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.     

On the relation between white shot noise,Gaussian white noise,and the dichotomic Markov process

It is shown that the dichotomic Markov process converges to a white shot noise (interpreted according to the Stratonovich integration rule) in the joint limit in which the average duration of one of the states goes to zero and the value at this state goes to infinity. A further limit procedure allows us to obtain Gaussian white noise from white shot noise. These results are applied to the problem of noise-induced transitions. It is shown that white shot noise can give rise to transitions which do not occur for Gaussian white noise. The above results are finally generalized in introducing compound dichotomic Markov processes.     

受迫薛罗格双匣化学反应模型的随机共振

为了在理论上揭示高斯白噪声激励的薛罗格双匣化学反应模型对弱周期扰动的线性与非线性响应 ,分四态近似和两态近似两种情形 ,基于绝热近似与速率方程方法 ,解析导出线性的和非线性的敏感性以及信噪比的表达式 ,并与数值模拟结果进行比较 ,在一次谐波的意义上得到了解析结果与数值模拟结果的定量一致性 .理论上讲 ,该模型只能表现出奇次谐波的随机共振 ,但数值模拟结果也出现了二次谐波的随机共振 ,其原因可能归结为在数值模拟中有限频率的截断引入了误差 ,也可能归结为信号的高次谐波与背景噪声难以区分所致 .     

基于空时级联滤波的拖船自噪声抵消方法

拖船自噪声属于近场多途强干扰信号,具有显著角度扩展现象,是影响拖曳阵探测性能的重要因素之一。在逆波束形成自噪声抵消方法基础上,结合空域和时域滤波,提出了空时级联滤波的拖船自噪声抵消方法。首先,由方位估计器估计拖船自噪声方位,经过波束形成空域滤波估计得到自噪声信号;然后,利用自噪声空域滤波输出设计最优维纳滤波器,将自噪声抵消在阵元级。基于简正波声场模型的仿真和实际海试数据的处理表明,该方法能够有效抵消拖船自噪声,性能优于逆波束形成方法。     

A new method of analysis of the effect of weak colored noise in nonlinear dynamical systems

A systematic method for obtaining the asymptotic behavior of a dynamical system forced by colored noise in the limit of small intensity is developed. It is based on the search of WKB solutions to the Fokker-Planck equation for the joint probability density of the system and noise, in which the perturbation expansion is continued to the first correction beyond the Hamilton-Jacobi limit. The method can be applied to noise with correlation time of order unity. It is illustrated on the normal form of a pitchfork bifurcation, where it is pointed out that additive noise can induce a shift of the most probable value. This prediction is confirmed by numerical simulation of the stochastic differential equations.     

Probability evolution method for exit location distribution

The exit problem in the framework of the large deviation theory has been a hot topic in the past few decades. The most probable escape path in the weak-noise limit has been clarified by the Freidlin–Wentzell action functional. However, noise in real physical systems cannot be arbitrarily small while noise with finite strength may induce nontrivial phenomena, such as noise-induced shift and noise-induced saddle-point avoidance. Traditional Monte Carlo simulation of noise-induced escape will take exponentially large time as noise approaches zero. The majority of the time is wasted on the uninteresting wandering around the attractors. In this paper, a new method is proposed to decrease the escape simulation time by an exponentially large factor by introducing a series of interfaces and by applying the reinjection on them. This method can be used to calculate the exit location distribution. It is verified by examining two classical examples and is compared with theoretical predictions. The results show that the method performs well for weak noise while may induce certain deviations for large noise. Finally, some possible ways to improve our method are discussed.     

