Determination of the thermal noise limit in test of weak equivalence principle with a rotating torsion pendulum

Thermal noise is one of the most fundamental limits to the sensitivity in weak equivalence principle test with a rotating torsion pendulum. Velocity damping and internal damping are two of many contributions at the thermal noise, and which one mainly limits the torsion pendulum in low frequency is difficult to be verified by experiment. Based on the conventional method of fast Fourier transform, we propose a developed method to determine the thermal noise limit and then obtain the precise power spectrum density of the pendulum motion signal. The experiment result verifies that the thermal noise is mainly contributed by the internal damping in the fiber in the low frequency torsion pendulum experiment with a high vacuum. Quantitative data analysis shows that the basic noise level in the experiment is about one to two times of the theoretical value of internal damping thermal noise.     

Time-correlation function for macroscopic observables in a classical gas

The state of a gas is characterized by occupation numbers of cells in-space. The mean values and fluctuations of these numbers are studied with the help of a master equation. The results are discussed within the framework of the theory of random forces. An equation of motion of the time-correlation function (TCF) is derived and it is shown that the temporal development of the TCF can be described by a linearized Boltzmann equation.The support of the Deutsche Forschungs-Gemeinschaft (DFG) is gratefully acknowledged.     

Evidence for structural damping in a high-stress silicon nitride nanobeam and its implications for quantum optomechanics

We resolve the thermal motion of a high-stress silicon nitride nanobeam at frequencies far below its fundamental flexural resonance (3.4 MHz) using cavity-enhanced optical interferometry. Over two decades, the displacement spectrum is well-modeled by that of a damped harmonic oscillator driven by a $1/f$ thermal force, suggesting that the loss angle of the beam material is frequency-independent. The inferred loss angle at 3.4 MHz, $?=4.5?{10}^{?6}$, agrees well with the quality factor (Q) of the fundamental beam mode ($?=Q^{?1}$). In conjunction with Q measurements made on higher order flexural modes, and accounting for the mode dependence of stress-induced loss dilution, we find that the intrinsic (undiluted) loss angle of the beam changes by less than a factor of 2 between 50 kHz and 50 MHz. We discuss the impact of such “structural damping” on experiments in quantum optomechanics, in which the thermal force acting on a mechanical oscillator coupled to an optical cavity is overwhelmed by radiation pressure shot noise. As an illustration, we show that structural damping reduces the bandwidth of ponderomotive squeezing.     

The power spectrum and correlation of flow noise for an axisymmetric body in water

Understanding the physical features of the flow noise for an axisymmetric body is important for improving the performance of a sonar mounted on an underwater platform. Analytical calculation and numerical analysis of the physical features of the flow noise for an axisymmetric body are presented and a simulation scheme for the noise correlation on the hydrophones is given. It is shown that the numerical values of the flow noise coincide well with the analytical values. The main physical features of flow noise are obtained. The flow noises of two different models are compared and a model with a rather optimal fore-body shape is given. The flow noise in horizontal symmetry profile of the axisymmetric body is non-uniform, but it is omni-directional and has little difference in the cross section of the body. The loss of noise diffraction has a great effect on the flow noise from boundary layer transition. Meanwhile, based on the simulation, the noise power level increases with velocity to approximately the fifth power at high frequencies, which is consistent with the experiment data reported in the literature. Furthermore, the flow noise received by the acoustic array has lower correlation at a designed central frequency, which is important for sonar system design.     

Influence of a uniform driving force on tracer diffusion in a one-dimensional hard-core lattice gas

The influence of a uniform driving force on tracer diffusion is investigated for a one-dimensional lattice gas where particles jump stochastically to unoccupied neighboring sites. A new, simple calculation is presented for the diffusion coefficient of a tracer particle with respect to its average drift, obtained recently by rigorous methods by De Masi and Ferrari. A theoretical expression describing the tracer particle mean square displacement approximately for all times is derived and found to be in excellent agreement with the results of Monte Carlo simulations.     

A random walker on a ratchet potential: effect of a non Gaussian noise

We analyze the effect of a colored non Gaussian noise on a model of a random walker moving along a ratchet potential. Such a model was motivated by the transport properties of motor proteins, like kinesin and myosin. Previous studies have been realized assuming white noises. However, for real situations, in general we could expect that those noises be correlated and non Gaussian. Among other aspects, in addition to a maximum in the current as the noise intensity is varied, we have also found another optimal value of the current when departing from Gaussian behavior. We show the relevant effects that arise when departing from Gaussian behavior, particularly related to current's enhancement, and discuss its relevance for both biological and technological situations.     

