Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system

We describe the asymptotic behavior as time goes to infinity of solutions of the 2 dimensional corotational wave map system and of solutions to the 4 dimensional, radially symmetric Yang-Mills equation, in the critical energy space, with data of energy smaller than or equal to a harmonic map of minimal energy. An alternative holds: either the data is the harmonic map and the soltuion is constant in time, or the solution scatters in infinite time

Nonlinear targeted energy transfer of two coupled cantilever beams coupled to a bistable light attachment

International audienceIn order to control the sound radiation by a structure, one aims to control vibration of radiating modes of vibration using " Energy Pumping " also named " Targeted Energy Transfer ". This principle is here applied to a simplified model of a double leaf panel. This model is made of two beams coupled by a spring. One of the beams is connected to a nonlinear absorber. This nonlinear absorber is made of a 3D-printed support on which is clamped a buckled thin small beam with a small mass fixed at its center having two equilibrium positions. The experiments showed that, once attached onto a vibrating system to be controlled, under forced excitation of the primary system, the light bistable oscillator allows a reduction of structural vibration up to 10 dB for significant amplitude and frequency range around the first two vibration modes of the system

Comparaison de techniques d'absorptions vibro-acoustiques

National audienceThis study presents the design of a test-rig built to caracterize a vibro-acoustical absorber. This experimental system is based on the properties of a short Kundt tube allowing low frequencies studies (below the first natural frequency of the tube). A precise measure method (surdetermined two-microphones method) is proposed in order to obtain the desired acoustical parameters of the absorber. Finally, we propose an energy balance of the obtanied frequency response (excitation frequency and its harmonics).Cette étude propose la conception d'un banc d'essai servant à la caractérisation d'absorbeurs vibro-acoustiques. Ce banc est conç u sur la propriété d'un tube de Kundt court permettant le travail en basses fréquences (en-dessous de la première fréquence de résonance du tube). Une méthode de me-sure fine (méthode à deux microphones surdéterminée) est mise en place afin d'extraire les paramètres acoustiques souhaités de l'absorbeur et in fine proposer un bilan énergétique résultant et sa répartition spectrale (fréquence d'excitation et ses harmoniques)

Stable self-similar blow-up dynamics for slightly L2L^2-supercritical generalized KdV equations

In this paper we consider the slightly $L^2$-supercritical gKdV equations $\partial_t u+(u_{xx}+u|u|^{p-1})_x=0$, with the nonlinearity $5<p<5+\varepsilon$ and $0<\varepsilon\ll 1$ . We will prove the existence and stability of a blow-up dynamic with self-similar blow-up rate in the energy space $H^1$ and give a specific description of the formation of the singularity near the blow-up time.Comment: 38 page

Strong Correlation to Weak Correlation Phase Transition in Bilayer Quantum Hall Systems

At small layer separations, the ground state of a nu=1 bilayer quantum Hall system exhibits spontaneous interlayer phase coherence and has a charged-excitation gap E_g. The evolution of this state with increasing layer separation d has been a matter of controversy. In this letter we report on small system exact diagonalization calculations which suggest that a single phase transition, likely of first order, separates coherent incompressible (E_g >0) states with strong interlayer correlations from incoherent compressible states with weak interlayer correlations. We find a dependence of the phase boundary on d and interlayer tunneling amplitude that is in very good agreement with recent experiments.Comment: 4 pages, 4 figures included, version to appear in Phys. Rev. Let

Skyrmion Dynamics and NMR Line Shapes in QHE Ferromagnets

The low energy charged excitations in quantum Hall ferromagnets are topological defects in the spin orientation known as skyrmions. Recent experimental studies on nuclear magnetic resonance spectral line shapes in quantum well heterostructures show a transition from a motionally narrowed to a broader `frozen' line shape as the temperature is lowered at fixed filling factor. We present a skyrmion diffusion model that describes the experimental observations qualitatively and shows a time scale of $\sim 50 \mu{\rm sec}$ for the transport relaxation time of the skyrmions. The transition is characterized by an intermediate time regime that we demonstrate is weakly sensitive to the dynamics of the charged spin texture excitations and the sub-band electronic wave functions within our model. We also show that the spectral line shape is very sensitive to the nuclear polarization profile along the z-axis obtained through the optical pumping technique.Comment: 6 pages, 4 figure

Model study on the photoassociation of a pair of trapped atoms into an ultralong-range molecule

Using the method of quantum-defect theory, we calculate the ultralong-range molecular vibrational states near the dissociation threshold of a diatomic molecular potential which asymptotically varies as $-1/R^3$. The properties of these states are of considerable interest as they can be formed by photoassociation (PA) of two ground state atoms. The Franck-Condon overlap integrals between the harmonically trapped atom-pair states and the ultralong-range molecular vibrational states are estimated and compared with their values for a pair of untrapped free atoms in the low-energy scattering state. We find that the binding between a pair of ground-state atoms by a harmonic trap has significant effect on the Franck-Condon integrals and thus can be used to influence PA. Trap-induced binding between two ground-state atoms may facilitate coherent PA dynamics between the two atoms and the photoassociated diatomic molecule.Comment: 11 pages, 4 figures, to appear in Phys. Rev. A (September, 2003

Kinematics of globular cluster systems and the formation of early-type galaxies

We numerically investigate the kinematic properties of globular cluster systems (GCSs) in E/S0 galaxies formed from dissipationless merging of spiral galaxies. The metal-poor globular clusters (MPCs) and metal-rich clusters (MRCs) in the merger progenitors are initially assumed to have spatial distributions consistent with the Milky Way GC system. Our principal results, which can be tested against observations, are as follows. Both MPCs and MRCs in elliptical galaxies formed from major mergers can exhibit significant rotation at large radii ($\sim$20 kpc) due to the conversion of initial orbital angular momentum into intrinsic angular momentum of the remnant. MPCs show higher central velocity dispersions than MRCs for most major merger models. $V_{\rm m}/{\sigma}_{0}$ (where $V_{\rm m}$ and ${\sigma}_{0}$, are the GCS maximum rotational velocity and central velocity dispersion of respectively) ranges from 0.2--1.0 and 0.1--0.9 for the MPCs and MRCs respectively, within $6R_{\rm e}$ for the remnant elliptical. For most merger remnant ellipticals, $V_{\rm m}/{\sigma}_{0}$ of GCSs within $6R_{\rm e}$ is greater than that of the field stars within $2R_{\rm e}$. The radial profiles of rotational velocities and velocity dispersions of the GCSs depend upon the orbital configuration of the merger progenitors, their mass-ratios, and the viewing angle. For example, more flattened early-type galaxies, formed through mergers with small mass ratios ($\sim$ 0.1), show little rotation in the outer MRCs. Two-dimensional (2D) velocity dispersion distributions of the GCSs of merger remnant ellipticals are generally flattened for both MPCs and MRCs, reflecting the fact that the GCSs have anisotropic velocity dispersions (abridged).Comment: 14 pages, 16 figures, accepted by MNRA