Approximate general solution of 2-degrees of freedom dynamical systems using `les solutions precieuses'     

C.L. Goudas  K.E. Papadakis  E. Valaris 《Astrophysics and Space Science》2003,286(3-4):461-486

This paper presents the procedure of a computational scheme leading to approximate general solution of the axi-symmetric,2-degrees of freedom dynamical systems. Also the results of application of this scheme in two such systems of the non-linear double oscillator with third and fifth order potentials in position variables. Their approximate general solution is constructed by computing a dense set of families of periodic solutions and their presentation is made through plots of initial conditions. The accuracy of the approximate general solution is defined by two error parameters, one giving a measure of the accuracy of the integration and calculation of periodic solutions procedure, and the second the density in the initial conditions space of the periodic solutions calculated. Due to the need to compute families of periodic solutions of large periods the numerical integrations were carried out using the eighth order, variable step, R-K algorithm, which secured for almost all results presented here conservation of the energy constant between 10^-9 and 10^-12 for single runs of any and all solutions. The accuracy of the approximate general solution is controlled by increasing the number of family curves and also by `zooming' into parts of the space of initial conditions. All families of periodic solutions were checked for their stability. The computation of such families within areas of `deterministic chaos' did not encounter any difficulty other than poorer precision. Furthermore, on the basis of the stability study of the computed families, the boundaries of areas of `order' and `chaos' were approximately defined. On the basis of these results it is concluded that investigations in thePoincaré sections have to disclose 3 distinct types of areas of `order' and 2 distinct types of areas of `chaos'. Verification of the `order'/`chaos' boundary calculation was made by working out several Poincaré surfaces of sections. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

太阳质量损失对高阶行星轨道的长期影响     

李林森  郁丽忠  郑学塘 《天文研究与技术》2003,(4):1-7

在文[1]研究的基础上给出了太阳质量损失对三阶行星轨道的影响解,并计算了二、三阶解的长期效应的数值结果。理论结果表明,在三阶解中对于质量变化模型k=3的情形,太阳质量损失对轨道半长轴继续产生长期项、混合项和周期项,但对轨道偏心率和近点角距只产生周期项,三阶解的效应值虽小,但有定性意义。  相似文献   

Mass transfer and preferred orientation development during extensional microcracking in slate-belt folds, Elura Mine, Australia     

J. A. DE ROO 《Journal of Metamorphic Geology》1989,7(3):311-322

Microstructures in slate belt rocks at the Elura Mine, near Cobar, south-eastern Australia, indicate that volume loss by syntectonic dissolution is coupled with mass accretion by reprecipitation of the dissolved material in dilational sites. The mass accretion is sustained primarily by repetitive tensile microfracturing at high pore-fluid pressures. Oriented growth in the inter- and intragranular microcracks is locally host-controlled, creating lattice- and shape-preferred orientations. The grain-scale crack-seal features throughout the rock reflect rhythmic fluid pressure fluctuations; a balance is achieved between the fracture-induced permeability (and consequent flushing rates), and the rate of fluid build-up in a relatively sealed environment.
Instability in the balancing factors can lead to localization and intensification of tensile failure (and hence, tension vein formation) in the grain aggregate. Growth of veins by crack-seal also reflects a steady state, but with more localized fluctuations of fluid flow on the aggregate scale. Still larger imbalances between flushing and fluid accumulation (i.e. pressure variations) induce breccia veining. The larger pressure gradients over greater distances, associated with dilation localization (from pervasive microfracturing to spaced breccia domains), allow fluid channelling with an increased potential for chemical fluid/rock disequilibrium. Therefore, large breccia vein systems tend to be sites of extensive fluid/rock interaction and replacement, as spectacularly illustrated by the syntectonic sulphide orebodies at Elura. The huge amounts of silicate, carbonate and sulphide accumulated during folding at Elura illustrate the large scale of source and sink couples possible in solute mass transfer.  相似文献   

Seismic moment distribution revisited: I. Statistical results   总被引：7，自引：0，他引：7  

Yan Y. Kagan 《Geophysical Journal International》2002,148(3):520-541

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Updated UBV Light-Curve and Period Analysis of Eclipsing Binary HS Herculis     

Zeynep Bozkurt  Ömer Lütfi Değirmenci 《Astrophysics and Space Science》2006,304(1-4):29-33

UBV light-curves of the eclipsing binary HS Herculis, obtained in 2002–2003 observational seasons, were analysed with Wilson-Devinney computer code. New absolute dimensions of the system were calculated using the results of the light-curve analysis. Period variation of the system was also investigated. Several new times of minima have been secured for this problematic system. An apsidal motion with a period of 80.7 years was confirmed and a third body in a pretty eccentric orbit (e ₃ = 0.90 ± 0.08) with a period of 85.4 years was found. The corresponding internal structure constants of the binary system, log k ₂, and the mass of the third body were derived.  相似文献   

