Transient oscillations in Soret-driven convection in a colloidal suspension

We present measurements of the transient stage of Soret-driven convective instability. The sample is a diluted colloidal suspension of silica spheres in water with an unusually large negative Soret coefficient S_T. A large temperature gradient (heating from above) is rapidly applied over the sample, while a shadowgraph imaging technique provides images of the convective flow. From the processing of the variance of the intensity of the images we are able to recover the time evolution of the overall intensity of the convective flow. A typical evolution of such signal exhibits, after a latency time, a peak followed by some damped oscillations leading to a steady-state value. Both the onset time _p (the temporal position of the first peak), and the oscillation period _osc show a power law dependence as a function of the solutal Rayleigh number R_s. The exponents found are compared with predictions from existing models.     

Effects of non-Gaussian noise on a calcium oscillation system

We investigate the effects of the non-Gaussian colored noise on a calcium oscillation system using stochastic simulation methods. It is found that the reciprocal coefficient of variance R has a maximum (R max ) with increasing noise intensity Q. The non-Gaussian noise parameter q has an important effect on the system. For some values of q (e.g., q = 0.9, q = 1.0), R has a maximum with increasing correlation time τ. Non-Gaussian noise induced spikes are more regular than Gaussian noise induced spikes when q is small and Q has large values. The R has a maximum with increasing q. Therefore, non-Gaussian noise could play more effective roles in the calcium oscillation system.     

External noise effects on the fluctuation line width

We calculate stationary state correlation functions of the anharmonic overdamped oscillator driven by multiplicative (white Gaussian) noise of strengthQ together with additive noise of relative strengthq. (i) We donot observe a particular slowing down at the so-called noise induced transition. But there is a region of the oscillator's stiffness parametera neara0 in which the decay time is typically enhanced. (ii) If the phase transition point is defined by the minimum of the decay rate, it lies within the ordered phasea>0 forq1 and shifts down toa=0 forq0. In our approximation it is even in the disordered regiona<0 for very smallq. (iii) As a function of the multiplicative noiseQ the decay ratedecreases with increasingQ if the system is well above or well below threshold. There seem to be experimental indications of this behavior. But within the proper threshold regime of smalla increasing noiseQ increases the decay rate. The valuesa _c where the cross-over occurs depend on the fluctuating variable and onq.     

色噪声间关联的周期调制对单模激光随机共振的影响

讨论色噪声驱动的单模激光系统在噪声间关联程度受时间周期调制情况下的随机共振.用线性化近似的方法计算了光强功率谱及信噪比.具体讨论色噪声情况下信噪比R受噪声强度D,Q,时间周期调制频率Ω_λ以及噪声自关联时间τ₁,τ₂和噪声间关联程度λ的影响.发现信噪比随噪声强度的变化呈单峰共振,信噪比随时间周期调制频率的变化呈周期性共振,而信噪比随 关键词： 色噪声 时间周期调制 噪声间关联程度 周期性随机共振     

非关联噪声驱动的单稳系统的平均首次穿越时间

基于非对称双稳系统的理论研究了偏单稳系统的平均首次穿越时间问题,并基于势函数分析了参数对平均首次穿越时间的影响.得出结论:1)当偏稳系数为零时,随着加性噪声强度和参数a的增加,两个方向的平均首次穿越时间相等且均单调减小,2)随着偏稳系数b的增加,势阱的对称性被破坏,粒子由xs1跃迁到xs2的时间线性地减小,而粒子由xs2跃迁到xs1的时间线性地增加.3)随着乘性噪声强度和加性噪声强度比率R的增加,两个方向平均首次穿越时间均单调增加.     

