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

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.     

太阳质量损失对高阶行星轨道的长期影响

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。     

A simplified analysis method for piled raft foundations in non‐homogeneous soils

A simplified method of numerical analysis based on elasticity theory has been developed for the analysis of axially and laterally loaded piled raft foundations embedded in non‐homogeneous soils and incorporated into a computer program “PRAB”. In this method, a hybrid model is employed in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. The interactions between structural members, pile–soil–pile, pile–soil–raft and raft–soil–raft interactions, are approximated based on Mindlin's solutions for both vertical and lateral forces with consideration of non‐homogeneous soils. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups and capped pile groups in non‐homogeneous soils. Thereafter, the solutions from this approach for the analysis of axially and laterally loaded 4‐pile pile groups and 4‐pile piled rafts embedded in finite homogeneous and non‐homogeneous soil layers are compared with those from three‐dimensional finite element analysis. Good agreement between the present approach and the more rigorous finite element approach is demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.     

一类非线性二阶奇异初值问题的正解

在简单的假定下。建立了一类非线性二阶奇异初值问题C^1[0,1]正解存在的充分必要条件，我们的奇异问题在有奇性。     

关于一类非线性微分系统周期解的存在性

本文应用映射不动点的方法,研究一类非线性微分系统周期解的存在性,得到了几个结果,并给出应用实例。     

The influence of deformation partitioning on dissolution and solution transfer in low-grade tectonic mélange

Abstract Dissolution of quartz and the recryst-allization and re-equilibration of phyllosilicates produce the dark anastomosing seams that dominate microstructures of tectonic melange which occur in a low-grade, imbricated and multiply deformed, mid-Palaeozoic, intracra-tonic fiysch sequence in northeastern Australia. Seams are composed of very closely spaced or coalesced cleavage lamellae, which are very thin layers of extremely fine-grained phyllosilicates. Cleavage seams enclose lenses of silt-stone or greywacke, which formerly occurred in continuous sedimentary layers, indicating extremely heterogeneous and disruptive deformation. Microphacoids enclosed by cleavage seams have subtle shape asymmetries analogous to those of porphyroclasts. Phyllosilicate-preferred orientations within microphacoids commonly lie at a low angle to enclosing seams, and asymmetric relationships occur within seams. The shape and fabric asymmetries appear to be constant, and are regarded as analgous to S and C planes. The number and extent of seams, the amount of dissolution they indicate, and the efficiency of deformation partitioning imply some enhancement of chemical activity and substantial silica loss from the system. This, in turn, suggests the passage of large amount of silica-undersaturated fluid, and melanges may be zones of high fluid flow. However, the microstructures and the disruptive nature of the fabrics may also reflect the influence of high bulk shear strains and suggest some relationship between the shearing component of deformation and the development of cleavages and foliations.     

An analytical solution for a jointed shield‐driven tunnel lining

This paper presents an analytical solution for the prediction of internal forces and displacements of a jointed segmental precast circular tunnel lining. The effects of joint stiffness on the performance of the tunnel lining are discussed. The ‘force method’ is used to determine the internal forces and displacements of jointed tunnel lining. Five shield‐driven tunnel cases are adopted to study the effects of joint stiffness, soil resistance, joint distribution and joint number on the internal forces and displacements of circular tunnels. Laboratory model tests are conducted to verify the proposed analytical solution. Copyright © 2001 John Wiley & Sons, Ltd.     

不适定方程正则化算法的谱分解式

从观测方程系数矩阵的谱分解着手探讨不适宜方程的正则化算法。利用谱分解式阐明了正则化的主要作用是平滑对参数估值比较敏感的观测误差的高频分量，完整给出了最小二乘平差、秩亏平差和病态方程正则化解的谱分解公式，证明了正则化解参数估值偏离真值的二次范数的期望值与均方误差是等价的。     

An Addendum to the Damour and Deruelle's Solution of the Post-Newtonian Two-Body Problem

A complement to the the analytical solution given by Damour and Deruelle (D&D) in order to solve the differential equations that describe the conic-like and rectilinear post-Newtonian two-body problem is presented. We show the geometric relation between the eccentric and true anomalies for the elliptic-like and hyperbolic-like cases and expressions for their velocities are obtained. A post-Newtonian version of the Lambert's theorem is shown. This revised version was published online in July 2006 with corrections to the Cover Date.     

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

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.