A time-domain probe method for three-dimensional rough surface reconstructions

The task of this paper is to develop a Time-Domain Probe Method for the reconstruction of impenetrable scatterers. The basic idea of the method is to use pulses in the time domain and the time-dependent response of the scatterer to reconstruct its location and shape. The method is based on the basic causality principle of timedependent scattering. The method is independent of the boundary condition and is applicable for limited aperture scattering data. In particular, we discuss the reconstruction of the shape of a rough surface in three dimensions from time-domain measurements of the scattered field. In practise, measurement data is collected where the incident field is given by a pulse. We formulate the time-domain fieeld reconstruction problem equivalently via frequency-domain integral equations or via a retarded boundary integral equation based on results of Bamberger, Ha-Duong, Lubich. In contrast to pure frequency domain methods here we use a time-domain characterization of the unknown shape for its reconstruction. Our paper will describe the Time-Domain Probe Method and relate it to previous frequency-domain approaches on sampling and probe methods by Colton, Kirsch, Ikehata, Potthast, Luke, Sylvester et al. The approach significantly extends recent work of Chandler-Wilde and Lines (2005) and Luke and Potthast (2006) on the timedomain point source method. We provide a complete convergence analysis for the method for the rough surface scattering case and provide numerical simulations and examples.

The drowned and the saved: shipwrecks and the 'cursus' of Latin love elegy

Throughout the corpus of Latin love elegy, the imaginary tombs envisaged by the elegists for their own personae and for other inhabitants of their poetic world display a striking tendency to take on the characteristic attributes and personalities of those interred within. The final resting-place of Propertius, for instance, that self-proclaimed acolyte of Callimachean miniaturism and exclusivity, is to be sequestered from the degrading attentions of the passing populace (Prop. 3.16.25–30) and crowned with the poet's laurel (2.13.33–4). What remains of his meagre form will rest in a ‘tiny little urn’ (paruula testa, 2.13.32) beneath a monument declaring the lover's slavery to a single passion (2.13.35–6), and the grave is to be attended, or so he hopes, by the object of that passion herself (3.16.23–4), or occasionally (though he is not so confident of this) by his patron Maecenas (2.1.71–8). Likewise the memorial designed by Ovid for Corinna's pet parrot - an imitatrix ales endowed with the most distinctive foibles of the elegiac tradition - in Amores 2.6, comprising a burial mound pro corpore magnus (2.6.59) topped with a tombstone described as exiguus (‘tiny’, 2.6.60; cf. Prop. 2.1.72, 2.13.33), exhibits an elegiac emphasis worthy of the parrot's human counterparts among Ovid's poetic predecessors.