数值求解常微分方程初值问题的偏差积分方法

在连续运动系统的设计、优化计算、实时仿真、系统识别等问题中,均需计算大量的系统运动轨道.这是相当费时间的,特别当精度要求比较高,而描写系统运动的常微分方程组右端函数相当复杂时,更是如此.前者要求采用较小的步长进行数值积分,因而积分的步数比较多.而后者表示每一步积分所需要的计算量相当大,这就使得一些问题由于轨道计算的总计算量太大,在通常的计算机上无法求解或实现,至少实时计算是无法进行     

用优选法推算柴油机配气凸轮运动方程

柴油机配气凸轮的设计是柴油机配气机构设计的核心.在实践中,我们经常遇到这样一种情况:即在具备了配气凸轮的实物时,如何求得凸轮的运动规律即凸轮的运动方程. 在鉴定一台柴油机的工作中,遇到了这类问题,为了评价它的设计,找出凸轮的运动规律,首先,我们对该柴油机的凸轮进行了测量.采用精度为0.001毫米的测长仪和精度     

薄壁结构动力计算中若干问题

本文讨论薄板和薄壳之类的薄壁结构受冲击荷载作用时的动力计算问题.主要是求动力因数.在计算中考虑了冲击物和被冲击的薄壁结构系统质量的影响;用相当质量法将薄壁结构的分布质量转化为只有一个集中的相当质量,从而导出薄壁结构系统在冲击力作用下的动力因数,计算比较方便.     

应力波放大器二维数值分析

运用动态有限元方法,对应力波在锥形应力波放大器中传播特性进行了二维数值分析,对影响透射波放大系数和波形的几何因素、输入脉冲形状、脉冲升时等进行了讨论,可供应力波铆接器设计之参考.计算结果与在Hopkinson杆上实验测得值以及特征线计算值进行了比较,其与实验结果吻合程度是令人相当满意的,与一维特征线方法相比.其计算精度也得到较大改善,特别是在透射波峰值压力附近.     

闭合圆柱壳在轴向冲击荷载下的某些动力计算问题

本文讨论了闭合圆柱形壳体在轴向冲击荷载作用下的某些动力计算问题,其中包括动应力的计算和稳定性问题.文中分析了冲击过程中动量及能量的变化,并计入冲击物和被冲击的闭合圆柱壳系统质量的影响;用相当质量法将整个圆柱形壳体的分布质量转化为只集中在壳体一端的“相当质量”,从而导出闭合圆柱形壳体在轴向冲击荷载作用下的动力因数,因而解决了在上述受力情况下计算动应力的问题和求出临界荷重的问题.     

Hill-n密码学的计算机代数研究

以模代数及矩阵变换技术为理论基础的 Hill-n密码学 ,作为线性代数知识的进一步应用 ,在大学数学的学习与应用中是具有相当价值的 ;但若想在当时的学习或以后的应用中得以迅速实现靠手工计算是相当困难的 ;本文借助于计算机代数系统 Mathematica的推导与计算功能 ,编写了相应的程序包 ,准确而迅速实现了编码、译码、破译加密矩阵及密文等系列工作 .     

有限分析系数的精确计算与插值算法

有限分析法是流体计算中一种有效的数值计算方法.但是在解高雷诺数的对流扩散方程时,有限分析系数计算将相当耗时且系数本身将严重失真.本文揭示了上述困难的成因,并提出一种改进算法.首先,建立了一套高精度计算系统,并利用它精确地求出所有基点上被称为“P_e”的函数值.在实际计算中,有限分析系数可通过插值得到的“P_e”值求出.实用算法在保证计算精度的同时,大大提高了有限分析系数的计算速度.     

瞬态接触动力学的三维问题

发展了三维瞬态接触动力学问题的分析解法,并且得到了广义Galin()定理.对于给定的相当普遍的接触应力,可以确定相应的接触位移,并且得到解析的形式;反过来,对于给定的相当普遍的接触位移,可以解析地确定其相应的接触应力.上述所指的普遍的给定物理量可以是X与y的任意阶多项式和时间t的任意瞬态函数.还针对不同接触区的几何特征和最典型的最常使用的7种固体介质进行了实例计算,所有计算结果均表明上述理论结果在数学上和物理上的精确性.     

