径向辛体系一种新的差分格式

通过对Hellinger-Reissner变分原理进行坐标变换,将径向模拟为时间,导向辛体系,得到Hamilton对偶方程组.将微分形式的有限差分法引入弹性力学极坐标系下径向辛体系,把对偶方程组中的微分方程直接改用差分方程代替,推导出极坐标系下问题的辛差分方程,从而得到一种全新的径向辛体系差分格式.求解方程组,可直接得到位移和应力.编程计算曲梁等算例,结果表明该辛差分格式是有效的,丰富了弹性力学辛体系差分法的内容.     

Conformal invariance and Hojman conserved quantities of canonical Hamilton systems

This paper discusses the conformal invariance by infinitesimal transformations of canonical Hamilton systems. The necessary and sufficient conditions of conformal invariance being Lie symmetrical simultaneously by the action of infinitesimal transformations are given. The determining equations of the conformal invariance are gained. Then the Hojman conserved quantities of conformal invariance by special infinitesimal transformations are obtained. Finally an illustrative example is given to verify the results.     

Exponential convergence rate in entropy

The exponential convergence rate in entroy is studied for symmetric forms, with a special attention to the Markov chain with a state space having two points only. Some upper and lower bounds of the rate are obtained and five examples with precise or qualitatively exact estimates are presented.      

Perturbation to Lie Symmetry and Hojman Exact and Adiabatic Invariants of Generalized Raitzin Canonical Equation of Motion

In this paper, firstly, we get the Hojman exact invariants by Lie symmetry for an undisturbed generalized Raitzin equation of motion. Secondly, we study the perturbation to Lie symmetry of generalized Raitzin canonical equation of motion and get Hojman adiabatic invariants. Lastly, an example is given to illustrate the application of the results.     

On Form Invariance,Lie Symmetry,and Three Kinds of Conserved Quantities of Generalized Lagrange's Equations

In this paper, the form invariance and the Lie symmetry of Lagrange's equations for nonconservative system in generalized classical mechanics under the infinitesimal transformations of group are studied, and the Noether's conserved quantity, the new form conserved quantity, and the Hojman's conserved quantity of system are derived from them. Finally, an example is given to illustrate the application of the result.     

The extended trace identity and its application

The trace identity is extended to the general loop algebra. The Hamiltonian structures of the integrable systems concerning vector spectral problems and the multi-component integrable hierarchy can be worked out by using the extended trace identity. As its application, we have obtained the Hamiltonian structures of the Yang hierarchy, the Korteweg-de--Vries (KdV) hierarchy, the multi-component Ablowitz--Kaup--Newell--Segur (M-AKNS) hierarchy, the multi-component Ablowitz--Kaup--Newell--Segur Kaup--Newell (M-AKNS--KN) hierarchy and a new multi-component integrable hierarchy separately.     

苯与丙烯在β分子筛上吸附行为的蒙特卡罗研究

采用巨正则统计系综蒙特卡罗模拟方法研究了β分子筛上苯与丙烯分子的吸附行为. 由分子筛内吸附质粒子云分布可知, 在100 kPa时, 丙烯在分子筛上的吸附量要远远大于苯的吸附量. 由吸附相互作用能分布来看, 苯与分子筛之间相互作用能比丙烯与分子筛之间的相互作用能更负, 这就使苯分子的吸附相对于丙烯分子稳定. 相对而言, 温度变化对丙烯吸附影响远大于对苯吸附的影响, 如100 kPa时, 温度由298 K升高至443 K导致丙烯分子吸附量明显减少, 由每8个晶胞吸附98个丙烯分子减少到80个; 而对苯分子吸附却没有显著的影响. β分子筛上存在着苯和丙烯的竞争吸附, 并且吸附分子之间存在相互作用使两者与分子筛之间的相互作用能分布改变. 在压力范围1×10－3～5.0 kPa, 不同温度下苯与丙烯在分子筛内吸附等温线的模拟结果表明, 在较高温度、较低压力下丙烯的吸附量要小于苯的吸附量.     

由分子的价电子总数判断中心原子轨道杂化方式的方法

提出了由分子的价电子总数判断中心原子轨道杂化方式的方法,探讨了该方法的理论依据,分析、归纳出了等电子分子系列中原子轨道杂化方式的周期性变化规律。     

Foucault Pendulum-like problems: A tensorial approach

The paper offers a comprehensive study of the motion in a central force field with respect to a rotating non-inertial reference frame. It is called Foucault Pendulum-like motion and it is a generalization of a classic Theoretical Mechanics problem. A closed form vectorial solution to this famous problem is presented. The vectorial time-explicit solution for the classic Foucault Pendulum problem is obtained as a particular case of the considerations made in the present approach. New interesting conservation laws for the Foucault Pendulum-like motion are deduced by using simple differential and vectorial computations. They help to visualize the shape of the trajectories. Exact vectorial expressions for the law of motion and the velocity are also offered. The case of the driven Foucault Pendulum is also analyzed, and a closed form solution is deduced based on the general considerations. In the end, an new tensorial prime integral for the Foucault Pendulum problem is offered. It helps to reveal in a concise form, within a single entity, all the scalar and vectorial conservation laws for the Foucault Pendulum motion.Two important engineering applications to this approach are presented: the motion of a satellite with respect to a rotating reference frame and the Keplerian relative orbital motion. The latter has a great importance in modeling the problems concerning satellite formation flying, satellite constellations and space terminal rendezvous. The classic problem of the harmonic oscillator in an electromagnetic field is also solved by using the instruments presented in this paper.     

New Rational Form Solutions to Coupled Nonlinear Wave Equations

The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown that more novel kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form,and so on.