Low-frequency fluctuations in stochastic processes with a 1/<Emphasis Type="Italic">f</Emphasis><Superscript>α</Superscript> spectrum

The results of numerical analysis of the Brownian movement of a particle in the force field of the potential corresponding to interacting subcritical and supercritical phase transitions are considered. If the white noise intensity corresponds to the critical intensity of the noise-induced transition, the system of stochastic differential equations describes random steady-state processes with fluctuation power spectra inversely proportional to frequency f, S(f) ∼ 1/f ^α, where exponent α varies in the interval 0.8 ≤ α ≤ 1.8. Exponent β of distribution function P(τ) ∼ τ^−β for the duration of low-frequency extremal fluctuations, which are analogous to avalanches considered in the models of self-organized criticality in many respects, varies between the same limits. It is shown that exponents α and β are connected through the relation α + β = 2.     

一种估计半导体激光器1/f噪声参数的新方法

对含白噪声的1/f分形信号小波变换系数的方差随尺度变化的关系进行适当的变换,提出了一种基于最小二乘法的估计半导体激光器1/f噪声参数的新方法.实验表明,该方法可以有效地提取出淹没在白噪声中的激光器1/f噪声,而且估计出的噪声信号的功率谱与对比仪器的测量结果有较好的一致性. 关键词： 半导体激光器 f噪声')" href="#">1/f噪声 参数估计 小波分析     

Generalized Fokker-Planck equation for a class of stochastic dynamical systems driven by additive Gaussian and Poissonian fractional white noises of order <Emphasis Type="Italic">α</Emphasis>

In a first stage, the paper deals with the derivation and the solution of the equation of the probability density function of a stochastic system driven simultaneously by a fractional Gaussian white noise and a fractional Poissonian white noise both of the same order. The key is the Taylor’s series of fractional order f(x + h) = E _α(h^αD _x ^α)f(x) where E _α() denotes the Mittag-Leffler function, and D _x ^α is the so-called modified Riemann-Liouville fractional derivative which removes the effects of the non-zero initial value of the function under consideration. The corresponding fractional linear partial differential equation is solved by using a suitable extension of the Lagrange’s technique involving an auxiliary set of fractional differential equations. As an example, one considers a half-oscillator of fractional order driven by a fractional Poissonian noise.      

1/f Noise in a nonequilibrium phase transition: Experiment and mathematical model

The results of an experimental investigation of a high-power source of broad-band 1/f noise, which can be generated in a system of two interacting nonequilibrium phase transitions, are presented. This process takes place when a normal conductor-superconductor phase transition is superposed on the critical liquid-vapor transition in a boiling coolant. A mathematical model describing a nonequilibrium phase transition in a complicated nonlinear system with two interacting order parameters, which involves the conversion of white noise into stochastic fluctuations of the order parameters with 1/f and 1/f ² spectra, is proposed. The properties of the model fluctuations with a 1/f spectrum agree qualitatively with the experimentally observed properties. A characteristic difference between the model fluctuations with a 1/f ² spectrum and random walks is also noted. Zh. éksp. Teor. Fiz. 113, 1748–1757 (May 1998)     

Capacity of Multivariate Channels with Multiplicative Noise: Random Matrix Techniques and Large-N Expansions (2)

