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Pitch is the most important auditory perception characteristic of sound with respect to speech intelligibility and music appreciation, and corresponds to a frequency of sound stimulus. However, in some cases, we can perceive virtual pitch, where the corresponding frequency component does not exist in the stimulating sound. This virtual pitch contains a deviation from the de Boer pitch shift formula, which is known as second pitch shift. It has been theoretically suggested that nonlinear dynamics in the cochlea or in the neural network produce a nonlinear resonance with a frequency corresponding to the virtual pitch; however, there is no direct experimental observation to support this theory. The second virtual pitch shift, expressed via basilar membrane nonlinear vibration temporal patterns, and consistent with psychoacoustic experiments, is observed in situ in the cochlea via laser interferometry.

The sense of mammalian hearing exhibits nonlinear phenomena which are most significant to hearing function, such as nonlinear dynamic compression, nonlinear tuning and combination tones. These nonlinear phenomena are suggested to originate from the Hopf amplification within the cochlea, while the mechanism underlying the Hopf amplification remains elusive. According to the experimental results of force-gating channel operation in hair cells, through a theoretic model, this work reveals a velocity-dependent open probability of force-gating channels in auditory hair cells, and a velocity-dependent active force produced by the force-gating channel operating, which makes sensors hear typical Hopf vibrators with nonlinear hearing phenomena.

A Brownian microscopic heat engine, driven by temperature difference and consisting of a Brownian particle moving in a sawtooth potential with an external load, is investigated. The heat flows, driven by both potential and kinetic energies, are taken into account. Based on the master equation, the expressions for efficiency and power output are derived analytically, and performance characteristic curves are plotted. It is shown that the heat flow via the kinetic energy of the particle decreases. The efficiency of the engine is enhanced, but the power output reduces as the α shape parameter of the sawtooth potential increases. The influence of the α shape parameter on efficiency and power output is then analyzed in detail.