University of Cambridge > > Isaac Newton Institute Seminar Series > Coherent elastic waves in multiple scattering media: influence of resonances and positional correlations of scatterers

Coherent elastic waves in multiple scattering media: influence of resonances and positional correlations of scatterers

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MWS - Mathematical theory and applications of multiple wave scattering

The propagation of elastic waves in heterogeneous media is a fundamental research topic that concerns composite materials, porous materials, colloids and emulsions, with the aim of characterising these materials or optimising their performance. This subject has benefited from renewed interest with the development in the 2000s of metamaterials and in particular locally resonant metamaterials. These materials consist of a fluid or solid matrix containing an ordered or random distribution of scatterers, whose resonances alter wave propagation. In some cases, the macroscopic mechanical properties of these materials are modified in non-ordinary ways, opening the way to wave control or damping. Other strategies have been implemented to control or guide waves, such as phononic crystals or topological metamaterials. Recently, the control of spatial correlations in random scatterer distributions has emerged as a new approach, and in particular the use of hyperuniform distributions has proven to be particularly relevant. In this context, the objective of the presented work is to study the influence of positional correlations between scatterers and strong sub-wavelength resonances on the propagation of coherent elastic waves. To achieve this, the work is based on the systematic comparison of results from statistical models, numerical simulations and experiments. The numerical results are obtained using the MuScat calculation code, developed in the laboratory. This code is based on the resolution of the multiple scattering equations as well as on the development of the incident and scattered fields on the cylindrical or spherical harmonics. It allows the treatment of various wave interaction problems with many scatterers, without any restriction on the distribution of the particles, nor on their polydispersity in size or elasticity. The MuScat code is used to study the influence of positional correlations between scatterers on coherent waves. Two types of correlation are investigated: short-range correlations, which are based simply on an exclusion distance between each pair of scatterers, and long-range correlations, which apply to the whole distribution. One type of material that exhibits these long-range correlations is hyperuniform media, which are characterised by the cancellation of density fluctuations as the volume of the medium tends towards infinity. Numerical simulations highlight the elastic wave transparency regime of hyperuniform media, as well as the existence of complete stop bands. Short-range correlations, which are much simpler to implement, lead to similar results. In a second step, we investigate the propagation of coherent elastic waves in a distribution of dense beads embedded in a softer solid matrix. This particle-matrix pair exhibits two sub-wavelength dipolar resonances: a translational resonance that affects both longitudinal and transverse waves and a rotational resonance that affects only transverse waves. Longitudinal coherent waves are then strongly influenced by the translational resonance and the study of statistical models shows that wave conversions are particularly important. Transverse coherent waves are influenced by translational and rotational dipole resonances, and increasing concentration leads to the simultaneous propagation of two coherent waves. The influence of spatial correlations, especially short-range correlations, finally allows to optimise these non-ordinary effects.

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

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