Neutral inclusions for diffusive acoustic fields

Abstract

We predict scattering cancellation in diffusive transport of acoustics waves propagating through multiple scattering media in the stationary limit. This would enable sensing of diffusive sound without disrupting the exterior acoustic field. We present design schemes for making spherical or cylindrical core-shell structures with multiple layers, characterized by homogenous and isotropic diffusion coefficients, neutral to an arbitrary applied multipole field. The double-layered sphere is found to support transparency to two concurrent multipole fields and unique cloaking solutions of arbitrary multipole order. One extra degree of freedom is provided by every layer added to the core-shell structure which may be exploited with our iterative formula for effective diffusivity for cloaking of additional field terms. From this we pass over to the long wavelength limit of ballistic sound and provide formulas for effective mass densities of multi-layered structures in spherical and cylindrical geometries with respect to multipole pressure fields.