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Controllability of a basic cochlea model
1. | Department of Mathematics, Iowa State University, Ames, IA 50011, United States |
References:
[1] |
G. von Békésy, Experiments in Hearing McGraw-Hill Inc., New York, 1960. |
[2] |
Isaak Chepkwony, Analysis and Control Theory of some Cochlea Models, Ph.D. thesis, Department of Mathematics, Iowa State University, Ames, IA, 2006. |
[3] |
S. W. Hansen, Exact controllability of an elastic membrane coupled with a potential fluid, Int. J. Appl. Math. Comput. Sci., 11 (2001), 1231-1248. |
[4] |
S. W. Hansen and A. Lyashenko, Exact controllability of a beam in an incompressible inviscid fluid, Disc. Cont. Dyn. Syst., 3 (1997), 59-78. |
[5] |
H. L. F. von Helmoltz, On the sensations of tone as a physiological basis for the theory of music, (Translation by A. J. Ellis of Die Lehre von den Tonempfindungen als physiologiche Grundlage für die Theorie der Musik: Verlag von Fr. Vieweg u. Sohn. 4th ed., 1877; originally published 1863) Dover, New York, 1954. |
[6] |
J. B. Keller and J. C. Neu, Asymptotic analysis of a viscous cochlear model, J. Acoust. Soc. Amer., 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. Applied Math., 45 (1988), 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. Applied Math., 48 (1988), 191-213.
doi: 10.1137/0148009. |
[9] |
J. Lighthill, Energy flow in the cochlea, J. Fluid Mech., 106 (1981), 149-213.
doi: 10.1017/S0022112081001560. |
[10] |
R. D. Luce, Sound and Hearing. A Conceptual Introduction, Lawrence Erlbaum Assoc. Inc., Publishers, Hillsdale, New Jersey, 1993. |
[11] |
G. A. Manley and R. R. Fay, Active Processes and Otoacoustic Emissions in Hearing, Springer Science & Business Media 30, 2007. |
[12] |
J. Nečas, Les Méthodes Directes en théorie des équations Elliptiques. Paris: Masson, 1967. |
[13] |
S. T. Neely, Mathematical modeling of cochlear mechanics, J. Acoust. Soc. Am., 78 (1985), 345-352.
doi: 10.1121/1.392497. |
[14] |
S. T. Neely and D. O. Kim, An active cochlear model showing sharp tuning and high sensitivity, Hearing Research, 9 (1983) 123-130.
doi: 10.1016/0378-5955(83)90022-9. |
[15] |
A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[16] |
O. F. Ranke, Theory of operation of cochlear: A contribution to the hydrodynamics of the cochlear, J. Acoust. Soc. Am., 22 (1950), 772-777. |
[17] |
W. S. Rhode, Observations of the vibration of the Basilar Membrane in squirrel monkeys using the Mössbauer technique, Journal of the Acoustical Society of America, 49 (1971), 1218-1231. |
[18] |
J. Xin, Dispersive instability and its minimization in time-domain computation of steady-state responses of cochlea models, J. Acoust. Soc. Am., 115 (2004), 2173-2177. |
show all references
References:
[1] |
G. von Békésy, Experiments in Hearing McGraw-Hill Inc., New York, 1960. |
[2] |
Isaak Chepkwony, Analysis and Control Theory of some Cochlea Models, Ph.D. thesis, Department of Mathematics, Iowa State University, Ames, IA, 2006. |
[3] |
S. W. Hansen, Exact controllability of an elastic membrane coupled with a potential fluid, Int. J. Appl. Math. Comput. Sci., 11 (2001), 1231-1248. |
[4] |
S. W. Hansen and A. Lyashenko, Exact controllability of a beam in an incompressible inviscid fluid, Disc. Cont. Dyn. Syst., 3 (1997), 59-78. |
[5] |
H. L. F. von Helmoltz, On the sensations of tone as a physiological basis for the theory of music, (Translation by A. J. Ellis of Die Lehre von den Tonempfindungen als physiologiche Grundlage für die Theorie der Musik: Verlag von Fr. Vieweg u. Sohn. 4th ed., 1877; originally published 1863) Dover, New York, 1954. |
[6] |
J. B. Keller and J. C. Neu, Asymptotic analysis of a viscous cochlear model, J. Acoust. Soc. Amer., 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. Applied Math., 45 (1988), 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. Applied Math., 48 (1988), 191-213.
doi: 10.1137/0148009. |
[9] |
J. Lighthill, Energy flow in the cochlea, J. Fluid Mech., 106 (1981), 149-213.
doi: 10.1017/S0022112081001560. |
[10] |
R. D. Luce, Sound and Hearing. A Conceptual Introduction, Lawrence Erlbaum Assoc. Inc., Publishers, Hillsdale, New Jersey, 1993. |
[11] |
G. A. Manley and R. R. Fay, Active Processes and Otoacoustic Emissions in Hearing, Springer Science & Business Media 30, 2007. |
[12] |
J. Nečas, Les Méthodes Directes en théorie des équations Elliptiques. Paris: Masson, 1967. |
[13] |
S. T. Neely, Mathematical modeling of cochlear mechanics, J. Acoust. Soc. Am., 78 (1985), 345-352.
doi: 10.1121/1.392497. |
[14] |
S. T. Neely and D. O. Kim, An active cochlear model showing sharp tuning and high sensitivity, Hearing Research, 9 (1983) 123-130.
doi: 10.1016/0378-5955(83)90022-9. |
[15] |
A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[16] |
O. F. Ranke, Theory of operation of cochlear: A contribution to the hydrodynamics of the cochlear, J. Acoust. Soc. Am., 22 (1950), 772-777. |
[17] |
W. S. Rhode, Observations of the vibration of the Basilar Membrane in squirrel monkeys using the Mössbauer technique, Journal of the Acoustical Society of America, 49 (1971), 1218-1231. |
[18] |
J. Xin, Dispersive instability and its minimization in time-domain computation of steady-state responses of cochlea models, J. Acoust. Soc. Am., 115 (2004), 2173-2177. |
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