关于电路系统与力学系统某些相似性的探讨

<物理通报>2001年第7期发表的<某些力学系统与电路系统的相似性>,该文作者的出发点是将力学中的质点与电容元件相类比,认为f外、m、v质分别与iC、C、uC相对应;将弹簧与电感元件相类比,认为f弹、1/k、υ弹分别与iL、L、uL相对应,并且认为质点的动能对应于电容的电场能量,弹簧的势能对应于电感的磁场能量.本文通过对电路系统和力学系统特性的分析,提出不同的类比方法以供广大读者探讨.     

力学系统的二阶梯度表示

研究力学系统运动微分方程的梯度表示以及二阶梯度表示. 将完整和非完整力学系统的微分方程在正则坐标下表出. 给出系统成为梯度系统以及二阶梯度系统的条件. 举例说明结果的应用.     

求解电路系统的另一途径

本文用分析力学的方法，取电荷为广义坐标，电流为广义速度，得到电路系统的功率函数表达式，该函数的极值，就是电路系统的唯一解．     

完整力学系统的统一对称性

函数对时间的全导数采用沿系统的运动轨线的方式, 建立了完整力学系统的统一对称性的定义和判据. 得到了由统一对称性导致的Noether守恒量、Hojman守恒量和新型守恒量. 举例说明结果的应用.     

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.     

相对论力学系统的形式不变性与Noether对称性

研究相对论力学系统的形式不变性与Noether对称性，给出相对论力学系统的Noether定理， 以及形式不变性的定义、判据和守恒量，得到形式不变性和Noether对称性的关系，并举例 说明结果的应用- 关键词： 相对论 力学系统 形式不变性 Noether对称性     

相对论力学系统的形式不变性与Lie对称性

研究相对论力学系统的形式不变性和Lie对称性.给出相对论力学系统在无限小变换下形式不变性和Lie对称性的定义、判据和守恒量,得到形式不变性和Lie对称性的关系,并举例说明结果的应用. 关键词： 相对论 力学系统 形式不变性 Lie对称性     

基于全局灵敏度的电路系统激励与测点优选

针对模拟电路系统级故障诊断问题,提出一种基于全局灵敏度的测试点与测试频率优选方法。利用Pspice软件进行参数分析,避免了电路的拓扑分析和冗繁的计算过程,节省了时间开销,综合考虑元件参数变化影响,定义了网络全局灵敏度的概念,并以此为依据比较不同频率下测点的故障诊断能力,实现测点与测试频率的优选。通过实验仿真验证了方法的有效性,结果表明新方法提高了对系统的故障识别率。     

相空间中力学系统的Lie-Mei对称性

研究了相空间中力学系统的一种新对称性——Lie-Mei对称性及其守恒量. 提出这种新对称性的定义, 给出了系统Lie-Mei对称性的判据, 得到了系统Lie-Mei对称性导致的广义Hojman守恒量和Mei守恒量. 举例说明了结果的应用. 关键词： 相空间 力学系统 Lie-Mei对称性 守恒量     

Connections Between the Thermodynamics of Classical Electrodynamic Systems and Quantum Mechanical Systems for Quasielectrostatic Operations

The thermodynamic behavior is analyzed of a single classical charged particle in thermal equilibrium with classical electromagnetic thermal radiation, while electrostatically bound by a fixed charge distribution of opposite sign. A quasistatic displacement of this system in an applied electrostatic potential is investigated. Treating the system nonrelativistically, the change in internal energy, the work done, and the change in caloric entropy are all shown to be expressible in terms of averages involving the distribution of the position coordinates alone. A convenient representation for the probability distribution is shown to be the ensemble average of the absolute square value of an expansion over the eigenstates of a Schrödinger-like equation, since the heat flow is shown to vanish for each hypothetical state. Subject to key assumptions highlighted here, the demand that the entropy be a function of state results in statistical averages in agreement with the form in quantum statistical mechanics. Examining the very low and very high temperature situations yields Planck's and Boltzmann's constants. The blackbody radiation spectrum is then deduced. From the viewpoint of the theory explored here, the method in quantum statistical mechanics of statistically counting the states at thermal equilibrium by using the energy eigenvalue structure, is simply a convenient counting scheme, rather than actually representing averages involving physically discrete energy states.     

