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

by H. Ammari and B. Davies

(Report number 2019-09)

Abstract
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 the acoustic pressure field due to scattering by a graded array of subwavelength resonators. Our set-up is designed to model the structure of cochlear hair cells on the surface of the basilar membrane. 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.

Keywords: subwavelength resonance, cochlear mechanics, coupled resonators, hybridisation, passive cochlea, signal processing

@Techreport{AD19_813,
  author = {H. Ammari and B. Davies},
  title = {A fully-coupled subwavelength resonance approach to modelling the passive cochlea},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2019-09},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2019/2019-09.pdf },
  year = {2019}
}

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