Performance of a snoring noise control system based on an active partition

This paper proposes an active partition that can be placed between a snorer and a non-snorer on a bed to reduce the snoring noise around the non-snorer ears by integrating a rigid finite size passive partition with a two channel active noise control system. The noise reduction performance of the passive partition on a bed with a headboard is studied first, where the effects of the height and the width of the partition are discussed. Due to the limited partition size, the attenuation for the low-frequency diffracted noise is not sufficient, so two loudspeakers are proposed to be installed on the partition as the secondary sources to increase the overall noise attenuation. Both numerical simulations and experiments are carried out to demonstrate the feasibility of the proposed integrated snoring noise control system, and the results show that the proposed active partition can achieve over 10 dB noise attenuation at non-snorer ears in the 1/3 octave bands from 80 to 1000 Hz.     

Active noise control in a duct by an analog neural network circuit

Conventional active noise control (ANC) in ducts has been realized with digital signal processing. The physical size of the conventional ANC systems is usually large owing to the signal processing interval, and the cost of the system depends on the price of the digital signal processor (DSP). This paper proposes a new ANC system with an analog neural network circuit, which will process signals in short time periods without DSP. The proposed neural network circuit has a simple structure consisting of analog multipliers and an integrator, and we simulated the performance of the circuit by HSPICE. We also fabricated a circuit connected to a real duct and confirmed operation of the proposed ANC system.     

A three-dimensional physical model of MRI noise based on current noise sources in a conductor

Magnetic flux noise is generated by any conductor in equilibrium with a bath as a result of random fluctuating currents. A physical model of this flux noise is proposed, based on allowable current patterns in the conductor, which we describe as natural current modes. This model gives insight into the spatial characteristics of the magnetic noise which is encountered in a variety of magnetic measurements and imaging modalities such as magnetic resonance imaging (MRI).     

Influence of vehicle noise emission directivity on sound level distribution in a canyon street. Part I: Simulation program test

Simulation programs may be useful tools for controlling an environmental noise. The computer simulation program PROP11 that enables predictions of the time-average sound level within an urban system is used here. A roadway as a noise source is represented by a sum of the sound exposures due to individual vehicle pass-bys. Different representations of equivalent point sources for various classes of vehicles are allowed including directivity characteristics other than omnidirectional. Propagation throughout an urban system contains multi-reflections from the walls and single and double diffraction at their edges. In this paper, the PROP11 program is used to predict the sound level between opposing façades of buildings in a canyon street. A multi-lane road is assumed to contain two classes of vehicles (light and heavy) ones. The equivalent source representing vehicles is defined by the source power spectrum, its position above the ground and directivity characteristics. The consequences of introducing equivalent source directivity are analyzed.     

New results on gas density, velocity field, and force field of a gasdynamic laser within a supersonic nozzle

Several new results are derived upon gas density as well as upon velocity and force fields relative to a gasdynamic laser within a supersonic nozzle. Evolution equations, including the continuity equation, are employed to obtain the above results. In particular, the continuity equation is used to determine the shape of the nozzle so that its cross-sectional area is calculated as a function of distance. This function is one of the ingredients to get our results relative to gas density, velocity, and force. In addition, the time-dependent power associated with the vibrational non-equilibrium expansion in the nozzle of hot gas at high pressure is evaluated.     

Impact of network activity on noise delayed spiking for a Hodgkin-Huxley model

In a Hodgkin-Huxley neuron model driven just above threshold, external noise can increase both jitter and latency of the first spike, an effect called “noise delayed decay” (NDD). This phenomenon is important when considering how neuronal information is represented, thus by the precise timing of spikes or by their rate. We examine how NDD can be affected by network activity by varying the model's membrane time constant, τ_m. We show that NDD is significant for small τ_m or high network activity, and decreases for large τ_m, or low network activity. Our results suggest that for inputs just above threshold, the activity of the network constrains the neuronal coding strategy due to, at least in part, the NDD effect.     