喷雾碰壁燃烧数值模拟研究北大核心CSCD

燃油喷雾碰壁是小型高压直喷式柴油机中普遍存在的现象.燃油碰壁会影响缸内燃烧过程,进而显著地影响柴油机的动力学、经济性和排放性.为了更好地认识燃油喷雾碰壁燃烧现象,该研究采用数值模拟的方法对该过程进行计算,探究其特殊的燃烧特性.研究结果表明:在碰壁喷雾的两阶段燃烧过程中,喷雾碰壁促进喷雾径向发展半径和卷吸高度的增加,促进近壁面油气混合,在近壁面形成有利于低温点火的条件.低温燃烧反应在混合气较为稀薄的近壁面区域开始,随后向碰壁喷雾中心浓混合气区域发展.随着低温氧化燃烧持续放热,碰壁喷雾雾束中心区域温度逐渐升高,同时积累大量甲醛.由于喷雾碰壁会导致碰壁雾束中心形成较浓混合气,并且低温燃烧放热量较少,导致部分碳氧化物无法完全燃烧,增加了碳烟的生成量.另外随着高温燃烧的进行,温度持续升高,碰壁喷雾卷吸更多环境气体,进而产生大量氮氧化物.     

Reissner厚板弹性弯曲的一般解析解

针对大型工程建设中的Reisner厚板弹性弯曲问题,本文采用复级数方法求解相应的常系数偏微分方程组的边值问题,并首次得到了任意边界条件下的一般解析解.该解形式简单,计算方便、可靠.以四边简支和三边固支一边自由两种支撑条件下厚板承受均布载荷为例进行了分析验算,与已有的计算结果相比,计算结果相当满意.同时本文还着重对解的收敛速度、正确性(合理性)及边界满足情况进行了考察.     

Analytical modelling for static stress analysis of pin-loaded lugs with bush fitting

Pin-loaded connections are widely used in the industry. Connecting rods of reciprocating engines in automotive applications or pin-loaded lugs of landing gears and airframe structures can be cited as examples. These systems are subject to thermomechanical cyclic loadings and fatigue mechanisms are often observed. The calculation of stresses in the lug is crucial in view of a fatigue lifetime analysis. Analytical modelling may be very helpful in the early design stage, by allowing fast parametric studies and the identification of the most influent parameters on the response in stresses. In this paper, we propose analytical models for bush fitting and pin-loading conditions, leading to the complete calculation of the stress distribution in the lug. In each case, the analytical solutions are compared with finite element simulations. In the last part, we perform a sensitivity analysis as an application of the presented analytical tools.     

High-frequency response of a calculation methodology for gas dynamics based on Independent Time Discretisation

A calculation methodology to solve the one-dimensional governing equations system is presented. This calculation methodology is based on the Independent Time Discretisation (ITD) of the ducts composing the system. The purpose is the improvement of the trade-off between the accuracy and the computational cost that the current 1D gas dynamic models can yield. The ITD methodology is applied to the specific problem of noise prediction in internal combustion engines in order to evaluate its performance in the frequency domain. The application of the ITD methodology to the well-known acoustic configurations which are representative of the main attenuation mechanisms in commercial mufflers shows its ability. The potential is evaluated in terms of reduction of the computational cost and the accuracy and robustness provided by the results as a function of the spatial mesh size and the family of finite difference numerical method applied.     

关键词广告支付模式的研究

关键词广告是主要用于搜索引擎的一种广告销售机制.所谓关键词既指搜索用户在搜索框内输入的检索词,也指机器程序从用户浏览的网页内容中抓取的词.广告主的广告依据关键词触发而展现在相应网页上.对搜索引擎来说,选择广告的支付模式是销售机制的核心命题.在互联网发展的实践中出现了许多支付模式,比如按展现付费(Pay-Per-Impression),接点击付费(Pay-Per-Click),按呼叫付费(Pay-Per-Call)和按销量付费(Pay-Per-Sale)等.如果实现这些支付模式的条件都具备,那么哪一种付费方式对搜索引擎是最有利的?试图回答这个问题.主要结论是对搜索引擎来讲,按点击付费是最优或近似最优的支付模式.     

