Shear induced anisotropy in two-dimensional liquids

The behavior of a dense two-dimensional soft disc liquid under shear is studied via nonequilibrium molecular dynamics. The structure factor for the liquid at a given shear rate is evaluated directly by plotting the particle positions, taken at random from the NEMD simulation at that shear, onto photographic film and using light scattering to obtain a diffraction pattern. The pair correlation function of this system is also extracted directly by histogramming the particle positions with respect to a given central particle as a function of separation and angle. The pair correlation function is compared to that approximated by a Fourier series expansion to rank ten. Results are reported as a function of shear rate from a shear rate of 0.1 (when the fluid is essentially Newtonian) to 10 (when the fluid can display a string phase). The appearance of the string phase is discussed and shown to be a consequence of the definition of temperature in the simulation algorithm. A modification of the algorithm is proposed. Comparisons between this work and previous work with three-dimensional liquids are given. The two-dimensional structure factor is compared with that obtained from a real colloidal suspension via light scattering.     

Attaining the Optimal Gaussian Diffusion Acceleration

Sampling from probability distributions in high dimensional spaces is generally impractical. Diffusion processes with invariant equilibrium distributions can be used as a means to generate approximations. An important task in such an endeavor is to design an equilibrium-preserving drift to accelerate the convergence. Starting from a reversible diffusion, it is desirable to depart for non-reversible dynamics via a perturbed drift so that the convergence rate is maximized with the common equilibrium. In the Gaussian diffusion acceleration, this problem can be cast as perturbing the inverse of a given covariance matrix by skew-symmetric matrices so that all resulting eigenvalues have identical real part. This paper describes two approaches to obtain the optimal rate of Gaussian diffusion. The asymptotical approach works universally for arbitrary Ornstein–Uhlenbeck processes, whereas the direct approach can be implemented as a fast divide-and-conquer algorithm. A comparison with recently proposed Lelièvre–Nier–Pavliotis algorithm is made.     

Fluctuations of the Increment of the Argument for the Gaussian Entire Function

The Gaussian entire function is a random entire function, characterised by a certain invariance with respect to isometries of the plane. We study the fluctuations of the increment of the argument of the Gaussian entire function along planar curves. We introduce an inner product on finite formal linear combinations of curves (with real coefficients), that we call the signed length, which describes the limiting covariance of the increment. We also establish asymptotic normality of fluctuations.     

RANDOM RESPONSE OF PREISACH HYSTERETIC SYSTEMS

An approximate method for analyzing the response of Preisach hysteretic systems with non-local memory under stationary Gaussian excitation is proposed. The covariance matrix equation of system response is derived. The cross correlation function of Preisach hysteretic force and response in the covariance equation is evaluated based on the switching probability analysis and the Gaussian approximation of response process and an explicit expression for the cross correlation function is given for the case of symmetric Preisach weighting function. It is shown that the numerical result obtained by using the proposed method is in good agreement with that from digital simulation.     

Intensity correlations in the presence of additive background noise

The mean value of the intensity correlation function and intensity spectrum of a bar object are evaluated when a spatialy random intensity is added to the deterministic object. The mean value of both functions depends upon two terms in addition to the usual term involving the deterministic object, one involves the mean and the other involves the covariance of the random background intensity.     

Lipschitz-Continuity of the Integrated Density of States for Gaussian Random Potentials

The integrated density of states of a Schrödinger operator with random potential given by a homogeneous Gaussian field whose covariance function is continuous, compactly supported and has positive mean, is locally uniformly Lipschitz-continuous. This is proven using a Wegner estimate.     

Introduction to light scattering by Gaussian random particles

Background, current status, and future prospects are offered for “Light scattering by Gaussian random particles: Ray-optics approximation” [1]. The stochastic geometry of the random particle is called the Gaussian random sphere. The radial distance of the Gaussian sphere is lognormally distributed. Two logarithmic radial distances at a given great-circle angle apart relate to one another according to the covariance function. Sample Gaussian particles can be conveniently generated using a Legendre polynomial expansion for the covariance function and a spherical harmonics expansion for the logarithmic radial distance. The ray-optics approximation consists of the geometric-optics and forward-diffraction parts fully accounting for polarization. It is valid for particles much larger than the wavelength of incident light and with central phase differences much larger than unity. The numerical ray-tracing algorithms are general and, in principle, applicable computationally to arbitrarily shaped non-spherical particles.     

