Time domain cochlear models have primarily followed a method introduced by Allen and Sondhi [J. Acoust. Soc. Am. 66, 123-132 (1979)]. Recently the "state space formalism" proposed by Elliott et al. [J. Acoust. Soc. Am. 122, 2759-2771 (2007)] has been used to simulate a wide range of nonlinear cochlear models. It used a one-dimensional approach that is extended to two dimensions in this paper, using the finite element method. The recently developed "state space formalism" in fact shares a close relationship to the earlier approach. Working from Diependaal et al. [J. Acoust. Soc. Am. 82, 1655-1666 (1987)] the two approaches are compared and the relationship formalized. Understanding this relationship allows models to be converted from one to the other in order to utilize each of their strengths. A second method to derive the state space matrices required for the "state space formalism" is also presented. This method offers improved numerical properties because it uses the information available about the model more effectively. Numerical results support the claims regarding fluid dimension and the underlying similarity of the two approaches. Finally, the recent advances in the state space formalism [Bertaccini and Sisto, J. Comp. Phys. 230, 2575-2587 (2011)] are discussed in terms of this relationship.

Particles suspended in a fluid that is exposed to an acoustic standing wave experience a time-averaged force that drives them to either the pressure nodes or anti-nodes of the wave. Several filter designs have been successfully implemented using this force to filter small particles in liquids with low flow rates and small cross-sectional areas. It has been suggested that the filtration of small solid particles out of a gas, such as carbon in air ͑smoke͒, would be a possible application of acoustic standing wave based particle separation. This study shows the limiting factors, in both power requirements and design factors, of an acoustic filter designed for filtering smoke particles across large cross-sectional areas. It is shown that while filtration is possible, the power needed is impractical. It is also shown that operating the filter within certain settling time parameters optimizes the energy usage of the filter.

The human cochlea is a fascinating transduction organ that illustrates the ingenious way in which engineering problems are solved in nature. A healthy cochlea has a dynamic range in the order of 120 dB; that is, the difference between the roar of the engines of a Boeing 747 and the faintest whisper. We discuss the recent assertion that the cochlea is governed by the dynamics of a Hopf bifurcation. In our cochlea model we discretise the basilar membrane into resonant sections with logarithmically decreasing characteristic frequencies. We show that the observed active behaviour of the cochlea can be modelled as a change in the quality factor of the individual resonant sections in a discretised model, and that this has dynamics which embody the Hopf bifurcation.

The cochlea is known to be a nonlinear system that shows strong fluid-structure coupling. In this work, the monolithic state space approach to cochlear modeling [Rapson et al., J. Acoust. Soc. Am. 131, 3925-3952 (2012)] is used to study the inherent nature of this coupling. Mathematical derivations requiring minimal, widely accepted assumptions about cochlear anatomy provide a clear description of the coupling. In particular, the coupling forces between neighboring cochlear partition segments are demonstrated, with implications for theories of cochlear operation that discount the traveling wave hypothesis. The derivations also reaffirm the importance of selecting a physiologically accurate value for the partition mass in any simulation. Numerical results show that considering the fluid properties in isolation can give a misleading impression of the fluid-structure coupling. Linearization of a nonlinear partition model allows the relationship between the linear and nonlinear fluid-structure interaction to be described. Furthermore, the effect of different classes of nonlinearities on the numerical complexity of a cochlear model is assessed. Cochlear models that assume outer hair cells are able to detect pressure will require implicit solver strategies, should the pressure sensitivity be demonstrated. Classical cochlear models in general do not require implicit solver strategies.

Controller design methodologies are commonly compared by publishing examples of individual controllers that were designed using competing approaches. In this paper, Pareto analysis is used to compare three methods of designing controllers for integrating second order plus dead time processes -a problem that has been discussed in the literature. The analysis shows that, in the example chosen, superior performance can be attained by adjusting the approach to tuning controllers. Solutions found by Pareto analysis that improve performance may be directly implemented. This finding demonstrates the usefulness of Pareto analysis in Control engineering, as either a design or research technique.