求正交曲线坐标系中速度和加速度的解析方法

引入“广义速度”和“广义加速度”的概念，把正交曲线坐标系或的速度加速度简化为广义坐标及其微商的偏导。     

Synchronization and Bifurcation of General Complex Dynamical Networks

In the present paper, synchronization and bifurcation of general complex dynamical networks are investigated. We mainly focus on networks with a somewhat general coupling matrix, i.e., the sum of each row equals a nonzero constant u. We derive a result that the networks can reach a new synchronous state, which is not the asymptotic limit set determined by the node equation. At the synchronous state, the networks appear bifurcation if we regard the constant u as a bifurcation parameter. Numerical examples are given to illustrate our derived conclusions.     

两个不相同系统的广义同步化

采用Temam无穷维动力系统的惯性流形理论，证明了两个不相同的系统能实现广义同步化.在两个系统具有吸收集和吸引子的基础上，通过定义在一个函数类上的压缩映射的不动点得到了广义同步化流形，该流形是Lipschitz光滑流形，而且具有不变性与指数吸引性.数值仿真证实了所建立理论的正确性.     

一类广义Birkhoff系统的广义正则变换

研究一类广义Birkhoff系统的广义正则变换.建立这类广义Birkhoff系统的运动微分方程,得到了该系统的广义正则变换以及保持广义正则变换的条件.最后,举例说明结果的应用.     

A New Conservation Law Derived from Mei Symmetry for the System of Generalized Classical Mechanics

A new conservation theorem derived directly from Mei symmetry of the generalized classical mechanical system is presented. First, the differential equations of motion of the system are established, and the definition and criterion of Mei symmetry for the system of generalized classical mechanics are given, which are based upon the invariance of dynamical functions under irdinitesimal transformations. Second, the condition under which a Mei symmetry can lead to a new conservation law is obtained and the form of the conservation law is presented. And finadly, an example is given to illustrate the application of the results.     

广义系统族的二次稳定与二次镇定

以系统族的方式描述了广义不确定系统的不确定性, 提出了广义系统“广义二次稳定锥”的概念. 利用矩阵不等式, 得到了广义系统族广义二次稳定和广义二次可镇定的充分必要条件. 关键词： 广义系统族 广义二次稳定 广义二次可镇定 矩阵不等式     

A New Generalized Riccati Equation Rational Expansion Method to Generalized Burgers-Fisher Equation with Nonlinear Terms of Any Order

In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order.     

广义Birkhoff系统的两类广义梯度表示

提出了两类广义梯度系统, 即广义斜梯度系统以及具有对称负定矩阵的广义梯度系统. 分别讨论了这两类梯度系统与动力学系统稳定性的关系. 研究了广义Brikhoff系统的两类广义梯度表示, 分别给出条件和表达式. 给出了广义Brikhoff系统稳定性的梯度判别法, 利用广义梯度系统的性质来研究广义Birkhoff系统的稳定性. 并举例说明了方法的应用.     

New exact solitary wave solutions to generalized mKdV equation and generalized Zakharov--Kuzentsov equation

In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov--Kuzentsov equation are constructed by the method of auxiliary equation with function transformation with aid of symbolic computation system Mathematica. The method is of important significance in seeking new exact solutions to the evolution equation with arbitrary nonlinear term.     

也谈一段电流磁场的安培环路定理是否成立?

本文通过全电流定理证明了毕－萨定理．同时也证明了一段传导电流包括其激发的位移电流在内所产生磁场的安培环路定理总是成立的．     

等离子体在任意强度的直流电场中产生电流的过程

通过Fokker-Planck模拟,研究了等离子体在任意强度的直流电场中产生电流的过程以及电子分布函数的演变过程.研究发现,不同强度的电场中等离子体的行为存在着明显的差别.在弱电场中,电流与电场满足Spitzer公式,且电流产生的响应时间约等于撤销电场后电流衰减的弛豫时间;在中等强度的电场中,电子分布函数呈现为静止Maxwell分布和漂移Maxwell分布之和,而且在中等强度或者强直流电场中弛豫时间也将远远大于响应时间.根据电子分布函数的演变规律,推导了一组类似于流体力学方程的公式,这组方程像Spitzer公式一样简便地描述了等离子体中电流与电场的关系,并且对电场强度没有限制.数值模拟显示这组方程比Spitzer公式更适用于等离子体的混合粒子模拟中. 关键词： 等离子体电流 电子分布函数 Fokker-Planck模拟 Spitzer公式     

对《位移电流不激发磁场简例》一文的补充

直接论证了位移电流不激发磁场.     

