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, ...     

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。     

拟线性椭圆方程变号解的存在性

使用Morse理论对一类超线性增长的拟线性椭圆方程进行了研究,得到了方程变号解的存在性.     

具有非线性边值条件的二阶脉冲积微分方程的解

脉冲微分方程在理论方面已取得重大进展,应用极其广泛.文中介绍了上下解的定义、单调迭代方法并给出几个引理.最后用上下解方法和单调迭代技巧讨论了具有非线性边值条件的二阶脉冲积微分方程,得到了最大解和最小解的存在性.     

具有非局部源和边界流抛物型方程组解的性质

研究了一类具有非局部源及边界流抛物型组解的性质,通过构造方程组的上、下解及运用比较定理,得到了方程组解整体存在及解在有限时刻爆破的充分条件。由此得到,当反应项和扩散项的指数满足不同条件时,方程组的解具有不同的性质。     

求解具有间断系数椭圆型方程的修正有限体积法

对经典的有限体积方法进行了修正,并用于求解具有间断系数的椭圆型方程.通过增加有限体积方法中通量函数泰勒展开式的项数来提高通量函数的计算精度,对与边界相邻的网格点改用中心差分离散,以使得边界处的精度更高.修正后的方法是有限体积方法和有限差分方法的结合形式.得到了格式二阶逐点收敛并且在界面处具有二阶精度.数值实验表明:新方法较经典有限体积方法中求解间断系数问题的算术平均法和调和平均法更具优势.     

A finite volume–finite difference method with a stiff ordinary differential equation solver for advection–diffusion–reaction equation

A model for atmospheric pollutant transport is proposed considering an advection–diffusion–reaction equation. A splitting method is used to decouple the advection, diffusion and reaction parts. A scheme based on finite volume, finite difference and backward differentiation formula is used for solving an atmospheric transport-chemistry problem.     

A pseudo-spectral scheme for the approximate solution of a time-fractional diffusion equation

We consider an initial-boundary-value problem for a time-fractional diffusion equation with initial condition u₀(x) and homogeneous Dirichlet boundary conditions in a bounded interval [0, L]. We study a semidiscrete approximation scheme based on the pseudo-spectral method on Chebyshev–Gauss–Lobatto nodes. In order to preserve the high accuracy of the spectral approximation we use an approach based on the evaluation of the Mittag-Leffler function on matrix arguments for the integration along the time variable. Some examples are presented and numerical experiments illustrate the effectiveness of the proposed approach.