Application de la méthode LSPIV pour la mesure de champs de vitesse et de débits de crue sur modèle réduit et en rivière

International audienceLSPIV technique enables the measurement of surface flow velocities using image sequence analysis. EDF and Irstea partnership made possible the development of Fudaa‑LSPIV freeware by DeltaCAD Company. Two software applications at flume and field scales are detailed: (i) bed shear stresses were calculated owing to LSPIV velocities, water depth and bathymetry for a physical model of the Old Rhine; (ii) the software was used to optimize the calculation parameters of LSPIV flood discharge measurement stations in Mediterranean rivers.La technique LSPIV (Large Scale Particle Image Velocimetry) permet de mesurer les vitesses de surface d'un écoulement par analyse de séquence d'images. Pour faciliter l'application opérationnelle de la méthode, un logiciel, Fudaa-LSPIV, a été développé par la société DeltaCAD dans le cadre d'une collaboration entre EDF et Irstea. Deux applications en laboratoire et en rivière sont présentées : (i) couplée avec des mesures de hauteur d'eau et de bathymétries, la LSPIV a permis d'estimer des paramètres de Shields sur le modèle physique à fond mobile du Vieux-Rhin ; (ii) le logiciel a été utilisé pour procéder à des analyses de sensibilité pour paramétrer ainsi au mieux les stations LSPIV de mesure de débit en crue de rivières cévenoles

On the stability of standing waves of Klein-Gordon equations in a semiclassical regime

We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.Comment: 9 page

Morphodynamics of the exit of a cutoff meander: experimental findings from field and laboratory studies

The morphological evolution of the entrances and exits of abandoned river channels governs their hydrological connectivity. The study focusses on flow and sediment dynamics in the exit of a cut-off meander where the downstream entrance is still connected to the main channel, but the upstream entrance is closed. Two similar field and laboratory cases were investigated using innovative velocimetry techniques (acoustic Doppler profiling, image analysis). Laboratory experiments were conducted with a mobile-bed physical model of the Morava river (Slovakia). Field measurements were performed in the exit of the Port-Galland cut-off meander, Ain river (France). Both cases yielded consistent and complementary results from which a generic scheme for flow patterns and morphological evolution was derived. A simple analogy with flows in rectangular side cavities was used to explain the recirculating flow patterns which developed in the exit. A decelerating inflow deposits bedload in the downstream part of the cavity, while the upstream part is eroded by an accelerating outflow, leading to the retreat of the upstream bank. In the field, strong secondary currents were observed, especially in the inflow, which may enhance the scouring of the downstream corner of the cavity. Also, fine sediment deposits constituted a silt layer in a transitional zone, located between the mouth of the abandoned channel and the oxbow-lake within the cut-off meander. Attempts at morphological prediction should consider not only the flow and sediment conditions in the cavity, but also the dynamics of the main channel

Stability and symmetry-breaking bifurcation for the ground states of a NLS with a δ′\delta^\prime interaction

We determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called (attractive) $\delta^\prime$ interaction, located at the origin. The time-dependent problem turns out to be globally well posed in the subcritical regime, and locally well posed in the supercritical and critical regime in the appropriate energy space. The set of the (nonlinear) ground states is completely determined. For any value of the nonlinearity power, it exhibits a symmetry breaking bifurcation structure as a function of the frequency (i.e., the nonlinear eigenvalue) $\omega$. More precisely, there exists a critical value \om^* of the nonlinear eigenvalue \om, such that: if \om_0 < \om < \om^*, then there is a single ground state and it is an odd function; if \om > \om^* then there exist two non-symmetric ground states. We prove that before bifurcation (i.e., for \om < \om^*) and for any subcritical power, every ground state is orbitally stable. After bifurcation (\om =\om^*+0), ground states are stable if $\mu$ does not exceed a value $\mu^\star$ that lies between 2 and 2.5, and become unstable for $\mu > \mu^*$. Finally, for $\mu > 2$ and \om \gg \om^*, all ground states are unstable. The branch of odd ground states for \om \om^*, obtaining a family of orbitally unstable stationary states. Existence of ground states is proved by variational techniques, and the stability properties of stationary states are investigated by means of the Grillakis-Shatah-Strauss framework, where some non standard techniques have to be used to establish the needed properties of linearization operators.Comment: 46 pages, 5 figure

Analytic theory of narrow lattice solitons

The profiles of narrow lattice solitons are calculated analytically using perturbation analysis. A stability analysis shows that solitons centered at a lattice (potential) maximum are unstable, as they drift toward the nearest lattice minimum. This instability can, however, be so weak that the soliton is ``mathematically unstable'' but ``physically stable''. Stability of solitons centered at a lattice minimum depends on the dimension of the problem and on the nonlinearity. In the subcritical and supercritical cases, the lattice does not affect the stability, leaving the solitons stable and unstable, respectively. In contrast, in the critical case (e.g., a cubic nonlinearity in two transverse dimensions), the lattice stabilizes the (previously unstable) solitons. The stability in this case can be so weak, however, that the soliton is ``mathematically stable'' but ``physically unstable''

The Air Microwave Yield (AMY) experiment - A laboratory measurement of the microwave emission from extensive air showers

The AMY experiment aims to measure the microwave bremsstrahlung radiation (MBR) emitted by air-showers secondary electrons accelerating in collisions with neutral molecules of the atmosphere. The measurements are performed using a beam of 510 MeV electrons at the Beam Test Facility (BTF) of Frascati INFN National Laboratories. The goal of the AMY experiment is to measure in laboratory conditions the yield and the spectrum of the GHz emission in the frequency range between 1 and 20 GHz. The final purpose is to characterise the process to be used in a next generation detectors of ultra-high energy cosmic rays. A description of the experimental setup and the first results are presented.Comment: 3 pages -- EPS-HEP'13 European Physical Society Conference on High Energy Physics (July, 18-24, 2013) at Stockholm, Swede

Orbital stability: analysis meets geometry

We present an introduction to the orbital stability of relative equilibria of Hamiltonian dynamical systems on (finite and infinite dimensional) Banach spaces. A convenient formulation of the theory of Hamiltonian dynamics with symmetry and the corresponding momentum maps is proposed that allows us to highlight the interplay between (symplectic) geometry and (functional) analysis in the proofs of orbital stability of relative equilibria via the so-called energy-momentum method. The theory is illustrated with examples from finite dimensional systems, as well as from Hamiltonian PDE's, such as solitons, standing and plane waves for the nonlinear Schr{\"o}dinger equation, for the wave equation, and for the Manakov system