Effect of noise and perturbations on limit cycle systems

This paper demonstrates that the influence of noise and of external perturbations on a nonlinear oscillator can vary strongly along the limit cycle and upon transition from limit cycle to stationary point behaviour. For this purpose we consider the role of noise on the Bonhoeffer-van der Pol model in a range of control parameters where the model exhibits a limit cycle, but the parameters are close to values corresponding to a stable stationary point. Our analysis is based on the van Kampen approximation for solutions of the Fokker-Planck equation in the limit of weak noise. We investigate first separately the effect of noise on motion tangential and normal to the limit cycle. The key result is that noise induces diffusion-like spread along the limit cycle, but quasistationary behaviour normal to the limit cycle. We then describe the coupled motion and show that noise acting in the normal direction can strongly enhance diffusion along the limit cycle. We finally argue that the variability of the system's response to noise can be exploited in populations of nonlinear oscillators in that weak coupling can induce synchronization as long as the single oscillators operate in a regime close to the transition between oscillatory and excitatory modes.     

Correlation method estimation of the modulation signal in the weak equivalence principle test

In a test of the weak equivalence principle(WEP) with a rotating torsion pendulum, it is important to estimate the amplitude of the modulation signal with high precision. We use a torsional filter to remove the free oscillation signal and employ the correlation method to estimate the amplitude of the modulation signal. The data analysis of an experiment shows that the uncertainties of amplitude components of the modulation signal obtained by the correlation method are in agreement with those due to white noise. The power spectral density of the modulation signal obtained by the correlation method is about one order higher than the thermal noise limit. It indicates that the correlation method is an effective way to estimate the amplitude of the modulation signal and it is instructive to conduct a high-accuracy WEP test.     

Analytic approximations of statistical quantities and response of noisy oscillators

Nonlinear oscillators have been utilized in many contexts because they encompass a large class of phenomena. For a reduced phase oscillator model with weak noise forcing that is necessarily multiplicative, we provide analytic formulas for the stationary statistical quantities of the random period. This is an important quantity which we term ‘response’ (i.e., the spike times, instantaneous frequency in neuroscience, the cycle time in chemical reactions, etc.) that is often analytically intractable in noisy oscillator systems. The analytic formulas are accurate in the weak noise limit so that one does not have to numerically solve a time-varying Fokker-Planck equation. The steady-state and dynamic responses are also analyzed with deterministic forcing. A second order analytic formula is derived for the steady-state response, whereas the dynamic response with time-varying forcing is more complicated. We focus on the specific case where the forcing is sinusoidal and accurately capture the frequency response with an analytic approximation that is obtained with a rescaling of the equation. By utilizing various techniques in the weak noise regime, this work leads to a better understanding of how the random period of nonlinear oscillators are affected by multiplicative noise and external forcing. Comparisons of the asymptotic formulas with a full oscillator system confirm the qualitative accurateness of the theory.     

一种Duffing弱信号检测新方法及仿真研究

研究了利用混沌相变进行弱信号检测的理论及仿真试验.对基于Duffing振子初值敏感性检测弱信号的方法分析后指出,过渡过程会影响检测性能,提出一种改进的弱信号检测方法.对仿真输入噪声生成和仿真步长选择进行研究后建立了仿真模型,在典型噪声背景下检测弱正弦信号.实验结果表明：所提出的方法有较好检测性能;混沌临界态的Duffing系统对噪声敏感导致相变方法难以精确确定最小检测幅值.指出了这类方法的局限性. 关键词： 混沌 信号检测 周期信号 白噪声     

Stationary and dynamic solutions of stochastic relaxation oscillators

Two different approaches are proposed to obtain explicit solutions for stochastic relaxation oscillator problems in the weak noise limit. The first method generalizes the idea of the cumulant expansion. It does not presuppose an analytical treatment of the deterministic motion. It is however restricted to the discussion of stationary situations. In the second method an adiabatic elimination of irrelevant variables allows for the computation of time dependent solutions. It can be carried through only if the deterministic limit cycle is known analytically. As special examples the stationary solutions of the stochastic van der Pol oscillator and time dependent solutions of a simple one dimensional model system have been obtained.This article is an excerpt from a dissertation presented at TH Darmstadt, Darmstädter Dissertation D17This work was performed within a program of the Sonderforschungsbereich 185 Darmstadt-Frankfurt, FRG     

