A note on weak stability boundaries

This paper is devoted to clarify the algorithmic definition of the weak stability boundary in the framework of the planar Restricted Three Body Problem. The role of the invariant hyperbolic manifolds associated to the central manifolds of the libration points L ₁ and L ₂, as boundary of the weak stability region, is shown.     

Modeling for the optimization of layout scenarios of cluster manifolds with pipeline end manifolds

The pipeline end manifold (PLEM) is an important subsea facility, which can greatly reduce the cost and risk of the development scenarios of deepwater oil and gas fields by declining the number of export pipelines and risers. However, the employment of PLEMs is a multidiscipline task involving substantial financial and technical factors. Due to various uncertainties of influencing factors, the evaluation process may take several months or years by the engineers with rich project experience. Thus, how to develop quantified reference tools using mathematical models to assist engineers in efficiently making their crucial decisions is essential. In this paper, the optimization of the layout scenarios of cluster manifolds with PLEMs is discussed, where a proposed mathematical model and its dedicated algorithm are illustrated. The optimal solution at the lowest cost can be obtained through in-house routine in MATLAB, including the optimal layout scenario, the number and locations of PLEMs, and the connection relations. Besides, the numerical simulations are performed to demonstrate the validity of the proposed mathematical model and its algorithm. The results show that this optimization layout problem in engineering can be described accurately by the presented mathematical model and the convergence rate of the given algorithm is efficient.     

离散小波变换与重力异常多重分解

小波变换多尺度分析是位场分解的有益工具.离散二维小波变换产生的低阶小波细节具有尺度不变的特征,它们不随小波变换的总阶数改变,而总阶数的增加仅增加高阶小波细节的个数和改变最后的高阶逼近.因此,用小波变换分解重力异常时,可根据地质目的来组合小波细节,从而实现有地质意义的异常分解.实验表明,用小波变换分解的重力异常小波细节,同样起到功率谱分解的作用,用分解之后的小波细节功率谱可以精确确定场源的埋深.中国大陆科学钻探场地的重力异常分解给出局部异常分解的典型例子.     

On target for Venus – set oriented computation of energy efficient low thrust trajectories

Recently new techniques for the design of energy efficient trajectories for space missions have been proposed that are based on the circular restricted three body problem as the underlying mathematical model. These techniques exploit the structure and geometry of certain invariant sets and associated invariant manifolds in phase space to systematically construct energy efficient flight paths. In this paper, we extend this model in order to account for a continuously applied control force on the spacecraft as realized by certain low thrust propulsion systems. We show how the techniques for the trajectory design can be suitably augmented and compute approximations to trajectories for a mission to Venus.     

Indirect approach to invariant point determination for SLR and VLBI systems: an assessment

We assess the accuracy of some indirect approaches to invariant point (IVP), or system reference point, determination of satellite laser ranging (SLR) and very long baseline interferometry (VLBI) systems using both observed and simulated survey data sets. Indirect IVP determination involves the observation of targets located on these systems during specific rotational sequences and by application of geometrical models that describe the target motion during these sequences. Of concern is that most SLR and VLBI systems have limited rotational freedom thereby placing constraint on the reliability of parameter estimation, including the IVP position. We assess two current approaches to IVP analysis using survey data observed at the Yarragadee (Australia) SLR and the Medicina (Italy) VLBI sites and also simulated data of a large rotationally constrained (azimuth-elevation) VLBI system. To improve reliability we introduce and assess some new geometric conditions, including inter-axis, inter-circle and inter-target conditions, to existing IVP analysis strategies. The error component of a local tie specifically associated with the indirect determination of SLR and VLBI IVP is less than 0.5 mm. For systems with significant rotational limits we find that the inter-axis and inter-circle conditions are critical to the computation of unbiased IVP coordinates at the sub-millimetre level. When the inter-axis and inter-circle geometric conditions are not imposed, we retrieve biased vertical coordinates of the IVP (in our simulated VLBI system) in the range of 1.2–3.4 mm. Using the new geometric conditions we also find that the axis-offset estimates can be recovered at the sub- millimetre accuracy (0.5 mm).     

复张量场扩散方程及其在PolSAR图像去噪中的应用

张量图像如极化合成孔径雷达(PolSAR)图像,它的每一个像素点都是一个3 阶的正定对称矩阵。对于张量图像的噪声抑制,目前普遍的做法是将它们看作多通道标量图像进行处理,但是,这样可能会破坏矩阵的正定性,从而造成信息的损失。本文主要研究基于扩散方程的张量图像的噪声抑制问题,将现有的基于扩散方程的实张量场去噪模型推广到复张量场,并给出了其数值迭代格式。模拟图像和PolSAR图像上的实验充分验证了本文算法的有效性。与现有算法相比,本文算法具有更好的去噪能力和边缘保持能力。     

Spinorial Field and Lyra Geometry

The Dirac field is studied in a Lyra space-time background by means of the classical Schwinger Variational Principle. We obtain the equations of motion, establish the conservation laws, and get a scale relation relating the energy-momentum and spin tensors. Such scale relation is an intrinsic property for matter fields in Lyra background.     

Sun-perturbed earth-to-moon transfers with low energy and moderate flight time

We construct a spacecraft transfer with low cost and moderate flight time from the Earth to the Moon. The motion of the spacecraft is modeled by the planar circular restricted three-body problem including a perturbation due to the solar gravitation. Our approach is to reduce computation of optimal transfers to a non-linear boundary value problem. Using a computer software called AUTO, we solve it and continue its solutions numerically to obtain the optimal transfers. Our result also shows that the use of the solar gravitation can further lower the transfer cost drastically.     

Diffusion Character in Four-Dimensional Volume-Preserving Map

Due to the existence of invariant tori, chaotic sea and hyperbolic structures in higher dimensional phase space of a volume-preserving map, the diffusion route of chaotic orbits will be complicated. The velocity of diffusion will be very slow if the orbits are near an invariant torus. In order to realize this complicated diffusion phenomenon, in this paper we study the diffusion characters in the different regions, i.e., chaotic, hyperbolic and invariant tori's regions. We find that for the three different regions, the diffusion velocities are different. The diffusion velocity in the vicinity of an invariant torus is the slowest one. This revised version was published online in July 2006 with corrections to the Cover Date.     

Lagrangian coherent structures in the planar elliptic restricted three-body problem

This study investigates Lagrangian coherent structures (LCS) in the planar elliptic restricted three-body problem (ER3BP), a generalization of the circular restricted three-body problem (CR3BP) that asks for the motion of a test particle in the presence of two elliptically orbiting point masses. Previous studies demonstrate that an understanding of transport phenomena in the CR3BP, an autonomous dynamical system (when viewed in a rotating frame), can be obtained through analysis of the stable and unstable manifolds of certain periodic solutions to the CR3BP equations of motion. These invariant manifolds form cylindrical tubes within surfaces of constant energy that act as separatrices between orbits with qualitatively different behaviors. The computation of LCS, a technique typically applied to fluid flows to identify transport barriers in the domains of time-dependent velocity fields, provides a convenient means of determining the time-dependent analogues of these invariant manifolds for the ER3BP, whose equations of motion contain an explicit dependency on the independent variable. As a direct application, this study uncovers the contribution of the planet Mercury to the Interplanetary Transport Network, a network of tubes through the solar system that can be exploited for the construction of low-fuel spacecraft mission trajectories. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.