混沌系统平均初始误差增长饱和特性研究

在非线性误差增长理论框架下研究了混沌系统平均初始误差增长饱和特性 以及误差饱和值同系统可预报期限的关系.首先探索了Lorenz96系统中平均相对初始误差增长饱和规律, 发现平均相对初始误差增长饱和值同初始误差的自然对数存在简单的线性关系: 其二者自然对数之和为一常量,且该常量同初始误差无关.实验表明该结论对其他混沌系统也适用. 因此对给定混沌系统,在计算出和常数后可以外推得到任意固定初始误差的平均相对误差增长饱和值. 为进一步研究误差饱和值同可预报期限的关系,给出了平均绝对误差增长的定义. 理论分析表明混沌系统平均绝对误差增长也会达到饱和.其饱和值为常量, 与初始误差无关,混沌系统控制参数确定,饱和值就固定.依据上述研究, 最后给出一个定量计算可预报期限的模型T_p=1/∧ln(E_s/δ₀)+c, E_s为绝对误差增长饱和值.实验研究表明对于复杂的高阶混沌系统,该预报期限模型都能较好地适用.     

“拐点法”测普朗克常量误差大的应对方法

由光电效应试验中得到的伏安特性曲线,用粗略简易的"拐点法"可以很快计算出普朗克常量,但计算出的数值误差比较大,针对误差较大,通过多次的取值分析计算,最后得出可以尽可能减小误差的"拐点"的确定。     

Zur Methodik der Messung der Aktivität von umschlossenen γ-Strahlungsquellen mittels Ionisationskammern

In der Arbeit wird über eine Empfehlung zur Methodik der Weitergabe der Aktivitätseinheit für umschlossene γ-Strahlungsquellen von den Normalen der metrologischen Slaatsämter der UdSSR (WNIIM) und der DDR (ASMW) an Normale niederer Ordnung berichtet. Die Weitergabe der Aktivitätseinheit geschieht durch Vergleich mittels Ionisationskammern. Die Empfehlung bezieht sich auch auf solche Fälle, in denen neben dem Hauptnuklid ein Verunreinigungsnuklid in der Quelle enthalten ist, sowie auf solche, bei denen unterschiedlicher Aufbau der zu vergleichenden Quellen vorliegt. Auβerdem umfaβt die Empfehlung die Methode der Fehlerrechnung.     

Meshing Requirements for Tidal Modeling in the Western North Atlantic

This paper presents an a posteriori approach to unstructured mesh generation via a localized truncation error analysis and applies it to the Western North Atlantic Tidal (WNAT) model domain. The WNAT model domain encompasses the Gulf of Mexico, the Caribbean Sea, and the North Atlantic Ocean east to the 60°W Meridian. Herein, we pay particular attention to the area surrounding the Bahamas.

A bathymetric data set with fine resolution is employed in seven separate linear, harmonic simulations of shallow water tidal flow for seven different tidal-forcing constituents. Each set of simulation results is used to perform a truncation error analysis of a linear, harmonic form of the depth-averaged momentum equations for each of the seven different tidal-forcing frequencies. Truncation error is then driven to a more uniform, domain-wide value by solving for local node spacing requirements. The process is built upon successful research aiming to produce unstructured grids for large-scale domains that can be used in the accurate and efficient modeling of shallow water flow. The methodology described herein can also be transferred to other modeling applications.     

FULLY SYMBOLIC GENERATION OF COMPLEX MULTIBODY MODELS*

Abstract

In this paper, a quasistatic finite element model of a spur gear pair is developed. A node-to-target contact formulation is given, where calculations of initial gaps are based upon the actual geometry of the gear flanks rather than upon a contact node and a facet or a line segment. By using a special contact search algorithm, profile modifications and mounting errors are easily incorporated in the analysis. The problem, which also includes friction, is solved by using a nonsmooth Newton method. The static transmission error can be calculated with accuracy with a relatively small number of nodes along the gear flanks. Several examples are given in order to demonstrate the model.     

测量噪声对波前重构精度的影响

 Hartmann-Shack波前传感器斜率测量误差是自适应光学系统中影响波前重构精度的一个主要误差来源。针对模式法波前重构算法,推导出了普遍适用的模式法波前重构误差传递系数计算公式;利用61单元自适应光学系统中的Hartmann-Shack波前传感器测量的斜率数据,验证了模式法波前重构误差传递系数计算公式的正确性。     

三类构型激光脉冲压缩器光栅拼接误差容限比较

建立了包含拼接光栅的三类典型构型(双程Z型、X型及菱型)激光脉冲压缩器的理论模型. 利用光线追迹法计算压缩器引入的相位变化,结合傅里叶变换的方法仿真分析并比较了各压缩器相应的光栅拼接误差容限. 以远场焦斑峰值能量下降到理想值的0.9倍为限确定了三类压缩器光栅拼接误差容限,明确了不同构型激光脉冲压缩器对拼接误差的敏感程度. 这对脉冲压缩器的选型和设计具有指导意义. 关键词： 光栅拼接 脉冲压缩 误差容限 光线追迹     

New lower bounds on 2-spontaneous emission error designs

The combinatorial object named $t$-spontaneous emission error design ($t$-SEED) was proposed by Beth et al. in 2003 in order to correct errors caused by quantum jumps. The newly rising category of $t$-SEEDs has been studied extensively in recent years. Especially, the maximal possible dimensions for 2-SEEDs with block size 3 were determined completely; lower bounds on 2-SEEDs were established by applying affine groups. In this paper we utilize the action of twisted affine groups on finite fields and obtain new lower bounds on the dimensions of 2-$(q^2,k;m)$ SEEDs, some of which outperform the known ones.     

Parametric error bounds for convex approximations of two-stage mixed-integer recourse models with a random second-stage cost vector

We consider two-stage recourse models with integer restrictions in the second stage. These models are typically non-convex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q. In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the ${?}_1$-norm of q.