Lie Symmetry and Conserved Quantity of Three-Order Lagrangian Equations for Non-conserved Mechanical System

Based on the infinitesimal and one parameter transformation, the problem of Lie symmetry of three-order Lagrangian equations has been studied. Under Lie transformation, the sufficient and necessary condition which keeps three-order Lagrangian equations to be unchanged and the invariant are obtained in this paper.     

Three-order pseudo-Hamilton canonical equations

Based on the three-order Lagrangian equations, Hamilton's function of acceleration $H^\ast$ and generalized acceleration momentum P_\alpha ^\ast are defined, and pseudo-Hamilton canonical equations corresponding to three-order Lagrangian equations are obtained. The equations are similar to Hamilton's canonical equations of analytical mechanics in form.     

The forms of three-order Lagrangian equation in relative motion

In this paper, the general expressions of three-order Lagrangian equations in a motional coordinate system are obtained. In coordinate systems with some specific forms of motion, the expressions corresponding to these equations are also presented.     

Three-order form invariance and conserved quantity

In this paper, the definition of three-order form invariance is given. Then the relation between the three-order form invariance and the three-order Lie symmetry is discussed and the sufficient and necessary condition of Lie symmetry, which comes from the three-order form invariance, is obtained. Finally a three-order Hojman conserved quantity is studied and an example is given to illustrate the application of the obtained results.     

光孤子对的振幅比与相位差对传输的影响

利用分步傅里叶变换法分别求解含三阶色散效应和不考虑三阶色散情况下的光孤子非线性薛定谔（NLS）方程,通过数值求解发现三阶色散效应会使孤子对脉冲发生单边振荡,并在振荡侧逐级产生次脉冲。讨论孤子对的两束孤子脉冲之间的振幅比与相位差对传输的影响,发现在不考虑三阶色散的情况下,振幅比与相位差均对孤子对的传输有显著影响,在考虑三阶色散效应时,只有相位差对孤子对的传输产生影响,并可以导致脉冲能量转移。     

辐射传输方程的三阶球谐展开(P3)近似的有限元法求解

从辐射传输方程出发,应用球谐函数方法对辐射率进行多项式展开,并利用球谐函数的正交性和递推性,在二维笛卡儿坐标下,导出了三阶展开的球谐函数微分方程组（P3近似）,改进了以往成像文献中忽略各项异性因子的P3近似,并用有限元方法对二维圆域均匀和非均匀两种情况做了数值模拟.与漫射近似模型相比较,P3近似能更准确地描述光源附近及吸收较强情况下边界的光辐射分布情况.     

一种8行任意扫描的电光扫瞄器

 针对激光的快速智能扫描,综合利用晶体的双折射效应和电光效应,提出一种电控集成8行任意扫瞄的高速光扫描方案。主要由三级数字电光偏转器和8×1的周期性极化电光棱镜组构成,其中3个电光快门和3块双折射晶体构成三级数字偏转器,通过半波电压的控制实现行位置的转换,一定数目的周期性极化电光棱镜级联组成单行偏转器,通过控制电压进行单行扫描,根据电场施加方式可实现数字型或者连续型扫描。利用梯形结构的电光棱镜组设计了最大电压为5.822 kV时,扫描视场为17.256°的可通过联机控制进行任意行扫描的高速激光扫描器。     

非球面零检验的镜式补偿器设计

根据三级像差理论，推导镜式补偿器在检验光路中初始结构参数计算公式，讨论计算机最佳优化设计方法，并给出设计实例。     

Dark Spatial Solitary Wave Due to Cascaded x^（2） Nonlinearity

The formation of the dark spatial solitary wave in cascaded second harmonic generation processes is numerically studied based on the nonlinear-coupled equations. It is shown that the solitary wave exists when the effective three-order nonlinearity induced by cascaded second-order nonlinearity is negative.     

Dark Spatial Solitary Wave Due to Cascaded x(2) Nonlinearity

The formation of the dark spatial solitary wave in cascaded second harmonic generation processes is numerically studied based on the nonlinear-coupled equations. It is shown that the solitary wave exists when the effective three-order nonlinearity induced by cascaded second-order nonlinearity is negative.     

二维MLSPH无网格方法

给出MLSPH无网格方法的控制方程、移动最小二乘近似、MLSPH守恒格式等,重点研究MLSPH守恒格式中MLS面积向量的数值求解方法,以提高求解的精度.对激波管问题和平面Noh问题进行模拟,得到较好的结果,确定用三次样条积分公式计算面积向量.     

