关于变摆长的单摆运动与相关的铅直运动的耦合

研究了一个变摆长单摆运动的例子,在平面极坐标系下给出了描述该运动的二阶微分方程组.采用微分方程高精度数值解法得到了随时间变化的摆角、摆长、摆长变化率以及运动轨迹的数值精确解.在小摆角近似下,采用迭代方法推导出摆角、摆角变化率的一级近似解析表达式和摆长、摆长变化率的二级近似解析表达式.由解析表达式得到的数值结果与数值精确解相比较,二者在前几个摆动周期内相吻合.     

基于三波耦合波方程数值精确解分析外腔高效和频对腔模的影响

基于外部谐振腔可以实现两基频激光的高效和频转换,通常可以采用泵浦不消耗近似(PUA)或小信号近似(SSA)来理论模拟实验结果。然而当基频光功率相近且转换效率较高时,此两种近似的误差就会变得不可接受,然而三波耦合波方程(TWCE)解析解通常需要进行椭圆积分,直接数值求解就变得简单易行。本文首先基于龙格-库塔方法求解准相位匹配下的TWEC,并与PUA和SSA下的解析解进行比较分析,确定了两种近似的适用条件;最后基于该精确数值解结合腔模理论对外腔高效和频对腔模线型的影响进行了研究。     

格栅式回热器换热性能解析解的误差分析

为探究格栅式回热器的换热性能,首先建立了近似的圆管解析模型,并采用数值法验证了圆管解析模型的正确性,数值解和解析解最大均方误差不超过0.025,基于此误差很小。然后分析了格栅式回热器六方管和圆管的温度分布和换热量,并对两种不同结构的温度分布和换热量进行误差分析。结果表明：六方管和圆管温度的最大均方误差为1.8,随着频率的越大,两种等效结构之间的温度误差和换热量误差就越大,圆管解析解和六方管数值解换热量的最大误差不超过0.026,在误差允许范围内用近似的圆管解析模型代替六方管是可行的。     

一维非定常流体力学数值模拟

非线性的流体偏微分方程中的激波间断解是物理中很有挑战的问题,其中的Riemann问题可采用解析的方法求出理论解,但采用近似解的方法进行流体动力学数值模拟也可以有效地追踪和捕捉激波.本文以一维激波管为例,对非定常流体基本方程组采用Roe通量差分裂格式,并进行数值模拟.通过与理论解对比,发现其符合度较好.     

单摆运动周期近似公式的数值推导及修正

运用MATLAB软件,采用数值计算的方法,得出单摆运动周期的两个新的近似公式.同时,对原有文献报道的运用解析方法推导出的近似公式进行比较和修正.     

随机共振问题Fokker-Planck方程的数值研究

本文用有限差分方法对一随机共振的Fokker-Planck方程的主要性质进行了广泛的数值研究。结果表明,当绝热近似条件ω?D△V和小信号近似条件A?1得到满足时,以往的解析近似理论结果与数值结果符合;当驱动强度增加时,则系统表现出明显的决定性非线性振动行为。然而,就随机共振问题本身而言,绝热近似解析理论概括了在双稳系统中发生的随机共振的主要性质。 关键词：     

基于 MAT LA B的强迫振动达芬 方程的非线性幅频响应分析

利用MAT LA B研究了强迫振动达芬( D u f f i n g) 方程的非线性幅频响应特性, 分析了达芬方程非线性幅 频响应近似解析求解和数值求解的方法和步骤, 给出了相应的 MAT LA B求解程序, 并将解析解与数值解结果进行 了比较. 仿真程序和结果能够加深学生对非线性振动相关知识的理解, 提高大学物理及相关力学课程的课堂教学效 果     

基于不可压缩光滑粒子动力学的黏性液滴变形过程仿真

应用基于投影算法的不可压缩光滑粒子动力学(incompressible smoothed particle hydrodynamics, ISPH)法对黏性液滴变形过程进行了数值仿真. 对于张力失稳导致的粒子非物理簇集问题, 采用粒子移位技术加以解决. 为了验证本文ISPH 算法的精度和稳定性, 分别模拟了圆形黏性液滴的拉伸变形过程以及方形液滴的旋转变形过程, 得到了不同时刻液滴内部的压力变化特征, 准确地捕捉了液滴自由面演化过程, 并将数值计算结果与文献中的解析解进行了比较.分析结果表明, 基于投影算法的不可压缩光滑粒子动力学方法结合粒子移位技术, 能够有效地模拟黏性液滴变形过程, 可以得到精确和稳定的结果. 关键词： 不可压缩光滑粒子动力学 黏性液滴 自由面流动 数值仿真     

精确计算非旋波近似下二能级系统的能谱和动力学性质

利用相干态正交化展开法,精确求解了非旋波近似下Jaynes-Cummings模型的能谱和动力学性质.与近似下解析解比较发现,在弱耦合和强耦合区近似解析解与数值精确解符合很好,但在中间耦合区符合较差. 关键词： 相干态正交化展开 非旋波近似 Jaynes-Cummings模型     

一类非线性微分方程的近似解析解

从理论上研究了一类广义扩散方程的求解问题. 利用相似变换和解析拆分技巧给出了求解该类非线性微分方程近似解的一种有效方法, 方程的解可以表示为一个收敛的幂级数. 近似解结果和数值结果非常符合，证明了所提出的方法的准确性和可靠性, 该方法可以用于解决其他科学和工程技术问题. 关键词： 广义扩散方程 非线性边界值问题 解析拆分 近似解析解     

Numerical Complexiton Solutions of Complex KdV Equation

In this paper, we directly extend the applications of the Adomian decomposition method to investigate the complex KdV equation. By choosing different forms of wave functions as the initial values, three new types of realistic numerical solutions: numerical positon, negaton solution, and particularly the numerical analytical complexiton solution are obtained, which can rapidly converge to the exact ones obtained by Lou et al. Numerical simulation figures are used to illustrate the efficiency and accuracy of the proposed method.     

