共查询到20条相似文献，搜索用时 93 毫秒
1.
几类辛方法的数值稳定性研究 总被引：1，自引：0，他引：1
主要对一阶隐式Euler辛方法M1、二阶隐式Euler中点辛方法M2、一阶显辛Euler方法M3和二阶leapfrog显辛积分器M4共4种辛方法及一些组合算法进行了通常意义下的线性稳定性分析．针对线性哈密顿系统,理论上找到每个数值方法的稳定区,然后用数值方法检验其正确性．对于哈密顿函数为实对称二次型的情况,为了理论推导便利,特推荐采用相似变换将二次型的矩阵对角化来研究辛方法的线性稳定性．当哈密顿分解为一个主要部分和一个小摄动次要部分且二者皆可积时,无论是线性系统还是非线性系统,这种主次分解与哈密顿具有动势能分解相比,明显扩大了辛方法的稳定步长范围． 相似文献
2.
当史瓦西黑洞周围存在渐近均匀的外部磁场时, 描述带电粒子在史瓦西黑洞附近运动的哈密顿系统会变为不可积系统. 类似于这样的相对论哈密顿系统不存在有显式分析解的2部分分离形式, 给显式辛算法的构建和应用带来困难. 近一年以来的系列工作提出将相对论哈密顿系统分解为具有显式分析解的2个以上分离部分形式, 成功解决了许多相对论时空构建显式辛算法的难题. 最近的工作回答了哈密顿系统显式可积分离数目对长期数值积分精度有何影响、哪种显式辛算法有最佳长期数值性能这两个问题, 指出哈密顿有最小可积分离数目即3部分分裂解形式并且应用于优化的4阶分段龙格库塔显式辛算法可取得最好精度. 由此选择上述数值积分方法并利用庞加莱截面、最大李雅普诺夫指数和快速李雅普诺夫指标研究在磁化史瓦西黑洞附近运动的带电粒子轨道动力学. 结果显示: 针对某特定的粒子能量和角动量, 较小的外部磁场很难形成混沌轨道; 较大的正磁场参数容易使轨道产生混沌, 并且随着磁场的增大, 轨道的混沌程度也随之加强; 粒子能量适当变大也可以加剧混沌程度, 但负磁场参数和粒子角动量变大都会减弱混沌. 相似文献
3.
《天文学进展》2021,(2)
辛算法作为研究哈密顿系统长期定性演化的最佳积分工具,自问世以来就受到了很大的关注。通过对哈密顿函数的截断误差分析,可以从不同角度构造出较高精度的辛算法,也可以通过引入正规化技术实现自动调整积分步长和改善数值稳定性。从辛算法的表现形式可以将它分为显式和隐式两种。当哈密顿系统能够分解为几个可积部分且每部分的解能用时间显函数来表示时,可以构造显式算法。显式算法有非力梯度显式辛算法、力梯度辛算法、辛校正、类高阶辛算法四种。当哈密顿系统变量不能分离时,适合应用隐式辛算法和扩充相空间对称算法求解。分别对这些算法的构造方法及其适用的物理模型进行归纳对比,分析了各种辛算法的优劣性和发展趋势,对如何选择辛算法高效高精度地解决实际问题提供了一定的理论和数值计算依据。 相似文献
4.
约束条件和数值积分 总被引：3，自引：1，他引：2
自治的哈密顿系统存在约束条件，例如能量积分或广义相对论中的4速度大小为常数，它能否在数值积分过程中始终满足将直接影响数值稳定性．在牛顿力学中哈密顿系统的动能一般为椭圆型，直接运用约束条件对方程进行降阶存在开平方判断正负号的困难，导致应用高精度的经典数值积分器时能量存在耗散．然而相对论力学的度规为双曲型，利用约束条件有可能实行方程降阶．在时空具有一定对称性的情况下，能够找到整个时空的一个全局变换使变换后的度规的主对角线某一元素为零，于是从约束方程中不需开平方能够解出某一动量，顺利实现运动方程的降阶．相对论力学中另一个可以降阶的模型是Mixmaster宇宙模型．数值实验表明将经典算法用于降阶后的运动方程能够严格地满足约束，但不一定能保持辛结构。 相似文献
5.
刘林 《紫金山天文台台刊》1997,16(2):82-94
太阳系小天体的运动对应—哈密顿(Hamilton)系统,对其轨道演化的数值研究宜采用哈密顿算法(即辛算法)。本文将仔细讨论这一问题,并以主带小行星的运动为例,较系统地介绍几种辛算法对应的显式辛差分格式。 相似文献
6.
7.
辛算法在动力天文中的应用（Ⅲ） 总被引：3，自引：0，他引：3
文［１］和文［２］从哈密顿系统的整体结构保持一角度阐明了辛算法［３－６］的主要功能，本文将从定量的角度进一步表明辛算法的另一独特优点－可以控制天体运动沿迹误差的快速增长，并对可分离哈密顿系统的显式辛差分格式稍加改进，推广应用到一般动力系统，该系统含有小耗散项或小的不可分离项，计算结果表明，效果极佳，因此，辛算法与传统的数值解法相比，确有很多优点。 相似文献
8.
近地小行星轨道演化的数值研究与辛算法有效性的探讨 总被引：2，自引：0，他引：2
本文采用改进的显式辛算法（symplecticalgorithm）和嵌套的RKF7（8）积分器对43颗已命名（或编号）的近地小行星的轨道演化进行数值研究．在力学模型上,除考虑各大行星的引力振动外,还增加了后牛顿效应,而在算法上则着重探索辛算法在近地小行星轨道演化研究中的应用前景,特别是当小行星与某一大行星靠近时辛算法的有效性．本文的结果可为了解近地小行星的轨道演化状况和对它们进行监测提供可靠的信息． 相似文献
9.
导航卫星历书参数拟合算法研究 总被引：1，自引：0，他引：1
对导航卫星历书问题进行了综合研究,并结合J2项分析解,提出了两套新的历书参数拟合方法和用户算法,与正常算法不同的是:8参数历书拟合算法以Ω=-3/2J2R2t/p2n cos I隐性直接代替历书参数Ω1 ;在用户算法中对MEO卫星以ωk=ω0-ω1·(△t/2-tk),对高轨卫星以ωk=ω0-ω1·(△t/2-tk)/2修正历书参数ωk,其中ω1=A2/p2n(2-5/2sin2 I).9参数历书拟合算法在8参数的基础上增加了一个历书参数M=(T_Errn-T_Err0)/△t/a参数,在用户算法中以ωk=ω0-ω1·(△t/2-tk),Mk=M0 n·tk-M·(△t/2-tk)修正ωk和Mk·通过多组模拟轨道和IGS精密轨道的历书拟合实验,结果表明,新8参数历书拟合方法具有参数少、迭代收敛速度快、对MEO卫星拟合精度高等优点;新9参数历书拟合算法,迭代收敛快,拟合精度优于其他算法. 相似文献
10.
EPIC 202060577是一个包含B型子星的食双星系统.根据K2测光数据获得了45个次极小时刻,确定其轨道周期为1.019648 d并给出了历元公式.基于大天区面积多目标光纤光谱望远镜(Large Sky Area Multi-Object Fiber Spectroscopic Telescope, LAMOST1,又称郭守敬望远镜)的光谱数据,使用ROTFIT程序获得了目标系统的主星光谱型、有效温度、金属丰度与表面重力加速度,并计算得到了视向速度曲线.通过PHOEBE (Physics Of Eclipsing Binaries)建模程序和emcee (Affine Invariant Markov chain Monte Carlo Ensemble Sampler)拟合程序,对EPIC 202060577进行了轨道求解并分析了RossiterMcLaughlin效应对视向速度曲线的影响.最终结果表明EPIC 202060577是一个质量比q=0.11的分离结构食双星系统(q=M2/M1, M1、M2分别为主星和伴星质量),主星的光谱型为B2/3,主星和伴星的质量、半径和有效温度分别为M1=12.56M⊙和M2=1.39M⊙,R1=4.58Rsun和R2=1.85Rsun, T1=18979 K和T2=8710 K, M⊙和Rsun分别为太阳质量和半径.根据所获得的物理参数,对EPIC 202060577的演化阶段进行了讨论. 相似文献
11.
