Multiple scattering by cylinders immersed in fluid: high order approximations for the effective wavenumbers

Acoustic wave propagation in a fluid with a random assortment of identical cylindrical scatterers is considered. While the leading order correction to the effective wavenumber of the coherent wave is well established at dilute areal density ($n_0$) of scatterers, in this paper the higher order dependence of the coherent wavenumber on $n_0$ is developed in several directions. Starting from the quasi-crystalline approximation (QCA) a consistent method is described for continuing the Linton and Martin formula, which is second order in $n_0$, to higher orders. Explicit formulas are provided for corrections to the effective wavenumber up to O$(n_0^4)$. Then, using the QCA theory as a basis, generalized self consistent schemes are developed and compared with self consistent schemes using other dynamic effective medium theories. It is shown that the Linton and Martin formula provides a closed self-consistent scheme, unlike some other approaches.Comment: 12 page

Effective wave numbers for thermo-viscoelastic media containing random configurations of spherical scatterers

The dispersion relation is derived for the coherent waves in fluid or elastic media supporting viscous and thermal effects and containing randomly distributed spherical scatterers. The formula obtained is the generalization of Lloyd and Berry's [Proc. Phys. Soc. Lond. 91, 678-688, 1067], the latter being limited to fluid host media, and it is the three-dimensional counterpart of that derived by Conoir and Norris [Wave Motion 47, 183-197, 2010] for cylindrical scatterers in an elastic host medium.Comment: 11 page

Dynamic effective properties of a random configuration of cylinders in a fluid

International audienceThe dynamic effective properties of a random medium consisting in a uniform concentration of cylindrical scatterers in an ideal fluid are looked for, with special focus on low frequencies. The effective medium is described as an isotropic viscous fluid whose mass density and dilation viscosity depend on frequency, and whose shear viscosity is nil. An explicit expression of the reflection coefficient of a harmonic plane wave incident upon the interface between the ideal fluid and the random medium may be obtained at low frequency, using the Fikioris and Waterman's approach, in two ways. In the first one, the low frequency assumption is introduced from the very beginning, while in the second one, the same hypotheses than those used by Linton et al. [J. Acoust. Soc. Am. 117 6, 2005] to calculate the effective wavenumber are used first, and, then, the low frequency assumption. In both cases, comparison of this reflection coefficient with that at the interface between the ideal fluid and the effective viscous fluid provides the effective density, which, coupled to the effective wavenumber, provides the effective dilatation viscosity. In the first case, the effective parameters found are identical to those found by Mei et al. [Phys. Rev. B 76, 2007] in a different way, while in the second case they are expressed in terms of form functions of the cylinders that reduce at low frequency to those found by Martin et al. [J. Acous. Soc. Am. 128, 2010]. PACS no. 43.20.Fn, 43.35.B

Experimental evidence of isotropic transparency and complete band gap formation for ultrasounds propagating in stealth hyperuniform media

Following on recent experimental characterization of the transport properties of stealth hyperuniform media for electromagnetic and acoustic waves, we report here measurements at ultrasonic frequencies of the multiple scattering of waves by 2D hyperuniform distributions of steel rods immersed in water. The transparency, for which the effective attenuation of the medium is cancelled, is first evidenced by measuring the transmission of a plane wave propagating in a highly correlated and relatively dense medium. It is shown that a band gap occurs in the vicinity of the first Bragg frequency. The isotropy of both transparency and bang gap are also evidenced for the case of waves generated by a point source in differently ordered and circular shaped distributions. In other words, we thus obtain a representation of the Green's function. Our results demonstrate the huge potential of hyperuniform as well as highly correlated media for the design of functional materials

Rayleigh limits for effective wavenumbers of randomly distributed porous cylinders in a fluid

We consider wave propagation in a fluid containing parallel porous cylinders randomly distributed in space. The effective wavenumber of the coherent wave in the medium is derived at the Rayleigh limit for explicit formulas ISA (Independent Scattering Approximation), Waterman and Truell (WT) and Linton and Martin (LM) as well as for implicit formulas, i.e. CPA (Coherent Potential Approximation) and GSCM (General Self Consistent Method) applied to WT and to LM. When the porosity of the cylinders tends to zero the well known cases of an assortment of random elastic cylinders in fluid is found

Effective wavenumbers and reflection coefficients for an elastic medium containing random configurations of cylindrical scatterers

Propagation of P and SV waves in an elastic solid containing randomly distributed inclusions in a half-space is investigated. The approach is based on a multiple scattering analysis similar to the one proposed by Fikioris and Waterman for scalar waves. The characteristic equation, the solution of which yields the effective wave numbers of coherent elastic waves, is obtained in an explicit form without the use of any renormalisation methods. Two approximations are considered. First, formulae are derived for the effective wave numbers in a dilute random distribution of identical scatterers. These equations generalize the formula obtained by Linton and Martin for scalar coherent waves. Second, the high frequency approximation is compared with the Waterman and Truell approach derived here for elastic waves. The Fikioris and Waterman approach, in contrast with Waterman and Truell's method, shows that P and SV waves are coupled even at relatively low concentration of scatterers. Simple expressions for the reflected coefficients of P and SV waves incident on the interface of the half space containing randomly distributed inclusions are also derived. These expressions depend on frequency, concentration of scatterers, and the two effective wave numbers of the coherent waves propagating in the elastic multiple scattering medium.Comment: 24 page

Influence of the microstructure of 2D-random heterogeneous media on the propagation of acoustic coherent waves

International audienceMultiple scattering of waves arises in all fields of physics either in periodic or random media. For random media the organization of the microstructure (uniform or non-uniform statistical distribution of scatterers) has effects on the propagation of coherent waves. Using a recent exact resolution method and different homogenization theories, the effects of the microstructure on the effective wavenumber are investigated over a large frequency range (ka between 0.1 and 13.4) and high concentrations. For uniform random media, increasing the configurational constraint makes the media more transparent for low frequencies and less for high frequencies. As a side but important result, we show that two of the homogenization models considered here appear to be very efficient at high frequency up to a concentration of 60%, in the case of uniform media. For non-uniform media, for which clustered and periodic aggregates appear, the main effect is to reduce the magnitude of resonances and to make network effects appear. In this case, homogenization theories are not relevant to make a detailed analysis

Diffusion acoustique par un cylindre : theorie modale et approximation de l'acoustique geometrique

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

DIFFUSION ACOUSTIQUE PAR UN OBJET CYLINDRIQUE A PROXIMITE D'UNE INTERFACE PLANE

LE HAVRE-BU Centrale (763512101) / SudocSudocFranceF

Multiple scattering by cylinders randomly located in a fluid: Effective properties

International audienceWe consider the interface between a homogeneous fluid and that same fluid with a random distribution of n0 cylinders per square meter inside. A harmonic plane wave, frequency v and wavenumber k, is incident upon that boundary under incidence angle α. The reflection coefficient obtained with the Fikioris and Waterman approach is expanded into powers of n0/K2 up to order 2, using Linton and Martin's expansion of the wavenumber of the coherent wave. This coefficient is then compared to that obtained when a homogeneous viscous fluid replaces the random medium. When the two reflection coefficients are equal, the random fluid is acoustically equivalent to the viscous one, which is called in that case the effective fluid. The coherent wave in the random medium is thus described as the acoustic mode in the effective fluid. Equating the two reflection coefficients provides expressions for the effective properties of the random medium: mass density ρeff, and coefficient of dilatation viscosity ρeff, as the shear viscosity is set to zero. Both depend on α and v, unless low frequencies only are considered, in which case the dependence on α vanishes