensitive to atmosphere-ocean coupled processes?
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Couplages hydromécaniques dans les roches argileuses : analyse par microscopie électronique environnementale et corrélation d'images
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Ocean Mixed Layer responses to intense meteorological events during HyMeX-SOP1 from a high-resolution ocean simulation
No full textInternational audienceKeywords: Air–sea fluxes Extreme events HyMeX Ocean Mixed Layer Western Mediterranean Sea a b s t r a c t The western Mediterranean Sea is a source of heat and humidity for the atmospheric low-levels in autumn. Large exchanges take place at the air–sea interface, especially during intense meteorological events, such as heavy precipitation and/or strong winds. The Ocean Mixed Layer (OML), which is quite thin at this time of year ($20 m-depth), evolves rapidly under such intense fluxes. This study investigates the ocean responses under intense meteorological events that occurred during HyMeX SOP1 (5 September–6 November 2012). The OML conditions and tendencies are derived from a high-resolution ocean simulation using the sub-regional eddy-resolving NEMO-WMED36 model (1/ 36°-resolution), driven at the surface by hourly air–sea fluxes from the AROME-WMED forecasts (2.5 km-resolution). The high space–time resolution of the atmospheric forcing allows the highly variable surface fluxes, which induce rapid changes in the OML, to be well represented and linked to small-scale atmospheric processes. First, the simulation results are compared to ocean profiles from several platforms obtained during the campaign. Then, this study focuses on the short-term OML evolution during three events. In particular, we examine the OML cooling and mixing under strong wind events, potentially associated with upwelling, as well as the surface freshening under heavy precipitation events, producing low-salinity lenses. Tendencies demonstrate the major role of the surface forcing in the temperature and/or salinity anomaly formation. At the same time, mixing [restratification] rapidly occurs. As expected, the sign of this tendency term is very dependent on the local vertical stratification which varies at fine scale in the Mediterranean. It also controls [disables] the vertical propagation. In the Alboran Sea, the strong dynamics redistribute the OML anomalies, sometimes up to 7 days after their formation. Elsewhere, despite local amplitude modulations due to internal wave excitation by strong winds, the integrated effect of the horizontal advection is almost null on the anom-alies' spread and decay. Finally, diffusion has a small contribution
Introduction à la génétique moderne : génomique, épigénétique, clonage, transgenèse, phylogénétique, évolution
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Estimation non paramétrique d'ensembles et de polytopes convexes
No full textIn this thesis, we are interested in statistical inference on convex bodies in the Euclidean space ℝ^d. Two models are investigated. The first one consists of the observation of n independent random points, with common uniform distribution on an unknown convex body. The second one is a regression model, with additive subgaussian noise, where the regression function is the indicator function of an unknown convex body. In the first model, our goal is to estimate the unknown support of the common uniform density of the observed points. In the second model, we aim either to estimate the support of the regression function, or to detect whether this support is nonempty, i.e., the regression function is nonzero. In both models, we investigate the cases when the unknown set is a convex polytope, and when we know the number of vertices. If this number is not known, we propose an adaptive method which allows us to obtain a statistical procedure performing asymptotically as well as in the case of perfect knowledge of that number. In addition, this procedure allows misspecification, i.e., provides an estimator of the unknown set, which is optimal in a minimax sense, even if the unknown set is not polytopal, in the contrary to what may have been thought. We prove a universal deviation inequality for the volume of the convex hull of the observations in the first model. We show that this inequality allows one to derive tight bounds on the moments of the missing volume of this convex hull, as well as on the moments of the number of its vertices. In the one-dimensional case, in the second model, we compute the asymptotic minimal size of the unknown set so that it can be detected by some statistical procedure, and we propose a decision rule which allows consistent testing of whether of that set is empty.Dans ce travail, nous nous intéressons à l'estimation d'ensembles convexes dans l'espace Euclidien ℝ^d, en nous penchant sur deux modèles. Dans le premier modèle, nous avons à notre disposition un échantillon de n points aléatoires, indépendants et de même loi, uniforme sur un ensemble convexe inconnu. Le second modèle est un modèle additif de régression, avec bruit sous-gaussien, et