The covariance response of linear systems to locally stationary random excitation

A simple method is given for calculating the covariance response of linear, time-invariant systems to random excitation processes which are locally stationary, or approximately so. As an illustration, the method is used to estimate the response of an idealized model of a ten-storey building to non-stationary ground acceleration; the accuracy of the estimated response is assessed by a comparison with the results of a less approximate, but lengthier, general calculation method, previously published.     

起伏海面环境下水声信道特性及估计方法*

为了研究随机起伏海面的散射对水声信道特性的影响,以及不同信道估计算法在该信道条件下的性能问题,该文从利用Monte Carlo方法模拟的基于PM海浪谱的二维随机起伏海面出发,提取了与风向不同夹角的一维随机起伏海面,并利用Kirchhoff近似法计算了其散射强度。将得到的声散射特性和海面环境信息融入到信道模型中,建立了基于PM海浪谱的随机信道模型。通过仿真分析了不同风速、传播距离条件下,声波的传播损失和信道冲激响应变化,并利用l_0-最小均方误差法、匹配追踪算法和正交匹配追踪算法进行了信道估计。给出了不同环境条件下,三种算法估计性能的综合比较结果,验证了算法针对该信道模型的有效性。     

Rules extraction in short memory time series using genetic algorithms

Data mining is performed using genetic algorithm on artificially generated time series data with short memory. The extraction of rules from a training set and the subsequent testing of these rules provide a basis for the predictions on the test set. The artificial time series are generated using the inverse whitening transformation, and the correlation function has an exponential form with given time constant indicative of short memory. A vector quantization technique is employed to classify the daily rate of return of this artificial time series into four categories. A simple genetic algorithm based on a fixed format of rules is introduced to do the forecasting. Comparing to the benchmark tests with random walk and random guess, genetic algorithms yield substantially better prediction rates, between 50% to 60%. This is an improvement compared with the 47% for random walk prediction and 25% for random guessing method. Received 29 August 2000     

相干激光雷达中最大似然离散谱峰值估计及Monte Carlo仿真

相干测风激光雷达中一个核心的问题是从微弱的气溶胶后向散射信号中估计出风速。基于零均值复高斯随机过程协方差矩阵统计模型的后向散射信号,首先讨论了最大似然(ML)离散谱峰值(DSP)风速估计算法的克拉美-罗下界(CRLB)与由Fisher信息矩阵论得到的精确CRLB之间的关系。其次,对于ML DSP估计应用于相干测风激光雷达中协方差矩阵统计模型的后向散射信号时,使用计算机Monte Carlo仿真的方法研究了风速估计的概率密度函数。分别讨论了信噪比、激光脉冲累积发数和发射激光脉冲宽度对ML DSP风速估计性能的影响。计算仿真结果表明:ML DSP风速估计的CRLB低于精确的CRLB;在信噪比为-20dB,100发激光脉冲累积和信噪比为-30dB,10 000发激光脉冲累积条件下,ML DSP风速估计中"坏"的估计值所占的比例都为0,"好"的估计值的标准差分别为0.62m/s和0.50m/s。     

Aspects of landau-level broadening using the path integral representation

Summary With the help of Wiener-type path integrals we accomplish a systematic study of two different, previously proposed versions of a first-order cumulant approximation to the averaged density of states for an electron in two dimensions under the influence of a perpendicular homogeneous magnetic field and a homogeneous isotropic random potential. Explicit results are given for a Gaussian random potential with a Gaussian covariance function. To speed up publication, the authors have agreed not to receive proofs which have been supervised by the Scientific Committee.     

Minimum-Covariance Estimates of Signal Parameters

We show the existence of the only procedure ensuring the absolute minimum of an arithmetic mean covariance in a certain parameter-variation range and coinciding identically with the algorithm for calculating the estimate minimizing the mean risk for a quadratic loss function and a uniform a priory distribution of parameters. This procedure is compared with the standard method for obtaining maximum likely estimates. In particular, it is shown that the procedure ensures a significantly smaller random scatter of estimates during the estimation of deterministic-signal parameters against the background of Gaussian interference. In the case where the estimate covariance is independent of the parameter estimated for physical reasons, the use of the above procedure with an arbitrary sample size allows us to reach the actual attainable variance bound.     

