Numerical study of one-dimensional and interacting Bose-Einstein condensates in a random potential

We present a detailed numerical study of the effect of a disordered potential on a confined one-dimensional Bose-Einstein condensate, in the framework of a mean-field description. For repulsive interactions, we consider the Thomas-Fermi and Gaussian limits and for attractive interactions the behavior of soliton solutions. We find that the disorder average spatial extension of the stationary density profile decreases with an increasing strength of the disordered potential both for repulsive and attractive interactions among bosons. In the Thomas Fermi limit, the suppression of transport is accompanied by a strong localization of the bosons around the state k=0 in momentum space. The time dependent density profiles differ considerably in the cases we have considered. For attractive Bose-Einstein condensates, a bright soliton exists with an overall unchanged shape, but a disorder dependent width. For weak disorder, the soliton moves on and for a stronger disorder, it bounces back and forth between high potential barriers.Comment: 13 pages, 13 figures, few typos correcte

Localisation d'Anderson des ondes dans les réseaux acoustiques unidimensionnels aléatoires

Après avoir résumé les quelques publications portant sur le phénomène de localisation d'Anderson en acoustique, nous présentons les propriétés générales de réseaux unidimensionnels aléatoires décrits par des chaînes de quadripôles à partir du théorème de Furstenberg, en distinguant variations de la constante de propagation et variations de l'impédance caractéristique. Nous étudions ensuite l'exemple de tuyaux sonores munis de cheminées latérales fermées résonnantes de dimensions aléatoires, en discutant les analogies présentées par cet exemple avec d'autres milieux macroscopiques ou microscopiques. L'expérience et la simulation numérique nous permettent de mettre en évidence le phénomène de localisation d'Anderson et de comparer les effets du désordre aux effets réactifs classiques et aux effets dissipatifs. Nous montrons en particulier l'élargissement des bandes d'arrêt « de résonance » par le désordre. Enfin, nous discutons le comportement de « super réseaux réguliers », constitués de blocs identiques de plusieurs cellules aléatoires

Introduction to aeroacoustics and self-sustained oscillations of internal flows

\u3cp\u3eAfter a review of basic equations of fluid dynamics, the Aeroacoustic analogy of Lighthill is derived. This analogy describes the sound field generated by a complex flow from the point of view of a listener immerged in a uniform stagnant fluid. The concept of monopole, dipole and quadrupole are introduced. The scaling of the sound power generated by a subsonic free jet is explained, providing an example of the use of the integral formulation of the analogy. The influence of the Doppler Effect on the radiation of sound by a moving source is explained. By considering the noise generated by a free jet in a bubbly liquid, we illustrate the importance of the choice of the aeroacoustic variable in an aeroacoustic analogy. This provides some insight into the usefulness of alternative formulations, such as the Vortex Sound Theory. The energy corrolary of Howe based on the Vortex Sound Theory appears to be the most suitable theory to understand various aspects of self-sustained oscillation due to the coupling of vortex shedding with acoustic standing waves in a resonator. This approach is used to analyse the convective energy losses at an open pipe termination, human whistling, flow instabilities in diffusers, pulsations in pipe systems with deep closed side branches and the whistling of corrugated pipes.\u3c/p\u3