@article{CML_2011__3_3_523_0, author = {Holmes, William R. and Jolly, Michael and Rubinstein, Jacob}, title = {Hydro-elastic waves in a cochlear model: {Numerical} simulations and an analytically reduced model}, journal = {Confluentes Mathematici}, pages = {523--541}, publisher = {World Scientific Publishing Co Pte Ltd}, volume = {3}, number = {3}, year = {2011}, doi = {10.1142/S1793744211000382}, language = {en}, url = {http://archive.numdam.org/articles/10.1142/S1793744211000382/} }
TY - JOUR AU - Holmes, William R. AU - Jolly, Michael AU - Rubinstein, Jacob TI - Hydro-elastic waves in a cochlear model: Numerical simulations and an analytically reduced model JO - Confluentes Mathematici PY - 2011 SP - 523 EP - 541 VL - 3 IS - 3 PB - World Scientific Publishing Co Pte Ltd UR - http://archive.numdam.org/articles/10.1142/S1793744211000382/ DO - 10.1142/S1793744211000382 LA - en ID - CML_2011__3_3_523_0 ER -
%0 Journal Article %A Holmes, William R. %A Jolly, Michael %A Rubinstein, Jacob %T Hydro-elastic waves in a cochlear model: Numerical simulations and an analytically reduced model %J Confluentes Mathematici %D 2011 %P 523-541 %V 3 %N 3 %I World Scientific Publishing Co Pte Ltd %U http://archive.numdam.org/articles/10.1142/S1793744211000382/ %R 10.1142/S1793744211000382 %G en %F CML_2011__3_3_523_0
Holmes, William R.; Jolly, Michael; Rubinstein, Jacob. Hydro-elastic waves in a cochlear model: Numerical simulations and an analytically reduced model. Confluentes Mathematici, Tome 3 (2011) no. 3, pp. 523-541. doi : 10.1142/S1793744211000382. http://archive.numdam.org/articles/10.1142/S1793744211000382/
[1] J. B. Allen and M. M. Sondhi, Cochlear macromechanics: Time domain solutions, J. Acoust. Soc. Am. 66 (1979) 123–132.
[2] G. V. Bekesy, Experiments in Hearing (McGraw-Hill, 1960).
[3] J. P. Boyd, Chebyshev and Fourier Spectral Methods, 2nd edn. (Dover, 2001).
[4] E. Givelberg and J. Bunn, A comprehensive three-dimensional model of the cochlea, J. Comput. Phys. 191 (2003) 377–391.
[5] J. Keener and J. Sneyd, Mathematical Physiology (Springer, 2001).
[6] J. B. Keller and J. C. Neu, Asymptotic analysis of a viscous cochlear model, J. Acoust. Soc. Am. 77 (1985) 2107–2110.
[7] Y. Kim and J. Xin, A two-dimensional nonlinear nonlocal feed-forward cochlear mode and time domain computation of multitone interactions, Multiscale Model. Simul. 4 (2005) 664–690.
[8] L. Landau and E. Lifshitz, Theory of Elasticity, Course of Theoretical Physics, Vol. 7, 3rd edn. (Elsevier, 1986).
[9] J. Lighthill, Energy flow in the cochlea, J. Fluid Mech. 106 (1981) 149–213.
[10] K.-M. Lim and C. R. Steele, A three-dimensional nonlinear active cochlear model analyzed by the WKB-numeric method, Hearing Res. 170 (2002) 190–205.
[11] D. Manoussaki, R. S. Chadwick, D. R. Ketten, J. Arruda, E. K. Dimitriadis and J. T. O’Malley, The influence of cochlear shape on low-frequency hearing, PNAS 105 (2008) 6162–6166.
[12] S. T. Neely, Finite difference solution of a two-dimensional mathematical model of the cochlea, J. Acoust. Soc. Am. 69 (1981) 1386–1393.
[13] C. S. Peskin, Partial Differential Equations in Biology. Courant Inst. Lecture Notes. (Courant Institute of Mathematical Sciences, 1975–76).
[14] L. C. Peterson and B. P. Bogert, A dynamical theory of the cochlea, J. Acoust. Soc. Am. 22 (1950) 369–381.
[15] J. O. Pickles, An Introduction to the Physiology of Hearing, 3rd edn. (Emerald, 2008).
[16] J. Rubinstein and M. Schatzman, Variational problems in multiply connected thin strips I: Basic estimates and convergence of the Laplacian spectrum, Arch. Rational Mech. Anal. 160 (2001) 271–308.
[17] C. R. Steele, Behavior of the basilar membrane with pure-tone excitation, J. Acoust. Soc. Am. 55 (1974) 148–162.
[18] J. W. Stephenson, Single cell discretizations of order two and four for biharmonic problems, J. Comput. Phys. 55 (1984) 65–80.
[19] J. Xin, Y. Qi and L. Deng, Time domain computation of a nonlinear nonlocal cochlear model with applications to multitone interaction in hearing, Comm. Math. Sci. 1 (2003) 211–227.
Cité par Sources :