D. Sornette
Lab. de Phys. de la Matiere Condensee, CNRS URA 190, Univ. de Nice---Sophia Antipolis, Parc Valrose, 06108 Nice Cedex, France
Lab. de Phys. Statist., CNRS and Univ. Paris VI and VII, Paris, France
J.-P. Bouchaud
Lab. Phys. Statist., Univ. Paris VI and VII, Paris, France
O. Legr
Univ. de Nice---Sophia Antipolis, Nice, France
X-RS, Parc-Club, Orsay, France
An inhomogeneous medium with scatterers presenting internal resonances has been suggested to be an efficient system to localize classical waves. Within a mean-field approach describing the internal degrees of freedom of the scatterers and their strong interactions in the near field regime, the existence of two longitudinal modes associated with the scatterers and embedding medium degrees of freedom is found. Anderson localization is shown to be reached in a rather large frequency interval for the ``slow'' mode, above the single scatterer resonant frequency, whereas the ``fast'' mode is never localized. An experimental situation is discussed where the localization of the ``slow'' mode could be observed. This work appeared in J. Phys. I France 2, 1861--1867 (1992). Also considered is the problem of the propagation of acoustic waves in a one-dimensional bubbly liquid, either periodic or random. The response of the bubbly liquid to an incident wave in any range of concentrations, bubble size polydispersity, and frequency range has been computed exactly. Three main regimes are found, depending on the average value of the bubble radius R, average distance d between bubbles, and wavelength (lambda) in the liquid: (1) ``phonon'' or ``mass-spring'' regime; (2) ``bubble'' regime; and (3) ``stratified'' regime. In the random systems, the Anderson localization length is computed both numerically and analytically in the limit of uncorrelated disorder, for various system realizations. This work is due to appear in J. Acoust. Soc. Am.