关于钻尖的变导程拟螺面磨法的研究

本文介绍了确保钻尖质量的变导程拟螺面磨法、相应的几何优化模型及其算法,由于经过实例计算和3659开刃机上的试验的验证,因而本文为磨得高质量钻尖提供了可靠依据。     

阻尼振动系统的强迫响应

本文讨论阻尼振动系统(离散或连续系统)在周期外激励作用下的强迫响应;系统的阻尼阵不能对角化.导出了强迫响应一般解的显式解析表达式.利用这些解式,本文对某些振动现象作了较普遍的解析讨论.如,从一般角度讨论了单阻尼振动系统特有的“固定振幅点”现象;讨论了同相位外激励作用下产生同相位响应的条件等等.本文导出的解式对一大类系统仅含很低阶的矩阵求逆运算,因而在计算机数值计算上.本方法比之于现有方法,具有程序简单、耗时少和精度高等优点.本方法可平行应用于转子动力学的不平衡响应分析.     

内外噪声扰动下放牧生态系统的稳态转换现象

生态系统的稳态转换可能会造成生态环境的退化和巨大的经济损失,研究稳态转换如何受随机因素影响非常必要.文章研究放牧模型在高斯噪声和Lévy噪声共同作用下的稳态转变现象.首先介绍了放牧模型的确定性方程,然后利用Janicki-Weron算法产生Lévy噪声,并通过四阶Runge-Kutta算法对放牧系统进行数值模拟,最后基于稳态概率密度分别分析了内噪声和外噪声对系统稳态转换行为的影响.研究发现两种噪声均可诱导系统产生稳态转换现象,但作用相反;高斯噪声强度的增大可以诱导放牧系统从高植被态向荒漠态转换,而Lévy噪声的强度、稳定性指标和偏斜参数的增大均可促进放牧系统从荒漠态向高植被态的恢复.     

一类含五次非线性恢复力的Duffing系统共振与分岔特性分析

考虑一类含有外激力和五次非线性恢复力的Duffing系统,运用多尺度法求解得到该系统的幅频响应方程,给出不同参数变化下的幅频特性曲线及变化规律,同时利用奇异性理论得到该系统在3种情形下的转迁集及对应的拓扑结构.其次确定系统的不动点,运用Hamilton函数给出该系统的异宿轨,在此基础上,利用Melnikov方法得到该系统在Smale马蹄意义下发生混沌的阈值.而后通过数值仿真给出了系统随外激力、五次非线性项系数变化下的动态分岔与混沌行为,发现存在周期运动、倍周期运动、拟周期运动及混沌等非线性现象.最后运用Lyapunov指数、相轨图和Poincaré截面等非线性方法对理论的正确性进行验证.上述研究结论为进一步提升对Duffing系统非线性特性及其演化规律的认识提供了一定的理论参考.     

广义Hamilton系统的有效稳定性

利用Lochak的同步逼近法证明了广义Hamilton系统的有效稳定性. 在考虑的系统中, 作用变量和角变量的维数可以不同.     

托卡马克中低模态到高模态转迁模型的混沌运动

利用Melnikov方法详细研究了在托卡马克(Tokamaks)中,等离子区边缘附近低模态到高模态转迁方程的混沌动力学.该转迁方程是一个含外激励和参数激励的系统.对含周期外激励和线性参数激励、三次参数激励的系统分别绘出了用来划分混沌区和非混沌区的临界曲线.得到的结果表明,含有线性或三次参数激励的系统存在不可控区域,在该区域中异宿轨分岔总是导致混沌发生.特别地,三次参数激励系统存在一个"可控频率",施以该频率的激励,不论激励的振幅多大,同宿轨分岔总是不会导致混沌发生.得到了这类系统的一些复杂的动力学行为.     

基于非线性能量阱的双频激励非线性系统减振

针对某型民用航空发动机双频带激励特点,建立了单自由度线性振子耦合非线性能量阱（nonlinear energy sink,NES）的动力学模型.根据典型双转子发动机在巡航状态下低、高特征频率比（1∶4.74）,为系统设定双频带简谐外激励.利用四阶Runge-Kutta算法,研究了耦合NES振子时系统的振动抑制特征,并从外激励频率对系统主振子动能、系统总体能量的影响等方面,与未耦合NES系统、耦合线性动力吸振器两种情况下的数值计算结果进行对比分析.研究结果表明NES对双频带外激励具有更好的振动抑制效果,用NES降低航空发动机振动有可行性.     

KdV方程的延拓结构

利用外微分形式系统和Lie代数表示理论提出了求解非线性波方程Lax对的延拓结构理论,该方法是构造非线性波方程Lax对的系统最有效的方法.其关键在于如何给出延拓代数的具体表示,如微分算子表示或矩阵表示.如果一个非线性波方程具有非平凡的延拓代数,则称其延拓代数可积,本篇论文主要利用延拓结构理论,讨论KdV方程的解,同时给出...     

一般脉冲系统的Melnikov函数构造方法及其应用

利用摄动法给出了一般脉冲系统Melnikov函数构造方法,得到脉冲信号作用下一般非线性系统Melnikov方法.为考察方法的有效性,将方法应用到脉冲信号作用下Duffing系统的混沌预测中去,通过方法得到脉冲信号作用下Duffing系统出现混沌的阈值曲线,数值实验结果验证理论结果的正确性.     

