广义Birkhoff系统的Birkhoff对称性与守恒量

研究广义Birkhoff系统的Birkhoff对称性问题,并给出此情形下相应的守恒量.将力学系统的等效Lagrange函数的一个定理推广到广义Birkhoff系统,证明了在一定条件下与两组动力学函数B,R_μ,Λ_μ和B,R_μ,Λ_μ分别给出的广义Birkhoff方程相关联的矩阵Λ 关键词： 广义Birkhoff系统 Birkhoff对称性 守恒量 矩阵迹     

相对论性力学系统的Birkhoff对称性与守恒量

提出了相对论性力学系统的一种新的对称性,并给出了此对称性导致的守恒量.提出了相对论性力学系统的Birkhoff对称性,即对应于相对论性力学系统的一组Birkhoff动力学函数的运动微分方程的解都满足从另一组Birkhoff动力学函数得到的运动微分方程.证明了与两组Birkhoff动力学函数分别给出的相对论性Birkhoff方程相关联的系数矩阵的各次幂的迹是系统的一个守恒量,从而将Currie和Saletan提出的力学系统的等效Lagrange函数定理拓展到了相对论性Birkhoff动力学系统.给出了两个例子以说明结果的正确性.     

Birkhoff系统约化的Routh方法

研究Birkhoff系统的约化.首先,列出系统的运动微分方程及其循环积分;其次,构造Birkhoff系统的Routh函数组,利用循环积分约化Birkhoff系统的运动微分方程,并使约化后的动力学方程仍保持Birkhoff方程的形式;最后,举例说明结果的应用. 关键词： Birkhoff系统 约化 循环积分     

广义Birkhoff系统的一类积分

将Birkhoff方程添加一附加项成为广义Birkhoff方程.将Birkhoff方程的一类积分推广并应用于广义Birkhoff方程.举例说明结果的应用. 关键词： Birkhoff方程 广义Birkhoff方程 积分     

相对论Birkhoff系统动力学研究

给出相对论系统的Birkhoff函数和Birkhoff函数组、Pfaff作用量、PfaffBirkhoff原理、Birkhoff方程;研究相对论动力学系统的Birkhoff表示方法;根据在无限小变换下相对论Pfaff作用量的不变性和相对论Birkhoff方程的不变性,得到相对论Birkhoff系统的Noether对称性理论和Lie对称性理论;研究相对论Birkhoff系统的代数结构和Poisson积分方法. 关键词： 相对论 Birkhoff系统 Noether对称性 Lie对称性 代数结构 Poisson积分     

Birkhoff系统的Hojman定理的几何基础

研究了Birkhoff系统的Hojman定理的几何基础.建立了系统的运动微分方程和Hojman守恒 定理，利用现代微分几何给出了Birkhoff系统的Hojman定理的一个证明. 关键词： Birkhoff系统 Hojman定理 对称性 微分几何     

相对论性Birkhoff系统的Lie对称性和守恒量

给出相对论性Birkhoff系统的Pfaff-Birkhoff原理和Birkhoff方程.由微分方程在无限小变换下的不变性,定义相对论性Birkhoff系统无限小变换生成元,建立Lie对称的确定方程,得到结构方程和守恒量.并研究该系统的Lie对称性逆问题.给出实例以说明结果的应用. 关键词：     

构造Birkhoff函数（组）的待定张量法

研究力学系统Birkhoff函数（组）的构造方法．基于自伴随条件和线性偏微分方程组的可积性条件给出构造Birkhoff函数（组）的待定张量法．举例说明结果的应用．     

转动系统相对论性Birkhoff动力学的基本理论

建立转动系统相对论性Birkhoff动力学的基本理论,给出其Birkhoff函数和Birkhoff函数组、Pfaff作用量、Pfaff-Birkhoff原理、Pfaff-Birkhoff-D’Alembert原理,以及Birkhoff方程.并研究转动系统相对论性Lagrange力学、Hamilton力学与转动系统相对论性Birkhoff动力学之间的关系,证明完整保守、完整非保守转动相对论系统都可纳入转动相对论Birkhoff系统 关键词： 转动系统 相对论 Birkhoff动力学 变分原理     

Birkhoff系统的守恒量与稳定性

利用Birkhoff系统的守恒量来研究系统的稳定性.如果守恒量的组合能够成为Liapunov函数，便可用来研究系统的平衡稳定性和运动稳定性. 关键词： Birkhoff系统 守恒量 Liapunov稳定性     

事件空间中Birkhoff系统的参数方程及其第一积分

研究事件空间中Birkhoff系统动力学.在(2n+1)维事件空间中,建立了Birkhoff系统的Pfaff-Birkhoff-d'Alembert原理和Birkhoff参数方程,研究了方程的第一积分,给出了第一积分及其存在条件. 关键词： Birkhoff系统 事件空间 参数方程 第一积分     

Poisson theory and integration method of Birkhoffian systems in the event space

<正>This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space.The Birkhoff's equations in the event space are given.The Poisson theory of the Birkhoffian system in the event space is established.The definition of the Jacobi last multiplier of the system is given,and the relation between the Jacobi last multiplier and the first integrals of the system is discussed.The researches show that for a Birkhoffian system in the event space,whose configuration is determined by(2n + 1) Birkhoff's variables,the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known.An example is given to illustrate the application of the results.     

