A new type of conserved quantity of Mei symmetry for the motion of mechanico electrical coupling dynamical systems

We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico-electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico-electrical coupling dynamical systems is obtained. Finally, an example is given to illustrate the application of the results.     

Whittaker方程的场方法

用场方法来求解Whittaker方程.将一个场变量取作为其余场变量和时间的函数并对这个函数建立基本偏微方程.如能求得它的完全积分，那么Whittaker方程的解可由解代数方程来得到. 关键词： 场变量 基本偏微分方程 场方法 积分     

场方法的改进及其在积分Riemann-Cartan空间运动方程中的应用

和Hamilton-Jacobi方法类似,Vujanovi?场方法把求解常微分方程组特解的问题转化为寻找一个一阶拟线性偏微分方程(基本偏微分方程)完全解的问题,但Vujanovi?场方法依赖于求出基本偏微分方程的完全解,而这通常是困难的,这就极大地限制了场方法的应用.本文将求解常微分方程组特解的Vujanovi?场方法改进为寻找动力学系统运动方程第一积分的场方法,并将这种方法应用于一阶线性非完整约束系统Riemann-Cartan位形空间运动方程的积分问题中.改进后的场方法指出,只要找到基本偏微分方程的包含m(m≤ n,n为基本偏微分方程中自变量的数目)个任意常数的解,就可以由此找到系统m个第一积分.特殊情况下,如果能够求出基本偏微分方程的完全解(完全解是m=n时的特例),那么就可以由此找到≤系统全部第一积分,从而完全确定系统的运动.Vujanovi?场方法等价于这种特殊情况.     

完整非保守系统Raitzin正则运动方程的积分因子和守恒定理

提出了经典非保守动力学系统守恒定律构成的一般途径.首先,给出积分因子的定义.其次,详细地研究了守恒量存在的必要条件,建立了完整非保守系统Raitzin正则运动方程的守恒定理及其逆定理,并举例说明结果的应用 关键词： 完整系统 Raitzin正则方程 积分因子 守恒定律     

Potential method of integration for solving the equations of mechanical systems

This paper is intended to apply a potential method of integration to solving the equations of holonomic and nonholonomic systems. For a holonomic system, the differential equations of motion can be written as a system of differential equations of first order and its fundamental partial differential equation is solved by using the potential method of integration. For a nonholonomic system, the equations of the corresponding holonomic system are solved by using the method and then the restriction of the nonholonomic constraints on the initial conditions of motion is added.     

Towards the continuum coupling in nuclear lattice effective field theory I: A three-particle model

Weakly bound states often occur in nuclear physics. To precisely understand their properties, the coupling to the continuum should be worked out explicitly. As the first step, we use a simple nuclear model in the continuum and on a lattice to investigate the influence of a third particle on a loosely bound state of a particle and a heavy core. Our approach is consistent with the Lüscher formalism.     

非线性非完整系统Raitzin正则方程的Hojman守恒定理

利用时间不变的无限小变换下的Lie对称性，研究非线性非完整系统Raitzin正则方程的Hojman守恒定理.列出系统的运动微分方程.建立时间不变的无限小变换下的确定方程.给出系统的Hojman守恒定理，并举例说明结果的应用. 关键词： 非线性非完整系统 Raitzin正则方程 Lie对称性 确定方程 Hojman守恒 定理     

Noether conserved quantities and Lie point symmetries of difference Lagrange--Maxwell equations and lattices

This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems, which leave invariant the set of solutions of the corresponding difference scheme. This approach makes it possible to devise techniques for solving the Lagrange--Maxwell equations in differences which correspond to mechanico-electrical systems, by adapting existing differential equations. In particular, it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical systems. As an application, it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone.     

基于多项式混沌方法的场线耦合响应不确定度量化

在传输线场线耦合的计算中,由于辐射场可能从不同方向入射,入射方位角和入射仰角会在一定范围内变化,可以将其看作不确定变量,因此传输线的响应也呈现出不确定性。针对输入参数服从非典型分布的情况,应用多项式混沌方法对传输线场线耦合频域响应进行不确定度量化。结合入射方位角和仰角的物理意义,给出其服从的分布类型并构建相应的正交多项式基底,并对该模型的传输线方程进行多项式混沌展开。最后结合含两个不确定参数的传输线场线耦合算例,给出远端电流响应的统计信息,对比蒙特卡罗方法,验证了该方法的正确性和高效性。     

Time-dependent molecular fields created by the interaction of an external electro-magnetic field with a molecular system: the derivation of the wave equations

This article continues a previous study (Int. J. Quantum Chem. 114, 1645 (2014)) in which is presented a theory that discusses the possibility to induce a novel field – to be called molecular field – via the interaction of an external electro-magnetic (EM) field and a molecular system. Assuming the molecular system is made up of two coupled adiabatic states the theory leads from three time-space curl equations and one time-space divergence equation to a set of decoupled wave equations usually encountered for fields. In the present study, wave equations are derived for an external field having two features: (1) the field intensity is relatively high enough; (2) the duration of the interaction is short enough.