Global Solution of Dynamical Systems a Report to Z. Kopal, on what Followed Since     

C. L. Goudas  K. E. Papadakis 《Astrophysics and Space Science》2005,296(1-4):79-89

Two basic problems of dynamics, one of which was tackled in the extensive work of Z. Kopal (see e.g. Kopal, 1978, Dynamics of Close Binary Systems, D. Reidel Publication, Dordrecht, Holland.), are presented with their approximate general solutions. The ‘penetration’ into the space of solution of these non-integrable autonomous and conservative systems is achieved by application of ‘The Last Geometric Theorem of Poincaré’ (Birkhoff, 1913, Am. Math. Soc. (rev. edn. 1966)) and the calculation of sub-sets of ‘solutions précieuses’ that are covering densely the spaces of all solutions (non-periodic and periodic) of these problems. The treated problems are: 1. The two-dimensional Duffing problem, 2. The restricted problem around the Roche limit. The approximate general solutions are developed by applying known techniques by means of which all solutions re-entering after one, two, three, etc, revolutions are, first, located and then calculated with precision. The properties of these general solutions, such as the morphology of their constituent periodic solutions and their stability for both problems are discussed. Calculations of Poincaré sections verify the presence of chaos, but this does not bear on the computability of the general solutions of the problems treated. The procedure applied seems efficient and sufficient for developing approximate general solutions of conservative and autonomous dynamical systems that fulfil the PoincaréBirkhoff theorems. The same procedure does not apply to the sub-set of unbounded solutions of these problems.  相似文献   

五维Einstein-Wesson引力理论的几个结果     

黄保法  王景昌 《中国天文和天体物理学报》1989,(4)

本文介绍五维广义相对论及Schwarzschild外部解,然后推导Schwarzschild内部解,最后着重采用五维引力理论计算水星近日点进动,光线在太阳附近的偏折,无线电信号延迟三个问题。结果表明,在现在实验条件下,五维理论对四维理论的修正是极其微小的,在与宇宙年龄相比拟情况下,两个理论的差别能显示出来。  相似文献   

Linear programming approach to moment tensor inversion of earthquake sources and some tests on the three-dimensional structure of the upper mantle     

Toshiro Tanimoto  Hiroo Kanamori 《Geophysical Journal International》1986,84(2):413-430

Summary. A new method of moment tensor inversion is developed, which combines surface wave data and P -wave first motion data in a linear programming approach. Once surface wave spectra and first motion data are given, the method automatically obtains the solution that satisfies first motion data and minimizes the L1 norm of the surface wave spectra. We show the results of eight events in which the method works and is stable even for shallow events. We also show one event in which surface wave data and P -wave first motion data seem to be incompatible. In such cases, our method does not converge or converges to a solution which has a large minor (second) double couple component. It is an advantage that the method can determine the compatibility of two data sets without trial and error.
Laterally heterogeneous phase velocity corrections are used to obtain spectra at the source. The method is also applied to invert moment tensors of eight events in two recent three-dimensional (3-D) upper mantle structures. In both 3-D models, variances of spectra are smaller than those in a laterally homogeneous model at 256 s. Statistical tests show that those reductions are significant at a high confidence level for five events out of eight examined. For three events, we examined those reductions at shorter periods, 197 and 151 s. The reduction of variances is comparable to the results at 256 s and is again statistically significant at a high confidence level. Orientation of fault planes does not change very much by incorporation of lateral variations of phase velocity or by doing inversions at different periods. This is mainly because of the constraints from P -wave first motion data. Scatter of phase spectra at shorter periods, especially at 151 s, is great and suggests that surface wave ray paths deviate from great circle paths substantially and these effects cannot be ignored.  相似文献   

清原南口前一带金矿床稳定同位素研究     

李庆章  刁乃昌 《国土资源》1989,(3)

南口前一带金矿床的稳定同位素研究表明,金矿成矿与太古宙花岗岩—绿岩带,南口前花岗岩体关系密切。依据金矿床硫、碳同位素组成判定金矿床属热液成因,热液体系处于 H_(?)S 占优势的化学环境。在成矿过程中成矿介质由弱酸性向酸性,再向碱性方向演化;氧逸度随着成矿介质温度降低,金属硫化物的沉淀而逐渐升高。氢、氧同位素组成显示了岩浆热液有天水混入。铅同位素组成表明金矿中的铅属古老正常铅,与花岗岩中长石铅为同源。据此,作者认为南口前一带金矿属再平衡岩浆热液矿床。  相似文献   

新疆托里齐Ⅱ金矿区岩石应变及体耗与矿脉关系初探     

王涛  宫同伦 《地球科学与环境学报》1989,(2)

在应变分析基础上,用本文提出的方法估算了岩石体耗,初步探讨了应变、体耗与矿脉的成因联系。认为矿脉主要是矿源层岩石在变形过程中,由压溶、压实作用产生体耗而排出的热液所形成的。  相似文献