Nonlinear least-squares analyses of complex impedance and admittance data for solid electrolytes

A nonlinear least-squares curve fitting technique, suitable for use with a laboratory minicomputer, is described for the analysis of a complex impedance (admittance) spectrum in which distortions of the various shapes constituting the complex plane plot occur because of overlapping time constants. With this technique, estimates of the parameter values occurring in an equivalent circuit are first obtained by a geometrical-fitting procedure and these are then used as the initial parametric values in a complex least-squares method which simultaneously fits the real and imaginary parts of the impedance (admittance) to a model (equivalent circuit), thereby yielding best-fit values of the circuit parameters as well as their confidence intervals. The method is illustrated by analyzing: (1) artificial, computer-generated impedance (admittance) data constructed for some simple RC circuits commonly used to model solid electrolyte behavior; and (2) measured admittance response of the fast sodium ion conductor NASICON at 486 K.     

跨音速定常势流计算中的解不唯一问题

本文采用近似因式分解(AF2)方法,数值求解二元跨音速小扰动速势方程。大量的数值实验表明:1.选取不同的松驰因子或加速收敛参数可能得到不唯一解。2.选取不同的初场,无论是采用Murman-Cole守恒或非守恒格式,还是采用Engquist-Osher格式,都可能得到不唯一解。     

Exact solutions of a Fokker-Planck equation

Exact explicit solutions are given for a one-dimensional Fokker-Planck equation with a particular potential form involving hyperbolic functions. This potential contains four arbitrary parameters that can be chosen so that the potential is bistable. The solutions also contain parameters that can be chosen so that the initial distribution is approximately Gaussian, centered either at the unstable potential maximum or in the neighborhood of the secondary minimum. The use of the solutions to approximate solutions for other potentials is considered.     

Infinite series symmetry reduction solutions to the modified KdV--Burgers equation

From the point of view of approximate symmetry, the modified Korteweg--de Vries--Burgers (mKdV--Burgers) equation with weak dissipation is investigated. The symmetry of a system of the corresponding partial differential equations which approximate the perturbed mKdV--Burgers equation is constructed and the corresponding general approximate symmetry reduction is derived; thereby infinite series solutions and general formulae can be obtained. The obtained result shows that the zero-order similarity solution to the mKdV--Burgers equation satisfies the Painlevé II equation. Also, at the level of travelling wave reduction, the general solution formulae are given for any travelling wave solution of an unperturbed mKdV equation. As an illustrative example, when the zero-order tanh profile solution is chosen as an initial approximate solution, physically approximate similarity solutions are obtained recursively under the appropriate choice of parameters occurring during computation.     

贯通导体及其电路对金属腔体内部电磁场的影响

为研究贯通导体及其负载电路对金属腔体内部电磁场的影响,建立了不同贯通导体端接负载模型,使用电磁仿真软件CST进行仿真,利用GTEM室、矢量网络分析仪、功率放大器、ETS电场探头组建实验测试系统,验证了仿真结果的正确性,揭示了贯通导体及其电路对金属腔体内部电磁场的影响规律。研究结果表明:腔体内部电磁场同时受到贯通导体与腔体谐振的影响,在谐振频点干扰场强取得极大值,屏蔽效能取得极小值甚至为负值。贯通导体端接负载不接地与贯通导体两端开路情形相似,贯通导体端接负载直接接地时内部场显著降低,谐振频点降低,贯通导体端接负载浮点接地时内部场变化规律低频时与开路模型相似,高频时与直接接地模型相似。贯通导体端接负载的电阻值、电容值也会影响腔体的内部场。     

The effect of transmission lines and switching action on theelectrical signals in a powerful capacitive discharge

A numerical model for the equivalent electrical circuit of a capacitive discharge that includes the effects of finite closure time of switches and finite transit time in the transmission line is presented. An approximate analytical method to predict the oscillations that can be excited in the circuit is developed. The model yields complex behavior over time of the magnitudes of currents and voltages in pulsed circuits in the simple circuit configurations studies. Some of the oscillations predicted by the calculations admit simple physical interpretations in limiting cases (and are then predictable without the need of complex calculations); however, the rest of the observed features are not amenable to easy interpretation. The numerical solutions of the model are compared with experimental signals measured in a plasma focus device. Good agreement with many of the observed features is noted. The model can be extended easily to other types of circuits (Marx generators, Blumlein lines, etc.)     