超混沌Lü系统的电路实现

在三维Lü系统的基础上增加一维状态,构建了一个新的四维超混沌Lü系统,简要地分析了该系统平衡点的性质、超混沌吸引子的相图、Lyapunov指数和Lyapunov维数等特性,并设计了一种实现四维超混沌系统的实际电路. 硬件电路实验表明,超混沌Lü系统具有丰富的动力学行为. 关键词： 超混沌Lü系统 Lyapunov指数 电路实现     

神光Ⅲ强激光光束远场诊断系统光学设计

介绍了神光Ⅲ光束远场诊断系统的基本组成,光学系统的工作原理,主要论述了光学系统的设计指标、设计思想、设计结果及其像质评价.研究表明:利用离轴非球面反射镜能很好地实现强激光光束的取样、缩束和衰减.通过切换弯月形离轴非球面透镜可分别实现对基频、三倍频激光光束的远场诊断.     

Extreme Lagrangian acceleration in confined turbulent flow

A Lagrangian study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the Lagrangian dynamics. It is found that the Lagrangian acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the Lagrangian acceleration as a function of the radius shows that the influence of the wall on the Lagrangian dynamics becomes negligible in the center of the domain, and it also reveals that the wall is responsible for the increased intermittency. The transition in the Lagrangian statistics between this region, not directly influenced by the walls, and a critical radius which defines a Lagrangian boundary layer is shown to be very sharp with a sudden increase of the acceleration flatness from about 5 to about 20.     

Polarization of an electron-positron vacuum by a strong magnetic field with an allowance made for the anomalous magnetic moments of particles

Given the anomalous magnetic moments of electrons and positrons in the one-loop approximation, we calculate the exact Lagrangian of an intense constant magnetic field that replaces the Heisenberg-Euler Lagrangian in traditional quantum electrodynamics (QED). We have established that the derived generalization of the Lagrangian is real for arbitrary magnetic fields. In a weak field, the calculated Lagrangian matches the standard Heisenberg-Euler formula. In extremely strong fields, the field dependence of the Lagrangian completely disappears and the Lagrangian tends to a constant determined by the anomalous magnetic moments of the particles.     

Lagrangian theoretical framework of dynamics of nonholonomic systems

By the generalized variational principle of two kinds of variables in general mechanics, it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then, one important formula of similar Lagrangian classical relationship called the popularized Lagrangian classical relationship was derived. From Vakonomic model, by two Lagrangian classical relationships and the popularized Lagrangian classical relationship, the result is the same with Chetaev's model, and thus Chetaev's model and Vakonomic model were unified. Simultaneously, the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples, it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.     

非旋转性自由表面重力驻波的Euler与Lagrange方法解间的转换

对于等深水中的非旋转性重力驻波流场,本文用Euler与Lagrange两种方法求得其至三阶的解,根据同一粒流体质点在相同时间与位置处其流速值为唯一与质量守恒及在自由表面水位的Euler形式解与Lagrange形式解相同等特性,来推导其间互可转换.由一系列连续的Taylor级数展开,在考虑波动场中各流体质点的运动轨迹与运动周期条件下,将已知的Euler解转换成完全未知的Lagrange形式解.接着再将所得的Lagrange解转换成对应的Euler形式,均可得到完全相同的结果.由此可得知,在考虑波动场各流体质 关键词： 重力驻波 Euler与Lagrange解间的转换 质点运动轨迹     

20～6000 K温度范围内二氧化碳配分函数的计算

在20～6000 K温度范围内,通过乘积近似计算了二氧化碳及其同位素的总的配分函数.其中振动配分函数用谐振子近似,转动配分函数考虑了离心扭曲修正.20～6000 K温度范围被划分为五个小区间.在每一个小区间,计算的总的配分函数被拟合到一个温度T的四阶或五阶多项式,从而获得五个或六个拟合系数.通过这些拟合系数可以快速准确的获得分子在所研究温度范围内任意温度下的总配分函数.     

Covariant Hamiltonian Field Theory: Path Integral Quantization

The Hamiltonian counterpart of classical Lagrangian field theory is covariant Hamiltonian field theory where momenta correspond to derivatives of fields with respect to all world coordinates. In particular, classical Lagrangian and covariant Hamiltonian field theories are equivalent in the case of a hyperregular Lagrangian, and they are quasi-equivalent if a Lagrangian is almost-regular. In order to quantize covariant Hamiltonian field theory, one usually attempts to construct and quantize a multisymplectic generalization of the Poisson bracket. In the present work, the path integral quantization of covariant Hamiltonian field theory is suggested. We use the fact that a covariant Hamiltonian field system is equivalent to a certain Lagrangian system on a phase space which is quantized in the framework of perturbative quantum field theory. We show that, in the case of almost-regular quadratic Lagrangians, path integral quantizations of associated Lagrangian and Hamiltonian field systems are equivalent.     

Low-Resistant Band-Passing Noise and Its Dynamical Effects

We propose an n-order noise, which is realized by driving an n-order linear differential equation with a Gaussian white noise. The time-derivative noise is a low-resistant band-passing noise. If the derivative noise is regarded as a thermal one, the system has a vanishing effective friction and it should induce ballistic diffusion of a free particle at long times. The simulation method for the generalized Langevin equation driven by the n-order noise is discussed systematically. The features of three-order derivative noises are presented when they are applied to a ratchet system.