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Online ISSN 1552-4485; Print ISSN 0033-569X
Reduced equations for an active model of hydroelastic waves in the cochlea
Authors:
Jacob Rubinstein and Peter Sternberg
Journal:
Quart. Appl. Math. 79 (2021), 395-408
MSC (2020):
Primary 92-10; Secondary 76M45
DOI:
https://doi.org/10.1090/qam/1584
Published electronically:
October 14, 2020
MathSciNet review:
4288589
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Building upon our earlier passive models for the cochlea (see L. Peres Hari, J. Rubinstein, and P. Sternberg [Quart. Appl. Math. 74 (2016), no. 4, 647–670] and J. Rubinstein and P. Sternberg [Pure Appl. Funct. Anal. 5 (2020), no. 2, 457–471]), here we enhance the model with an active mechanism. Starting with a one-chamber simplification leading to a system of a time-dependent PDE in two spatial variables for the pressure coupled to a PDE in one spatial variable for the oscillation of the basilar membrane, we rigorously establish the validity of a dimension reduction to a system to two ODE’s. We then present numerical simulations demonstrating the ability of this reduced active system to distinguish and amplify multi-frequency input signals.
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Additional Information
Jacob Rubinstein
Affiliation:
Department of Mathematics, Technion, I.I.T., 32000 Haifa, Israel
MR Author ID:
204416
Email:
koby@technion.ac.il
Peter Sternberg
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405
MR Author ID:
167150
Email:
sternber@indiana.edu
Received by editor(s):
August 7, 2020
Received by editor(s) in revised form:
August 17, 2020
Published electronically:
October 14, 2020
Additional Notes:
The first author acknowledges the support from a grant supplied by the Israel Science Foundation.
The second author acknowledges the support from a Simons Collaboration grant 585520.
Article copyright:
© Copyright 2020
Brown University