Evolution of a Network of Vortex Loops in the Turbulent Superfluid Helium; Derivation of the Vinen Equation

The evolution a network of vortex loops due to the fusion and breakdown in the turbulent superfluid helium is studied. We perform investigation on the base of the “rate equation” for the distribution function n(l) of number of loops in space of their length l. There are two mechanisms for change of quantity n(l). Firstly, the function changes due to deterministic process of mutual friction, when the length grows or decreases depending on orientation. Secondly, the change of n(l) occurs due to random events when the loop crosses itself breaking down into two daughter or two loops collide merging into one larger loop. Accordingly the “rate equation” includes the “collision” term collecting random processes of fusion and breakdown and the deterministic term. Assuming, further, that processes of random colliding are fastest we are in position to study more slow processes related to deterministic term. In this way we study the evolution of full length of vortex loops per unit volume—so-called vortex line density ℒ(t). It is shown this evolution to obey the famous Vinen equation. In conclusion we discuss properties of the Vinen equation from the point of view of the developed approach.     

Modified Berlekamp-Massey algorithm and modelling of discrete-time signals

The objective of the present paper is the study of models which view the given 1-D data as the impulse response of a minimal order discrete linear filter with data and coefficients confined to a finite field. This representation is known as “minimal partial realization” problem in linear system theory and has been tackled successfully by Ho and Kalman. Interestingly, the same problem is addressed and solved in a coding theory context by the well-known Berlekamp-Massey (bm) algorithm. We present a modified recursive version of thebm algorithm specially suited to our task of signal modelling. By introducing an absolute error bound, one can further solve the approximation problem computationally. The paper includes a number of examples and a mention of the software for this purpose.     

EKF和PF算法及其在目标跟踪中的应用

基于贝叶斯滤波的目标跟踪原理,介绍了扩展卡尔曼滤波(Extended Kalman Filter,EKF)和粒子滤波(ParticleFilter,PF)的基本思想和算法实现步骤。在非线性环境下对比分析了EKF算法和PF算法的估计精度,并给出两种方法的适用条件。EKF算法采用Taylor展开的线性变换来近似非线性模型,而PF算法采用一些带有权值的随机样本来表示所需要的后验概率密度。仿真结果表明,在强非线性非高斯环境下,PF算法的跟踪性能远优于EKF算法,当系统非线性强度不大时,EKF算法和PF算法的估计精度相差不大,但PF算法计算复杂,跟踪时间长,实时性差。     

一种新的自适应非线性卡尔曼滤波算法

为避免由于系统噪声统计特性不准确所导致的滤波性能下降问题,改进了一种基于新息的系统噪声方差调整方法,并将其与扩展卡尔曼滤波、Unscented 卡尔曼滤波和差分滤波相结合,形成自适应非线性卡尔曼滤波.将此方法应用到非线性测量光电跟踪系统中,并与采用基本非线性卡尔曼滤波进行性能对比.仿真实验结果证明该方法可以实时调整系统噪声方差,有效地避免由于系统噪声统计特性不准确所带来的滤波性能下降的问题,而且其性能明显优于基本非线性卡尔曼滤波.     

Ore Principal Subresultant Coefficients in Solutions

The principal subresultant coefficients of polynomials play a fundamental role in elimination theory and computer algebra. Recently they have been extended to Ore polynomials. They are defined by an expression in the coefficients of Ore polynomials. In this paper, we provide another expression for them. This expression is written in terms of the “solutions” of Ore polynomials (in “generic” case). It can be viewed as a generalization of the well known expression for resultants of two commutative polynomials: the product of the pair-wise differences of their roots. Received: August 16, 1999; revised version: July 3, 2000     

Experimental fundamentals of tribofatigue. Part 2

We present a general survey of the experimental results that can be regarded as fundamental for tribofatigue (the theory of wear-fatigue damage to power systems of machines). In Part 2, we describe and analyze basic regularities of the inverse effect under the conditions of friction-mechanical fatigue. “Tribofatigue” Scientific-Industrial Concern, Gomel, Belarus. Translated from Problemy Prochnosti, No. 4, pp. 17–20, July–August, 1997.     

Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell

One of the essential questions in the area of granular matter is, how to obtain macroscopic tensorial quantities like stress and strain from “microscopic” quantities like the contact forces in a granular assembly. Different averaging strategies are introduced, tested, and used to obtain volume fractions, coordination numbers, and fabric properties. We derive anew the non-trivial relation for the stress tensor that allows a straightforward calculation of the mean stress from discrete element simulations and comment on the applicability. Furthermore, we derive “elastic” (reversible) mean displacement gradient, based on a best-fit hypothesis. Finally, different combinations of the tensorial quantities are used to compute some material properties. The bulk modulus, i.e. the stiffness of the granulate, is a linear function of the trace of the fabric tensor which itself is proportional to the density and the coordination number. The fabric, the stress and strain tensors are not co-linear so that a more refined analysis than a classical elasticity theory is required. Received: 23 July 1999     

FASTSIM2: a second-order accurate frictional rolling contact algorithm

In this paper we consider the frictional (tangential) steady rolling contact problem. We confine ourselves to the simplified theory, instead of using full elastostatic theory, in order to be able to compute results fast, as needed for on-line application in vehicle system dynamics simulation packages. The FASTSIM algorithm is the leading technology in this field and is employed in all dominant railway vehicle system dynamics packages (VSD) in the world. The main contribution of this paper is a new version “FASTSIM2” of the FASTSIM algorithm, which is second-order accurate. This is relevant for VSD, because with the new algorithm 16 times less grid points are required for sufficiently accurate computations of the contact forces. The approach is based on new insights in the characteristics of the rolling contact problem when using the simplified theory, and on taking precise care of the contact conditions in the numerical integration scheme employed.     

A dirichlet process elaboration diagnostic for binomial goodness of fit

Useful model checking tools can be constructed by measuring the distance between a prior distribution that concentrates most of its mass around a model of interest, and the resulting posterior distribution. In this paper we use this approach to construct a diagnostic measure for detecting lack of fit in discrete data, with special focus on binomial data. We begin by constructing a suitable probability model “around” the model of interest, via a Dirichlet Process elaboration. We derive the resulting diagnostic and show that, approximately, it is the sum of two terms: the first is the logarithm of the Bayes factor and the second is proportional to the Pearson chi-square statistics. We give details of a simulation algorithm for computing the diagnostic and illustrate its use in an application to biomedical data.     

Application of the energy criterion to the numerical analysis of pipelines for “leak prior to fracture”

We consider an energy fracture criterion in the form of an integral over the crack surface. The basic variational equation enables one to describe both critical and subcritical states of cracked bodies under monotonic loads by introducing special variations of crack length. By using this criterion, we deduce an equation which describes the subcritical growth of through and nonthrough cracks in pipelines, compute the amount of water flowing through the crack, and propose a generalized fracture diagram which enables one to estimate pipelines according to the the “leak-prior-to-fracture” criterion. Moscow Institute of Physical Engineers. Moscow. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 1, pp. 67–75, January–February, 1996.     

Experimental fundamentals of tribofatigue. Part 3

We present a general survey of the experimental results that can be regarded as fundamental for tribofatigue (the theory of wear-fatigue damage to power systems of machines). In Part 3, we describe and analyze basic regularities of damage and the limiting states under the conditions of contact-mechanical fatigue. “Tribofatigue” Scientific-Industrial Concern, Gomel, Belarus. Translated from Problemy Prochnosti, No. 4, pp. 21–29, July–August, 1997.     

基于信息融合方法的切削颤振状态识别技术

讨论了切削颤振状态识别的信息融合方法．分别给出了基于基本概率分配函数和基于证据区间值的颤振状态识别方法。试验中，在同一个测量区内使用了功率传感器和加速度传感器，利用Dempster—Shafer证据论方法对两种传感器信息进行了分析融合。试验与理论分析表明：经过信息融合得到的基本概率分配函数可以作为一种颤振状态识别参数。如果同时考虑证据区间P1(A)-Bel(A)值进行识别会减小识别的不确定性．提高颤振状态识别的精度。     

基于物理参数贝叶斯更新的桥梁剩余强度估计研究

考虑系统参数的随机性,将基于广义卡尔曼滤波的子结构法与贝叶斯更新方法相结合,提出了桥梁结构基于贝叶斯更新物理参数的剩余强度估计两步法:第一步,将子结构法与广义卡尔曼滤波算法相结合,成功识别出子结构及其相邻单元的物理参数;第二步,视识别出的结构物理参数为更新信息,对以蒙特卡罗仿真实验结果作为先验分布的参数进行贝叶斯更新并分别基于蒙特卡罗仿真参数和贝叶斯更新物理参数对结构进行了剩余强度估计。数值算例表明:基于贝叶斯更新物理参数估计得到的结构剩余强度明显低于基于蒙特卡罗仿真参数估计得到的结构剩余强度。该方法为测量响应信息不完备条件以及小样本抽样情况下桥梁结构剩余强度估计提供了一个较好的解决思路。     

不同信息融合方法在结构损伤识别上的应用和分析

在工程结构的损伤探测领域,不同的信息融合方法和方式对结构的损伤敏感程度以及计算的复杂程度往往不同,而且适用条件也不同。为了解决以上问题,描述了基于结构损伤识别的功能信息融合模型,并在此基础之上采用了多种融合方法进行了数值仿真和分析。数值仿真结果表明,采用了信息融合技术的结构多损伤位置识别,可以产生比单一信息源更精确、更完全的估计和判决,而且不同的信息融合算法的应用往往取决于研究对象和实际条件的要求。     

Bayesian parametric inference in a nonparametric framework

This paper considers the problem of reporting a “posterior distribution” using a parametric family of distributions while working in a nonparametric framework. This “posterior” is obtained as the solution to a decision problem and can be found via a well-known optimization algorithm.      

