Consider the time-harmonic acoustic scattering from an extended elastic body surrounded by a finite number of point-like obstacles in a fluid. We assume point source waves are emitted from arrayed transducers and the signals of scattered near-field data are recorded by receivers not far away from the scatterers (compared to the incident wavelength). The forward scattering can be modeled as an interaction problem between acoustic and elastic waves together with a multiple scattering problem between the extend solid and point scatterers. We prove a necessary and sufficient condition that can be used simultaneously to recover the shape of the extended elastic solid and to locate the positions of point scatterers. The essential ingredient in our analysis is the outgoing-to-incoming (OtI) operator applied to the resulting near-field response matrix (or operator). In the first part, we justify the MUSIC algorithm for locating point scatterers from near-field measurements. In the second part, we apply the factorization method, the continuous analogue of MUSIC, to the two-scale scattering problem for determining both extended and point scatterers. Numerical examples in 2D are demonstrated to show the validity and accuracy of our inversion algorithms.

In this article we develop a posteriori error estimates for second orderlinear elliptic problems with point sources in two- and three-dimensional domains. Weprove a global upper bound and a local lower bound for the error measured in a weightedSobolev space. The weight considered is a (positive) power of the distance to the supportof the Dirac delta source term, and belongs to the Muckenhoupt’s class A2. The theoryhinges on local approximation properties of either Clément or Scott–Zhang interpolationoperators, without need of modifications, and makes use of weighted estimates forfractional integrals and maximal functions. Numerical experiments with an adaptivealgorithm yield optimal meshes and very good effectivity indices.

The AMANDA neutrino telescope, prototype instrument of the IceCube neutrino observatory at South Pole, has collected data since 2000 in its final configuration. A period of 1001 days of livetime between 2000 and 2004 has been analysed in order to find evidence of a neutrino signal coming from point-like sources such as microquasars, active galactic nuclei, supernovae remnants or gamma ray bursts. A sensitivity to fluxes of νμ + νμ + ντ + ντ of dΦ/dE =1.0 · 10−10 (E/TeV)−2 · TeV−1 cm−2 s−1 was reached in the energy range between 1.6 TeV and 1.6 PeV. No significant excess over the background has been found so far. Flux upper limits infered from this study can constrain certain neutrino emission models of X-ray binaries. IceCube will have a substantially higher sensitivity. Currently at 10% of its final extension, it will comprise 4800 optical sensors deployed along 80 strings by early 2011, instrumenting one cubic kilometre volume of ice and 1 km2 at the surface.