Effects of correlation time between noises on the noise enhanced stability phenomenon in an asymmetric bistable system

The effects of the correlation time τ between noises on the noise-enhanced stability (NES) phenomenon in an asymmetric bistable system driven by cross-correlated noise are investigated. The expressions for the average escape time from the left metastable state T_L and from the right metastable state T_Rare derived. The results indicate that: i) The NES effect is suppressed as the correlation time τ increases for two metastable states; ii) The increase in τ speeds up the escape process from the right state for positively correlated noise, whereas its role is reverses for negatively correlated; iii) In the escape process from the left state, the role of τ is opposite to that in escape from the right state.     

Stochastic multiresonance in a bistable sawtooth potential driven by correlated multiplicative and additive noise

We present an analytic investigation of the signal-to-noise ratio (SNR) by studying the bistable sawtooth system driven by correlated Gaussian white noises. The analytic expression of SNR is obtained. Based on it, we detect the phenomenon of stochastic multiresonance, which arises from the dependence of SNR upon the noises correlation coefficient. Furthermore, there exists not only resonance, but also suppression in the SNR∼D (the additive noise intensity) curve and the SNR∼Q (the multiplicative noise intensity) curve. Received 26 February 2002 / Received in final form 12 July 2002 Published online 17 September 2002     

Causality study on a feedforward active noise control headset with different noise coming directions in free field

A systematic analysis is proposed to predict the performance of a typical feedforward single channel ANC headset in terms of the delay, especially the non-causal delay caused by different noise coming directions. First, the performance of a non-causal feedforward system for a band-limited noise is analyzed by using a simplified pure delay model, where it is found that the noise reduction bandwidth is narrowed and the maximum noise reduction is decreased with the increase of the non-causal delay. Second, a systematic method is developed, which can be used to predict the system performance with measured primary and secondary path transfer functions in most practical sound fields and to study the effects of the control filter length and the path delay on the performance. Then, the causality of a typical feedforward active noise control headset with the primary source at 0° and 90° positions in an anechoic chamber is analyzed, and the performance for the two locations predicted by the systematic analysis is shown in good agreements with the experiment results. Finally, an experiment of a typical feedforward active noise control headset in a reverberation chamber is carried out, which shows the validity of the proposed systematic analysis for other more practical sound fields.     

Growth in a restricted solid on solid model with correlated noise

We introduce correlated growth into a restricted solid on solid model (RSOS), a stochastic deposition model with a constraint on neighboring height differences. A two-dimensional lattice model is used in which particles are deposited via horizontal Levy flight steps with a step length distribution exponentf. Though RSOS is in the same universality class as ballistic deposition for uncorrelated deposition, it appears to depart from it for strong correlations. Forf=1, the short-range limit is reached and both exponents and, which describe the dependence of surface width on time and strip length, tend to 1. Forf>1 we retreat to an enhanced algorithm, searching for growth sites which become excessively rare. We find an unusual short-time dependence, but still tends to 1. The number of growth sitesG shows saturation forf<1, while forf1 we observeG/L0 as the strip lengthL increases. Finally, we test directly the relationship of noise-noise correlation strength tof, and find that a direct comparison between correlated growth models and theoretical predictions for growth with correlated noise is so far unjustified.     

Effects of an oscillating field on a diffusion process in the presence of a trap

Consider a diffusion process on an infinite line terminated by a trap and modulated by a periodic field. When the frequency is equal to zero the mean time to trapping will be finite or infinite, depending on the sign of the field. We ask whether this behavior can be changed by an oscillatory field, and show that it cannot for pure Brownian motion. We suggest that transition can appear when the signal propagation velocity is finite as for the telegrapher's equation. We further suggest that the asymptotic time dependence of the survival probability is proportional tot ^–1/2 just as in the case of ordinary diffusion. The same conclusion is shown to hold for a system whose dynamics is governed by the equation , whereL is a constant.     

Phase noise suppression in a DPSK transmission system by the use of an attenuation-imbalanced NOLM

A nonlinear optical loop mirror (NOLM) imbalanced by attenuation has been used for the suppression of nonlinear phase noise in a DPSK transmission system. It has been experimentally shown that such a passive, NOLM-based regenerator can significantly improve the performance of a phase-encoded transmission when it is limited by nonlinear phase noise. A brief overview over the advantages und limitations of different NOLM-based phase-preserving amplitude regenerators is also given.