Velocity spectrum for non-Markovian Brownian motion in a periodic potential

Non-Markovian Brownian motion in a periodic potential is studied by means of an electronic analogue simulator. Velocity spectra, the Fourier transforms of velocity autocorrelation functions, are obtained for three types of random force, that is, a white noise, an Ornstein—Uhlenbeck process, and a quasimonochromatic noise. The analogue results are in good agreement both with theoretical ones calculated with the use of a matrix-continued-fraction method, and with the results of digital simulations. An unexpected extra peak in the velocity spectrum is observed for Ornstein-Uhlenbeck noise with large correlation time. The peak is attributed to a slow oscillatory motion of the Brownian particle as it moves back and forth over several lattice spaces. Its relationship to an approximate Langevin equation is discussed.     

One-Dimensional Poisson Growth Models With Random and Asymmetric Growth

Suppose there is a Poisson process of points X _i on the line. Starting at time zero, a grain begins to grow from each point X _i , growing at rate A _i to the left and rate B _i to the right, with the pairs (A _i , B _i ) being i.i.d. A grain stops growing as soon as it touches another grain. When all growth stops, the line consists of covered intervals (made up of contiguous grains) separated by gaps. We show (i) a fraction 1/e of the line remains uncovered, (ii) the fraction of covered intervals which contain exactly k grains is (k–1)/k!, (iii) the length of a covered interval containing k grains has a gamma(k–1) distribution, (iv) the distribution of the grain sizes depends only on the distribution of the total growth rate A _i +B _i , and other results. Similar theorems are obtained for growth processes on a circle; in this case we need only assume the pairs (A _i , B _i ) are exchangeable. These results extend those of Daley, et al. (2000) who studied the case where A _i =B _i =1. Simulation results are given to illustrate the various theorems.     

全20CrMnTi表面激光重熔的组织与性能研究

本文对激光重熔20CrMnTi材料表明改性层显微组织分布特征、表面硬度分布规律以及残余应力状态作了研究,结果表明,表面改性层由熔融层、相变硬化层及过渡层组成,且材料表面显微硬度得到大幅度提高,表面硬度达到HV841,约提高4倍。硬化层深度约1mm。残余应力测试得出最大残余应力出现在熔凝带中心,表现为压应力。随着离中心距离的增大,残余应力逐步降低,到熔化带边缘,表现为低幅值压应力;而熔池的外边缘应力在热影响区则转变为拉应力状态。     

Some Invariance Principles for Random Vectors in the Generalized Domain of Attraction of the Multivariate Normal Law

For independent identically distributed random vectors belonging to the generalized Domain of Attraction of the multivariate normal law, we define two partial sum processes analogous to that of Donsker's Theorem. We prove that each converges in distribution to a Brownian Motion in the space of continuous functions. One process uses nonrandom operator normalization, and the other is a studentization of the first, using normalization by the empirical covariance operator.     

基于主元分析的多变量统计过程的故障辨识技术

为了更好的进行故障检测与诊断，介绍了主元分析理论，给出了基于主元分析的过程故障辨识机理及策略。仿真实例表明，利用此方法建立的故障诊断模型，能够在不依赖过程机理的前提下高效抽取原始数据空间的主要变化信息，对过程的非正常变化做出反应，同时还能较正确地找出发生故障的原因以及相应环节。     

DDS技术在数字激光相位测距仪中的应用

本文介绍了直接数字合成(DDS)技术在激光相位测距仪中的应用。使用该技术研制的数字激光相位测距仪具有操作简便、携带方便、性能可靠的特点，测相精度优于干分之一。     

化学镀工艺在微电子材料中的研究和应用

简要综述了化学镀工艺在微电子材料中的应用,讨论了影响化学镀镍、铜、锡、钴和贵金属等的主要因素,阐述了化学镀微电子材料的特性、存在问题及研究动态。     

A note about the Gaussian property of the Brownian bridge

The Gaussian property of the Brownian bridge is characterized as an application of Ramachandran's theorem in terms of the independence of the random variables that appear in the Karhunen-Loéve expansion of the process. A reference about the construction of the Brownian bridge by means of functional transformations is also included.     

动态模糊随机信息处理的数学方法

本文系统地概述了我们近年来提出的动态模糊随机信息处理的数学方法,内容包括模糊随机变量、模糊随机过程和模糊随机微分方程的基本解法等方面的基本概念、基本定义和某些重要的定理,以及动态系统的模糊随机响应与可靠性分析的方法等。这些方法是为我们研究工程实际问题的需要逐步发展起来的,对于处理某些类型的问题简便实用。