A General Approach to Dyadic Periodic Interpolation Based on Discrete Sigma-Pi Orthogonality

Starting with some well known formulas of discrete sigma-pi orthogonality of bipolar vectors we introduce a quite general and easy strategy to obtain periodic interpolation schemes on dyadic grids including fast algorithms for explicit calculation. As special cases of our presented approach we mention dyadic trigonometric and Walsh-type interpolation.     

关于方阵高次幂计算方法的一个注记

一般地,求方阵的幂总是先将其标准化,然后通过相似变换得到.然而矩阵的标准化过程却是十分复杂的,所以应用范围受到很大的局限性.利用凯莱-哈密顿(Cayley-Hamilton)定理,可以得到计算方阵高次幂的一种非特征值方法.     

Supersymmetry-inspired low-energy <Emphasis Type="Italic">α</Emphasis>–<Emphasis Type="Italic">p</Emphasis> elastic scattering phases

We consider an effective potential model consisting of an electromagnetic part plus a nuclear part as the ground state interaction for an α–p system. The next few higher partial wave interactions are generated using the formalism of supersymmetric quantum mechanics. We adapt the phase function method to compute α–p elastic scattering phases up to 12 MeV, including the effect of the electromagnetic interaction quite rigorously in our phase shift calculation. With the further incorporation of some energy-dependent correction factors to our interactions, we obtain a good agreement with the experimental data.     

Product-type block preconditioners for electromagnetic cavity problems

In a radar detecting system, the radar cross section (RCS) of a target is an important application in electromagnetics computation. Cavity prediction is usually required in the computation process. When wavelengths of electromagnetic field are large, cavity calculation is a challenging problem. The main aim of this paper is to employ the preconditioned GMRES method to solve linear systems arising in cavity calculation of the transverse magnetic and transverse electric problems. We develop new preconditioners based on fast transforms and Toeplitz solvers. Our numerical results show that the proposed preconditioners are quite efficient and effective, especially when the wavelength is large.     

Cost of ownership model for spare engines purchase for the Korean navy acquisition program

Major weapon system acquisition programmes often require high initial purchase cost which can be a burden for the procurement of a highly reliable system. In order to avoid the tendency of acquiring a less expensive weapon system with lower performance, a cost of ownership (COO) model can be applied to assess the lifetime cost of the weapon system. In many existing cost estimation models for weapon systems, the failure rate of the system is assumed to be constant and the functional relationship between the initial purchase cost and maintenance cost is not well defined. In this paper, we propose a revised COO model where random effects models are employed to accommodate the variations of the system failure frequency and repair time. It is expected that our model can contribute to the cost-effective procurement of spare engines for the Korean Navy acquisition programme within the limited national defence budget.     

On control of a dynamical system by rotors

In this paper, we consider a solution of the space reorientation problem for a body by one plane rotation for the case where the number of flywheel engines can be arbitrary. The algorithm obtained for the solution of the problem defines the program of change of control influence at the entrance of flywheel engines.     

Factorization and Resultants of Partial Differential Operators

Comparatively little is known about commutative rings of partial differential operators, while in the ordinary case, concrete examples and an algebraic(-geometric) structure can be algorithmically determined for large classes. In this note, by the calculation of the partial μ-shifted differential resultant which we defined in a previous paper, we produce algebraic equations of spectral surfaces for commutative rings in two variables, and Darboux transformations of Airy-type operators that correspond to morphisms of surfaces. There are, however, many elementary differential-algebraic statements that we only observe experimentally, thus we offer open questions which seem to us quite significant in differential algebra, and access to Mathematica code to enable further experimentation.