A Bayesian approach for optimal reinsurance and investment in a diffusion model

A Bayesian adaptive control approach to the combined optimal investment/reinsurance problem of an insurance company is studied. The insurance company invests in a money market and a capital market index with an unknown appreciation rate, or “drift”. Using a Bayesian approach, the unknown drift is described by an unobservable random variable with a known (prior) probability distribution. We assume that the risk process of the company is governed by a diffusion approximation to the compound Poisson risk process. The company also purchases reinsurance. The combined optimal investment/reinsurance problem is formulated as a stochastic optimal control problem with partial observations. We employ filtering theory to transform the problem into one with complete observations. The control problem is then solved by the dynamic programming Hamilton–Jacobi–Bellman (HJB) approach. Semi-analytical solutions are obtained for the exponential utility case.     

Padé approximants for the numerical solution of singular integral equations

Summary A method for accelerating the convergence of the numerical solution of a singular integral equation, based on Padé Approximants, is given in this paper. At first the general form of the Padé Table and of the “epsilon” algorithm are presented. Taking into consideration the classical quadrature method, based on the Gauss-Jacobi quadrature rule, an approximate formula is derived for the unknown density function of the Cauchy-type singular integral equation or of the equivalent Fredholm integral equation. In this formula applying the “epsilon” algorithm to the solution for the stress intensity factors, the convergence is achieved after a few operations. The number of numerical operations required for the determination of stress intensity factors is considerable reduced, when compared to the number of operations required for a classical type of solution. Illustrative examples are given, indicating the efficiency of the method.     

Effect of interaction between deep impurity traps on thermally stimulated currents in semiconductors

We demonstrate that the problem of determining the concentrations of free and trapped charge carriers in wide-gap semiconductors from their thermally stimulated current (TSC) curves for m interacting levels in an implicit difference scheme for numerically solving differential rate equations of TSCs reduces to finding the roots of an algebraic equation of degree m + 1. For two interacting trap levels of the same nature (electron or hole traps), we present an algorithm for numerically solving differential rate equations of TSCs which allows the concentrations of free and trapped charge carriers to be determined. TSC curves can be divided into four types according to their shape (dependent on trap parameters and experimental conditions): “splitting” (two well-resolved peaks separated by a temperature range), “saddle” (a well-defined minimum between two peaks), shoulder (on the high- or low-energy side), and “coalescence-absorption” (one peak). The modeling results are used to interpret an experimental TSC curve for semiconducting InSe and to demonstrate that, to adequately interpret experimental TSC data, one should use a model for the interaction between levels.     

The structural strength of glass: hidden damage

We discuss “hidden damage” of glass by the rolling process, which results in heterogeneous distribution of microcracks on the edge surface of glass element, which are the fracture source deteriorating glass element strength. It is shown that removal of this damage on the edges of glass elements increases the engineering strength of float glass significantly. Using the “hidden damage” approach, we provide strength determination for the weakest specimens that is statistically relevant and is based on a reliable engineering parameter.     

基于二阶转换测量Kalman滤波的目标跟踪算法(英文)

为了减小传统跟踪滤波算法线性化误差,提高光电跟踪系统的跟踪速度和跟踪精度,本文在三维空间中,提出了二阶去偏转换测量卡尔曼滤波算法.该算法利用二阶泰勒展开的方法,推导出了光电跟踪系统观测方程的转换测量值误差的均值和协方差矩阵表达式,并对测量误差进行去偏差补偿处理,再经过转换测量卡尔曼滤波,可显著减小传统滤波算法的线性化误差.仿真结果表明,二阶去偏转换测量卡尔曼滤波(SCMKF)算法的跟踪精度优于非去偏转换测量卡尔曼滤波(CMKF)和扩展卡尔曼滤波(EKF),以及unscented卡尔曼滤波(UKF)算法,并且具 有更快的收敛速度,和采用统计方法的去偏转换测量卡尔曼滤波(DCMKF)的跟踪精度相当,但计算简单,提高了跟踪速度.