相关变量随机数序列产生方法

当采用蒙特卡罗方法对很多问题进行研究时,有时需要对多维相关随机变量进行抽样.之前的研究表明:在协方差矩阵满足正定条件时,可以采用Cholesky分解方法产生多维相关随机变量.本文首先对产生多维相关随机变量的理论公式进行了推导,发现采用Cholesky分解并不是产生多维相关随机变量的唯一方法,其他的矩阵分解方法只要能满足协方差矩阵的分解条件,同样可以用来产生多维相关随机变量.同时给出了采用协方差矩阵、相对协方差矩阵和相关系数矩阵产生多维随机变量的公式,以方便以后使用.在此基础上,利用一个简单测试题和Jacobi矩阵分解方法对上述理论进行了验证.通过对大亚湾中微子能谱进行抽样分析,Jacobi矩阵分解和Cholesky矩阵分解结果一致.针对核工程中的不确定性分析常用的~(238)U辐射俘获截面协方差矩阵进行分解时,由于协方差矩阵的矩阵本征值有负值,导致很多矩阵分解方法无法使用,在引入置零修正以后发现,与Cholesky对角线置零修正相比,Jacobi负本征值置零修正的误差更小.     

Airy Kernel with Two Sets of Parameters in Directed Percolation and Random Matrix Theory

We introduce a generalization of the extended Airy kernel with two sets of real parameters. We show that this kernel arises in the edge scaling limit of correlation kernels of determinantal processes related to a directed percolation model and to an ensemble of random matrices.     

The effect of ocean wave on the vertical spatial correlation of ocean ambient noise

The effect of the correlation function of noise sources derived from the ocean wave spectrum on the vertical spatial correlation of ocean ambient noise is investigated. The spatial correlation models of ocean ambient noise usually assume that the surface noise sources are uncorrelated. This assumption can be used to explain some physical phenomena, but it is not consistent with the real situation. Considering the relation between the ocean wave motion and the ambient noise generated by wind, the spectrum of ocean wave is introduced to calculate the vertical correlation of ocean ambient noise as the correlation function of noise sources by using the Kuperman-Ingenito(K/I) noise model. The comparison of the simulations and the experimental data shows that the simulations of vertical correlation of ambient noise have some differences with the experimental data by assuming the noise sources are uncorrelated and the simulations of vertical correlation of ambient noise have a good agreement with the experimental data by using the correlation function of noise sources derived from the ocean wave spectrum under the situation of high wind speed.     

Smooth decomposition of random fields

The Smooth Decomposition (SD) method was introduced to analyze discrete-time signals and generalized to continuous-time vector-valued random processes. The SD is obtained solving a generalized eigenproblem defined from the covariance matrix of the random process and the covariance matrix of the associated time-derivative random process which defines the decomposition basis. This paper presents a new extension of the SD to continuous-time and continuous-space vector-valued random processes, classically named random fields. This generalization is a major step since one now deals with operators in infinite-dimensional spaces and not matrices. It is shown that in this new context the main properties of the SD are preserved. Applied to the responses of randomly excited continuous mechanical systems, the SD can be considered as an output-only analysis tool. Moreover, two natural orderings are defined to classify the decomposition terms which permit to interpret the SD in terms of modal analysis or in terms of Karhunen–Loève analysis.     

一种新的卫星钟差Kalman滤波噪声协方差估计方法

采用Kalman滤波方法进行钟差参数计算和预报时, 需确定Kalman滤波噪声协方差矩阵. 针对这一问题, 提出了一种新的卫星钟差Kalman滤波噪声协方差估计方法, 通过建立新息的相关函数序列与未知的噪声参数间的线性函数模型, 采用最小二乘法进行噪声参数估计. 采用精密钟差数据进行钟差参数估计和预报分析, 结果表明, 该方法具有较好的收敛性, 并与顾及随机噪声模型的开窗分类因子自适应抗差估计方法进行对比分析, 验证了新方法的正确性和有效性.     

First-order probability density function of the laser speckle phase

An expression for the first-order probability density function of the laser speckle phase is analytically derived under the assumption that the speckle field obeys a non-circular, complex Gaussian, random process with a certain correlation between the real and imaginary parts of its complex amplitude. The probability density function of the speckle phase is actually evaluated for various cases and shown three-dimensionally as a function of the standard deviation of random object phase variations. The effect of random object phase variations on the probability density function is also investigated in detail.     

Fluctuations in the Weakly Asymmetric Exclusion Process with Open Boundary Conditions

We investigate the fluctuations around the average density profile in the weakly asymmetric exclusion process with open boundaries in the steady state. We show that these fluctuations are given, in the macroscopic limit, by a centered Gaussian field and we compute explicitly its covariance function. We use two approaches. The first method is dynamical and based on fluctuations around the hydrodynamic limit. We prove that the density fluctuations evolve macroscopically according to an autonomous stochastic equation, and we search for the stationary distribution of this evolution. The second approach, which is based on a representation of the steady state as a sum over paths, allows one to write the density fluctuations in the steady state as a sum over two independent processes, one of which is the derivative of a Brownian motion, the other one being related to a random path in a potential.