Laura Schaefer 《Icarus》2004,169(1):216-241
We modified the MAGMA chemical equilibrium code developed by Fegley and Cameron (1987, Earth Planet. Sci. Lett. 82, 207-222) and used it to model vaporization of high temperature silicate lavas on Io. The MAGMA code computes chemical equilibria in a melt, between melt and its equilibrium vapor, and in the gas phase. The good agreement of MAGMA code results with experimental data and with other computer codes is demonstrated. The temperature-dependent pressure and composition of vapor in equilibrium with lava is calculated from 1700 to 2400 K for 109 different silicate lavas in the ONaKFeSiMgCaAlTi system. Results for five lavas (tholeiitic basalt, alkali basalt, Barberton komatiite, dunite, and a molten type B1 Ca, Al-rich inclusion) are discussed in detail. The effects of continuous fractional vaporization on chemistry of these lavas and their equilibrium vapor are presented. The predicted abundances (relative to Na) of K, Fe, Si, Al, Ca, and Ti in the vapor equilibrated with lavas at 1900 K are lower than published upper limits for Io's atmosphere (which do not include Mg). We predict evaporative loss of alkalis, Fe, and Si during volcanic eruptions. Sodium is more volatile than K, and the Na/K ratio in the gas is decreased by fractional vaporization. This process can match Io's atmospheric Na/K ratio of 10±3 reported by Brown (2001, Icarus 151, 190-195). Silicon monoxide is an abundant species in the vapor above lavas. Spectroscopic searches are recommended for SiO at IR and mm wavelengths. Reactions of metallic vapors with S- and Cl-bearing volcanic gases may form other unusual gases including MgCl2, MgS, MgCl, FeCl2, FeS, FeCl, and SiS. 相似文献
12.
13.
《中国天文和天体物理学报》2014,(10)
正Research in Astronomy and Astrophysics publishes original research papers and reviews on all branches of astronomy and astrophysics.Reviews are by invitation only.Important new results that require rapid publication can be submitted as a Letter(Letters must be restricted in length to 6 printed pages).Authors who submit a paper are expected to be able to certify that the paper is original work, 相似文献
14.
15.
Laura Schaefer 《Icarus》2005,173(2):454-468
We use chemical equilibrium calculations to model the speciation of alkalis and halogens in volcanic gases emitted on Io. The calculations cover wide temperature (500-2000 K) and pressure (10−6 to 10+1 bars) ranges, which overlap the nominal conditions at Pele (T=1760 K, P=0.01 bars). About 230 compounds of 11 elements (O, S, Li, Na, K, Rb, Cs, F, Cl, Br, I) are considered. The elemental abundances for O, S, Na, K, and Cl are based upon observations. CI chondritic elemental abundances relative to sulfur are used for the other alkalis and halogens (as yet unobserved on Io). We predict the major alkali species in Pele-like volcanic gases and the percentage distribution of each alkali are LiCl (73%), LiF (27%); NaCl (81%), Na (16%), NaF (3%); KCl (91%), K (5%), KF (4%); RbCl (93%), Rb (4%), RbF (3%); CsCl (92%), CsF (6%), Cs (2%). Likewise the major halogen species and the percentage distribution of each halogen are NaF (88%), KF (10%), LiF (2%); NaCl (89%), KCl (11%); NaBr (89%), KBr (10%), Br (1%); NaI (61%), I (30%), KI (9%). We predict the major halogen condensates and their condensation temperatures at P=0.01 bar are NaF (1115 K), LiF (970 K); NaCl (1050 K), KCl (950 K); KBr (750 K), RbBr (730 K), CsBr (645 K); and solid I2 (200 K). We also model disequilibrium chemistry of the alkalis and halogens in the volcanic plume. Based on this work and our prior modeling for Na, K, and Cl in a volcanic plume, we predict the major loss processes for the alkali halide gases are photolysis and/or condensation onto grains. Their estimated photochemical lifetimes range from a few minutes for alkali iodides to a few hours for alkali fluorides. Condensation is apparently the only loss process for elemental iodine. On the basis of elemental abundances and photochemical lifetimes, we recommend searching for gaseous KCl, NaF, LiF, LiCl, RbF, RbCl, CsF, and CsCl around volcanic vents during eruptions. Based on abundance considerations and observations of brown dwarfs we also recommend a search of Io's extended atmosphere and the Io plasma torus for neutral and ionized Li, Cs, Rb, and F. 相似文献
16.
