非线性LC电路方程的李群分析和精确解

应用李群分析方法、(G'/G )-展开法和幂级数法求解非线性LC电路方程. 通过李 群分析求得了方程的对称. 并且结合李群分析方法、齐次平衡方法和(G'/G )-展开法求得了非线性LC电 路方程的全部(G'/G ) 解. 最后, 又给出了非线性LC电路方程的精确幂级数解.     

(2+1)维色散长波方程组新的无穷序列精确解

为了获得非线性发展方程的无穷序列新精确解, 给出Riccati方程的一些新解和B\"{a}cklund变换以及解的非线性叠加公式, 并Riccati方程与函数变换相结合,借助符号计算系统Mathematica,构造了 (2+1)维维色散长波方程组新的无穷序列精确解. 这些解包括无穷序列类孤子解、无穷序列复合型解等. 这种方法构造非线性发展方程无穷序列精确解领域具有普遍意义.     

Optimal functional expansion for estimation from counting observations

A systematic method to develop approximate nonlinear estimators is presented, in the form of a functional series, for the signal that modulates the rate of a counting process. The estimators are optimal for the given structure and approach the minimum variance (MV) estimator when the approximation order increases. Two kinds of functional series, the iterated integral (II) series and the Fourier-Charlier (FC) series, are used. Product-to-sum formulas for the II and FC functionals are derived. By using the formulas, the MV estimate is projected onto the Hilbert subspaces of the II and the FC series driven by the counting observations with the given index set. The projection results in a Wiener-Hopf type equation for the II kernels and a system of linear algebraic equations for the FC coefficients. The FC series estimator consists of finitely many single Wiener integrals of the counting observations and a nonlinear postprocessor. The nonlinear postprocessor, however, is not memoryless.     

激光大气传输非线性效应数值模拟与分析

对激光通过大气传输的主要非线性过程进行数值模拟，列出大气的流体动力学方程组和与大气互作用的波方程．推导出受激热瑞利散射引起的小扰动不稳定性的波与大气的耦合方程，还对湍流作了处理，依据这些理论基础，编制了一套四维程序，用来模拟热晕及补偿、小扰动不稳定性、热晕与湍流的互作用过程．理论结果和实验十分符合．     

Effect of nonlinear collector capacitance on collector current rise time

The collector capacity, C, of a junction transistor is known to vary as a nonlinear function of the voltage, V, across it. A calculation is made of the collector current rise time of a grounded emitter alloy junction transistor for which C = kV^-1/2. A comparison is then made with linear analyses in which C is assumed to have one of the following constant values. 1) C = Ccc, where Cccis the small signal capacity measured at the collector supply voltage, Vcc. 2) C = 1.52Ccc. This capacity is one which displaces the same charge as the nonlinear capacity as the voltage across it changes from 0-90 per cent of its final value. 3) C - 2Ccc. This capacity is one which displaces the same charge as the nonlinear capacity as the voltage across it changes from 0-100 per cent of its final value. The linear analysis using the latter two capacity values gives 0-90 per cent and 0-100 per cent rise times which are very close to those given by a numerical solution of the nonlinear circuit equation. The usual linear analysis using C = Ccc, on the other hand, is very much in error for predicting rise time. Experimental results show that the 2Cccvalue, in a linear analysis, predicts the 0-100 per cent rise time almost exactly. In addition, analog computer solutions of the nonlinear circuit equation give results almost identical with the shape of the experimental curves.     

Gross-Pitaevskii方程的复行波解

Hyperbolic tangent法是研究非线性微分方程的有力工具,通过利用hyperbolic tangent法得到非线性Gross-Pitaevskii方程的复行波解.     

非线性协调控制系统状态方程的级数解

针对非线性系统,为了合理利用变量间的有益耦合、消除有害的关联,提出了具有扰动补偿的非线性协调控制原则.根据控制原则,建立了非线性协调控制系统的状态方程,基于该方程导出了对于外界扰动的完全补偿条件,进而给出了完全补偿协调控制系统非线性状态方程.采用直接试探法,求得了该方程的任意阶级数解析解,这是一种有效的非线性系统状态方程的近似求解方法.     

Formulas for the distribution of sums of independent exponential random variables

This paper derives a new type of formula for the probability that, among a collection of items with s-independent exponential times to failure, a certain subset of them fails in a given order before a certain time, and all the remaining items survive beyond that time. This formula is in the form of a power series that satisfies a certain constant coefficient linear differential equation with specified initial conditions. This provides an alternative to existing closed-form formulas of the "exponomial" variety, viz., a nonlinear combination of exponential terms, where the coefficients of the exponential terms are polynomials in the mission time. Some results are given which quantify the computation effort required to achieve a specified accuracy using partial sums of the infinite series; a simple example illustrates these results. This approach can be very efficient for system reliability analysis where the product of the mission time and the sum of the failure rates down any path leading to system failure is small. Further work is needed to expand the practical applicability of this approach to cases where some rates are large and/or the mission time is long.     

FDTD analysis of wave propagation in nonlinear absorbing and gainmedia

An explicit finite-difference time-domain (FDTD) scheme for wave propagation in certain kinds of nonlinear media such as saturable absorbers and gain layers in lasers is proposed here. This scheme is an extension of the auxiliary differential equation FDTD approach and incorporates rate equations that govern the time-domain dynamics of the atomic populations in the medium. For small signal intensities and slowly varying pulses, this method gives the same results as frequency-domain methods using the linear susceptibility function. Population dynamics for large signal intensities and the transient response for rapidly varying pulses in two-level (absorber) and four-level (gain) atomic media are calculated to demonstrate the advantages of this approach     

Adaptive Fuzzy Control for Stochastic Nonlinear Systems via Sliding Mode Method

In this paper, an adaptive fuzzy controller is designed for a nonlinear stochastic system to track the given reference via the sliding mode method. The nonlinear stochastic system is modeled by a deterministic nonlinear system with white noise obtained from the derivative of a Wiener process, which eventually generates an Itô differential equation. Compared with existing results, the main advantage is that information of the nonlinear functions is not required. Under the designed controller with the proposed update laws, the tracking error trajectories converge to an arbitrary small region around zero in the mean square norm. Simulations to show the efficiency of the proposed controller are provided.     