dont la fonction de régression est l'indicatrice d'Euler d'un ensemble convexe ici aussi inconnu. Dans le premier modèle, notre objectif est de construire un estimateur du support de la densité des observations, qui soit optimal au sens minimax. Dans le second modèle, l'objectif est double. Il s'agit de construire un estimateur du support de la fonction de régression, ainsi que de décider si le support en question est non vide, c'est-à-dire si la fonction de régression est effectivement non nulle, ou si le signal observé n'est que du bruit. Dans ces deux modèles, nous nous intéressons plus particulièrement au cas où l'ensemble inconnu est un polytope convexe, dont le nombre de sommets est connu. Si ce nombre est inconnu, nous montrons qu'une procédure adaptative permet de construire un estimateur atteignant la même vitesse asymptotique que dans le cas précédent. Enfin, nous démontrons que ce même estimateur pallie à l'erreur de spécification du modèle, consistant à penser à tort que l'ensemble convexe inconnu est un polytope. Nous démontrons une inégalité de déviation pour le volume de l'enveloppe convexe des observations dans le premier modèle. Nous montrons aussi que cette inégalité implique des bornes optimales sur les moments du volume manquant de cette enveloppe convexe, ainsi que sur les moments du nombre de ses sommets. Enfin, dans le cas unidimensionnel, pour le second modèle, nous donnons la taille asymptotique minimale que doit faire l'ensemble inconnu afin de pouvoir être détecté, et nous proposons une règle de décision, permettant un test consistant du caractère non vide de cet ensemble
Self-Propulsion of Pure Water Droplets by Spontaneous Marangoni-Stress-Driven Motion
No full textInternational audienceWe report spontaneous motion in a fully biocompatible system consisting of pure water droplets in an oil-surfactant medium of squalane and monoolein. Water from the droplet is solubilized by the reverse micellar solution, creating a concentration gradient of swollen reverse micelles around each droplet. The strong advection and weak diffusion conditions allow for the first experimental realization of spontaneous motion in a system of isotropic particles at sufficiently large Péclet number according to a straightforward generalization of a recently proposed mechanism [S. Michelin, E. Lauga, and D. Bartolo, Phys. Fluids 25, 061701 (2013); S. Michelin and E. Lauga, J. Fluid Mech. 747, 572 (2014)]. Experiments with a highly concentrated solution of salt instead of water, and tetradecane instead of squalane, confirm the above mechanism. The present swimming droplets are able to carry external bodies such as large colloids, salt crystals, and even cells
Sensitivity of aerodynamic forces in laminar and turbulent flow past a square cylinder
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A model of the magnetosheath magnetic field during magnetic clouds
No full textInternational audienceMagnetic clouds (MCs) are huge interplanetary structures which originate from the Sun and have a paramount importance in driving magnetospheric storms. Before reaching the magnetosphere, MCs interact with the Earth's bow shock. This may alter their structure and therefore modify their expected geoeffectivity. We develop a simple 3-D model of the magnetosheath adapted to MCs conditions. This model is the first to describe the interaction of MCs with the bow shock and their propagation inside the magnetosheath. We find that when the MC encounters the Earth centrally and with its axis perpendicular to the Sun–Earth line, the MC's magnetic structure remains mostly unchanged from the solar wind to the magnetosheath. In this case, the entire dayside magnetosheath is located downstream of a quasi-perpendicular bow shock. When the MC is encountered far from its centre, or when its axis has a large tilt towards the ecliptic plane, the MC's structure downstream of the bow shock differs significantly from that upstream. Moreover, the MC's structure also differs from one region of the magnetosheath to another and these differences vary with time and space as the MC passes by. In these cases, the bow shock configuration is mainly quasi-parallel. Strong magnetic field asymmetries arise in the mag-netosheath; the sign of the magnetic field north–south component may change from the solar wind to some parts of the magnetosheath. We stress the importance of the B x component. We estimate the regions where the magnetosheath and magnetospheric magnetic fields are anti-parallel at the mag-netopause (i.e. favourable to reconnection). We find that the location of anti-parallel fields varies with time as the MCs move past Earth's environment, and that they may be situated near the subsolar region even for an initially northward magnetic field upstream of the bow shock. Our results point out the major role played by the bow shock configuration in modifying or keeping the structure of the MCs unchanged. Note that this model is not restricted to MCs, it can be used to describe the magnetosheath magnetic field under an arbitrary slowly varying interplanetary magnetic field