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On the Betti numbers of level sets of solutions to elliptic equations
Paradoxical waves and active mechanism in the cochlea
1. | Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, United States, United States |
References:
[1] |
R. P. Beyer, A computational model of the cochlea using the immersed boundary method, J. Computational Physics, 98 (1992), 145-162. |
[2] |
P. J. Dallos, The active cochlea, J. Neuroscience, 12 (1992), 4575-85. |
[3] |
E. Givelberg and J. Bunn, A comprehensive three-dimensional model of the cochlea, J. Computational Physics, 191 (2003), 377-391.
doi: 10.1016/S0021-9991(03)00319-X. |
[4] |
A. J. Hudspeth, Integrating the active process of hair cells with cochlear function, Nature Reviews Neuroscience, 15 (2014), 600-614.
doi: 10.1038/nrn3786. |
[5] |
E. Isaacson, A Numerical Method for a Finite-Depth, Two-Dimensional Model of the Inner Ear, Ph.D thesis, New York University, 1979. |
[6] |
R. J. LeVeque, C. S. Peskin and P. D. Lax, Asymptotic analysis of a viscous cochlear model, J. Acoustical Society of America, 77 (1985), 2107-2110.
doi: 10.1121/1.391735. |
[7] |
R. J. LeVeque, C. S. Peskin and P. D. Lax, Solution of a two-dimensional cochlea model using transform techniques, SIAM J. Appl. Math., 45 (1985), 450-464.
doi: 10.1137/0145026. |
[8] |
R. J. LeVeque, C. S. Peskin and P. D. Lax, Solution of a two-dimensional cochlea model with fluid viscosity, SIAM J. Appl. Math., 48 (1988), 191-213.
doi: 10.1137/0148009. |
[9] |
C. S. Peskin, Flow patterns around heart valves: A numerical method, J. Computational Physics, 10 (1972), 252-271. |
[10] |
C. S. Peskin, Lectures on Mathematical Aspects of Physiology (II) The Inner Ear, in Mathematical Aspects of Physiology (eds. F.C. Hoppensteadt), American Mathematical Society, (1981), 38-69. |
[11] |
C. S. Peskin, The immersed boundary method, Acta Numerica, 11 (2002), 479-517.
doi: 10.1017/S0962492902000077. |
[12] |
J. J. Stoker, Water Waves, Interscience Publishers Inc, New York, 1957. |
[13] |
G. von Bekesy, Experiments in Hearing, Robert E. Krieger Publishing Company, Huntington, New York, 1960. |
show all references
References:
[1] |
R. P. Beyer, A computational model of the cochlea using the immersed boundary method, J. Computational Physics, 98 (1992), 145-162. |
[2] |
P. J. Dallos, The active cochlea, J. Neuroscience, 12 (1992), 4575-85. |
[3] |
E. Givelberg and J. Bunn, A comprehensive three-dimensional model of the cochlea, J. Computational Physics, 191 (2003), 377-391.
doi: 10.1016/S0021-9991(03)00319-X. |
[4] |
A. J. Hudspeth, Integrating the active process of hair cells with cochlear function, Nature Reviews Neuroscience, 15 (2014), 600-614.
doi: 10.1038/nrn3786. |
[5] |
E. Isaacson, A Numerical Method for a Finite-Depth, Two-Dimensional Model of the Inner Ear, Ph.D thesis, New York University, 1979. |
[6] |
R. J. LeVeque, C. S. Peskin and P. D. Lax, Asymptotic analysis of a viscous cochlear model, J. Acoustical Society of America, 77 (1985), 2107-2110.
doi: 10.1121/1.391735. |
[7] |
R. J. LeVeque, C. S. Peskin and P. D. Lax, Solution of a two-dimensional cochlea model using transform techniques, SIAM J. Appl. Math., 45 (1985), 450-464.
doi: 10.1137/0145026. |
[8] |
R. J. LeVeque, C. S. Peskin and P. D. Lax, Solution of a two-dimensional cochlea model with fluid viscosity, SIAM J. Appl. Math., 48 (1988), 191-213.
doi: 10.1137/0148009. |
[9] |
C. S. Peskin, Flow patterns around heart valves: A numerical method, J. Computational Physics, 10 (1972), 252-271. |
[10] |
C. S. Peskin, Lectures on Mathematical Aspects of Physiology (II) The Inner Ear, in Mathematical Aspects of Physiology (eds. F.C. Hoppensteadt), American Mathematical Society, (1981), 38-69. |
[11] |
C. S. Peskin, The immersed boundary method, Acta Numerica, 11 (2002), 479-517.
doi: 10.1017/S0962492902000077. |
[12] |
J. J. Stoker, Water Waves, Interscience Publishers Inc, New York, 1957. |
[13] |
G. von Bekesy, Experiments in Hearing, Robert E. Krieger Publishing Company, Huntington, New York, 1960. |
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