大平板瞬态热传导问题的一种新的近似解法

１引言大平板瞬态热传导问题有着广泛的工程应用背景。对于复杂的初边值条件或含内热源问题,以及工程上常见的多层复合平壁对象,分析求解难度很大甚至无法求解。在此类情况下往往采用数值方法。但是单纯的数值解不便于理解影响该问题的各种参数的物理意义。因此,各种近似分析方法得到了发展［１,２］。但在近似精度上,往往难以对整个时间坐标范围都达到较高的精度,这就使得近似解更多地局限于定性分析。此外,对于不同的初边值条件或含内热源问题,近似解的形式相异,降低了解的通用性。增加了求解的工作量。本文提出一种基于矩阵理论…     

Significant parameters affecting a lightning stroke to a horizontal conductor

This paper studies different parameters affecting a lightning stroke to a horizontal conductor. An electromagnetic model has been constructed to consider the influences of different lightning and horizontal conductor parameters and ambient conditions on the lateral striking distance. The results show that lightning leader parameters, horizontal conductor voltage, horizontal conductor height, and ground slope have a series effect on the lateral striking distance. Based on the results, recommendations are made to decrease the lightning stroke to the horizontal conductor.     

Direct Perturbation Method for Derivative Nonlinear Schrödinger Equation

We extend Lou's direct perturbation method for solving the nonlinear Schrödinger equation to the case of the derivative nonlinear Schrödinger equation (DNLSE). By applying this method, different types of perturbation solutions are obtained. Based on these approximate solutions, the analytical forms of soliton parameters, such as the velocity, the width and the initial position, are carried out and the effects of perturbation on solitons are analyzed at the same time. A numerical simulation of perturbed DNLSE finally verifies the results of the perturbation method.     

忆阻电路降维建模与特性分析

通过对蔡氏忆阻电路的数学建模分析,提出了忆阻电路动力学建模的降维问题.以包含两个磁控忆阻器的忆阻电路为例,进行了忆阻电路降维建模,由此建立了一个三维系统模型.基于该模型,分析了忆阻电路的平衡点和稳定性,研究了电路参数变化时忆阻电路的动力学特性.进一步,对包含两个磁控忆阻器的忆阻电路常规模型的分析结果和其降维模型的分析结果进行了比较.结果表明:忆阻电路降维模型的维数只与电容器的数量和电感器的数量有关,而与忆阻器的数量无关;当电路参数变化时忆阻电路存在分岔模式共存等非线性现象;降维建模降低了系统建模复杂度,有利于系统的动力学特性分析,但消除了忆阻器内部状态变量的初始条件对忆阻电路动力学特性的影响.     

单周期控制Cuk功率因数校正变换器中的中尺度不稳定现象分析

基于单周期控制的自治性,建立了描述单周期控制Cuk功率因数校正(PFC)变换器动力学行为的非线性状态平均模型.在此基础上,采用谐波平衡法得出了该系统周期平衡态的近似解析表达式,继而通过判定Floquet乘子的变化趋势,准确地预测了该变换器首次失稳时分岔点的位置和类型,揭示了系统出现中尺度不稳定现象的物理机理.研究结果表明,该变换器周期闭轨稳定性的丧失,即Neimark-Sacker分岔的发生是最终导致中尺度振荡现象产生的根本原因.最后,电路实验验证了理论分析的正确性.这些研究结果不仅揭示了单周期控制CukPFC变换器中的中尺度分岔行为的本质,而且为系统电路参数的设计提供了理论依据.     

Conformal Invariant Asymptotic Expansion Approach for Solving (3+1)-Dimensional JM Equation

The (3+1)-dimensional Jimbo-Miwa (JM) equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new (3+1)-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.     

