MULTISCATT

We report the first experiments using the reversibility of a transient acoustic wave in a multiple-scattering medium to simulate either a stationary or a dynamic acoustic lens. The method is based on time reversal experiments performed in a backscattering configuration. In the stationary case, we show that we take advantage of multiple scattering to focus better than with a perfect reflecting interface. In the dynamic case, we explain the refocused spot time evolution by a simple model based on the time-dependent ability to recover the angular spectrum thanks to both single- and multiple-scattering paths.

Effects of the disorder (or free-orientation) on the multiple scattering situation by using discrete velocity models for the possible (dynamical) localization and/or delocalization of (plane) sound waves propagating in dilute monatomic hard-sphere gases are presented. After comparing with previous free-orientation (n = 2) results, we show that there also exists a certain gap of the spectra for the relevant periodic (wave-propagating) operator when the disorder or free-orientation exists and when a periodic medium with a gap (in spectra) is (slightly) randomized (like our orientation-free 6- and 8-velocity cases) then possible localization and/or delocalization occur in a vicinity of the edges of the gap, even when multiple scattering is being considered.

Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this geometry, using both periodic orbit theory and the short-term semi-classical behavior of wave packets. We also discuss wave packet revivals and show that there are exact revivals, for all wave packets, at times given by (Eq) where a and µ are the length of one side and the mass of the point particle, respectively. We find additional cases of exact revivals with shorter revival times for zero-momentum wave packets initially located at special symmetry points inside the billiard. Finally, we discuss simple variations on the equilateral (60°-60°-60°) triangle, such as the half equilateral (30°-60°-90°) triangle and other foldings, which have related energy spectra and revival structures.

In the framework of a two-scale scattering model, radar backscattering from the rough sea surface was considered. The sea surface was modelled as a superposition of a nonlinear, large-scale Gerstner's wave and small-scale resonant Bragg scattering ripples. The zero-order diffracted field was found by a geometrical optics approach, with shadowing taken into account, and by an `exact' solution of the diffraction problem obtained numerically. For vertical and horizontal polarizations, the spatial distribution of specific scattering cross sections along the large-scale wave was obtained. The spatially averaged specific backscattering cross sections, as well as the mean Doppler frequency shifts at both polarizations, obtained by the geometrical optics approach are compared with those obtained by using the `exact' solution of the large-scale diffraction problem. The roles of shadowing and multiple wave scattering processes are discussed, and qualitative explanations of the difference between these two approaches are given.

Elementary function representations of Schlömilch series introduced by Twersky (Twersky V 1961 Arch. Ration. Mech. Anal. 8 323-32) are used to construct the exact analytical expressions for the classical electromagnetic problem of transverse electric multiple scattering by an infinite array of insulating dielectric circular cylinders at oblique incidence.

Recently time-reversal techniques have emerged as a new, important and fascinating discipline within wave propagation. Many of the problems involved can best be understood, analysed and optimized based on a random field model for the medium. Here we discuss stable refocusing of second-order time-reversed reflections. This phenomenon may appear as surprising at first. However, we show how it can be understood in very simple terms viewing the wavefield as a stochastic process. We give sufficient conditions on Green's function of the propagation problem for the phenomenon to happen. In particular we discuss acoustic wave propagation in the regime of weak random medium fluctuations and explicitly give the derivation of stable refocusing in this case, illustrating it with numerical examples.

We consider the Friedel sum rule (FSR) in the context of the scattering theory for the Schrödinger operator -D _x

We study multiple scattering of elastic waves using a generalized diffusion approximation of the radiative transfer equation applied to spherically symmetric scatterers. This generalized diffusion equation allows us to keep track of the two elastic wave types as well as the mode conversions. It describes the process towards equipartition and fills, as such, a gap between the radiative transfer equation and the conventional diffusion approximation. The effects of boundary conditions and dissipation on the energy partitioning are studied.