Low-frequency instabilities of electron-hole plasmas in crossed fields

Using local point-contact probes, we observed two types of low-frequency instabilities inn-InSb at 85 K if the samples were exposed to crossed fields. One is a local density instability with threshold frequencies off = 1 20 Mc, the other a more turbulent current instability. The threshold values ofU ₀ andB for the onset of these instabilities and the dependence of their amplitudes on the fields have been measured.If a rectangular semiconductor slab is placed in crossed fields, regions of high electric field strength at opposite edges of the contacts are caused by the distortion of the Hall field, giving rise to the generation of electron-hole plasmas by impact ionization. These plasmas are the sources of the observed instabilities. This is especially evident in the case of the local density instability, which originates at the anode high field corner. Several possible reasons for the development of the instabilities are discussed.     

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     

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.     

Squeezed two-mode lasers without and with inversion

On the basis of the nondegenerate quantum-beat laser model, we introduce a coherent field which drives the transition between the upper lasing level and an auxiliary level. We demonstrate that such a four-level system can produce squeezed two-mode laser without and with inversion. When the laser is operated well above threshold, the intensity fluctuation in the average mode is reduced below the shot noise with an optimum Mandel parameter Q=- 1/2. At the same time, the noises in the relative amplitude and the relative phase drop to their vaccum noise levels. Furthermore, regardless of inversion, noninversion, and transition between inversion and noninversion, the optimum Mandel Q parameter of Q=- 1/2 is retained when the system operates well above threshold. A simple physical explanation of the squeezing mechanism for two-mode squeezing is given. Received: 22 December 1997 / Revised: 25 March 1998 / Accepted: 9 September 1998     

CMOS 1/f noise: n-channel versus p-channel

This note reports on the noise of CMOS devices. It is shown experimentally that a weak boron threshold implant (10¹² cm^–3) can influence the 1/f noise levels. For wafers with threshold adjustment the p-channel noise decreases whilst the n-channel noise increases. The changes in the n/p noise ratio with/without threshold implantation are predicted using a simple model in conjunction with carrier profile simulations.     

Stationary Properties and Stochastic Resonance for a Saturation Laser Model with Cross-correlation Between Quantum Noise Terms

The stationary properties of a saturation laser model with cross-correlation between the real and imaginary parts of the quantum noise are investigated theoretically. Using the Novikov theorem and the Sargent technique, we obtain the analytic expressions of the stationary probability density distribution, the mean, the variance and the skewness of the saturation laser model. The cross-correlation coefficient λ and other parameters can make the stationary probability density distribution P _st (I) generate interesting two-extrema structure, one-extremum structure, or no-extremum structure. It is clearly found that a first- order-like-transition is induced by the coupling strength |λ| of the complex quantum noise terms in the saturation laser model. When the laser system is operated above the threshold, the mean 〈I〉 becomes larger and the output of the laser intensity increases; however the coupling strength |λ| attenuates the output of the laser intensity. When the laser is operated near and below the threshold, the mean 〈I〉 becomes smaller, the output of the laser intensity decreases, and |λ| still attenuates the output of the laser intensity. When a periodic signal is added to a saturation laser model with cross-correlation between quantum noise terms, the interesting stochastic resonance phenomena occur at λ=0. The noise intensity Q decreases the values of the resonance peak, however, the amplitude of the periodic signal B enhances the values of the resonance peak.     

Effects of colored noise and noise delay on a calcium oscillation system

As a calcium oscillations system is in steady state, the effects of colored noise and noise delay on the system is investigated using stochastic simulation methods. The results indicate that: (1) the colored noise can induce coherence bi-resonance phenomenon. (2) there exist three peaks in the R–_τ0$R\text{–}{\tau }_0$ (R$R$ is the reciprocal coefficient of variance, and _τ0${\tau }_0$ is the self-correlation time of the colored noise) curves. For the same noise intensity Q=1$Q=1$, the Gaussian colored noise can induce calcium spikes but the white noise cannot do this. (3) the delay time can improve noise induced spikes regularity as _τ0${\tau }_0$ is small, and R$R$ has a significant minimum with increasing τ$\tau$ as _τ0${\tau }_0$ is large. (4) large values of ζ$\zeta$ reduce noise induced spikes regularity.     

