A new explicit multisymplectic integrator for the Kawahara-type equation

We derive a new multisymplectic integrator for the Kawahara-type equation which is a fully explicit scheme and thus needs less computation cost. Multisympecticity of such scheme guarantees the long-time numerical behaviors. Nu- merical experiments are presented to verify the accuracy of this scheme as well as the excellent performance on invariant preservation for three kinds of Kawahara-type equations.     

居中热库蛙跳算法的大尺度模拟测试

分子动力学模拟一个必不可少的要素是对运动方程的准确高效积分. 尽管在动力学传播框架内的现代计算工具中大量使用了传统的蛙跳算法,研究表明蛙跳算法仍然可以进一步改进以获得更好的性能. 居中控温方案中蛙跳的改进版本(蛙跳-middle)实现了更高的精度和效率,即使积分时间步长扩大了几倍,也能保持稳定的动力学传播. 本文使用常规和增强采样模拟中对两个积分算法(蛙跳和蛙跳-middle)进行大尺度模拟测试,旨在标定由时间步长引起的全局性质(例如,详细的势能项)的变化行为以及复杂系统的实际模拟中的局部可观察量(例如,自由能变化或键长). 测试集由六个化学和生物相关系统组成,包括$N$-甲基乙酰胺和A₇-T₇DNA中二面角翻转的构象变化、丙二醛内的分子内质子转移、苯和苯酚针对T4溶菌酶L99A的结合自由能计算、乙胺醇低共熔溶剂中的羟基键长变化以及蓝光受体蛋白的势能计算. 所有结果显示蛙跳-middle积分算法中时间步长引起的误差较小. 蛙跳-middle相对传统蛙跳积分算法的性能提高对于全局属性比局部可观测量更大. 总体而言,目前的工作结果表明,在实际化学和生物系统的模拟中,应优先应用蛙跳-middle算法以获得准确的热力学行为和性质.     

Klein-Gordon-Schr(o)dinger方程的辛Fourier拟谱格式

主要讨论Klein-Gordon-Sehrodinger方程的Fourier拟谱辛格式,包括中点公式和Stormer/Vedet格式.首先构造一个哈密尔顿方程,针对此哈密尔顿方程,在空间方向用Fourier拟谱离散得到一个有限维的哈密尔顿系统,对此有限维系统在时间方向用St(o)rmer/Verlet方法离散得到KGS...     

Nonlinear vibration of embedded single-walled carbon nanotube with geometrical imperfection under harmonic load based on nonlocal Timoshenko beam theory

Based on the nonlocal continuum theory, the nonlinear vibration of an embedded single-walled carbon nanotube (SWCNT) subjected to a harmonic load is investigated. In the present study, the SWCNT is assumed to be a curved beam, which is unlike previous similar work. Firstly, the governing equations of motion are derived by the Hamilton principle, meanwhile, the Galerkin approach is carried out to convert the nonlinear integral-differential equation into a second-order nonlinear ordinary differential equation. Then, the precise integration method based on the local linearzation is appropriately designed for solving the above dynamic equations. Besides, the numerical example is presented, the effects of the nonlocal parameters, the elastic medium constants, the waviness ratios, and the material lengths on the dynamic response are analyzed. The results show that the above mentioned effects have influences on the dynamic behavior of the SWCNT.     

量测带噪声的多个体二阶系统聚集控制

考虑在含有量测噪声情况下的二阶多个体系统聚集控制问题.目的是使得系统中每个个体根据邻居信息构造控制,在只有部分个体能够观测到目标的情况下到达目标.和以前许多多个体同步及聚集问题的研究模型中所考虑的一阶系统不同, 系统的每个个体都只能量测到其邻居个体的部分状态信息,如位置, 并且这些量测还带有噪声.根据这些信息设计了基于局部规则的分散控制律,并且证明当量测噪声和状态量测本身相关时,只要系统在任意给定的时间区域段之内能够保持联合连通,就能够实现系统对目标的跟踪和达到目标.     

具有低通滤波的改进电压型磁链观测器

针对现有算法在PWM波反电动势输入时磁链观测精度很差的问题,采用了一种改进的电压型磁链观测算法,在现有算法的基础上增加了一个低通滤波器和一个用于补偿低通滤波器引起的幅值和相位误差的补偿环节.根据所采用的低通滤波器形式,利用时间相量分析方法,推出了滤波误差补偿公式,并在不同的同步速情况下分析比较,确定最佳补偿系数.仿真结果证明,新算法在PWM波反电动势输入情况下仍具有很高的磁链观测精度,可以有效地消除积分漂移误差.将新算法用于一永磁同步电动机无位置传感器控制系统,仿真证明了新算法的可行性及有效性.     

改进的高性能级联积分梳状滤波器

为解决应用于采样率变换系统中的级联积分梳状(CIC)滤波器通带失真大和阻带衰减小对其应用的限制,在分析传统CIC滤波器传输函数和频谱特性的基础上,引入二级可调参数简单滤波器,设计一种高性能CIC滤波器。仿真结果表明,它与同级数规模的内插二阶多项式CIC滤波器、锐化CIC滤波器相比,阻带衰减分别提高20dB、80dB;通带性能得到较大改善;实现复杂度较低。因此,它适用于对通带、阻带性能和实现复杂度要求较高的采样率变换系统。     

Symplectic Euler Method for Nonlinear High Order Schrödinger Equation with a Trapped Term

In this paper, we establish a family of symplectic integrators for a class of high order Schrödinger equations with trapped terms. First, we find its symplectic structure and reduce it to a finite dimensional Hamilton system via spatial discretization. Then we apply the symplectic Euler method to the Hamiltonian system. It is demonstrated that the scheme not only preserves symplectic geometry structure of the original system, but also does not require to resolve coupled nonlinear algebraic equations which is different from the general implicit symplectic schemes. The linear stability of the symplectic Euler scheme and the errors of the numerical solutions are investigated. It shows that the semi-explicit scheme is conditionally stable, first order accurate in time and $2l^{th}$ order accuracy in space. Numerical tests suggest that the symplectic integrators are more effective than non-symplectic ones, such as backward Euler integrators.     

NURBS曲线插补的离散比例积分器速度规划算法

传统NURBS(Non-uniform rational B-spline,NURBS)曲线插补算法忽略了弧长与曲线的参数关系,造成无法在线对速度进行实时调节,针对这个问题,该文提出一种NURBS曲线插补的离散比例积分器速度规划算法.该方法分2个步骤实现速度规划:①使用数值方法计算NURBS曲线弧长及给定速度的运行时间;二、使用具有加减速的对称性和信号转换功能的离散比例积分器,完成对NURBS曲线插补的在线速度规划.在离散比例积分器的速度规划方法中,起始段、结束段的轨迹速度能够得到实时控制,系统以不超过机床要求的加速度运行.实验结果表明,该文速度规划算法能有效地满足系统约束,保证机床平稳运行.另外,相较于其他算法,该文算法在插补精度、插补实时性及速度波动率性能方面优于现有方法,说明该文方法的有效性和先进性.