Detection performance of trigger-controlled Geiger-mode avalanche photodiodes in weak optical signal detection

This Letter introduces a trigger-controlled Geiger-mode avalanche photodiode(GM-APD). A hierarchical lookback-upon tree recurrence method is given to predict the performance of trigger-controlled GM-APDs under different trigger-count upper limits. In addition, the normalized detection probability is defined to evaluate the detection performance of trigger-controlled GM-APDs in typical weak optical signal detection(impulse noise and continuous noise situations). Theoretical analyses show that the trigger-controlled GM-APD improves the detection performance of GM-APDs in weak optical signal detection via the optimization of the trigger-count upper limit, compared with single-trigger and multi-trigger GM-APDs.     

Comparison of maximum entropy and filtered back-projection methods to reconstruct rapid-scan EPR images

Reconstruction of two-dimensional images by filtered back-projection (FBP) and by the maximum entropy method (MEM) was compared for spectral-spatial EPR images with differing signal-to-noise ratios. Experimental projections were recorded using direct-detected rapid scans in the presence of a series of magnetic field gradients. The slow-scan absorption lineshapes were calculated by Fourier deconvolution. A Hamming filter was used in conjunction with FBP, but not for MEM. Imperfections in real experimental data, as well as random noise, contribute to discrepancies between the reconstructed image and experimental projections, which may make it impossible to achieve the customary MEM criterion for convergence. The Cambridge MEM algorithm, with allowance for imperfections in experimental data, produced images with more linear intensity scales and more accurate linewidths for weak signals than was obtained with another MEM method. The more effective elimination of noise in baseline regions by MEM made it possible to detect weak trityl (13)C trityl hyperfine lines that could not be distinguished from noise in images reconstructed by FBP. Another advantage of MEM is that projections do not need to be equally spaced. FBP has the advantages that computational time is less, the amplitude scale is linear, and there is less noise superimposed on peaks in images. It is useful to reconstruct images by both methods and compare results. Our observations indicate that FBP works well when the number of projections is large enough that the star effect is negligible. When there is a smaller number of projections, projections are unequally spaced, and/or signal-to-noise is lower MEM is advantageous.     

Renormalized Fokker-Planck equation for the problem of the beam-beam interaction in electron storage rings

It is shown that the beam-beam interaction in electron storage rings is equivalent to an additional source of noise for the particle betatron oscillations. A weak white noise acting upon a nonlinear oscillator causes a fast loss of coherence in its phase. This loss of coherence induces a broadening of the resonances, thus avoiding the problem of the divergent perturbative series which arises in the study of nonintegrable Hamiltonian systems. A “renormalized” Fokker-Planck equation is established which contains new diffusive terms corresponding to the presence of resonances. The solution of this equation is exhibited explicitly in a simplified case. This allows an analytical approach to the problem of the beam-beam instability, which sets an upper limit to the maximum attainable luminosity in storage rings.     

Energy diffusion controlled reaction rate of reacting particle driven by broad-band noise

The energy diffusion controlled reaction rate of a reacting particle with linear weak damping and broad-band noise excitation is studied by using the stochastic averaging method. First, the stochastic averaging method for strongly nonlinear oscillators under broad-band noise excitation using generalized harmonic functions is briefly introduced. Then, the reaction rate of the classical Kramers' reacting model with linear weak damping and broad-band noise excitation is investigated by using the stochastic averaging method. The averaged It? stochastic differential equation describing the energy diffusion and the Pontryagin equation governing the mean first-passage time (MFPT) are established. The energy diffusion controlled reaction rate is obtained as the inverse of the MFPT by solving the Pontryagin equation. The results of two special cases of broad-band noises, i.e. the harmonic noise and the exponentially corrected noise, are discussed in details. It is demonstrated that the general expression of reaction rate derived by the authors can be reduced to the classical ones via linear approximation and high potential barrier approximation. The good agreement with the results of the Monte Carlo simulation verifies that the reaction rate can be well predicted using the stochastic averaging method.     

