A family of lower- and higher-order transversal linearization techniques in non-linear stochastic engineering dynamics

Sample pathwise numerical integration of noise-driven engineering dynamical systems cannot generally be performed beyond a limited level of accuracy, especially when the noise processes are modelled using (filtered) white noises. Recently, a locally transversal linearization (LTL) strategy has been proposed by the author (Proc Roy Soc London A 2001; 457 :539–566) for direct integration of deterministic and stochastic non-linear dynamical systems. The present effort is focussed on a host of extensions along with detailed theoretical error analyses of the linearization approach, especially as applied to problems in non-linear stochastic engineering dynamics. Thus, to begin with, estimates of local and global error orders in the basic LTL scheme are obtained separately for the displacement and velocity vectors when the system is driven either by a set of additive noises or by an arbitrary combination of (independently evolving) additive and multiplicative noises. Following this, a new family of higher-order LTL schemes is proposed in order to improve upon the basic LTL method and the associated error orders are established. A stepwise implementation of the lower- and higher-order versions of the LTL method, along with certain computational aspects, is also outlined. The proposed schemes are numerically illustrated, to a limited extent, for a single degree-of-freedom (SDOF) and a two degree-of-freedom (TDOF) non-linear engineering systems under additive and/or multiplicative white noise excitations. Copyright © 2004 John Wiley & Sons, Ltd.     

Stability of Circular Cylindrical Shells with a Single Local Dent

The theoretical-and-experimental investigation has been performed on the stability of smooth cylindrical shells of steel with a single local dent. All the shells manufactured using the same process were tested with the fulfillment of identical conditions for observations and measurements. Theoretical calculations were carried out by the mesh method with the use of the nonlinear theory of shells. A comparison of the experimental and theoretical values of the critical loads has been made. The theoretical-and-experimental approach proposed enables one to evaluate the quality of shells by studying local dents and other specific imperfections.     

Adaptive Edge Detectors for Piecewise Smooth Data Based on the minmod Limiter

We are concerned with the detection of edges—the location and amplitudes of jump discontinuities of piecewise smooth data realized in terms of its discrete grid values. We discuss the interplay between two approaches. One approach, realized in the physical space, is based on local differences and is typically limited to low-order of accuracy. An alternative approach developed in our previous work [Gelb and Tadmor, Appl. Comp. Harmonic Anal., 7, 101–135 (1999)] and realized in the dual Fourier space, is based on concentration factors; with a proper choice of concentration factors one can achieve higher-orders—in fact in [Gelb and Tadmor, SIAM J. Numer. Anal., 38, 1389–1408 (2001)] we constructed exponentially accurate edge detectors. Since the stencil of these highly-accurate detectors is global, an outside threshold parameter is required to avoid oscillations in the immediate neighborhood of discontinuities. In this paper we introduce an adaptive edge detection procedure based on a cross-breading between the local and global detectors. This is achieved by using the minmod limiter to suppress spurious oscillations near discontinuities while retaining high-order accuracy away from the jumps. The resulting method provides a family of robust, parameter-free edge-detectors for piecewise smooth data. We conclude with a series of one- and two-dimensional simulations.To David Gottlieb, on his 60th birthday, with friendship and appreciation.     

The experimental determination of the neutron cross section for selected solvents

An experiment was conducted in order to determine the macroscopic neutron cross section of various solvents useful in neutron radiographic inspection. These solvents are used to dissolve the salts of high cross-section elements in order to formulate a fluid of maximal neutron cross section. The resulting fluid could then be used as a contrast enhancing agent in neutron radiographic inspection. This experiment was planned using statistical experimental design techniques. The results of this experiment provided a quantitative measure of the mean and standard deviation of the macroscopic neutron cross section for the nine fluids investigated. A control fluid was found to be in close agreement with published values.     

河道冲刷和清水水流河床冲刷率

在冲积河流里。水流条件变化如洪水、水库泄放清水、河道渠化等使挟沙力不饱和引起冲刷，称为河道冲刷。这与水工建筑造成的局部冲刷不同。河道冲刷深度主要决定于冲刷率和冲刷历时。本研究通过对各种泥沙大量实验，证明了河床冲刷率正比于水流提供的冲刷功率并依赖于泥沙粒径和容重，首次提出了冲刷率公式。经验证，该公式可以用于非恒定流输沙和河流洪水冲刷计算。     

基于非线性规划的指数自回归模型的辨识

讨论了指数自回归模型的辨识问题，证明了该模型最小二乘估计的目标函数的非凸性，并给出了使该函数为凸的条件，最后给出了辨识该模型的算法及该算法的收敛性，并以数值例子加以说明。     

Fe73.5Cu1Nb3Si13.5B9非晶合金的晶化动力学

用ＤＴＡ结合ＸＲＤ了Ｆｅ７３．５Ｃｕ１Ｎｂ３Ｓｉ１３．５Ｂ９晶合金的晶化动力学。表明，该事金在５００℃时析出α－Ｆｅ（Ｓｉ）相。晶化初期激活能最小为２４２ｋＪ／ｍｏｌ，它随晶化量的增加，在ＸＣ为０．４－０．８时，呈极大值为５２０ｋＪ／ｍｏｌ。在６２４℃时析出Ｆｅ２Ｂ相。     

Locally Weighted Learning

This paper surveys locally weighted learning, a form of lazy learning and memory-based learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, assessing predictions, handling noisy data and outliers, improving the quality of predictions by tuning fit parameters, interference between old and new data, implementing locally weighted learning efficiently, and applications of locally weighted learning. A companion paper surveys how locally weighted learning can be used in robot learning and control.     

分子振动态及其跃迁的激光相干控制

讨论了激光合成相干叠加态的原理及其性质 ,针对 XY2 型分子 ,证明了合成局域模振动的可行性 ,然后给出相干叠加态的跃迁几率特征 ,发现它仍表现出相干的特性 ,对之进行分析研究表明 ,分子的振动态具有可控性 ,态跃迁几率具有可控性。     

原料扩重的中压加氢改质装置投产

介绍燕山石化公司为扩大1Mt／a中压加氢改质装置的原料来源，改用大庆减二线油和重油催化裂化柴油组成的混合料开工投产的经验以及装置初期的运行条件。中压加氢改质技术可以生产优质柴油和蒸汽裂解制乙烯的原料，还可增产喷气燃料。