We study memoryless, discrete time, matrix channels with additive white Gaussian noise and input power constraints of the form Y i = ∑ _j H _ij X _j + Z _i , where Y _i , X _j and Z _i are complex, i = 1… m, j = 1… n, and H is a complex m× n matrix with some degree of randomness in its entries. The additive Gaussian noise vector is assumed to have uncorrelated entries. Let H be a full matrix (non-sparse) with pairwise correlations between matrix entries of the form E[H ik H ^* jl] = 1/n C ij D kl, where C, D are positive definite Hermitian matrices. Simplicities arise in the limit of large matrix sizes (the so called large-n limit) which allow us to obtain several exact expressions relating to the channel capacity. We study the probability distribution of the quantity f(H) = log (1+PH ^† SH) . S is non-negative definite and hermitian, with TrS = n and P being the signal power per input channel. Note that the expectation E[f(H)], maximised over S, gives the capacity of the above channel with an input power constraint in the case H is known at the receiver but not at the transmitter. For arbitrary C, D exact expressions are obtained for the expectation and variance of f(H) in the large matrix size limit. For C = D = I, where I is the identity matrix, expressions are in addition obtained for the full moment generating function for arbitrary (finite) matrix size in the large signal to noise limit. Finally, we obtain the channel capacity where the channel matrix is partly known and partly unknown and of the form α; I+ β H, α,β being known constants and entries of H i.i.d. Gaussian with variance 1/n. Channels of the form described above are of interest for wireless transmission with multiple antennae and receivers.     

Photoinduced current noise ina-Si: H solar cells

Summary Measurements of photoinduced current noise in amorphous silicon solar cells are reported. A 1/f ⁿ (n≈1) component, superimposed to a frequency-independent one due to simple shot noise, is attributed to the presence of defects limiting the conversion efficiency of the cell. In particular, large defects, such as local shorts or pin holes, can easily be detected since they are characterized by a very large increase of the 1/f ⁿ component. In general, even in the absence of such large defects, a correlation between the intensity of the 1/f ⁿ component and the cell conversion efficiency is found.     

1/f noise at a critical nonequilibrium phase transition

The generation of 1/f noise is demonstrated experimentally in a system consisting of a superconducting film carrying a transport current in contact with a boiling liquid coolant. It is found that wide-band 1/f noise with a large amplitude of the fluctuations is observed over a wide range of parameters. This noise is attributed to the fact that the sub-systems in contact have the same character of the relaxational dependences δT(t)∼ t ^−1/2. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 739–742 (10 May 1996)     

On Stephany's theory of origin of 1/f bulk noise

Summary Stephany's treatment is not correct since he neglects the friction force proportional to the velocity, which we show to be universal,i.e. present in any mechanism of electric conduction. Moreover his predicted power spectral density is in some cases three orders of magnitude larger than the observed one. Finally, his noise cannot be the true 1/f noise because it should predict a low cut-off of ∼5·10⁻² Hz due to the transit time of the electron-linked lattice (ELL) carriers through a distance of 20 μm while no cut-off has been observed down to 10⁻³ Hz.     

Does the weak interaction constant depend on time?

A comparison is made of the probability of the process of two-neutrino double β decay for ⁸²Se and ⁹⁶Zr in direct (counter) and geochemical experiments. The experimental data for ¹³⁰Te are analyzed. It is shown that this probability is systematically lower in geochemical experiments, which characterize the probability of 2 β(2 v) decay 10⁹ yr ago. It is proposed that this could be due to a change in the weak-interaction constant with time. It is proposed that a series of new, precise measurements be performed with the aid of counters and geochemical experiments. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 3–8 (10 July 1998)     

Asymptotic behavior of the β function in the ϕ<Superscript>4</Superscript> theory: A scheme without complex parameters

The previously-obtained analytical asymptotic expressions for the Gell-Mann-Low function β(g) and anomalous dimensions in the ϕ⁴ theory in the limit g → ∞ are based on the parametric representation of the form g = f(t), β(g) = f ₁(t) (where t ∝ g ₀^−1/2 is the running parameter related to the bare charge g ₀), which is simplified in the complex t plane near a zero of one of the functional integrals. In this work, it has been shown that the parametric representation has a singularity at t → 0; for this reason, similar results can be obtained for real g ₀ values. The problem of the correct transition to the strong-coupling regime is simultaneously solved; in particular, the constancy of the bare or renormalized mass is not a correct condition of this transition. A partial proof has been given for the theorem of the renormalizability in the strong-coupling region.     