非线性RLC电路的频响特性与稳定性分析

针对非线性RLC电路的频响特性和周期解稳定性等问题,建立了电感非线性RLC串联电路的动力学方程。利用谐波平衡法,导出了电感非线性RLC串联电路的频率响应方程,研究了频率响应特性曲线的跳跃和滞后现象及其不产生谐振现象的条件;分析了该电路周期解的稳定性,得出了稳定区和不稳定区的分界线方程;讨论了非线性因素的影响,得出了忽略RLC串联电路的电感非线性因素的条件。     

Determination of nonlinearity from its harmonic response

A simple method is given for determining the equation of an instantaneous single-valued nonlinear characteristic from measurement of the magnitude of its output harmonics in response to a sinusoidal input. The method, which relies on the orthogonality of the Cheby?shev polynomials, gives the nonlinear characteristic as a power series in these polynomials, with the normalised input magnitude as argument. If desired, this can easily be written in terms of powers of the input.     

Synthesis of stable digital sine wave generators

A digital oscillator having a unique limit cycle, independent of the initial conditions, is described. The oscillator is synthesized by discretizing a continuous oscillatory system described by a nonlinear difference-differential equation. Simulation results for a system utilizing a word length ranging from 8 to 12 b are in good agreement with analytical results.     

Nonlinear dynamics of femtosecond optical solitary wave propagationat the zero dispersion point

A perturbed nonlinear Schrodinger equation, describing nonlinear pulse propagation of femtosecond duration in optical fibers at the zero dispersion point, is considered. This equation is reduced to an ordinary differential equation, which is treated by means of Hamiltonian dynamics techniques. Conditions for solitary wave formation, as well as the solutions themselves, namely, a bright soliton, a rarefaction soliton, and a pair of dark solitons, are derived analytically. The shifts of the solitary wave velocity, the angular frequency, and the wavenumber, as well as the peak power required to launch a bright soliton are also obtained. The connection among the point initial conditions of the pulse and the type of solitary wave that can be excited is finally presented     

Design of wave absorber for small conducting sphere

An electromagnetic wave absorber for a small sized conducting sphere is designed by applying the Newton-Raphson method to the eigenfunction series solution for a coated conducting sphere. The parameters for the perfect absorbing condition are the constitutive parameters and the thickness of coating for a given radius of conducting sphere. The wave absorber designed by this method exhibits a superior absorption performance to that designed using flat plate absorber theory     

General nonlinear analysis of second-order oscillators

A general nonlinear analysis of second-order oscillators is presented. The oscillator equation is given in perturbation form, involving a small perturbation parameter, and its periodic solution derived, if any exists, which is calculated using an asymptotic method. Analytical relations between design constraints and circuit parameters are deduced and applied     

Analysis of the harmonic gyrotron traveling wave amplifier

A single nonlinear differential equation is derived for describing the spatial evolution of the wave field in a gyrotron amplifier of the cylindrical guide geometry. This equation is then used to determine the efficiencies and the optimized interaction lengths for gyrotrons operated with TE_N1 modes at the N-th cyclotron harmonic.     

Solitary wave formation through mth-order parametric interaction

Using a solitary wave solution for the Klein-Gordon equation with mth-order nonlinear term, a model of soliton formation is demonstrated in which the nonlinearity mediates the parametric generation of sum and difference frequencies.     

卷筒纸印刷机折页机构运动学方程直接积分解法

针对运动副间隙和轴承滚子变形引起的折页机构非线性动态响应问题,提出刚性杆与弹簧组合假设,建立了折页机构间隙动力学模型.对含二阶偏微分方程组的含间隙折页机构动力学模型,采用非线性系统直接积分法进行求解.非线性系统分析的核心归结为系统状态方程的求解问题,对于一般非线性控制系统,通过引入由状态量、控制量与自变量时间t为坐标构成的"广义状态空间",在广义状态空间处将方程的右端展开为关于时间的Taylor级数,进一步直接积分获得非线性控制系统状态方程关于自变量时间的级数解.以卷筒纸印刷机折页机构这种存在耦合的非线性系统为例,利用本文提出的解法得出了输入量与输出量的解析解,并仿真验证了方法的正确性.     

胶印机齿轮系统非线性模型直接积分解法

卷筒纸印刷机折页机构是一种存在耦合的非线性齿轮系统.运用集中质量法、牛顿第二定律、微分方程及级数理论和方法，考虑变啮合刚度、齿侧间隙、动态传递误差等非线性因素，建立卷筒纸印刷机折页机构齿轮系统单自由度非线性动力学模型.引入由状态量、控制量与自变量时间为坐标构成的"广义状态空间"，将卷筒纸印刷机折页机构齿轮系统动力学模型变为广义状态空间上的系统状态方程.在广义状态空间将方程的右端展开为时间的Taylor级数，进一步直接积分获得非线性控制系统状态方程关于自变量时间的级数解，最终获得状态方程的解析解.使用Matlab软件，对状态方程的解析解进行仿真，得到齿轮转动的角速度与角加速度与时间关系曲线.得到的曲线与实际情况进行对比，验证了动力学模型与状态方程解析解的正确性.