Scaling of 1/<Emphasis Type="Italic">f</Emphasis> noise in nonequilibrium phase transitions

Investigation of the dynamics of fluctuations of heat and mass transfer reveals that its crisis and transient modes exhibit high-energy pulsations with a power spectrum that is inversely proportional to frequency (flicker or 1/f fluctuations). Such a spectrum suggests energy transfer from high-to low-frequency modes and the possibility of large-scale catastrophic outbursts in the system being considered. The theory shows that such fluctuations arise in the system owing to the simultaneous occurrence of interacting phase transitions in the presence of white noise having a sufficiently high intensity. The distribution of fluctuations for scale transformations of the set of stochastic equations that describe the generation of 1/f noise is investigated. It is shown that, under a scale transformation, the Gaussian distribution of a random process having a 1/f spectrum passes to an exponential distribution, which is characteristic of the statistics of extreme outbursts. The probability of such outbursts must be taken into account in predicting the stability of various heat-transfer modes.     

Correlation of power variables

Cross correlation functions between input power fluctuations and system power fluctuations are derived for a Gaussian process and sine wave process. These cross correlation functions are referred to as power correlations and they contain both a constant term plus a fluctuating quantity. The derivations show that for a linear system with no uncorrelated noise normalized correlations of squared fluctuations between the input and output should be equal to one. Experimental data obtained from tests on an electrical circuit validated analytically derived power correlation formulas. Power correlation functions can be used for determination of propagation times, for power transmission, and for other applications such as resonance testing.     

Effects of the Low Frequencies of Noise on On–Off Intermittency

A bifurcating system subject to multiplicative noise can exhibit on–off intermittency close to the instability threshold. For a canonical system, we discuss the dependence of this intermittency on the Power Spectrum Density (PSD) of the noise. Our study is based on the calculation of the Probability Density Function (PDF) of the unstable variable. We derive analytical results for some particular types of noises and interpret them in the framework of on-off intermittency. Besides, we perform a cumulant expansion (N. G. van Kampen, 24, 171 (1976).) for a random noise with arbitrary power spectrum density and we show that the intermittent regime is controlled by the ratio between the departure from the threshold and the value of the PSD of the noise at zero frequency. Our results are in agreement with numerical simulations performed with two types of random perturbations: colored Gaussian noise and deterministic fluctuations of a chaotic variable. Extensions of this study to another, more complex, system are presented and the underlying mechanisms are discussed. PACS Number: 05.40.-a, 05.45.-a, 91.25.-r     

Criticality in the relaxation phase of a spontaneously contracting atria isolated from a frog's heart

We investigate the spontaneous contraction generated by the atria of a frog's heart isolated in a physiological solution. In the relaxation phase, the recorded time series for two different sampling rates possesses an intermittent component similar to the dynamics of the order parameter's fluctuations of a thermal critical system belonging to the mean field universality class. This behavior is not visible through conventional analysis in the frequency space due to the presence of Brownian noise dominating the corresponding power spectrum.     

Power Spectrum of a Noisy System Close to a Heteroclinic Orbit

We consider a two-dimensional dynamical system that possesses a heteroclinic orbit connecting four saddle points. This system is not able to show self-sustained oscillations on its own. If endowed with white Gaussian noise it displays stochastic oscillations, the frequency and quality factor of which are controlled by the noise intensity. This stochastic oscillation of a nonlinear system with noise is conveniently characterized by the power spectrum of suitable observables. In this paper we explore different analytical and semianalytical ways to compute such power spectra. Besides a number of explicit expressions for the power spectrum, we find scaling relations for the frequency, spectral width, and quality factor of the stochastic heteroclinic oscillator in the limit of weak noise. In particular, the quality factor shows a slow logarithmic increase with decreasing noise of the form \(Q\sim [\ln (1/D)]^2\). Our results are compared to numerical simulations of the respective Langevin equations.     

