Stochastic Optimal Linear Control for Generalized Cost Functions With Time-Invariant Stochastic Parameters.

This study presents the design of feedback controllers for generalized cost functions to deal with stochastic optimal control problems. Target linear systems contain time-invariant stochastic parameters that describe system uncertainty. The cost functions involve nonlinear mappings and polynomial forms of the system states and inputs to express various performance metrics.

Periodic switching of acoustic radiation force with beat created by multitone field.

Acoustic radiation force plays a key role in microfluidic systems for particle and cell manipulation. In this study, we investigate the acoustic radiation force resulting from synthesized ultrasounds that are emitted from multiple sound sources with slightly different oscillation frequencies. Due to the synthesized field, the acoustic radiation force is expressed as the sum of a dc component and harmonics of fundamental frequencies of a few hertz.

Noise-induced switching from a symmetry-protected shallow metastable state.

We consider escape from a metastable state of a nonlinear oscillator driven close to triple its eigenfrequency. The oscillator can have three stable states of period-3 vibrations and a zero-amplitude state. Because of the symmetry of period-tripling, the zero-amplitude state remains stable as the driving increases.

Dependence of enhancement factor on electrode size for field emission current from carbon nanotube on silicon wafer.

This work studies the enhancement factor associated with a current emitted from a multi-wall carbon nanotube to an extremely small counter electrode. The experimental data show that the field enhancement factor increases by 1.15 times when the width of the counter electrode increases from 50 to 200 nm.

Driven nonlinear nanomechanical resonators as digital signal detectors.

Because of their nonlinearity, vibrational modes of resonantly driven nanomechanical systems have coexisting stable states of forced vibrations in a certain range of the amplitude of the driving force. Depending on its phase, which encodes binary information, a signal at the same frequency increases or decreases the force amplitude. The resulting force amplitude can be outside the range of bistability.

Design and characterization of nonlinear functions for the transmission of a small signal with non-Gaussian noise.

We design nonlinear functions for the transmission of a small signal with non-Gaussian noise and perform experiments to characterize their responses. Using statistical design theory [A. Ichiki and Y.

Relation between optimal nonlinearity and non-Gaussian noise: enhancing a weak signal in a nonlinear system.

In the study of stochastic resonance, it is often mentioned that nonlinearity can enhance a weak signal embedded in noise. In order to give a systematic proof of the signal enhancement in nonlinear systems, we derive an optimal nonlinearity that maximizes a signal-to-noise ratio (SNR). The obtained optimal nonlinearity yields the maximum unbiased signal estimation performance, which is known in the context of information theory.

Singular probability distribution of shot-noise driven systems.

We study the stationary probability distribution of a system driven by shot noise. We find that both in the overdamped and underdamped regime, the coordinate distribution displays power-law singularities in its central part. For sufficiently low rate of noise pulses they correspond to distribution peaks.

Singular response of bistable systems driven by telegraph noise.

We show that weak periodic driving can exponentially strongly change the rate of escape from a potential well of a system driven by telegraph noise. The analysis refers to an overdamped system, where escape requires that the noise amplitude θ exceed a critical value θ(c). For θ close to θ(c), the exponent of the escape rate displays a nonanalytic dependence on the amplitude of an additional low-frequency modulation.