SOLUTION OF A TWO-DIMENSIONAL COCHLEA MODEL USING TRANSFORM TECHNIQUES.

Randall J. LeVeque, Charles S. Peskin, Peter D. Lax

Research output: Contribution to journalArticlepeer-review

Abstract

The authors study the propagation of waves on the basilar membrane, a thin elastic plate immersed in the fluid-filled inner ear, using a two-dimensional linear model. Since the basilar membrane has an exponentially increasing compliance, Fourier transforming these equations gives rise to an unusual boundary value problem for an analytic function in the complex plane. They describe a general technique for solving such equations and apply it to the cochlea model. The resulting expression for the Fourier transform can be used to deduce important features of the cochlea wave. This approach also serves as the basis for an efficient numerical method to approximate the cochlea wave using fast Fourier transforms.

Original languageEnglish (US)
Pages (from-to)450-464
Number of pages15
JournalSIAM Journal on Applied Mathematics
Volume45
Issue number3
DOIs
StatePublished - 1985

ASJC Scopus subject areas

  • Applied Mathematics

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