力梯度辛方法在圆型限制性三体问题中的应用

旋转坐标系下的圆型限制性三体问 题因含非惯性系所附加的影响部分使得动能不是动量的严格二次型, 可能导致力梯度辛积分算法的应用遇到困难. 从Lie算子运算出发, 严格论证了力梯度算子在这种情形下的物理意义 仍然像质心惯性坐标系下的圆型限制性三体问题那样是引力的梯度, 而不是引力与非惯性力所得合力的梯度, 表明了力梯度辛方法适合求解旋转坐标系下的圆型限制性三体问题. 通过应用四阶力梯度辛方法、最优化四阶力梯度辛方法和Forest-Ruth 辛方法分别求解该问题, 进行了数值对比研究, 结果显示最优化型力梯度算法能够取得最好精度. 还应用最优化型算法计算两邻近轨道的Lyapunov指数和快速Lyapunov指标, 确保高精度辛方法能够贯穿于这些混沌指标计算的全过程, 以便准确刻画此系统的动力学定性性质. 关键词： 辛积分器 圆型限制性三体问题 混沌 Lyapunov指数     

半隐Euler法和隐中点法嵌入混合辛积分器的比较

当Hamilton函数分解为可积和不可积两部分时,前者能用分析方法给出解析解,而后者可借助一阶半隐Euler法或二阶隐中点法等数值求解,将这种解析和数值解法组合能构造二阶混合辛积分器.理论分析表明Euler嵌入法的稳定区要小于中点嵌入法的.再分别以圆形限制性三体问题和相对论自旋致密双星后牛顿Hamilton构型为例,详细比较了两嵌入法的性能特点.二者的数值精度、稳定性及计算效率与Hamilton的分解方式和轨道类型有关.就圆形限制性三体问题而言,当Hamilton采用势能和含坐标与动量混合项在内的动能分解 关键词： 辛积分器 后牛顿近似 自旋致密双星 混沌     

辛算法在Ba+HF反应准经典轨线计算中的应用

将辛算法应用于准经典轨线理论,模拟了Ba HF反应在扩展的London-Eyring-Polanyi-Sato (LEPS)势能面上的动力学行为.比较哈密顿体系在RK4-AMH4积分,四阶辛积分,六阶辛积分下的总能量守恒情况,结果表明六阶辛算法能最好地保持反应体系的能量守恒,且用时间最短,能够很好地节省计算资源.得到的六阶辛算法下生成物BaF的振动分布高于以前计算的结果,进一步证明六阶辛算法能最好保持能量守恒的特点.     

磁性液体一阶磁浮力原理实验研究

基于伯努利方程推导了磁性液体的一阶磁浮力,实验研究了不同轴线上一阶磁浮力的变化规律,便于学生理解一阶磁浮力变化的本质原因.磁性液体一阶磁浮力受磁场强度、磁场梯度,以及磁性液体的饱和磁化强度和磁化率影响.沿z轴方向随磁场强度和磁场梯度减弱,一阶磁浮力逐渐变小并趋于零,磁性液体悬浮能力变弱.MFP-1磁性液体的饱和磁化强度和磁化率大于MFP-2磁性液体,其一阶磁浮力较大;电流为3.00 A时,MFP-1磁性液体将玻璃、铝、黄铜、紫铜和铅球悬浮,并出现Rosensweig尖峰,而MFP-2磁性液体仅将玻璃、铝和黄铜球悬浮.沿r轴方向不同高度处磁场强度和磁场梯度变化规律不同,随高度增加,磁场梯度逐渐趋于零,此时一阶磁浮力主要受磁场强度影响,测试杯壁处一阶磁浮力最小,出现了非磁性测试球上升过程中向测试杯壁移动现象.     