Origin of laser-output noise of cataphoretic HeSe+ lasers

We investigated noise and fluctuations of the output power of cataphoretic HeSe⁺ lasers in positive column plasma. Direct coupling of laser output power noise and fluctuations of the local population inversion was found. An investigation of the positive column plasma showed moving striations being responsible for the gain fluctuations. Whereas the local plasma properties are dominated by high frequency striations in the 100 kHz range, integrated quantities such as laser gain per pass are most strongly influenced by low-frequency waves with a continuous noise spectrum below 200 kHz. External modulation of the discharge voltage or current at a frequency near thehf striations reduces laser noise and increases laser output power.     

Auditory masking of a 10 kHz tone with environmental, comodulated, and Gaussian noise in bottlenose dolphins (Tursiops truncatus)

The pattern of auditory masking derived from Gaussian noise is often cited and used to predict the detrimental effects of masking noise on marine mammals. However, environmental noise (both anthropogenic and natural) may not always be Gaussian distributed. Some noise sources are highly structured with complex amplitude fluctuations that extend across frequency regions, which are often termed comodulated noise. Recent evidence with bottlenose dolphins using comodulated noise demonstrated a significant release from masking compared to Gaussian maskers of the same bandwidth and pressure spectral density level, a result known as comodulation masking release. The present study demonstrates a pattern of masking where both temporally fluctuating comodulated noise and environmental noise produce lower masked thresholds compared to Gaussian noise of the same spectral density level and bandwidth. Furthermore, a threshold reduction or "masking release" occurred when the environmental noise bandwidth increased beyond a critical band. These results provide further evidence that conventional models of auditory masking using Gaussian maskers (i.e., the power spectrum model) do not fully describe the masking effects that occur in realistic environments.     

Fluctuations in doubly scattered laser light

Fluctuations in laser light, doubly scattered by brownian particles, were analysed by measuring the spectral noise power of the photodetector current. Scattering took place at two spatially separated systems of spherical particles. Analytic expressions for the field and intensity correlations are derived. The analytic expressions for the spectrum of the intensity fluctuations of the doubly scattered laser light demonstrate that the frequency dependence of the spectrum depends strongly of the geometry of the experimental arrangement. This is not the case for singly scattered light where in good approximation the spatial and temporal correlations can be separated analytically.Our measurements show that the noise spectrum of the doubly scattered radiation may have the same frequency dependence as the spectrum of the singly scattered light. However, there are conditions where the frequency dependence of the noise of the doubly scattered light diverges markedly from that of the singly scattered light.     

Deviation of 1/f voltage fluctuations from scale-similar Gaussian behavior

Recent measurements on thin metal films suggest a pulse model of resistance fluctuations in which scale similarity and power law spectra are only approximate. We show that such a pulse model is consistent with stationary Gaussian resistance fluctuations. This is to be contrasted with the phenomenological behavior, of fluctuations near phase transitions and in turbulent fluids where the fluctuations are non-Gaussian, but exhibit scale similarity of deep physical origin. We then critically examine other tests of the Gaussian behavior of the fluctuating voltageV(t) across a resistor. These include the relaxation of the conditional mean V(t)¦V(0)=V ₀, and the spectrum ofV ²(t). We consider also the question of time reversal invariance. We further ask under what conditions 1/f noise can be measured through fluctuations of the Johnson noise power with no applied voltage. We emphasize that this possibility, suggested and observed by Voss and Clarke, requires thatV(t) contain a non-Gaussian component.     

On low frequency and 1/f noise from diffusion like processes

The noise spectrum resulting from diffusion like processes is calculated in two and three dimensions for two different forms of free energy fluctuation. For example it is shown that in a three dimensional system with ideal non-interacting particles the noise is almost white up to a certain frequency. In a two dimensional system where the free energy fluctuations are proportional to the gradient of a parameter modulating the electrical conductivity a 1/f noise power spectrum is expected in a certain frequency interval.     

