Dynamical causes of asymmetry in the arrangement of gaps in the asteroid belt

The centers of the gaps observed in the asteroid belt are displaced toward Jupiter from their positions that correspond to the exact commensurability between the mean motions of an asteroid and Jupiter. Using the current theory of stability and nonlinear oscillations of Hamiltonian systems, we point out the dynamical causes of this asymmetry. Our analysis is performed in terms of the plane circular restricted three-body problem. The orbits that correspond to Poincaré periodic solutions of the first kind are taken as unperturbed asteroid orbits.     

On the Relationship Between Fast Lyapunov Indicator and Periodic Orbits for Continuous Flows

It is already known (Froeschlé et al., 1997a) that the fast Lyapunov indicator (hereafter FLI), i.e. the computation on a relatively short time of a quantity related to the largest Lyapunov indicator, allows us to discriminate between ordered and weak chaotic motion. Using the FLI many results have been obtained on the standard map taken as a model problem. On this model we are not only able to discriminate between a short time weak chaotic motion and an ordered one, but also among regular motion between non resonant and resonant orbits. Moreover, periodic orbits are characterised by constant FLI values which appear to be related to the order of periodic orbits (Lega and Froeschlé, 2001). In the present paper we extend all these results to the case of continuous dynamical systems (the Hénon and Heiles system and the restricted three-body problem). Especially for the periodic orbits we need to introduce a new value: the orthogonal FLI in order to fully recover the results obtained for mappings.     

Classes of Families of Generalized Periodic Solutions to the Beletsky Equation

For the equation describing plane oscillations and rotations of a satellite, we consider families of symmetric generalized periodic solutions with integral rotation number p. We give new confirmations of the hypothesis: there are only four classes of these families with topologically different structures, namely, the classes of families of periodic solutions with p≥ 1, p= 0, p=−1, and p≤−2. Besides, we demonstrate that the vertices of cusps of these families are placed on some analytical curves, and the same is true for the multiple intersections of these families with other families.     

Motion close to the Hopf Bifurcation Of the vertical family of periodic orbits of L4

The paper deals with different kinds of invariant motions (periodic orbits, 2D and 3D invariant tori and invariant manifolds of periodic orbits) in order to analyze the Hamiltonian direct Hopf bifurcation that takes place close to the Lyapunov vertical family of periodic orbits of the triangular equilibrium point L₄ in the 3D restricted three-body problem (RTBP) for the mass parameter, μ greater than (and close to) μ_R (Routh’s mass parameter). Consequences of such bifurcation, concerning the confinement of the motion close to the hyperbolic orbits and the 3D nearby tori are also described.     

Topology of the Two Fixed Centers Problem

In this paper we give a complete topological characterization of the Two Fixed Centers (TFC) problem flow. This characterization is based on the link formed by some basic periodic orbits. The Restricted Circular Three-Body (RCTB) problem is considered as a perturbation of the TFC in the case of two primaries with equal masses. The basic periodic orbits of the integrable problem can be continued in the non-integrable one.This revised version was published online in October 2005 with corrections to the Cover Date.     

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。     

The planar Hill problem with oblate primary

The regularized equations of motion of the planar Hill problem which includes the effect of the oblateness of the larger primary body, is presented. Using the Levi-Civita coordinate transformation as well as the corresponding time transformation, we obtain a simple regularized polynomial Hamiltonian of the dynamical system that corresponds to that of two uncoupled harmonic oscillators perturbed by polynomial terms. The relations between the synodic and regularized variables are also given. The convenient numerical computations of the regularized equations of motion, allow derivation of a map of the group of families of simple-periodic orbits, free of collision cases, of both the classical and the Hill problem with oblateness. The horizontal stability of the families is calculated and we determine series of horizontally critical symmetric periodic orbits of the basic families g and g'. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.