测量软X射线脉冲信号的门控积分器

 研制了满足ICF诊断中软X射线能量测量精度要求的具有限定时间积分功能的门控积分器。测试结果表明, 门控积分器的门有效导通时间约为7.8ns; 用信号源做被积信号, 门控积分器与示波器同时测量, 积分非线性小于3%; 门控积分器与示波器测量对比, 最大误差小于门控积分器满量程的5%。     

算法对混沌体系逃逸率的影响

以Hénon-Heiles体系为例，研究算法对混沌体系运动轨道和逃逸率计算结果的影响.比较了新发现的四阶辛算法和一种非辛的高阶算法得到的结果.发现两种算法给出的轨迹之间的距离随时间增大，增加的速度可以作为体系相空间混沌的度量.通过跟踪大数量的粒子轨迹，提取出了逃逸率随体系能量的变化.发现由两种算法得到的逃逸率相互符合得很好. 关键词： 逃逸率 Hénon-Heiles体系 辛算法     

含时Schrdinger方程的高阶辛FDTD算法研究

提出了一种新的算法—高阶辛时域有限差分法(SFDTD(3,4):symplectic finite-difference time-domain)求解含时薛定谔方程.在时间上采用三阶辛积分格式离散,空间上采用四阶精度的同位差分格式离散,建立了求解含时薛定谔方程的高阶离散辛框架;探讨了高阶辛算法的稳定性及数值色散性.通过理论上的分析及数值算例表明:当空间采用高阶同位差分格式时,辛积分可提高算法的稳定度;SFDTD(3,4)法和FDTD(2,4)法较传统的FDTD(2,2)法数值色散性明显改善.对二维量子阱和谐振子的仿真结果表明:SFDTD(3,4)法较传统的FDTD(2,2)法及高阶FDTD(2,4)法有着更好的计算精度和收敛性,且SFDTD(3,4)法能够保持量子系统的能量守恒,适用于长时间仿真.     

含时Schrödinger方程的高阶辛FDTD算法研究

提出了一种新的算法——高阶辛时域有限差分法(SFDTD(3, 4): symplectic finite-difference time-domain)求解含时薛定谔方程.在时间上采用三阶辛积分格式离散, 空间上采用四阶精度的同位差分格式离散, 建立了求解含时薛定谔方程的高阶离散辛框架;探讨了高阶辛算法的稳定性及数值色散性.通过理论上的分析及数值算例表明:当空间采用高阶同位差分格式时, 辛积分可提高算法的稳定度;SFDTD(3, 4)法和FDTD(2, 4)法较传统的FDTD(2, 2)法数值色散性明显改善.对二维量子阱和谐振子的仿真结果表明: SFDTD(3, 4)法较传统的FDTD(2, 2)法及高阶FDTD(2, 4)法有着更好的计算精度和收敛性, 且SFDTD(3, 4)法能够保持量子系统的能量守恒, 适用于长时间仿真.     

利用GOCE卫星数据确定全球重力场模型

利用GOCE卫星观测数据确定全球静态重力场是当前大地测量学的研究热点.本文联合2011-02-28至2012-03-05共12个月的GOCE卫星轨道和梯度数据采用直接法恢复了210阶次的重力场模型SWJTUGO01S,利用零相位的有限脉冲带通数字滤波器对GOCE梯度数据进行滤波处理,直接在梯度仪坐标系中建立梯度观测方程,避免了坐标转换过程中高精度梯度观测分量精度的损失;采用短弧积分法处理轨道数据,并利用方差分量估计确定联合解的最优权,Kuala正则化方法用于处理数据极空白问题.基于EGM2008模型和北美地区的GPS水准观测数据,对SWJTU-GO01S模型进行内外符合精度分析,结果表明:SWJTU-GO01S模型在210阶次的大地水准面误差和累计误差分别为2.1 cm和13.7 cm,整体上优于欧空局公布的第二代时域法和空域法模型的精度,在150阶以后优于ITG-GRACE2010S的精度;本文的研究为进一步联合多类卫星观测数据恢复重力场模型提供参考.     