Birkhoff意义下Hénon-Heiles方程的离散变分计算

在Birkhoff意义下研究了非线性不可积Hamilton系统——Hénon-Heiles方程的离散变分计算方法,并和辛算法及Runge-Kutta方法相比较,说明在Birkhoff意义下采用离散变分算法研究非线性不可积系统的动力学行为是合理和可行的. 关键词： Hénon-Heiles方程 离散变分方法 自治Birkhoff方程     

Generalized energy integral and reduction of rotational relativistic Birkhoffian system

We study the order reduction method of the rotational relativistic Birkhoffian equations.For a rotational relativistic autonomous Birkhoffian system,if the conservative law of the Birkhoffian holds,the conservative quantity can be called the generalized energy integral.Through the eneralized energy integral,the order of the system can be reduced.If the rotational realtivistic Birkhoffian system has a generalized energy integral,then the Birkhoffian equations can be reduced by at least two degrees and the Birkhoffian form can be kept.An example is given to illustrate the application of the result.     

Cyclic integrals and reduction of rotational relativistic Birkhoffian system

The order reduction method of the rotational relativistic Birkhoffian is studied.For a rotational relativistic Birkhoffian system.the cyclic integrals can be found by using the perfect differential method.Through these cyclic integrals,the order of the system can be reduced.If the rotational relativistic Birkhoffian system has a cyclic integral,then the Birkhoffian equations can be reduced at least two degrees and the Birkhoffian form can be kept.An example is given to illustrate the application of the results.     

Thermal transport property of Ge34 and d-Ge investigated by molecular dynamics and the Slack’s equation

In this study,we evaluate the values of lattice thermal conductivity κ L of type II Ge clathrate (Ge 34) and diamond phase Ge crystal (d-Ge) with the equilibrium molecular dynamics (EMD) method and the Slack's equation.The key parameters of the Slack's equation are derived from the thermodynamic properties obtained from the lattice dynamics (LD) calculations.The empirical Tersoff's potential is used in both EMD and LD simulations.The thermal conductivities of d-Ge calculated by both methods are in accordance with the experimental values.The predictions of the Slack's equation are consistent with the EMD results above 250 K for both Ge34 and d-Ge.In a temperature range of 200-1000 K,the κ L value of d-Ge is about several times larger than that of Ge 34.     

Letter: Solutions of All One-Dimensional Wave Equations with Time Independent Potential and Separable Variables

Solutions, in terms of special functions, of all wave equations u _xx – u _tt = V(x) u(t,x), characterised by eight inequivalent time independent potentials and by variables separation, have been found. The real valueness and the properties of the solutions produced by computer algebra programs are not always manifest and in this work we provide ready to use solutions. We discuss especially the potential (m ₁ + m ₂ sinh x)cosh^–2x. Such potential approximates the Schwarzschild black hole potential and its use for determining black holes quasi-normal modes is hinted to.     

Analytical and numerical study of coupled atomistic-continuum methods for fluids

The stability and convergence rate of coupled atomistic-continuum methods are studied analytically and numerically. These methods couple a continuum model with molecular dynamics through the exchange of boundary conditions in the continuum-particle overlapping region. Different coupling schemes, including velocity–velocity, flux–velocity, velocity–flux and flux–flux, are studied. It is found that the velocity–velocity and flux–velocity schemes are stable. The flux–flux scheme is weakly unstable. The stability of the velocity–flux scheme depends on the parameter T_c which is the length of the time interval between successive exchange of boundary conditions. It is stable when T_c is small and unstable when T_c is large. For steady-state problems, the flux–velocity scheme converges faster than the other coupling schemes.     

The sub master equation

Three postulates are proposed concerning the probabilistic dynamics of chemically reactive systems: the occurrence of the elementary event is a random variable characterized by a Poisson process; the state of the chemical system is a multivariate random variable characterized by a Markov process; the identity of any chemical species in the system is an independent random variable. These postulates when applied to chemically reactive systems in a uniform manner lead to a hierarchy of equations describing in detail how eachk subpopulation varies with time. By summing over all permutations of the equation forf _n ⁽ⁿ⁾ (e ₁, ...,e _n ;t) we obtain the usual master equation. This paper focuses on the simple isomerization reaction.     

P–V–T equation of state of rhodium oxyhydroxide

A high pressure X-ray diffraction study of RhOOH was carried out up to 17.44?GPa to investigate the compression behavior of an oxyhydroxide with an InOOH-related structure. A fit to the third-order Birch–Murnaghan equation of state gave K₀?=?208?±?6?GPa, and K′?=?9.4?±?1.3. The temperature derivative of the bulk modulus was found to be ?K/?T?=??0.06?±?0.02?GPa K^?1. The refined parameters for volume thermal expansion were α₀?=?2.7?±?0.3?×?10^?5 K^?1; α₁?=?1.7?±?1.1?×?10^?8 K^?2 in the polynomial form (α(T)?=?α_0?+?α₁(T?300)). Our results show that RhOOH is very incompressible, and has a higher bulk modulus than other InOOH-structured oxyhydroxides (e.g. δ-AlOOH, ε-FeOOH, and γ-MnOOH).