Wavelength-modulation-spectroscopy for real-time, in situ NO detection in combustion gases with a 5.2 μm quantum-cascade laser

A mid-infrared absorption strategy with calibration-free wavelength-modulation-spectroscopy (WMS) has been developed and demonstrated for real-time, in situ detection of nitric oxide in particulate-laden combustion-exhaust gases up to temperatures of 700 K. An external-cavity quantum-cascade laser (ECQCL) near 5.2 μm accessed the fundamental absorption band of NO, and a wavelength-scanned, 1f-normalized WMS with second-harmonic detection (WMS-2f/1f) strategy was developed. Due to the external-cavity laser architecture, large nonlinear intensity modulation (IM) was observed when the wavelength was modulated by injection-current modulation, and the IM indices were also found to be strongly wavelength-dependent as the center wavelength was scanned with piezoelectric tuning of the cavity. A quantitative model of the 1f-normalized WMS-2f signal was developed and validated under laboratory conditions. A sensor was subsequently designed, built and demonstrated for real-time, in situ measurements of NO across a 3 m path in the particulate-laden exhaust of a pulverized-coal-fired power plant boiler. The 1f-normalized WMS-2f method proved to have better noise immunity for non-absorption transmission, than wavelength-scanned direct absorption. A 0.3 ppm-m detection limit was estimated using the R15.5 transition near 1927 cm⁻¹ with 1 s averaging. Mid-infrared QCL-based NO absorption with 1f-normalized WMS-2f detection shows excellent promise for practical sensing in the combustion exhaust.     

An exactly solvable linear model giving indication of stochastic resonance

The linear stochastic equation dx _β /dt+[1+f _β (t)]x _β (t)=A sin (Ωt) is discussed. The functionƒ _β (t) is defined as a Poissonian noise dependent on a parameterβ>0,ƒ _β (t)=β Σ _j [δ(t − t _j ⁺ ) −δ (t − t _j ⁻ )]. The mean frequency of the delta-pulses is chosen asβ-dependent in the formλ(β)=2γ(β ⁻² + 1) exp(−β) whereγ is a constant from the interval (0, 0.974). With the stochastic functionƒ _β (t) defined in this way, attention is paid on the oscillational term of the averaged function 〈x(t)〉, 〈x(t)〉_osc=Āsin(Ωt − α). It is found that the dependenceĀ=Ā(β) exhibits one maximum and one minimum. The occurrence of these extrema seems to affirm the presence of stochastic resonance. This work has been supported by the Slovak Grant Agency VEGA under contract No. 1/4319/97.     

Fine structure of the strength function for the β<Superscript>+</Superscript>/EC decay of the <Superscript>160<Emphasis Type="Italic">m</Emphasis></Superscript>Ho (5.02 h) isomer

The strength function for the β⁺/EC decay of the deformed nucleus of the ^160m Ho (5.02 h) isomer is obtained from the experimental data, The fine structure of the strength function S _β(E) is analyzed. It has a pronounced resonance structure for Gamow-Teller transitions and is found to exhibit a resonance structure for first-forbidden transitions. It is shown that for some excitation energies of the 160Dy daughter nucleus the probability of first-forbidden β⁺/EC transitions in the decay of the ^160m Ho isomer is comparable with the probability of Gamow-Teller β⁺/EC transitions.     

Fluctuations with a 1/f α spectrum in film boiling

1/f and 1/f ² noise were observed experimentally in film boiling of water on vertically oriented platinum heater. Fluctuations with a 1/f _α spectrum were observed in a wide range of controlling parameters and seen over five orders of magnitude in frequency. It was noted that the process investigated is similar to the phenomenon of self-organized criticality. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 8, 590–593 (25 April 1999)     

Doppler experiments with Cassini radio system

Summary The proposedK _a band link on the Cassini orbiter can be used for very accurate Doppler tracking. A two-wayK _a band coherent link, near opposition, or more complex schemes involving theX-band link also, can virtually eliminate the noise due to interplanetary plasma, giving an accuracy Δf/f better than 10⁻¹⁵ for time scales of (10³÷10⁴) s. To achieve this accuracy, the other error sources, mainly the tropospheric delay and the clock stability, must be accurately controlled. This sensitivity will allow for the first time for a search for gravitational waves of reasonable amplitude. Paper presented at the V Cosmic Physics National Conference, S. Miniato, November 27–30, 1990.     

