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Title: Active noise control has been around since the pioneering work of Paul Lueg in 1936. The idea is to use active sources to prevent scattering of sound or to keep a closed region quiet. Over the last twenty years active metamaterials have become an important part of metamaterial science, leading to (amongst other things) what are now known as active cloaks. The idea is to distribute active sources in a way that both prevents scattering and keeps a region quiet. Achieving both of these feats is highly non-trivial! Furthermore knowing how to distribute sources spatially in three dimensions, whilst also calculating the required amplitudes of those sources is a highly complex computational challenge.
In our work we re-visited this problem and realised that distributing the active sources at the vertices of an imaginary Platonic solid surrounding the region that needs to be made quiet is highly effective and efficient. Why? One can exploit the rotational symmetry properties of the Platonic solids to show that we only need to find the required amplitude at one of the source locations in order to know the amplitudes at every other source location. This speeds up computations of the required amplitudes significantly.
The image illustrates the implementation of our active noise control technique in the case of acoustic scattering from a sphere. The bottom left image illustrates a cross-section of the pressure field due to scattering from a sphere due to plane wave incidence, without any active control. This is contrasted with the image in the bottom right, in which we have used the Platonic distribution of sources in the top right image to control the field. There is almost no scattering outside the active source region and almost complete quiet inside.
For more details see our current arxiv paper on this topic:
https://arxiv.org/abs/2109.14552

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Description: Active noise control has been around since the pioneering work of Paul Lueg in 1936. The idea is to use active sources to prevent scattering of sound or to keep a closed region quiet. Over the last twenty years active metamaterials have become an important part of metamaterial science, leading to (amongst other things) what are now known as active cloaks. The idea is to distribute active sources in a way that both prevents scattering and keeps a region quiet. Achieving both of these feats is highly non-trivial! Furthermore knowing how to distribute sources spatially in three dimensions, whilst also calculating the required amplitudes of those sources is a highly complex computational challenge. In our work we re-visited this problem and realised that distributing the active sources at the vertices of an imaginary Platonic solid surrounding the region that needs to be made quiet is highly effective and efficient. Why? One can exploit the rotational symmetry properties of the Platonic solids to show that we only need to find the required amplitude at one of the source locations in order to know the amplitudes at every other source location. This speeds up computations of the required amplitudes significantly. The image illustrates the implementation of our active noise control technique in the case of acoustic scattering from a sphere. The bottom left image illustrates a cross-section of the pressure field due to scattering from a sphere due to plane wave incidence, without any active control. This is contrasted with the image in the bottom right, in which we have used the Platonic distribution of sources in the top right image to control the field. There is almost no scattering outside the active source region and almost complete quiet inside. For more details see our current arxiv paper on this topic: https://arxiv.org/abs/2109.14552