半离散Newton分裂方法的Kantorovich型定理

本文在Kantorovich型定理的条件下,给出了一种半离散Newton型分裂方法的存在性收敛性定理.     

基于面搭接多重网格技术的全机增升装置绕流数值模拟

文章在多块结构化框架下,采用面积加权平均的方法进行通量守恒传递,并成功地应用于存在"剪刀差"的全机增升装置复杂外形绕流N-S方程数值分析。通过对某民机全机低速构形所进行的气动力数值分析,计算结果与风洞实验结果吻合良好,表明该方法可以比较好地模拟如此复杂外形的流动细节,从而验证了文中所采用的面搭接多重网格技术、网格生成策略及流场计算方法的有效性。     

一类有理差分方程的全局渐近稳定性

通过研究一类有理差分方程的唯一的正平衡解的性态,进一步证明了此类差分方程的唯一正平衡解是全局渐近稳定的.     

高维力学系统的能量方程

在低维系统中,能量方程因其明晰的物理意义而得到广泛的应用,而研究高维力学系统的能量方程也同样具有理论价值和实际意义,如位移对时间的导数是速度,速度对时间的导数是加速度,这些具有明显的物理意义,而加速度的导数其物理意义就不是很清晰了,但具有理论上的意义.本文应用广义经典力学中关于广义拉格朗日函数、广义动量和广义哈密顿函数等概念,推导了高维系统的能量方程,文中举了实例具体说明新方程的应用,为力学数学系统能量方程的推广提供了一种途经.     

p-moment stability of stochastic impulsive differential equations and its application in impulsive control

The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impulsive differential system. As an application of the theorem proposed, the problem of controlling chaos of Lorenz system which is excited by parameter white-noise excitation is considered using impulsive control method. Finally, numerical simulation results are given to verify the feasibility of our approach. Supported by the National Natural Science Foundation of China (Grant No. 10772046)     

Equilibrium equations for nonlinear buckling analysis of drill-strings in 3D curved well-bores

With the development of drilling technology, the oil/gas well has evolved from its early vertical straight form to the inclined, horizontal, plane curved, or even 3D curved well-bore. Understanding of the buck-ling behavior of a drill-string in a well-bore is crucial for the success of a drilling operation. Therefore, equilibrium equations for analyzing the buckling behavior of a drill-string in a 3D curved well-bore are required. Based on Love’s equilibrium equations for a curved and twisted rod in space, ...     

具有分布时滞的Liénard型方程周期解的存在性

考察了具有分布时滞的Liénard型方程,利用重合度理论研究其周期解问题,得到了该方程周期解存在的充分条件,结论丰富了现有文献的结果．     

基于物理的波浪实时模拟方法

为解决广域范围内波浪状态的实时计算和可视化问题,结合无粘滞流体力学的物理模型,提出了一种以三角形为控制单元的有限体积简化算法。该算法的优点在于：以不规则边界区域的非规则三角网格为基础,通过简化通量向量分裂方法获得三角形控制单元的边界数值通量,能快速逼近二维浅水方程的解进而模拟非规则边界浅水的实时流动。实验结果显示,所提方法能在符合现实世界物理规律的前提下较好地实现大规模波浪的实时可视化模拟。     

Positivity and stability of mixed fractional‐order systems with unbounded delays: Necessary and sufficient conditions

This article provides a comprehensive study on quantitative properties of linear mixed fractional‐order systems with multiple time‐varying delays. The delays can be bounded or unbounded. We first obtain a result on existence and uniqueness of solutions to these systems. Then, we prove a necessary and sufficient condition for their positivity. Finally, we provide a necessary and sufficient criterion to characterize asymptotic stability of positive linear mixed fractional‐order systems with multiple time‐varying delays.     

双极完全可压缩Navier-Stokes-Maxwell方程组整体光滑解的渐近行为

考虑等离子体物理中的双极完全可压缩Navier-Stokes-Maxwell方程组,借助经典的能量方法和对称子技巧,研究了三维全空间中的Cauchy问题.在初值为一个小摄动的条件下,证明了当时间趋于无穷大时,该问题的整体光滑解收敛到平衡态.