PHYSICAL MATHEMATICS SEMINAR



TITLE:		COMPUTATION AND ANALYSIS OF A NONLINEAR 
		NONOCAL COCHLEAR MODEL WITH APPLICATIONS
		TO MULTITONE INTERACTION IN HEARING

SPEAKER:	JACK XIN
		DEPARTMENT OF MATHEMATICS AND TICAM 
		THE UNIVERSITY OF TEXAS AT AUSTIN



ABSTRACT:

A nonlinear nonlocal cochlear model of the transmission line type is studied to capture the multitone
interactions and resulting tonal suppression effects.  The model can serve as a module for voice signal 
processing.  It is a one dimensional (in space) damped dispersive nonlinear partial differential equation
(PDE) based on mechanics and phenomenology of hearing.  It describes the motion of basilar membrane 
(BM) in the cochlea driven by input pressure waves.  The elastic damping is a nonlinear and nonlocal
functional of BM displacement, and plays a key role in capturing tonal interactions.  The initial boundary 
value problem is numerically solved with a semi-implicit second order finite difference method.  Solutions
reach a multi-frequency quasi-steady state.  Numerical results are shown on two tone suppression from 
both high frequency and low-frequency sides, consistent with known behavior of two tone suppression.  
Suppression effects among three tones are demonstrated by showing how the response magnitudes of the
fixed two tones are reduced as the third tone is varied in frequency and amplitude.  Qualitative agreement 
of model solutions with existing cat auditory neural data is observed.  The model is thus simple and efficient 
as a processing tool for voice signals.  Mathematical analysis of global well-posedness of the model PDE 
and the existence of tonal solutions will also be shown using a-priori estimates and fixed point theory.

TUESDAY, OCTOBER 1ST , 2002
2:30 pm
Building 2, Room 338

Refreshments will be served at 3:30 PM in Room 2-349


Massachusetts Institute of Technology
Department of Mathematics
Cambridge, MA  02139