Extended Weak Coupling Limit for Pauli-Fierz Operators

We consider the weak coupling limit for a quantum system consisting of a small subsystem and reservoirs. It is known rigorously since [10] that the Heisenberg evolution restricted to the small system converges in an appropriate sense to a Markovian semigroup. In the nineties, Accardi, Frigerio and Lu [1] initiated an investigation of the convergence of the unreduced unitary evolution to a singular unitary evolution generated by a Langevin-Schrödinger equation. We present a version of this convergence which is both simpler and stronger than the formulations which we know. Our main result says that in an appropriately understood weak coupling limit the interaction of the small system with environment can be expressed in terms of the so-called quantum white noise.     

Synchronization of periodic self-oscillations by common noise

We consider the effect of external noise on the stability properties of self-oscillations. A stochastic equation for the phase is derived at the limit of weak noise (in the appropriate sense). The stationary probability-density distribution is used for an analytic calculation of the Lyapunov exponent. We show that the exponent is always negative for the small noise level, which corresponds to synchronization of self-oscillations.     

基于随机共振进行弱信号探测的实验研究

非线性随机共振系统可利用噪声增强微弱信号检测的能力,为强噪声背景下微弱信号的检测开创了新方法.基于随机共振的基本原理设计了硬件电路系统,并将其应用于检测单频和多频微弱信号;通过输入模拟工程实际的带噪信号,采样所得的输出信号的频谱分析结果表明,利用随机共振技术可从强噪声背景下有效地提取出单频和多频弱信号.多频弱信号的有效提取拓展了基于随机共振原理的弱信号检测技术的应用领域,结合数字滤波处理技术有效地消除了低频噪声对信号识别的影响.基于随机共振的弱信号检测技术在信息识别与信息处理方面具有巨大的潜在的应用价值.     

The shot noise of a strongly correlated quantum dot coupled to the Luttinger liquid leads

We study the shot noise of a strongly correlated quantum dot weakly coupled to Luttinger liquid leads in the Kondo regime by means of the extended equation of motion method. A general zero-frequency shot noise formula with good convergence is derived. The shot noise exhibits a non-monotonic dependence on voltage for weak intralead interaction. There is a peak around the Kondo temperature at low voltage when the interaction is very weak, and its height decreases rapidly with the intralead interaction increasing. When the interaction is moderately strong the peak disappears and the shot noise scales as a power law in bias voltage, indicating that the intralead electron interaction suppresses the shot noise. It is possible that the measurements of the shot noise spectrum can extract the information of the intralead interaction.     

Extinction and flame bifurcations of stretched dimethyl ether premixed flames

Extinction limits and flame bifurcation of lean premixed dimethyl ether–air flames are numerically investigated using the counterflow flame with a reduced chemistry. Emphasis is paid to the combined effect of radiation and flame stretch on the extinction and flammability limits. A method based on the reaction front is presented to predict the Markstein length. The predicted positive Markstein length agrees well with the experimental data. The results show that flow stretch significantly reduces the flame speed and narrows the flammability limit of the stretched dimethyl ether–air flame. It is found that the combined effect of radiation and flow stretch results in a new flame bifurcation and multiple flame regimes. At an equivalence ratio slightly higher than the flammability limit of the planar flame, the distant flame regime appears at low stretch rates. With an increase in the equivalence ratio, in addition to the distant flame, a weak flame isola emerges at moderate stretch rates. With a further increase in the equivalence ratio, the distant flame and the weak flame branches merge together, resulting in the splitting of the weak flame branch into two weak flame branches, one at low stretch and the other at high stretch. Flame stability analysis demonstrates that the high stretch weak flame is also stable. Furthermore, a K-shaped flammability limit diagram showing various flame regimes and their extinction limits is obtained.