Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.

Pollen-based biome reconstructions for Latin America at 0, 6000 and 18000 radiocarbon years

The biomisation method is used to reconstruct Latin American vegetation at 6000±500 and 18 000±1000 radiocarbon years before present (14C yr BP) from pollen data. Tests using modern pollen data from 381 samples derived from 287 locations broadly reproduce potential natural vegetation. The strong temperature gradient associated with the Andes is recorded by a transition from high altitude cool grass/shrubland and cool mixed forest to mid-altitude cool temperate rain forest, to tropical dry, seasonal and rain forest at low altitudes. Reconstructed biomes from a number of sites do not match the potential vegetation due to local factors such as human impact, methodological artefacts and mechanisms of pollen representivity of the parent vegetation.

How to apologise in Latin: a case study

Recent years have seen an increase in sociolinguistic studies of the Latin language devoted to aspects and forms of politeness as part of general linguistic behaviour, and considerable progress has been made overall. One area, albeit central to the notion of politeness, has been conspicuously neglected so far, and this area is best summarised by the term ‘apologies’. This paper aims to remedy this situation and to provide a first extensive case study, based on the textual corpus of Terence.