Power spectrum of density fluctuations in a finite reactive-diffusive system: resistance fluctuation spectroscopy

The measurement in thermal equilibrium of the vacancy contribution to the residual resistivity of metals has posed certain difficulties. The recent experiment of Celasco and co-workers represents a new, powerful approach to this problem, via the measurement of the power spectrum of the voltage noise generated by resistivity fluctuations. The latter originate in vacancy number fluctuations. We develop a theory for the power spectrum, incorporating three basic features. Vacancies can be annihilated in the material and they diffuse. Grain boundaries act as sources and sinks for vacancies. Both annihilation (a form of reaction) and diffusion are noisy processes. We therefore set up and solve a reactive-diffusive stochastic equation for the instantaneous density, with appropriatefinite boundary conditions. Assuming for simplicity that the grains are spherical, the power spectrum is evaluated exactly, in closed form. A detailed comparison with experiment is made. The physical origins of different time scales in the problem and the consequent frequency regimes in the power spectrum are analysed. Recognising the very general applicability of our theory, we also mention possible applications to other problems.     

高斯白噪声相位调制的激光光谱展宽

激光器是现代光学中一种常用的光源,分析其谱宽特性对于激光的研究具有重要意义.由于高性能窄线宽激光的半高全宽通常在几十M Hz以内,难以直接满足宽光谱领域的应用需求,因而无法发挥其在成本和性能方面的优势,这在一定程度上限制了激光的发展.如果在激光内部直接进行调制实现线宽展宽,又会导致频率的严重漂移,破坏稳频特性.为了在激...     

Noise measurements in bilayer lipid membranes during electroporation

A study of voltage fluctuations in bilayer lipid membranes during electroporation and under current-clamp conditions is presented. Qualitative considerations based on the electroporation theory are used in order to explain the phenomenon on long time scale. Indeed, the current-clamp condition induces a feedback mechanism on the pore formation and therefore on the macroscopic conductance. Voltage fluctuations can thus be recorded. These fluctuations are nonstationary long-living and have a flicker power spectrum over nearly four decades of frequency between about 10^-2 and 10²Hz. The study of the fluctuations in the time domain has been performed by introducing an electrical model of the system formed by the membrane and the circuit under current-clamp configuration. The analysis of the time series gives a characteristic time of 100ms for the circuitry response to the fragments of electroporation signals with characteristic times faster than 100ms. During electroporation, the response to an external periodic stimulus in the frequency range 10^-1-10Hz shows that the system behaves linearly, even if voltage fluctuations are present. Received 1 June 1999 and Received in final form 1 October 1999     

An entropy-based stability analysis of extreme fluctuations in a system featuring a 1/<Emphasis Type="Italic">f</Emphasis> spectrum

Extreme fluctuations are modeled by a point system of stochastic equations, in which power spectra inversely proportional to the frequency are produced under the effect of white noise. The distribution of extreme fluctuations corresponds to the maximum of statistical entropy, which points to their stability in nature. By calculating the spectral entropy of random processes, it becomes possible to investigate their stability directly from power spectra without the need to calculate the amplitude distribution functions. The spectral entropy as a function of white noise amplitude has a minimum. The position of the spectral entropy minimum corresponds to the critical state of the system in which the spectra of fluctuating quantities are inversely proportional to the frequency.     

Noise power fluctuations and the masking of sine signals

This article is concerned with fluctuations in noise power and with the role that such fluctuations play in the masking of sine signals by noise. Several measures of noise fluctuations are discussed: the fourth moment of the waveform, the fourth moment of the envelope, and the crest factor. Relationships among these quantities are found for cases of equal-amplitude random-phase noise and Rayleigh-distributed-amplitude noise. Of particular interest is a special non-Gaussian noise called low-noise noise in which the fluctuations are small by any of our measures. The results of frozen-noise masking experiments are reported, where the noise waveform was fixed for all stimulus presentations. In separate experiments, equal-amplitude random-phase Gaussian noise, with typical fluctuations, and low-noise noise, with almost no fluctuations were used. The data show that for a noise bandwidth less than the critical bandwidth, the masked threshold is about 5 dB lower for low-noise noise than for Gaussian noise. When the noise bandwidth is larger than the critical bandwidth, the masked threshold is the same for both kinds of noise. It is concluded that noise power fluctuations increase masked threshold by about 5 dB and that filtering by the auditory system reintroduces fluctuations into broadband low-noise noise.     

