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Acoustic waves propagation in disordered media : Influence of spatial correlations on coherent wave

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MWSW02 - Theory of wave scattering in complex and random media

Adrien Rohfritsch, Tony Valier-Brasier, Régis Marchiano, Jean-Marc Conoir. This work deals with the propagation of acoustic waves through heterogeneous structures. An originalnumerical modelisation is developped that offers the possibility to treat problems that bring into play severalthousands of particles, either spherical of cylindrical. This tool takes into account the size of the scatterersand their exact distribution in space that characterizes the microstructure. The results presented focuse on the effective properties of the mean field, or coherent wave, driven bya complex wavenumber keff. Different spatial correlations are inserted in the microstructure, with the ideato deeply understand the link between the nature of the correlations and the modifications induced on keff.The study of isotropic microstructures lead us to use our numerical tool to validate several homogeneizationmodels from the literature that include correlations thanks to the pair-correlation function. The model developped by Fikioris and Waterman (FW) is precisely analyzed in a novel manner andconnections with Keller’s model based on diagrammatic expansion are drawn. Short-range correlations (SRC)and long range correlation (or stealth hyperuniform, SHU ) are compared and studied one after the other.The SRC media appear then as a transition between uncorrelated media and SHU media. For the first time,low frequency transparency of the SHU media are analyzed taking into account multiple scattering, highconcentration and particles anisotropic scattering effects. The frequency limit for transparency is expressedthanks to the concentration and the degree of stealthiness. For the microstructures SRC and SHU , FW modelis valid for concentration up to 50%, which is much higher than the value commonly accepted. This surprisingresult is confirmed thanks to experimental measures of keff through SRC slabs made of steel rods and ofdifferent thicknesses. Finally, propagation through two complex correlated microstructures is presented. The first one is made ofsub-wavelength resonators and offers selective filtering possibilities at low frequency. The second is composed of a combination of two distinct microstructures. By mixing short and long range correlations, we demonstrate the possibility to modify effective phase velocity without impacting effective attenuation, which is of great interest for wave front shaping.

This talk is part of the Isaac Newton Institute Seminar Series series.

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