By J. B. Allen (auth.), Mark H. Holmes, Lester A. Rubenfeld (eds.)
The articles of those lawsuits come up from a NSF-CBMS neighborhood convention at the mathematical modeling of the listening to technique, that used to be held at Rensselaer Polytechnic Institute in the summertime of 1980. to place the a=ticles in standpoint, you should in brief assessment the background of suc~ modeling. It has proceeded, roughly, in 3 levels. the 1st was once initiated by way of Herman Helmholtz within the 1880's, whose theories ruled the topic for years. notwithstanding, as a result of his loss of exact experimental facts and his heuristic arguments it turned obvious that his types wanted revision. for this reason, in line with the experimental observations of von Bekesy, the "long wave" theories have been built within the 1950's via investigators similar to Zwislocki, Peterson, and Bogert. although, because the ex?eri~ents turned extra sophisticated (such as Rhode's ~wssbauer Measurements) even those versions got here into query. This has prompted a flurry of 'activity lately into tips on how to expand the types to account for those more moderen eXT. lerimental observations. One technique is thru a tool co~monly refered to as a moment filter out (see Allen's article) and one other is thru a extra tricky hydroelastic version (see Chadwick's article). at the side of this latter process, there was a few fresh paintings on constructing a low frequency version of the cochlea (see Holmes' article).
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Extra info for Mathematical Modeling of the Hearing Process: Proceedings of the NSF-CBMS Regional Conference Held in Troy, NY, July 21–25, 1980
Fluid Mech. 51, 497-512. J. (1980) Energy flow in the cochlea, to appear in J. Fluid Mech. 12. T. (1980). A two-dimensional mathematical model of the mechanics of the cochlea, submitted to J. Acoust. Soc. Am. 13. F. (1950). Theory of operation of the cochlea: A contribution to the hydrodynamics of the cochlea, J. Acous't. Soc. Am. 22, 772-777. 14. S. (1945). Theory of Sound, vol. I. Dover Publications, New York. 15. M. (1974). Ranke revisited - a simple short wave cochlea model, J. Soc. Am. 56, 594-600.
Math. 18. R. A. (1979). Comparison of WKB and finite differences calculations for a two dimensional cochlear model, J. Acoust. Soc. Am. 65, 10011006. - 54 19. A. (980). Mechanics of the Inner Ear. Delft University Press, The Netherlands. 20. Voldrich, L. (1978). Mecchanical properties of the basilar membrane. Acta Oto larygl. 86, 331-335. A HYDROELASTIC MODEL OF THE COCHLEA: AN ANALYSIS FOR LOW FREQUENCIES Mark H. Holmes Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy, New York 12181 Introduction A number of mathematical models of the low frequency behavior of the cochlea have appeared over the years, beginning with Helmholtz (1885), and continuing with Peterson and Bogert (1950) and Zwislocki (1965).
For example, for humans, £2 ~ 10- 3 • The appropriate asymptotic expansions in this case are -+- v ~ p ~ -+- (vo'O,O) + £v I + ... po(x,y,z,t) + £Pl + ... and Introducing these into (1) one finds from the 0(1) problem that + + (2) Po = P~ (x,t) a + CltVo - (3) and (4) 59 where 1;0 1 2 2 2 2 (x,y) = - 24 [y - G (x) 1 [y - 5G (x) 1 (5) The +, - refer to the upper and lower chambers, respectively. Also, + The equation for p~ is obtained by applying Green's theorem to the O(S2) continuity equation.