Dynamical Phase Transition in a Neural Network Model with Noise: An Exact Solution

The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same value. It is shown that, under very general conditions, there exists a critical value _c of the noise, below which the network remains organized and above which it behaves randomly. The existence and nature of the phase transition are computed analytically, showing that the critical exponent is 1/2. The dependence of _c on the parameters of the network is obtained. These results are then compared with two numerical realizations of the network.     

Energy characteristics of photothermal vibrational instability at stimulated Raman and Mandelstam-Brillouin scattering in aerosol droplets

The threshold intensity and the combination frequencies for photothermal vibrational instability in high-Q aqueous aerosol droplets in the two-mode regime have been calculated. The selection rules for coupling electromagnetic and temperature modes in a droplet are obtained. A comparative analysis of the threshold excitation intensities of photothermal vibrational instability, stimulated Mandelstam-Brillouin scattering, and stimulated Raman scattering in droplets is performed. It is shown that photothermal vibrational instability in the two-mode regime can be developed at a pump intensity of about 10⁴ W/cm² for droplets with radii of 2–20 μm for a pump wavelength of 0.532 μm. A method of remote measurement of the microphysical droplet parameters from the additional periodic temperature shift of droplet eigenfrequencies in the spectrum of stimulated Raman scattering and lasing is proposed.     

噪声间关联程度的时间周期调制对单模激光随机共振的影响

用线性化近似的方法研究了噪声间关联程度λ受时间周期性调制的单模激光增益模型的光强功率谱及信噪比.具体讨论信噪比R受加法噪声强度D,乘法噪声强度Q及噪声间关联程度λ的影响,以及受周期调制频率Ω_λ,输入信号频率Ω的影响.发现了一些新颖的现象. 关键词： 时间周期调制频率 噪声间关联程度 随机共振 信噪比     

Control of the perturbation-wave-vector range of modulation instability of dispersive electromagnetic waves in the nonlocal Josephson electrodynamics of a thin superconducting film

Modulation instability of dispersive electromagnetic waves propagating through a Josephson junction in a thin superconducting film is investigated in the framework of the nonlocal Josephson electrodynamics. A dispersion relation is found for the time increment of small perturbations of the amplitude. For dispersive waves, it is first established that spatial nonlocality suppresses the modulation instability in the range of perturbation wave vectors 0≤Q≤Q_B1(k), i.e., in the long-wavelength range of experimental interest. The modulation instability range Q_B1(k)<Q<Q_B2(k, A, L) can be controlled (which is a unique possibility) by varying a dispersion parameter, namely, the wave vector k [or the frequency ω(k)] of linear-approximation waves. In the wave-vector ranges 0≤Q≤Q_B1(k) and Q≤Q_B2(k, A, L), waves are shown to be stable.     

Depth distribution of x-rays in electron microprobe analysis

The dependence of the relative intensityk on the thin film thickness has been measured. This dependence has enabled us to verify the Monte Carlo simulation. From the experimentally determined dependence, distributions of X-rays in the specimen ((z) functions) have been derived. It has been found that the intensities calculated by the present Monte Carlo model are always higher than those measured.The authors wish to thank Prof. R. Kuel of the Faculty of Mathematics and Physics, Charles University, Prague, for the measurement of the sputtered thin films thickness.     

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.     

A stochastic return map for stochastic differential equations

A method is presented for constructing a stochastic return map from a stochastic differential equation containing a locally stable limit cycle and small-amplitude [O()] additive Gaussian colored noise. The construction is valid provided the correlation time isO() orO(1). The effective noise in the return map has nonzeroO( ²) mean and is state dependent. The method is applied to a model dynamical system, illustrating how the effective noise in the return map depends on both the original noise process and the local deterministic dynamics.     

Some first passage time problems for shot noise processes

It has recently been shown that the first passage time problem for a certain class of one-dimensional processes that includes shot noise can be formulated in terms of a set of integral equations. These are found by exact enumeration of all possible trajectories. We show that the equations can be found by more direct means for processes described by the evolution equation , wheren(t) is time-localized shot noise.