For this situation, the study reveals that the just mentioned interaction creates two fields that coexist within a molecule: one is just a scalar EM field essentially identical to the external EM field and the other, a vectorial field, produced by the non-adiabatic coupling terms. In addition, we mention that the wave velocities related to these two fields are identical to the wave velocity, c, of the external EM field.     

海-气耦合动力系统的改进变分迭代解法

研究了一个描述厄尔尼诺和南方涛动振荡物理机理的海-气耦合动力系统.利用改进变分迭代方法 (MVIM)简捷地得到了该非线性模型近似解的展开式.通过与特殊情形下模型精确解的比较,说明获得的MVIM 近似解具有非常好的准确度.     

Effects of quantum coupling on the performance of metal-oxide-semiconductor field transistors

Based on the analysis of the three-dimensional Schrödinger equation, the effects of quantum coupling between the transverse and the longitudinal components of channel electron motion on the performance of ballistic MOSFETs have been theoretically investigated by self-consistently solving the coupled Schrödinger-Poisson equations with the finite-difference method. The results show that the quantum coupling between the transverse and the longitudinal components of the electron motion can largely affect device performance. It suggests that the quantum coupling effect should be considered for the performance of a ballistic MOSFET due to the high injection velocity of the channel electron.     

Variational principle and dynamical equations of discrete nonconservative holonomic systems

By analogue with the methods and processes in continuous mechanics, a Lagrangian formulation and a Hamiltonian formulation of discrete mechanics are obtained. The dynamical equations including Euler--Lagrange equations and Hamilton's canonical equations of the discrete nonconservative holonomic systems are derived on a discrete variational principle. Some illustrative examples are also given.     

Quantum coherence in A-three-level system driven by bichromatic coupling field

<正>We present a theoretical study of quantum coherent effects in a A-three-level system with a strong bichromatic coupling field and a weak probe field.When one component of the strong bichromatic coupling field is resonant with a corresponding transition and the other is detuning with an integer fraction of the Rabi frequency of the resonant field, the absorption spectrum exhibits a series of symmetrical doublets.While two frequencies of the strong bichromatic coupling field are symmetrically detuned from the transition,the position and the relative intensity of the absorption peak are both affected by the coupling field intensity and detuning.An explanation of the spectrum is given in term of the dressed-state formalism.     

Integrating factors and conservation theorems for Hamilton‘s canonical equations of motion of variable mass nonholonmic nonconservative dynamical systems

We present a general approach to the construction of conservation laws for variable mass noholonmic nonconservative systems.First,we give the definition of integrating factors,and we study in detail the necessary conditions for the existence of the conserved quantities,Then,we establish the conservatioin theorem and its inverse theorem for Hamilton‘s canonical equations of motion of variable mass nonholonomic nonocnservative dynamical systems.Finally,we give an example to illustrate the application of the results.     

Equations of motion from field equations and a gauge-invariant variational principle for the motion of charged particles

New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is proposed. It differs from the standard, gauge-dependent, first-order Lagrangian by boundary terms only. A new method of deriving equations of motion from field equations is developed. When applied to classical electrodynamics, this method enables us to obtain unambiguously the above, second-order Lagrangian from the general energy-momentum conservation principle.     

Quantum coherence in λ-three-level system driven by bichromatic coupling field

We present a theoretical study of quantum coherent effects in a λ-three-level system with a strong bichromatic coupling field and a weak probe field. When one component of the strong bichromatic coupling field is resonant with a corresponding transition and the other is detuning with an integer fraction of the Rabi frequency of the resonant field, the absorption spectrum exhibits a series of symmetrical doublets. While two frequencies of the strong bichromatic coupling field are symmetrically detuned from the transition, the position and the relative intensity of the absorption peak are both affected by the coupling field intensity and detuning. An explanation of the spectrum is given in term of the dressed-state formalism.     

多导体传输线高频场线耦合渐近法分析

基于理想地面上单导体传输线渐近法,提出了改进的多导体传输线渐近法。与已有多导体传输线渐近法相比,所提方法步骤简单,求解效率高。利用所提方法计算电磁波与不同结构多导体传输线网络之间的耦合,结果与全波分析方法计算结果吻合很好。在此基础上,分析了多导体传输线导线间距对沿线感应电流的影响。结果表明,随着导线间距变化,矩形网络和平行网络沿线感应电流波形变化趋势不同,且当间距大于一个波长后,平行网络和理想地面上相同结构的单导线具有相同的沿线感应电流。     

Variational iteration method for solving integro-differential equations

In this Letter, the variational iteration method is applied to solve integro-differential equations. Some examples are given to illustrate the effectiveness of the method, the results show that the method provides a straightforward and powerful mathematical tool for solving various integro-differential equations.     

Exact solutions for nonlinear evolution equations using Exp-function method

In this Letter, the Exp-function method is used to construct solitary and soliton solutions of nonlinear evolution equations. The Klein-Gordon, Burger-Fisher and Sharma-Tasso-Olver equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations.