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A fully-coupled subwavelength resonance approach to modelling the passive cochlea

The aim of this paper is to understand the behaviour of a large number of coupled subwavelength resonators. We use layer potential techniques in combination with numerical computations to study an acoustic pressure wave scattered by a graded array of subwavelength resonators. Our set-up is inspired by the structure of cochlear hair cells on the surface of the basilar membrane and promotes the assumption that such cells are sensitive to pressure changes. We compute the resonant modes of the system and explore the model's ability to decompose incoming signals. Significantly, we are able to offer a mathematical explanation for the cochlea's so-called travelling wave behaviour and tonotopic frequency map.