LpL^p compression of some HNN extensions

Using recent developments on locally compact groups, we are able to obtain quantitative results on embeddings into Lebesgue spaces for a large class of HNN extensions

Dispersive hydrodynamics of nonlinear polarization waves in two-component Bose-Einstein condensates

We study one dimensional mixtures of two-component Bose-Einstein condensates in the limit where the intra-species and inter-species interaction constants are very close. Near the mixing-demixing transition the polarization and the density dynamics decouple. We study the nonlinear polarization waves, show that they obey a universal (i.e., parameter free) dynamical description, identify a new type of algebraic soliton, explicitly write simple wave solutions, and study the Gurevich-Pitaevskii problem in this context

No consistent cross-interactions for a collection of massless spin-2 fields

We report a no-go theorem excluding consistent cross-couplings for a collection of massless, spin-2 fields described, in the free limit, by the sum of Pauli-Fierz actions (one for each field). We show that, in spacetime dimensions >2, there is no consistent coupling, with at most two derivatives of the fields, that can mix the various "gravitons". The only possible deformations are given by the sum of individual Einstein-Hilbert actions (one for each field) with cosmological terms. Our approach is based on the BRST-based deformation point of view.Comment: 12+1 pages, to appear in the Proceedings of the Meetings "Spring School in QFT and Hamiltonian Systems" (Calimanesti, Romania, 2-7 May 2000) and "Quantization, Gauge Theory and Strings" (Moscow, Russia, 5-10 June 2000

Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula

Factorizing low-rank matrices has many applications in machine learning and statistics. For probabilistic models in the Bayes optimal setting, a general expression for the mutual information has been proposed using heuristic statistical physics computations, and proven in few specific cases. Here, we show how to rigorously prove the conjectured formula for the symmetric rank-one case. This allows to express the minimal mean-square-error and to characterize the detectability phase transitions in a large set of estimation problems ranging from community detection to sparse PCA. We also show that for a large set of parameters, an iterative algorithm called approximate message-passing is Bayes optimal. There exists, however, a gap between what currently known polynomial algorithms can do and what is expected information theoretically. Additionally, the proof technique has an interest of its own and exploits three essential ingredients: the interpolation method introduced in statistical physics by Guerra, the analysis of the approximate message-passing algorithm and the theory of spatial coupling and threshold saturation in coding. Our approach is generic and applicable to other open problems in statistical estimation where heuristic statistical physics predictions are available

Sideband Injection Locking in Microresonator Frequency Combs

Frequency combs from continuous-wave-driven Kerr-nonlinear microresonators have evolved into a key photonic technology with applications from optical communication to precision spectroscopy. Essential to many of these applications is the control of the comb's defining parameters, i.e., carrier-envelope offset frequency and repetition rate. An elegant and all-optical approach to controlling both degrees of freedom is the suitable injection of a secondary continuous-wave laser into the resonator onto which one of the comb lines locks. Here, we study experimentally such sideband injection locking in microresonator soliton combs across a wide optical bandwidth and derive analytic scaling laws for the locking range and repetition rate control. As an application example, we demonstrate optical frequency division and repetition rate phase-noise reduction to three orders of magnitude below the noise of a free-running system. The presented results can guide the design of sideband injection-locked, parametrically generated frequency combs with opportunities for low-noise microwave generation, compact optical clocks with simplified locking schemes and more generally, all-optically stabilized frequency combs from Kerr-nonlinear resonators.Comment: 13 pages, 6 figure

Modèle de simulation 3DoF et capacités spécifiques de controle d'un véhicule de rentrée atmosphérique de type SpaceX Starship

International audienceIn September 2018, a novel design of reusable atmospheric reentry vehicle was proposed: SpaceX's Starship (SXS). Its main difference with comparable vehicles lays in its aerodynamic actuators that allow for stable flight at angles of attack (AoA) up to 90°. In this work, we propose a 3DoF simulation model of this vehicle, and present preliminary reentry simulation results. A study of the center of mass location's implications on longitudinal stability is presented. The modulation of the aerodynamic forces at a given equilibrium AoA allowed by the multiactuator configuration is discussed and demonstrated on a reentry trajectory simulation.En septembre 2018, un nouveau design de véhicule de rentrée atmosphérique as été présenté : le Starship de l'entreprise SpaceX. Sa différence principale avec des véhicules de fonction similaire réside dans ses actionneurs aérodynamiques qui permettent un vol stabilisé a des incidences très élevées, jusqu'à 90° en avant et en arrière.On propose ici un modèle de simulation de ce véhicule avec son actionnement aérodynamique particulier. Une étude de de l'équilibre de la voie de tangage est présentée. La configuration multi-actionneur permettant un nouveau degré de liberté sous la forme de la variation de portance et de traînée à une incidence donnée, cette capacité est discutée et démontrée sur une trajectoire de rentrée atmosphérique

Understanding the catalytic carbonylation of epoxides for the valorization of carbon monoxide

International audienceSmall molecules released as gaseous wastes by the industries, such as CO and CO2, are attractive C1 building blocks for the production of chemicals. They can indeed reduce our dependence on fossil feedstocks. The catalytic insertion of carbon dioxide into epoxides has been developed over the last decades for the production of cyclic and polymeric carbonates, with industrial success. The same strategy can be used for the production of polyester from epoxides and carbon monoxide, possibly released from the production of steel. The catalytic carbonylation of epoxides with gaseous CO leads to $\beta$-lactones and this reaction has attracted a particular attention over the past few years. Yet, only few catalytic systems have been developed, all containing a cobalt carbonyl complex assisted by a Lewis acid. Herein, we disclose a theoretical study to understand the mechanism6 of carbonylation of epoxides using a cobalt catalyst with Lewis acids. The influence of the Lewis acidy on the activity was investigated through various boron compounds. The DFT calculations, linked with a Lewis acidity scale, can thus be used as a guide for the development of a novel catalytic system