带状电缆的直流X射线辐照响应

对真空环境下带状电缆模型直流X射线辐照响应进行了实验和数值模拟研究;研制了电缆直流X射线辐照实验系统;使用蒙特卡罗模拟软件计算了直流X光机产生的X射线能谱、通量等参数;建立了带状电缆X射线辐照响应一维计算模型,该计算模型包括电缆导体与介质层间隙和介质层电导率模型。实验测量了两个带状电缆模型的直流X射线辐照响应电流波形,并对其进行了数值模拟。结果显示,在一定的电缆导体与介质层间隙大小假设条件下,采用带状电缆X射线辐照响应计算模型计算的结果与实验测量结果在波形特征和绝对幅度方面比较接近,说明了利用该模型描述电缆直流X射线辐照响应具有其合理性。     

Quantum Theory of Vibron Soliton

A quantum mechanical treatment of Takeno model for energy transport in protein is presented and the cubic anharmonicity of the hydrogen-bonded interaction is also taken into account. Under the continuum approximation, two coupled nonlinear differential equations are obtained, and then exact and approximate solitary wave solutions are found. The ideal parameters for protein are used to show whether the soliton solutions can exist for real protein molecules.     

Approximate Symmetries and Infinite Series Symmetry Reduction Solutions to Perturbed Kuramoto-Sivashinsky Equation

Starting from Lie symmetry theory and combining with the approximate symmetry method, and using the package LieSYMGRP proposed by us, we restudy the perturbed Kuramoto-Sivashinsky （KS） equation. The approximate symmetry reduction and the infinite series symmetry reduction solutions of the perturbed KS equation are constructed. Specially, if selecting the tanh-type travelling wave solution as initial approximate, we not only obtain the general formula of the physical approximate similarity solutions, but also obtain several new explicit solutions of the given equation, which are first reported here.     

A new approach for modelling the damped Helmholtz oscillator:applications to plasma physics and electronic circuits

In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.     

一种二次型忆阻器四阶混沌电路

由HP实验室研制的无源忆阻器得到的荷控二次型忆阻器模型,与有源磁控分段线性和三次光滑忆阻器模型相比,更符合实际.利用此模型并基于蔡氏混沌电路演化而来的拓扑对偶结构设计了一种新型忆阻器四阶混沌电路.理论分析、仿真及电路实现表明,该电路具有依赖于忆阻器初始状态的复杂动力学行为,也会产生随时间和系统参数变化的状态转移等非线性动力学现象,在相轨图中出现"涡眼"和"环眼".     

APPROXIMATE ANALYTICAL SOLUTIONS FOR PRIMARY CHATTER IN THE NON-LINEAR METAL CUTTING MODEL

This paper considers an accepted model of the metal cutting process dynamics in the context of an approximate analysis of the resulting non-linear differential equations of motion. The process model is based upon the established mechanics of orthogonal cutting and results in a pair of non-linear ordinary differential equations which are then restated in a form suitable for approximate analytical solution. The chosen solution technique is the perturbation method of multiple time scales and approximate closed-form solutions are generated for the most important non-resonant case. Numerical data are then substituted into the analytical solutions and key results are obtained and presented. Some comparisons between the exact numerical calculations for the forces involved and their reduced and simplified analytical counterparts are given. It is shown that there is almost no discernible difference between the two thus confirming the validity of the excitation functions adopted in the analysis for the data sets used, these being chosen to represent a real orthogonal cutting process. In an attempt to provide guidance for the selection of technological parameters for the avoidance of primary chatter, this paper determines for the first time the stability regions in terms of the depth of cut and the cutting speed co-ordinates.     

Evolution of two-dimensional lump nanosolitons for the Zakharov-Kuznetsov and electromigration equations

The evolution of lump solutions for the Zakharov-Kuznetsov equation and the surface electromigration equation, which describes mass transport along the surface of nanoconductors, is studied. Approximate equations are developed for these equations, these approximate equations including the important effect of the dispersive radiation shed by the lumps as they evolve. The approximate equations show that lump-like initial conditions evolve into lump soliton solutions for both the Zakharov-Kuznetsov equation and the surface electromigration equations. Solutions of the approximate equations, within their range of applicability, are found to be in good agreement with full numerical solutions of the governing equations. The asymptotic and numerical results predict that localized disturbances will always evolve into nanosolitons. Finally, it is found that dispersive radiation plays a more dominant role in the evolution of lumps for the electromigration equations than for the Zakharov-Kuznetsov equation.