Stochastic response of van der Pol oscillator with two kinds of fractional derivatives under Gaussian white noise excitation

This paper aims to investigate the stochastic response of the van der Pol(VDP) oscillator with two kinds of fractional derivatives under Gaussian white noise excitation.First,the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique.Then,the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution.Finally,the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator.The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order,the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator.An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary.     

Soliton self-frequency shift decelerated by self-steepening

Self-steepening of ultrashort light pulses is shown to reduce the soliton self-frequency shift (SSFS) induced by the Raman effect in an optical fiber. We derive an analytical expression for the SSFS that conserves the number of photons and allows the SSFS to be calculated for arbitrary frequency profiles of fiber dispersion and Raman gain without a numerical solution of the pulse evolution equation. The accuracy of this analytical approach to SSFS calculation is tested by numerical simulations based on the generalized nonlinear Schr?dinger equation.     

Numerical solution of differential equations with colored noise

Using the general theory of numerical integration of stochastic differential equations, a constructive approach to numerical methods for a system with colored noise is proposed. Efficient methods up to the 5/2 strong order and up to the third weak order, including Runge-Kutta and implicit schemes, are presented. The algorithms are tested on the Kubo oscillator.     

颗粒碰撞的直接模拟算法

为研究细微颗粒间平均碰撞率,构建了直接模拟三维空间内颗粒碰撞的数值方法.对剪切流内夹带的无惯性颗粒和自由运动颗粒的碰撞过程分别进行了数值模拟,得到的颗粒平均碰撞率的模拟值与理论值的相对误差小于1%.在碰撞颗粒对的搜索过程中,引入网络排除法等优化措施,使计算量降低两个量级以上,而不增大相对误差.采用不同的Δt模拟同一颗粒群的运动,发现较小的时间步长可以避免因为截断误差增大的相对误差.在不遗失颗粒碰撞的条件下,较密的计算网格可明显减少计算量.     

混凝土HJC模型抗侵彻参数敏感性数值模拟研究

 混凝土是一种应用广泛的复合材料,其动态性能及抗侵彻毁伤效应的研究越来越依赖于数值模拟,其中混凝土HJC模型是应用最广泛的本构模型之一。在介绍HJC模型的基础上,应用LS-DYNA数值模拟方法进行HJC本构模型抗侵彻性能的参数敏感性研究,通过大量数值模拟得出HJC模型的抗侵彻敏感参数有：无侧限单轴抗压强度f_c、压实点压力p_lock、特征化粘性强度A、特征化压力硬化因子B和压力硬化指数N。在混凝土的抗侵彻数值模拟过程中,重点是确定敏感参数的取值,以提高数值模拟的精度和质量,做到合理地选择试验方法和安排试验量。     

载流直螺线管磁场的三维数值解

本文利用严格的解析和数值方法讨论了载流直螺线管产生的三维磁场 ,并在计算机上进行了高精度的数值计算。     

Numerical simulation of quasi-multifractal diffusion process

The properties of quasi-multifractal diffusion process are discussed. A discrete model of the process is constructed, and a method is proposed for calculating the quasi-multifractal spectrum, based on statistical processing of its realizations. An analysis of multifractal properties performed by numerical simulation of the quasi-multifractal spectrum is qualitatively substantiated by examining realizations of the simulated process. The results of numerical simulations suggest that there are three distinct scaling regions. Special attention is given to comparative analyses between numerical and analytical results and between realizations of the proposed process and the well-known multifractal random walk.     

Stochastic joint time–frequency response analysis of nonlinear structural systems

A novel approximate analytical approach for determining the response evolutionary power spectrum (EPS) of nonlinear/hysteretic structural systems subject to stochastic excitation is developed. Specifically, relying on the theory of locally stationary processes and utilizing a recently proposed representation of non-stationary stochastic processes via wavelets, a versatile formula for determining the nonlinear system response EPS is derived; this is done in conjunction with a stochastic averaging treatment of the problem and by resorting to the orthogonality properties of harmonic wavelets. Further, the nonlinear system non-stationary response amplitude probability density function (PDF), which is required as input for the developed approach, is determined either by utilizing a numerical path integral scheme, or by employing a time-dependent Rayleigh PDF approximation technique. A significant advantage of the approach relates to the fact that it is readily applicable for treating not only separable but non-separable in time and frequency EPS as well. The hardening Duffing and the versatile Preisach (hysteretic) oscillators are considered in the numerical examples section. Comparisons with pertinent Monte Carlo simulations demonstrate the reliability of the approach.