Essential nonlinearities in hearing

Our hearing organ, the cochlea, evidently poises itself at a Hopf bifurcation to maximize tuning and amplification. We show that in this condition several effects are expected to be generic: compression of the dynamic range, infinitely shrap tuning at zero input, and generation of combination tones. These effects are "essentially" nonlinear in that they become more marked the smaller the forcing: there is no audible sound soft enough not to evoke them. All the well-documented nonlinear aspects of hearing therefore appear to be consequences of the same underlying mechanism.Comment: 4 pages, 3 figure

The Cochlear Tuning Curve

The tuning curve of the cochlea measures how large an input is required to elicit a given output level as a function of the frequency. It is a fundamental object of auditory theory, for it summarizes how to infer what a sound was on the basis of the cochlear output. A simple model is presented showing that only two elements are sufficient for establishing the cochlear tuning curve: a broadly tuned traveling wave, moving unidirectionally from high to low frequencies, and a set of mechanosensors poised at the threshold of an oscillatory (Hopf) instability. These two components suffice to generate the various frequency-response regimes which are needed for a cochlear tuning curve with a high slope

Displacement-based dynamometer for milling force measurement

This project will study the design and testing of a low-cost dynamometer for milling dynamic force measurement. The monolithic design is based on constrained-motion/flexure-based kinematics, where force is inferred from displacement measured using a low-cost optical interrupter (i.e., a knife edge that partially interrupts the light beam in an emitter-detector pair). The time-dependent displacement of the dynamometer’s moving platform caused by the milling force is converted to the frequency domain, multiplied by the inverse of the dynamometer’s ideally single degree of freedom (SDOF) frequency response function (FRF), and converted back into the time-domain to obtain the time-dependent cutting force. The basic science to be examined is the process dynamics and vibration behavior of the innovative dynamometer design and the ability to measure dynamic cutting forces by applying a structural deconvolution technique. A vibration transducer with high resolution, signal-to-noise ratio, and linearity is therefore able to accurately deconvolve dynamic forces from the measured displacement using the dynamometer’s FRF. This dynamometer will enable accurate and repeatable static and dynamic force measurement for milling operations; however, this approach can be extended to turning, grinding, and drilling as well. A SDOF constrained-motion dynamometer will be designed, manufactured, and evaluated against a commercially available, piezoelectric dynamometer system to validate the displacement-based cutting force approach. A milling process model will be implemented through the solution of second-order, time-delay differential equations of motion that describe the milling behavior [1]. Experiments will be performed to identify the critical stability limit for the various dynamometer systems and mechanistic cutting force coefficients The sensor selection, monolithic constrained-motion design, and companion structural deconvolution technique will provide an innovative, low-cost, high fidelity cutting force dynamometer for use in both production and research environments This approach offers the potential for reduced uncertainty cutting force measurement and significant advancement of metrology for machining operations including the in-process assessment of tool wear and the corresponding machining process health

Analysis and simulation methods for free-running, injection-locked and super-regenerative oscillators

RESUMEN: En los últimos años, muchos esfuerzos han sido dedicados al desarrollo de técnicas complementarias para el análisis de circuitos autónomos de microondas. Estas técnicas están pensadas para su uso en combinación con balance armónico, ampliamente usado para el análisis a frecuencias de microondas. De hecho, balance armónico sufre de restricciones cuando se utiliza para el análisis de circuitos autónomos, en su mayoría debidos a su falta de sensibilidad a las propiedades de estabilidad de la solución que se genera o se extingue mediante bifurcaciones. En esta tesis doctoral se presentan nuevos métodos de simulación y análisis para la caracterización y modelado de osciladores libres, sincronizados y superregenerativos. Todos los resultados obtenidos mediante los nuevos métodos de simulación y análisis han sido comparados satisfactoriamente con otras técnicas de simulación y con medidas.ABSTRACT: In the last years, numerous efforts have been devoted to the development of complementary analysis tools for autonomous microwave circuits. They are intended to be applied in combination with the harmonic-balance (HB) method, widely used at microwave frequencies. In fact, HB suffers from a number of shortcomings when dealing with autonomous circuits, mostly due the fact that it is insensitive to the stability properties of the solution, generated and extinguished through bifurcation phenomena. Here, new simulation and analysis methodologies for the characterization and modeling of free-running, injection-locked and super-regenerative oscillators have been proposed to overcome these problems when using commercial software. Results from the different new analysis methodologies have been successfully compared with independent simulations and with measurements