General Volume-Preserving Mechanical Systems

We present the general form of equations that generate a volume-preserving flow on a symplectic manifold M, ) via the highest Euler–Lagrange cohomology. It is shown that for every volume-preserving flow there are some 2-forms that play a similar role to the Hamiltonian in Hamilton mechanics. The ordinary canonical equations are included as a special case with a 2-form 1/(n - 1)H, where H is the corresponding Hamiltonian.     

Some Similarity Reduction Solutions to Two-Dimensional Incompressible Navier-Stokes Equation

We investigate the symmetry reduction for the two-dimensional incompressible Navier Stokes equation in conventional stream function form through Lie symmetry method and construct some similarity reduction solutions. Two special cases in [D.K. Ludlow, P.A. Clarkson, and A.P. Bassom, Stud. Appl. Math. 103 （1999） 183] and a theorem in [S.Y. Lou, M. Jia, X.Y. Tang, and F. Huang, Phys. Rev. E 75 （2007） 056318] are retrieved.     

与下雨相关的几个力学问题

1 雨滴对伞的压力 雨中行进需撑伞挡雨，雨滴会对伞产生一个持续的压力，压力的大小与雨滴的质量、单位体积内雨滴的数量和雨滴的下落速度（大小和方向）有关．     

Some Similarity Reduction Solutions to Two-Dimensional Incompressible Navier-Stokes Equation

We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equation in conventional stream function form through Lie symmetry method and construct some similarity reduction solutions. Two special cases in [D.K. Ludlow, P.A. Clarkson, and A.P. Bassom, Stud. Appl. Math. 103 (1999) 183] and a theorem in [S.Y. Lou, M. Jia, X.Y. Tang, and F. Huang, Phys. Rev. E 75 (2007) 056318] are retrieved.     

Information Between Quantum Systems via POVMs

The concepts of conditional entropy and information between subsystems of a composite quantum system are generalized to include arbitrary indirect measurements (POVMs). Some properties of those quantities differ from those of their classical counterparts; certain equalities and inequalities of classical information theory may be violated. PACS: 03.67.-a.     

Supersymmetry and Integrability in Planar Mechanical Systems

We present an N=2-supersymmetric mechanical system whose bosonic sector, with two degrees of freedom, exhibits the most general possible supersymmetric fourth order potential, including the interesting case of SU(2) Yang–Mills theory. The Painlevé test is adopted to discuss integrability and we focus on the rôle of supersymmetry and parity invariance in two space dimensions for the attainment of integrable or non-integrable models, with some remarks on the chaotic behavior. Our result shows that, for the model studied here, the relationships among the parameters, as imposed by supersymmetry, restrict the parameter space in such a way that the reduction on its non-integrable sector is much more severe than on its integrable sector (especially on the non-separable subset of the latter), thus suggesting that supersymmetry may favor (mainly non-separable) integrability.     

Twin-Bladed Microelectro Mechanical Systems Variable Optical Attenuator

The design and evaluation of a microelectro mechanical systems (MEMS) based variable optical attenuator is reported. The device contains two blades, which are each driven by a separate electrostatic comb microactuator, and move independently to form a variable slit. This device has been fabricated in silicon-on-insulator material which has been back-etched. Electro-mechanical design considerations, including factors to minimise the side instability of the comb drive, are described. Finite element modelling (FEM) of the variable optical attenuator (VOA) is backed up by theoretical results, and the results from the theoretical work verify the findings from the FEM. Optical modelling of the VOA using near field diffraction theory is also reported. Experimentally, the device was driven from 0-34V DC to measure its static characteristics. For dynamic characterisation, the device was operated from 0-28 V AC and its fundamental resonant frequency was measured to be 3 kHz. Optical measurements including wavelength dependent attenuation are also presented.     

On General Volume-Preserving Mechanical Systems via Cohomology

We present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M,ω) via the highest Euler-Lagrange cohomology.It is shown that for every volume-preserving flow there are some 2-forms that play a similar role to the Hamiltonian in the Hamilton mechanics and the ordinary canonical equations with Hamiltonian H are included as a special case with a 2-form Hω/(n-1).     

Synthesized AI LMI-based Criterion for Mechanical Systems

This paper proposes a novel artificial intelligence sythethized controller in the mechanical system which has high speed computation because of the LMI type criterion. The proposed membership functions are adopted and stabilization criterion of the closed-loop T-S fuzzy systems are obtained through a new parametrized LMI (linear matrix) inequality which is rearranged by machine learning membership functions.