17.
In this paper, we investigate the dynamics of Born–Infeld (B–I) phantom model in the ω–ω′ plane, which is defined by the equation of state parameter for the dark energy and its derivative with respect to N (the logarithm of the scale factor a). We find the scalar field equation of motion in ω–ω′ plane, and show mathematically the property of attractor solutions which correspond to ω
φ
∼−1, Ω
φ
=1, which avoid the “Big rip” problem and meets the current observations well.
相似文献
18.
In astronomical observations at optical wavelengths, a fast image tracking system can be adopted to reduce the effects of the atmospheric seeing and telescopic tracking error, and therefore improve the observing efficiency. Aiming at the need of astronomical observations, totally 5 kinds of algorithms in two categories were selected to make a comparative study on their accuracies and stabilities under different noise conditions by both numerical experiment and laboratory test. The results indicate that the normalized cross-correlation method and barycenter method have not only a higher accuracy but also a better reliability against interferences, they will be applied to the high-resolution spectrograph of the Xinglong 2.16 m telescope and the scienti?c instruments of the SONG (Stellar Observations Network Group) project, respectively. 相似文献
19.
Marcelo Samuel Berman 《Astrophysics and Space Science》2008,314(1-3):79-82
A combined BCDE (Brans-Dicke and Einstein-Cartan) theory with lambda-term is developed through Raychaudhuri’s equation, for
inflationary scenario. It involves a variable cosmological constant, which decreases with time, jointly with energy density,
cosmic pressure, shear, vorticity, and Hubble’s parameter, while the scale factor, total spin and scalar field increase exponentially.
The post-inflationary fluid resembles a perfect one, though total spin grows, but the angular speed does not (Astrophys. Space
Sci. 312: 275, 2007d).
相似文献
20.
Li Xin-nan Zhang Hai-ying Cui Xiang-qun Jiang Zi-bo Zheng Yi Liu Xing-tao Ni Hou-kun 《Chinese Astronomy and Astrophysics》2012
A special stressed annular polishing technique is proposed to mill the off-axis aspheric sub-mirrors of a large segmented mirror with an annular polishing machine. Based on the basic principle of stressed annular polishing technique, a set of special stressing mechanisms are designed to convert milling the aspheric surfaces of sub-mirrors with different off-axis distances into milling the spherical surfaces with identical radii of curvature, so that they can be pol- ished simultaneously on a continuous polishing machine. It took about contin- uous 40 hours to polish a scaled-down mirror of the planning Chinese Future Giant Telescope (CFGT) using this technique. This mirror has the 330 mm di- ameter, 3.6 m off-axis distance, and the 21.6 m radius of curvature, and its max- imum asphericity is 16 micron. The experiment shows that this method has a high effciency, suits batch manufacturing, especially the batch manufacturing of aspheric sub-mirrors of the segmented primary mirror of an extremely large aperture telescope. 相似文献