一族Liouville可积的有限维Hamilton系统

本文生成了一族Liouville可积的Hamilton相流彼此可交换的有限维Hamilton系统,并且给出了一串对合的显式公共运动积分及其一组对合的显式生成元.     

平面运动学位似运动Steiner公式的推广

对单参数闭平面复意义位似运动，给出了Muller提出的Steiner公式和混合面公式的表达式。利用推广的Steiner公式得到了位似运动的Holditch定理．作为特例，给出了Muller位似比h≡1时的结果。     

非退化扩散过程的极性与相交性

本文讨论非退化扩散过程的极性，得到了几个较好的充分条件，它可看作[1]的进一步深化，此外，我们将这些结果用来研究两个独立的非退化扩散过程的相交性，得到了一些有意思的结果。     

Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model

In many applications materials are modeled by a large number of particles (or atoms) where any one of particles interacts with all others. Near or nearest neighbor interaction is expected to be a good simplification of the full interaction in the engineering community. In this paper we shall analyze the approximate error between the solution of the simplified problem and that of the full-interaction problem so as to answer the question mathematically for a one-dimensional model. A few numerical methods have been designed in the engineering literature for the simplified model. Recently much attention has been paid to a finite-element-like quasicontinuum (QC) method which utilizes a mixed atomistic/continuum approximation model. No numerical analysis has been done yet. In the paper we shall estimate the error of the QC method for this one-dimensional model. Possible ill-posedness of the method and its modification are discussed as well.

     

用二维欧拉方法模拟滑移爆轰作用下金属圆筒的收敛运动

本文用二维流体-弹塑性欧拉编码对金属圆筒在滑移爆轰作用下的收敛运动作了数值模拟。文中考虑了起爆端对金属圆筒运动的影响,给出了圆筒自由面不同时刻的运动姿态和自由面速度随时间变化规律。计算结果与实验结果符合较好。     

我国运动稳定性研究的新进展

综述了近年来我国运动稳定性(包括力学系统、控制系统、人口系统、生态系统和大系统的稳定性)及其一般理论的研究进展。      

Observation of sharp resistance anomalies near Tc in granular superconductors

Granular films prepared from well-defined In clusters embedded in Kr (? 10-40 at % Kr) show sharp resistance anomalies very close to the superconducting transition temperature. The observed resistance peak(s), which go(es) above the normal state resistance R_N and which can be as high as ? 1.5 R_N, can be explained by a “mesoscopic” effect: Superconducting percolation aggregates of size ξ_ρ, larger than the superconducting coherence length ξ_S, but smaller than the quasiparticle relaxation length λ_Q*, have a superconducting gap, but are not yet able to carry a supercurrent.     

阻尼落体运动的分析力学研究

应用分析力学理论和方法,研究了两种情况下的阻尼落体运动:1)阻力大小与速度成正比;2)阻力大小与速度平方成正比.对两种运动分别给出了等效的Lagrange函数和Hamilton函数,并应用第一积分法、点变换法、正则变换法和Ham-ilton-Jacobi方程法等不同的求解方法进行了求解.     

利用杨辉三角形对称性推导高阶运动微分方程

利用Mathematica数学软件计算函数r=r(q(t),t)各变量之间偏导和高阶导数的关系，发现具有杨辉三角形对称性.结合杨辉三角形的对称性规律和牛顿第二定律推导出了高阶运动微分方程，并讨论了理想约束系统下的高阶运动微分方程. 关键词： 杨辉三角形 牛顿第二定律 高阶运动微分方程 高阶力变率 高阶速度能量 理想约束