Simulated acoustic emissions from coupled strings

We consider traveling transverse waves on two identical uniform taut strings that are elastically coupled through springs that gradually decrease their stiffness over a region of finite length. The wave system can be decomposed into two modes: an in-phase mode ( + ) that is transparent to the coupling springs, and an out-of-phase mode ( − ) that engages the coupling springs and can resonate at a particular location depending on the excitation frequency. The system exhibits linear mode conversion whereby an incoming ( + ) wave is reflected back from the resonance location both as a propagating ( + ) wave and an evanescent ( − ) wave, while both types emerge as propagating forward through the resonance location. We match a local transition layer expansion to the WKB expansion to obtain estimates of the reflection and transmission coefficients. The reflected waves may be an analog for stimulated emissions from the ear

The Portable Parallel Implementation of Two Novel Mathematical Biology Algorithms in ZPL

This paper shows that mathematical models of biological pattern formation are ideally suited to data parallelism. We present two new algorithms, one for simulating the dynamic structure of fibroblasts, and the other for studying the self-organization of motile bacteria. We describe implementations of these algorithms using a high level data parallel language called ZPL, and we give performance results for the Kendall Square Research KSR-2 and the Intel Paragon that include comparisons against sequential Fortran. 1 Introduction Mathematical biology is one of the fastest growing and most exciting applications of modern mathematics. As biology becomes more quantitative, the increased use of mathematical modeling is inevitable. Many of these problems involve extensive numerical computations over large computational domains and are easily amenable to data-parallelism. For example, in the field of pattern formation in biological systems, the equations that one derives are generally continuu..

Effects of coiling on the micromechanics of the mammalian cochlea

The cochlea transduces sound-induced vibrations in the inner ear into electrical signals in the auditory nerve via complex fluid–structure interactions. The mammalian cochlea is a spiral-shaped organ, which is often uncoiled for cochlear modelling. In those few studies where coiling has been considered, the cochlear partition was often reduced to the basilar membrane only. Here, we extend our recently developed hybrid analytical/numerical micromechanics model to include curvature effects, which were previously ignored. We also use a realistic cross-section geometry, including the tectorial membrane and cellular structures of the organ of Corti, to model the apical and basal regions of a guinea-pig cochlea. We formulate the governing equations of the fluid and solid domains in a curvilinear coordinate system. The WKB perturbation method is used to treat the propagation of travelling waves along the coiled cochlear duct, and the O(1) system of the governing equations is solved in the transverse plane using finite-element analysis. We find that the curvature of the cochlear geometry has an important functional significance; at the apex, it greatly increases the shear gain of the cochlear partition, which is a measure of the bending efficiency of the outer hair cell stereocilia

The influence of cochlear shape on low-frequency hearing

The conventional theory about the snail shell shape of the mammalian cochlea is that it evolved essentially and perhaps solely to conserve space inside the skull. Recently, a theory proposed that the spiral's graded curvature enhances the cochlea's mechanical response to low frequencies. This article provides a multispecies analysis of cochlear shape to test this theory and demonstrates that the ratio of the radii of curvature from the outermost and innermost turns of the cochlear spiral is a significant cochlear feature that correlates strongly with low-frequency hearing limits. The ratio, which is a measure of curvature gradient, is a reflection of the ability of cochlear curvature to focus acoustic energy at the outer wall of the cochlear canal as the wave propagates toward the apex of the cochlea