Dynamics of two satellites in the 2/1 Mean–Motion resonance: application to the case of Enceladus and Dione

The dynamics of a pair of satellites similar to Enceladus–Dione is investigated with a two-degrees-of-freedom model written in the domain of the planar general three-body problem. Using surfaces of section and spectral analysis methods, we study the phase space of the system in terms of several parameters, including the most recent data. A detailed study of the main possible regimes of motion is presented, and in particular we show that, besides the two separated resonances, the phase space is replete of secondary resonances.     

Influences of overburden pressure and soil dilation on soil nail pull-out resistance

Soil nailing is the most popular technique for stabilizing newly formed and existing sub-standard slopes in Hong Kong because of its economic and technical advantages. The nail–soil interface shear resistance is an important parameter in design of soil nailed structures. A three-dimensional finite element model was established and used for simulating soil nail pull-out tests. The finite element model was verified by comparing simulated results with measured data. The agreement between the experimental and simulated results in terms of both average pull-out shear stress and stress variation was very good. Using this finite element model, a parametric study was carried out to study the influences of the overburden pressure and soil dilation angle on the soil nail pull-out resistance. The simulated peak pull-out resistance was not directly related to the overburden pressure, which was coincident with the observations in laboratory pull-out tests. The simulated pull-out resistance increased significantly with the increase in dilation angle of the shearing zone. This analysis indicated that the constrained dilatancy of the nail–soil interface and the soil surrounding the nail contributed a lot to the development of peak pull-out resistance.     

一类信号恢复问题的投影迭代硬阈值算法

本文给出了基于L₀模求解该问题的非凸模型,借助于稀疏正则化方法来克服问题的不适定性。该模型利用紧小波框架对信号进行稀疏逼近,并利用L₀模度量稀疏性。提出了求解该模型的投影迭代硬阈值算法,并证明了算法的全局收敛性。该算法每一步都有闭式解,计算过程简洁高效。数值实验表明,方法在重建信号的视觉质量和量化指标方面均优于所对比的pFISTA方法。     

A water movement study in Lianzhou Bay,Guangxi Province,China

This study investigates the physical conditions (water depth, current speed, salinity, temperature) in Lianzhou Bay, a shallow coastal bay in southern China, during two expeditions in the dry and wet seasons of 2011. Based on these expedition data, basic hydrodynamic parameters like Brunt-Väisälä Frequency, Richardson Number, Rossby radius, and Resonance Period are calculated. The results show that Lianzhou Bay is characterized by comparatively small quantity of freshwater input and weak stratification. Strong tides, which are spatially uniform within the bay, cause turbulent mixing. Residence time of the water is shorter in winter due to a stronger coastal current in that season. Consideration of the water movement may help to reduce the harmful ecological impact of aquaculture waste water discharge.     

青海唐古拉沱沱河地区晚更新世河流阶地沉积特征及意义

青海沱沱河地区水系密布、河网交织,沿主干水系河流阶地发育。对沱沱河沿岸不同地段河流阶地进行物质成分及古植物孢粉进行研究,确定了自63.1 kaB.P.(ESR)以来的晚更新世草本植物与木本植物两个古植被演化阶段,相应气候由温凉较干向温和较湿转变。详细的测年(TL、ESR)数据显示,位于基座阶地之上的阶地堆积物为晚更新世97.78 KaB.P.以来堆积而成,推断长江水系在研究区的形成与外泄地质时期为晚更新世早期。     

液氮冻结条件下岩石孔隙结构损伤试验研究

液氮温度极低,约在-195.56^-180.44℃之间,当与岩石接触时会对岩石孔隙结构产生损伤。根据这一特点,低温液氮有望作为压裂流体对储层进行压裂改造。为了研究液氮冻结对岩石孔隙结构损伤的影响,选取两种不同砂岩岩样,分别在不同初始含水饱和度条件下进行液氮冻结处理。对冻结前、后的岩样进行孔隙度以及核磁共振测试,得到岩样在冻结前、后的孔隙度、横向弛豫时间T2分布以及T2谱面积变化情况。试验结果表明:液氮冻结会对岩石的孔隙结构产生损伤,损伤程度受到岩性、孔隙度和岩石含水饱和度等因素影响;岩石含水饱和度越大,损伤就越严重,当岩石含水饱和度达到100%时,岩石表面产生了明显裂纹;岩石在液氮冻结下损伤形式主要是微孔隙的发育和扩展,微孔隙的增加会使岩石孔隙结构的连通性增强,甚至会产生新的大尺寸孔隙,从而对孔隙结构造成严重损伤。     

The influence of the orbital eccentricity of a primary on the chaotic region

Applying the resonance overlap theory to the elliptic three-body model, it is shown that the effect of the eccentricity is to increase the size of the chaotic region.     

Stable Manifolds and Homoclinic Points Near Resonances in the Restricted Three-Body Problem

The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses 1− μ and μ that circle each other with period equal to 2π. For small μ, a resonant periodic motion of the massless particle in the rotating frame can be described by relatively prime integers p and q, if its period around the heavier primary is approximately 2π p/q, and by its approximate eccentricity e. We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions. We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with q/p equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances. We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2 resonances for any μ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist for μ small enough in the unaveraged restricted three-body problem.     

The integrable cases of the planetary three-body problem at first-order resonance

This paper investigates the stability of the motion in the averaged planar general three-body problem in the case of first-order resonance. The equations of the averaged motion of bodies near the resonance surface is obtained and is analytically integrated by quadratures. The stability of the averaged motion is analytically investigated in relation to the semi-major axes, the eccentricities and the resonance phases. An autonomous second-order equation is obtained for the deviation of semiaxes from the resonance surface. This equation has an energy integral and is analytically integrated by quadratures. The quasi-periodic dependence on time with two-frequency basis of the averaged motion of bodies is found. The basic frequencies are analytically calculated. With the help of the mean functionals calculated along integral curves of the averaged problem the new analytic first integrals are constructed with coefficients periodic in time. The analytic conditions of librations of resonance phases are obtained.     

Mapping models for near-conservative systems with applications

A systematic method is presented to construct a mapping model for a near-conservative system, based on that of Hadjidemetriou for a Hamiltonian system [1]. The mapping we constructed preserves the basic features of the actual system. We apply this method to the forced oscillating system and to the 3 : 1 resonant grain motion in the presence of Poynting-Robertson drag.Supported by the National Natural Science Foundation of China.