HREELS signal processing via wavelets

In spectroscopy, the recorded spectra can often be modelled as the noisy convolution product of an instrumental function with the ‘true’ signal to be estimated. Such models have often been used for high‐resolution electron energy‐loss spectroscopy (HREELS). In this article, a new method is suggested to estimate the ‘true’ HREELS signal, i.e. the original electronic diffusion function with ‘true’ peak intensities. Our method relies upon the use of wavelets that, because they exhibit simultaneous time and frequency localization, are well‐suited for signal analysis. Firstly, a wavelet shrinkage algorithm is used to filter the noise. This is achieved by decomposing the noisy signal into an appropriate wavelet basis and then thresholding the wavelet coefficients that contain noise. This algorithm has a particular threshold related to frequency and time. Secondly, the broadening due to the instrumental response is eliminated through a deconvolution process. This step mainly rests on the existing relation between the Lipschitz regularity of the signal and the decay with scale of its wavelet coefficients and on least squares. The efficiency of this technique is highlighted by comparing the results obtained with those provided by other published methods. This work is the second in a series of three papers in this issue. The first one presents background knowledge on the wavelets required to understand the estimation methods. The third paper explores the application of wavelet filtering and deconvolution techniques to x‐ray photoelectron spectroscopy. Copyright © 2004 John Wiley & Sons, Ltd.     

Active control and a simple estimation method for the onset of Rayleigh-Bénard convection in temperature-dependent-viscosity liquids

Active feedback control for the onset of Rayleigh-Bénard Convection in temperature-dependent-viscosity liquids is investigated. In this paper, three major problems are addressed: (1) The results of Tang-Bau control are improved by considering the effects of temperature-dependent viscosity; (2) A more efficient two-plate control strategy is presented. A phenomenon of coalescence of the unstable modes is observed as the controller gain is large enough; (3) A simple way to estimate the critical Rayleigh number under the effects of temperature-dependent viscosity is described. Numerical results show that the effects of temperature-dependent viscosity on the critical Rayleigh number should be taken into account in some cases and the onset of Rayleigh-Bénard convection can be effectively delayed or advanced by the active feedback control strategies studied here.     

Relative intensity noise of mode-locked fiber grating external cavity semiconductor lasers

The noise of hybrid soliton pulse source (HSPS) with linearly chirped Gaussian apodized fiber Bragg grating is analyzed by couple-mode equations including spontaneous emission noise when the HSPS is mode-locked. Relative intensity noise is calculated using numerical solutions of these equations. It is shown that transform limited pulses are generated over a wide tuning range around the fundamental mode-locking frequency with low spontaneous noise. However, a high noise level affects the operation of device, and therefore transform-limited pulses are not obtainable over a wide tuning range. It is also shown that noise is extremely sensitive to the RF and DC currents, linewidth enhancement factor, gain saturation parameter and spontaneous coupling factor.     

奇偶相干态的Wehrl熵和Shannon熵

研究了奇、偶相干态的Ｗｅｈｒｌ熵和Ｓｈａｎｎｏｎ熵，结果表明，其Ｗｅｈｒｌ熵随总噪声的增加而增大，并趋向同一个常数。Ｓｈａｎｎｏｎ熵随力学量起伏的减小而减小，且这两种态的Ｓｈａｎｎｏｎ熵均可小于相干态的Ｓｈａｎｎｏｎ熵，但这时并不与压缩效应的出现相对应，因而Ｓｈａｎｎｏｎ熵不能成为压缩存在的判据。     

调制不稳定性对级联放大光纤传输系统信噪比的影响

在考虑光纤损耗和级联放大器的情况下，推导了调制不稳定性的产生条件和增益的普适解析表达式，分析了调制不稳定性对信噪比的影响，给出了一个新的计算信噪比的表达式。     

Flicker noise in degenerately doped Si single crystals near the metal-insulator transition

In this paper we report some of the important results of experimental investigations of the flicker noise near the metal-insulator (MI) transition in doped silicon single crystals. This is the first comprehensive work to study low-frequency noise in heavily doped Si over an extensive temperature range (2 K<T<500 K). The measurements of conductance fluctuations (flicker noise) were carried out in the frequency range 10⁻²<f<4 × 10¹ Hz in single crystalline Si across the MI transition by doping with phosphorous and boron. The magnitude of noise in heavily doped Si is much larger than that seen in lightly doped Si over the whole temperature range. The extensive temperature range covered allowed us to detect two distinct noise mechanisms. At low temperatures (T<100 K) universal conductance fluctuations (UCF) dominate and the spectral dependence of the noise is determined by dephasing the electron from defects with two-levels (TLS). At higher temperatures (T>200 K) the noise arises from activated defect dynamics. As the MI transition is approached, the 1/f spectral power, typical of the metallic regime, gets modified by the presence of discrete Lorentzians which arise from generation-recombination process which is the characteristic of a semiconductor.     

Noise-induced asymptotic periodicity in a piecewise linear map

We examine asymptotically periodic density evolution in one-dimensional maps perturbed by noise, associating the macroscopic state of these dynamical systems with a phase space density. For asymptotically periodic systems density evolution becomes periodic in time, as do some macroscopic properties calculated from them. The general formalism of asymptotic periodicity is examined and used to calculate time correlations along trajectories of these maps as well as their limiting conditional entropy. The time correlation is shown to naturally decouple into periodic and stochastic components. Finally, asymptotic periodicity is studied in a noise-perturbed piecewise linear map, focusing on how the variation of noise amplitude can cause a transition from asymptotic periodicity to asymptotic stability in the density evolution of this system.     

置换环上的稳定矩阵

本文证明了置换环上的正则稳定矩阵是幂等矩阵和可逆矩阵的积,进一步证明了置换环上的正则稳定矩阵可以对角化。     

Soluble models for dynamics driven by a super-diffusive noise

We explicitly discuss scalar Langevin type of equations where the deterministic part is linear, but where the integrated noise source is a non-linear diffusion process exhibiting superdiffusive behavior. We calculate transient and stationary probabilities and study the possibility of noise induced transitions from a unimodal to a bimodal probability shape. Illustrations from finance and dynamical systems are given.     

负关联噪声驱动下单模激光的定态分析

研究了负关联的加法和乘法高斯白噪声驱动下单模激光损失模型的定态情况。文中推导了负关联情况下，定态时的激光场幅的几率分布，光强的平均值，光强的协方差以及光强的偏斜率。并和文献〔１，２〕中正关联时的定态分析作了比较，发现了有意义的新现象。