Numerical investigation of scaling regimes in a model of an anisotropically advected vector field

Influence of strong uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of a passive transverse vector field advected by an incompressible turbulent flow is investigated by means of the field theoretic renormalization group. Turbulent fluctuations of the velocity field are taken to have the Gaussian statistics with zero mean and defined noise with finite correlations in time. It is shown that stability of the inertial-range scaling regimes in the three-dimensional case is not destroyed by anisotropy, but the corresponding stability of the two-dimensional system can be corrupted by the presence of anisotropy. A borderline dimension d _c below which the stability of the scaling regime is not present is calculated as a function of anisotropy parameters. The text was submitted by the authors in English.     

电子直线加速器磁控管频率稳定的自适应线性神经元方法

 电子直线加速器电子束能量的稳定与否取决于功率源工作频率的稳定性,磁控管在短时间内的散谱和轻微跳谱造成稳频系统的控制精度下降,最后电子束的扫描均匀度下降。引入自适应线性神经元方法(ADALINE)和噪声对消技术以消除对工作频率长期稳定性的影响,从而保证了电子束的扫描均匀度。     

Fluctuations and Correlations of Pure Quantum Turbulence in Superfluid 3He-B

We describe the first measurements of line-density fluctuations and spatial correlations of quantum turbulence in superfluid 3He-B. All of the measurements are performed in the low-temperature regime, where the normal-fluid density is negligible. The quantum turbulence is generated by a vibrating grid. The vortex-line density is found to have large length-scale correlations, indicating large-scale collective motion of vortices. Furthermore, we find that the power spectrum of fluctuations versus frequency obeys a -5/3 power law which verifies recent speculations that this behavior is a generic feature of fully developed quantum turbulence, reminiscent of the Kolmogorov spectrum for velocity fluctuations in classical turbulence.     

Kolmogorov spectrum of renewable wind and solar power fluctuations

With increasing the contribution of renewable energies in power production, the task of reducing dynamic instability in power grids must also be addressed from the generation side, because the power delivered from such sources is spatiotemporally stochastic in nature. Here we characterize the stochastic properties of the wind and solar energy sources by studying their spectrum and multifractal exponents. The computed power spectrum from high frequency time series of solar irradiance and wind power reveals a power-law behaviour with an exponent ～ 5/3 (Kolmogorov exponent) for the frequency domain 0.001?Hz < f < 0.05?Hz, which means that the power grid is being fed by turbulent-like sources. Our results bring important evidence on the stochastic and turbulent-like behaviour of renewable power production from wind and solar energies, which can cause instability in power grids. Our statistical analysis also provides important information that must be used as a guideline for an optimal design of power grids that operate under intermittent renewable sources of power.     

Brownian motion in a solitary potential well in a bounded solid structure

The motion of a heavy Brownian particle in a low-dimensional bounded solid structure under the effect of a phonon’s excitation fluctuations is considered. Because of the finiteness of the system, the fluctuation spectrum has zero spectral density at zero frequency. The effect of this kind of noise, which is conditionally called “green” noise, is studied both analytically by using the averaging method and numerically on the basis of predictor-corrector algorithms. The effective potential is introduced, and its form is shown to govern the particle dynamics. Considering a Gaussian potential well (a trap) as an example, it is demonstrated that green noise leads to abrupt phase transitions in the system as a result of very small parameter variations (a catastrophe-type effect). The results are compared with the case of white noise in an unbounded structure. From numerical calculations, it follows that the boundedness of the structure, which changes the noise spectrum, favors a considerable increase in the lifetime of the particle in the trap.