线性广义系统的P型、PD型和PID型迭代学习控制

本文研究了线性定常广义系统在P型、PD型和PID型学习律作用下的迭代控制问题,利用矩阵理论和微分不等式方法,得到了其迭代控制收敛性结果.不仅对于时变系统也成立,而且,可以移植到线性定常广义离散时间系统.     

一个关于二次规划问题的分段线性同伦算法

本文发展了一个关于二次规划问题的分段线性同伦算法。该算法可看作是外点罚函数法的一个变体。凡是符合外点罚函数法收敛条件的二次规划问题用该算法均可经有限次轮回运算得到稳定解。大量的关于随机的凸二次规划问题的数值实验结果表明它的计算效率是高的，在某些条件下可能是多项式时间算法。     

A new penalty function algorithm for convex quadratic programming

In this paper, we develop an exterior point algorithm for convex quadratic programming using a penalty function approach. Each iteration in the algorithm consists of a single Newton step followed by a reduction in the value of the penalty parameter. The points generated by the algorithm follow an exterior path that we define. Convergence of the algorithm is established. The proposed algorithm was motivated by the work of Al-Sultan and Murty on nearest point problems, a special quadratic program. A preliminary implementation of the algorithm produced encouraging results. In particular, the algorithm requires a small and almost constant number of iterations to solve the small to medium size problems tested.     

Local energy decay for the damped Klein-Gordon equation in exterior domain

We prove uniform local energy decay for the solution of the dissipative Klein–Gordon equation on an exterior domain under some geometric condition called “exterior geometric control”.     

Geometric modeling and validation of twist drills with a generic point profile

Traditionally, twist drills with a few specific point geometry, such as planar, conical, cylindrical, ellipsoidal or hyperboloidal, have been designed and adapted for specific applications. Using CAD, the point geometry can be given a generic definition which will enhance the freedom to design drills with different point profiles and optimize them for multiple objectives. Such a definition can also be used for several downstream applications. This paper presents a methodology to model the twist drills with generic point geometry using NURBS. To begin with, a detailed basic model for a fluted twist drill with sectional geometry made up of arcs and straight lines has been presented in terms of bi-parametric surface patches. The coordinates of cutting lips and chisel edge of the drill have been obtained as solution to a surface-curve intersection problem using optimization algorithm. Subsequently, the model has been generalized by employing NURBS to represent the curves whereby the cutting edges and angles can be altered simply by changing the control points or their respective weights. Using this methodology, the generic definitions of the conventional angles on the drill point have been derived and presented. The proposed model has been illustrated in MATLAB environment and validated experimentally for a conical and an arbitrary point geometry. The experiments show a good conformity with the theoretical evaluations.     

Identification of objects in an acoustic wave guide inversion II: Robin–Dirichlet conditions

In this paper we investigate the unknown body problem in a wave guide where one boundary has a pressure release condition and the other an impedance condition. The method used in the paper for solving the unknown body inverse problem is the intersection canonical body approximation (ICBA). The ICBA is based on the Rayleigh conjecture, which states that every point on an illuminated body radiates sound from that point as if the point lies on its tangent sphere. The ICBA method requires that an analytical solution be known exterior to a canonical body in the wave guide. We use the sphere of arbitrary centre and radius in the wave guide as our canonical body. We are lead then to analytically computing the exterior solution for a sphere between two parallel plates. We use the ICBA to construct solutions at points ranging over the suspected surface of the unknown object to reconstruct the unknown object using a least‐squares matching of computed, acoustic field against the measured, scattered field. Copyright © 2005 John Wiley & Sons, Ltd.     

Stabilisation d'ondes électromagnétiques dans un domaine extérieur 2D

We consider the stabilization of Maxwell equations in two dimensional on the exterior of an arbitrary bounded obstacle. Using some results concerning of wave equations with Neumann boundary condition in the exterior domain. We deduce under the ‘exterior geometric control condition’ the behavior of the solution for large time. To cite this article: A. Moulahi, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

关于Helmholtz外问题的边界积分方程解的唯一性问题

本文用能量分析的观点探讨了用边界积分方程描述Helmholtz外问题时,解的唯一性不能保持的原因.文中证明了,当利用积分方程来描述问题时,实际上将无穷远处的Sommerfeld条件改成了既适合于外向波(辐射波),又适合于内向波(吸收波),即整个系统的能量保持守恒.并根据此观点解释了保持唯一性的算法.     

Variational procedures for a class of exterior interface problems

The problem under consideration is that of determining a function which is a solution of the Helmholtz equation in a planar region exterior to a simple closed curve and of an inhomogeneous Helmholtz equation inside the curve. Jump conditions on the function and its normal derivative across the cruve are given. The problem is first transformed into one involving the inner region only with a boundary condition which is non-local. This means that the solution at a point on the boundary is a functional of its values elsewhere. This second problem is further transformed into a variational form with all boundary conditions natural. It is shown that the variational problem has a solution. Finite dimensional approximate problems are defined and they are shown to have solutions converging to the solution of the variational problem.     

The exterior sphere condition for the Ventcel-Freidlin quasi-potential function

This paper is essentially an addendum to a previous paper [3] on the regularity properties of the Ventcel-Freidlin quasipotential function. We give here a proof of our conjecture regarding an exterior sphere condition for level sets.This work was supported in part by the National Science Foundation under grant DMS-8420755.