Center Manifold Dynamics in Randomly Coupled Oscillators and in Cochlea

In dynamical systems theory, a fixed point of the activity is called nonhyperbolic if the linearization of the system around the fixed point has at least one eigenvalue with zero real part. The center manifold existence theorem guarantees the local existence of an invariant subspace of the activity, known as a center manifold, around nonhyperbolic fixed points. A growing number of theoretical and experimental studies suggest that neural systems utilize dynamics on center manifolds to display complex, nonlinear behavior and to flexibly adapt to wide-ranging sensory input parameters. In this thesis, I will present two lines of research exploring nonhyperbolicity in neural dynamics

Applications of Nonlinear Dynamics in Semiconductor Lasers With Time-Delayed Feedback in Microwave Photonics

The main objective of this research is to investigate the rich nonlinear dynamics of a semiconductor \gls{LD} subjected to time-delayed optoelectronic (OE) feedback, emphasizing applications in microwave photonics and communications. A semiconductor LD based OE feedback constitutes an oscillator that produces self-sustained optical output modulation through the intrinsic nonlinearities of the system without needing any external modulators. To explore the wide variety of dynamics in the optical intensity, the LD needs to be perturbed out of the steady-state free-running behavior, so the photodetected optical signal is appropriately amplified prior to feeding it back into the LD injection terminal. The complex dynamics of such an oscillator have been studied theoretically and experimentally in recent decades. In this work, however, we report several novel dynamical effects by re\"{e}xamining this rich nonlinear system with state-of-the-art experiments and supported that by comprehensive modelling. In particular, we have identified operating conditions that exhibit high-order locking between LD relaxation oscillations with harmonics of the feedback delay frequency for a OE feedback with large delay. We also observe that this system exhibits a stepwise change in LD oscillation frequency as the feedback level is varied. Further, upon varying the injection current near threshold, we also can generate a periodic pulse train with repetition rate at the feedback delay frequency arising from gain-switching between the on and off states of LD. This pulse train grows into pulse clusters as we increase the current. In addition, driving an LD at very high currents and strong feedback results in square-wave pulses whose repetition rate is determined by the feedback delay of the OE loop. The square-waves at a fixed current have been shown to exhibit a double-peaked optical spectrum that depends on the feedback level. These interesting discoveries advance the understanding of the nonlinear OE oscillator and could find applications in communications, sensing, measurement, and spectroscopy.Ph.D

Synchronization of Micromechanical Oscillators Using Light

Synchronization, the emergence of spontaneous order in coupled systems, is of fundamental importance in both physical and biological systems. We demonstrate the synchronization of two dissimilar silicon nitride micromechanical oscillators, that are spaced apart by a few hundred nanometers and are coupled through optical radiation field. The tunability of the optical coupling between the oscillators enables one to externally control the dynamics and switch between coupled and individual oscillation states. These results pave a path towards reconfigurable massive synchronized oscillator networks

Power Amplification and Frequency Selectivity in the Inner Ear: A New Physical Model

This Chapter presents a new physical model for signal processing phenomena (power amplification and frequency selectivity) occurring in the inner ear (Cochlea). It is generally accepted that Outer Hair Cells (OHCs) play a pivotal role in the Cochlear signal processing. In the proposed new model we postulate that all signal processing phenomena in the Cochlea are due to electrical currents flowing in the Cochlea structure. Three crucial characteristics of the OHCs are: 1) a forward mechanoelectrical transduction, 2) a strong piezoelectric effect (direct and inverse), and 3) a transmembrane nonlinear capacitance. The new model postulates existence of a biological electromechanical transistor (EMT) in each of the OHCs (based on a forward mechanoelectrical transduction phenomenon), which enhances the power of an incoming acoustic signal. Consequently, the nonlinear capacitance of the appropriate OHCs is charged (pumped) by an AC current source generated at the output of the proposed EMT transistor. Power amplification and frequency selectivity are realized on the nonlinear capacitance, which constitutes an essential part of a parametric amplifier circuit. The amplified and sharpened in frequency electric signal is then converted to a mechanical signal by the OHCs (inverse piezoelectric effect) and transferred to the Inner Hair Cells that transform this mechanical signal into an output electrical signal supplied to the afferent nerves

Mode locking in an optomechanical cavity

We experimentally study a fiber-based optical ring cavity integrated with a mechanical resonator mirror and an optical amplifier. The device exhibits a variety of intriguing nonlinear effects including synchronization and self-excited oscillation. Passively generated optical pulses are observed when the frequency of the optical ring cavity is tuned very close to the mechanical frequency of the suspended mirror. The optical power at the threshold of this process of mechanical mode locking is found to be related to quantum noise of the optical amplifier