Padé approximants for the acoustical properties of rigid frame porous media with pore size distributions

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with fixed cross-sectional shape, but of variable pore size distribution. The lowand high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coefficients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade´ approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned

Padé approximants for the acoustical characteristics of rigid frame porous media

In this paper it is shown that a number of theoretical models of the acoustical properties of rigid frame porous media, especially those involving ratios of Bessel functions of complex argument, can be accurately approximated and greatly simplified by the use of Padé approximation techniques. In the case of the model of Attenborough [J. Acoust. Soc. Am. 81, 93–102 (1987)] rational approximations are produced for the characteristic impedance, propagation constant, dynamic compressibility, and dynamic density, as a function of frequency and the material parameters. The model proposed by Stinson and Champoux

Novel European free-living, non-diazotrophic Bradyrhizobium isolates from contrasting soils that lack nodulation and nitrogen fixation genes - a genome comparison

The slow-growing genus Bradyrhizobium is biologically important in soils, with different representatives found to perform a range of biochemical functions including photosynthesis, induction of root nodules and symbiotic nitrogen fixation and denitrification. Consequently, the role of the genus in soil ecology and biogeochemical transformations is of agricultural and environmental significance. Some isolates of Bradyrhizobium have been shown to be non-symbiotic and do not possess the ability to form nodules. Here we present the genome and gene annotations of two such free-living Bradyrhizobium isolates, named G22 and BF49, from soils with differing long-term management regimes (grassland and bare fallow respectively) in addition to carbon metabolism analysis. These Bradyrhizobium isolates are the first to be isolated and sequenced from European soil and are the first free-living Bradyrhizobium isolates, lacking both nodulation and nitrogen fixation genes, to have their genomes sequenced and assembled from cultured samples. The G22 and BF49 genomes are distinctly different with respect to size and number of genes; the grassland isolate also contains a plasmid. There are also a number of functional differences between these isolates and other published genomes, suggesting that this ubiquitous genus is extremely heterogeneous and has roles within the community not including symbiotic nitrogen fixation.