人造地球卫星运动方程的代数动力学算法数值解

代数动力学算法首次被用于求人造地球卫星运动方程的数值解，在四阶算法下，与Runge-Kutta算法和辛算法的计算结果作了比较.结果表明，代数动力学算法对于人造地球卫星长期轨道的计算有较高的精度.并讨论了地球四极和八极带谐项对卫星轨道的影响. 关键词： 人造地球卫星运动方程 代数动力学算法数值解 地球四极和八极带谐项对卫星轨道的影响     

Dynamics of Charged Particles Around a Magnetized Black Hole with Pseudo–Newtonian Potential

The linear stability of equilibria of charged particles moving near a compact object with a dipole magnetic field and a pseudo-Newtonian potential is analyzed detailedly.An optimal fourth-order force gradient symplectic method,as a global symplectic integrator that can simultaneously solve both the equations of motion and the variational equations,is used to calculate fast Lyapunov indicators.In this way,dynamical structures are described,and parameter domains for causing chaos are found.     

Dynamics of Charged Particles Around a Magnetized Black Hole with Pseudo-Newtonian Potential

The linear stability of equilibria of charged particles moving near a compact object with a dipole magnetic field and a pseudo-Newtonian potential is analyzed detailedly. An optimal fourth-order force gradient symplectic method, as a global symplectic integrator that can simultaneously solve both the equations of motion and the variational equations, is used to calculate fast Lyapunov indicators. In this way, dynamical structures are described, and parameter domains for causing chaos are found.     

Symplectic integrators from composite operator factorizations

I derive fourth order symplectic integrators by factorizing the exponential of two operators in terms of an additional higher order composite operator with positive coefficients. One algorithm requires only one evaluation of the force and one evaluation of the force and its gradient. When applied to Kepler's problem, the energy error function associated with these algorithms are approximately 10 to 80 times smaller than the fourth order Forest-Ruth, Candy-Rozmus integrator.     

Electron acceleration considering pondermotive force effect in a plasma-filled rectangular waveguide by microwave radiation

The electron acceleration inside the plasma-filled rectangular waveguide is numerically investigated for the externally injected single-electron model considering the effects of density modification under a balance between the ponderomotive force and the pressure gradient force. Using Maxwell’s equations, we evaluate the field components of the fundamental mode in the plasma-filled rectangular waveguide, where the obtained equations are solved numerically using the fourth-order Runge–Kutta method for the electric field amplitude of the microwave. Besides, by solving the relativistic momentum and energy equations using the fourth-order Runge–Kutta method, the deflection angle and the total energy of the electron in the waveguide are obtained. Furthermore, it is shown that the electron energy gain can be controlled using superposing microwave fundamental modes. Effects of various parameters on the results are graphically presented.     

基于多步高阶差分格式求解时域Maxwell方程

提出基于无穷维哈密尔顿系统及分裂算子理论的多步高阶差分格式,求解时域Maxwell方程.在时间方向上,针对Maxwell方程采用不同阶数的辛算法进行差分离散;在空间方向上,采用四阶差分格式进行差分离散.探讨多步高阶差分格式的稳定性及数值色散性,最后给出数值计算结果.结果表明,五级四阶格式为最有效的多步高阶差分格式,具有高精度、占用较少的计算机资源等优点,适用于长时间的数值模拟.     

On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications

In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechanics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.     

Semi-classical smoothing in a non-monotonic field

It is pointed out that the semi-classical method of Jennings, Bhaduri and Brack for smoothing the total energy of a system of non-interacting fermions in a potential wellV(r) breaks down in the fourth-order term if this potential is non-monotonic. This means that the method as it stands can only be used by neglecting the Coulomb force on protons. We propose a modified treatment for the fourth-order term which appears to be entirely satisfactory.     

On gradient field theories: gradient magnetostatics and gradient elasticity

In this work, the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared. For gradient magnetostatics, non-singular expressions for the magnetic vector gauge potential, the Biot–Savart law, the Lorentz force and the mutual interaction energy of two electric current loops are derived and discussed. For gradient elasticity, non-singular forms of all dislocation key formulas (Burgers equation, Mura equation, Peach–Koehler stress equation, Peach–Koehler force equation, and mutual interaction energy of two dislocation loops) are presented. In addition, similarities between an electric current loop and a dislocation loop are pointed out. The obtained fields for both gradient theories are non-singular due to a straightforward and self-consistent regularization.