基于同相第二代电流传输器的网格多涡卷混沌电路研究

通过简化广义Jerk系统,构建了一个三维网格多涡卷混沌系统,利用同相第二代电流传输器(CCII+)设计并实现了该系统的模拟电路,将该电路与传统运放实现的混沌电路进行了对比,发现基于CCII+的混沌电路能在更高频段产生网格多涡卷吸引子,且电路结构更简单,使用器件更少,最后,通过示波器观测到了网格多涡卷混沌吸引子,验证了混沌电路的物理可实现性,电路实验结果与数值仿真结果一致。     

Full current statistics of incoherent "cold electrons"

We evaluate the full current statistics (FCS) in the low-dimensional (1D and 2D) diffusive conductors in the incoherent regime eV>E(Th)=D/L(2), E(Th) being the Thouless energy. It is shown that the Coulomb interaction substantially enhances the probability of big current fluctuations for short conductors with E(Th)>1/tau(E), tau(E) being the energy relaxation time, leading to the exponential tails in the current distribution. The current fluctuations are most strong for low temperatures, provided E(Th) approximately [(eV)(2)/Dnu(2)(1)](1/3) for 1D and E(Th) approximately (eV/g)ln(g for 2D, where g is a dimensionless conductance and nu(1) is a 1D density of states. The FCS in the "hot electron" regime is also discussed.     

氢原子的总电流及其经典对应

定态下氢原子平均电流密度只有一个沿纬线的分量非零,本文在这一结果的基础上计算了氢原子的总电流,发现它与经典力学中行星运动的开普勒定律之间有明确的对应关系．     

夹断开关对“荧光-1”实验装置电流特性的影响

主要探讨了夹断开关对“荧光-1”实验装置输出电流特性的影响,利用Pspice软件对其在装置中起到的作用进行功能建模并分析其参数影响,同时开展初步调试实验并分析多组夹断开关导通性能及其同步性对负载电流的影响。仿真与实验结果表明:夹断开关可有效改善负载电流脉宽,可使脉宽从原有3 μs展宽至100 μs,其导通电阻与电感参数均能明显影响电流幅值与脉宽。由实验波形结合仿真可知,夹断开关实际导通电阻约4 mΩ, 两支路耦合电感分别约为60,125 nH,调试结果验证了夹断开关功能建模的正确性及其对脉宽展宽的有效性。     

Rotational analog of the Hall effect: Coriolis contribution to electric current

A galvanogyroscopic effect which is the rotational analog of the gravitomagnetic Hall effect has been proposed. As a consequence of Ohm’s law in the rotating frame, the effect of the Coriolis force on the conduction current is predicted to give rise to an azimuthal potential differenceV _gg about 10^-3V in a spinning rotor carrying radial electric currenti _r. The potential difference developed by the galvanogyroscopic effect is proportional both to angular velocity Ω and to the electric current.     

光与介质作用下的一种分子电流机制

光与介质分子相互作用是一个活跃的研究领域,新的现象、技术和理论不断出现,原有理论对解释某些新的现象遇到困难.本文应用法拉第电磁感应原理研究了分子中电子云与光波之间的相互作用,提出了在光波作用下介质中存在的一种分子电流机制,这种电流的密度随磁场的时间变化率增加而增大,它不同于介质分子的极化电流和磁化电流.这些工作有助于深入认识光波与介质之间的相互作用.     

Ion current density profiles in negative corona gaps versus EHD confinements

This paper deals with the electric and hydrodynamic confinement of negative ions in a point-to-plane corona discharge gap. Radial ion current density profiles have been measured on the earthed planar electrode, drilled in the axis of the point. The experimental setup is first validated by comparison with the Warburg's law without injected gas flow rate. The gas injected in the gap and blown from the discharge gap through the hole located at the centre of the plane affects neither the electric field close to the point nor the subsequent electric wind. However, it leads to the confinement of ions flux towards the central symmetry axis in the low electric field region up to a critical gas velocity, which for no more effect is measurable. Hence, electro hydro-dynamics confinement of ions can be achieved by limiting the outward radial expansion of ions to increase ion current densities on specific locations close to the low field planar electrode.