Quality assessments of electrochromic devices: the possible use of 1/<Emphasis Type="Italic">f</Emphasis> current noise

Electrochromic (EC) devices, capable of modulating their optical transmittance by charge insertion/extraction, were produced by laminating films comprised of nanoporous W oxide and Ni–V oxide by a polymer electrolyte and having this three-layer stack between transparent conducting In₂O₃:Sn films backed by polyester foils. 1/f noise in the current (I) was observed when the charged (colored) EC device was discharged via a resistor. The power spectral density S _i at fixed frequency scaled as S _i  ∼ I ². Extended color/bleach cycling degraded the optical quality and homogeneity of the device and concomitantly increased the 1/f noise intensity. These initial data indicate that 1/f noise has a potential to serve as a quality measure for EC devices.     

A Random Matrix Decimation Procedure Relating <Emphasis Type="Italic">β</Emphasis> = 2/(<Emphasis Type="Italic">r</Emphasis> + 1) to <Emphasis Type="Italic">β</Emphasis> = 2(<Emphasis Type="Italic">r</Emphasis> + 1)

Classical random matrix ensembles with orthogonal symmetry have the property that the joint distribution of every second eigenvalue is equal to that of a classical random matrix ensemble with symplectic symmetry. These results are shown to be the case r = 1 of a family of inter-relations between eigenvalue probability density functions for generalizations of the classical random matrix ensembles referred to as β-ensembles. The inter-relations give that the joint distribution of every (r + 1)^st eigenvalue in certain β-ensembles with β  =  2/(r + 1) is equal to that of another β-ensemble with β  =  2(r + 1). The proof requires generalizing a conditional probability density function due to Dixon and Anderson.     

Non-dynamical stochastic resonance: Theory and experiments with white and various coloured noises

Summary We describe the simplest system which shows stochastic resonance. A linear(ized) theory for white and (almost) arbitrarily coloured noise is presented. The presented new system has new, unique properties which originate from itsnon-dynamical character; for example, the strength and phase shift of periodic response of the system is independent of the frequency. Experiments have been carried out with the following noise processes: (physical) white noise, (physical) Lorentzian noise and (physical) 1/f noise. With a small extension of the system, its linear-response regime can be significantly increased. As the system is similar to some simple models of neurones, the new results might have not only physical but also biological importance. Paper presented at the International Workshop “Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena”, Elba, 5–10 June 1994.     

Stretched exponential relaxation in the Coulomb glass

The relaxation of the specific heat and the entropy to their equilibrium values is investigated numerically for the three-dimensional Coulomb glass at very low temperatures. The long time relaxation follows a stretched exponential function, f (t) = f ₀exp - (t/τ)^β , with the exponent β increasing with the temperature. The relaxation time diverges as an Arrhenius law when T→ 0. Received 24 May 2001 and Received in final form 12 September 2001     

Noise color and asymmetry in stochastic resonance with silicon nanomechanical resonators

Stochastic resonance with white noise has been well established as a potential signal amplification mechanism in nanomechanical two-state systems. While white noise represents the archetypal stimulus for stochastic resonance, typical operating environments for nanomechanical devices often contain different classes of noise, particularly colored noise with a 1/f spectrum. As a result, improved understanding of the effects of noise color will be helpful in maximizing device performance. Here we report measurements of stochastic resonance in a silicon nanomechanical resonator using 1/f noise and Ornstein-Uhlenbeck noise types. Power spectral densities and residence time distributions provide insight into asymmetry of the bistable amplitude states, and the data sets suggest that 1/f^α noise spectra with increasing noise color (i.e. α) may lead to increasing asymmetry in the system, reducing the achievable amplification. Furthermore, we explore the effects of correlation time τ on stochastic resonance with the use of exponentially correlated noise. We find monotonic suppression of the spectral amplification as the correlation time increases.