Stability of motion in the Sitnikov 3-body problem

We study the stability of motion in the 3-body Sitnikov problem, with the two equal mass primaries (m ₁ = m ₂ = 0.5) rotating in the x, y plane and vary the mass of the third particle, 0 ≤ m ₃ < 10⁻³, placed initially on the z-axis. We begin by finding for the restricted problem (with m ₃ = 0) an apparently infinite sequence of stability intervals on the z-axis, whose width grows and tends to a fixed non-zero value, as we move away from z = 0. We then estimate the extent of “islands” of bounded motion in x, y, z space about these intervals and show that it also increases as |z| grows. Turning to the so-called extended Sitnikov problem, where the third particle moves only along the z-axis, we find that, as m ₃ increases, the domain of allowed motion grows significantly and chaotic regions in phase space appear through a series of saddle-node bifurcations. Finally, we concentrate on the general 3-body problem and demonstrate that, for very small masses, m ₃ ≈ 10⁻⁶, the “islands” of bounded motion about the z-axis stability intervals are larger than the ones for m ₃ = 0. Furthermore, as m ₃ increases, it is the regions of bounded motion closest to z = 0 that disappear first, while the ones further away “disperse” at larger m ₃ values, thus providing further evidence of an increasing stability of the motion away from the plane of the two primaries, as observed in the m ₃ = 0 case.     

The Non-Linear Stability of L4 in the Restricted Three-Body Problem when the Bigger Primary is a Triaxial Rigid Body

The non-linear stability of L ₄ in the restricted three-body problem has been studied when the bigger primary is a triaxial rigid body with its equatorial plane coincident with the plane of motion. It is found that L ₄ is stable in the range of linear stability except for three mass ratios:

The accelerated Kepler problem

The accelerated Kepler problem (AKP) is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed using physical as well as parabolic coordinates. The latter naturally separate the problem’s Hamiltonian into two unidimensional Hamiltonians. In particular, we identify the origin of the secular resonance in the AKP and determine analytically the radius of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary systems as well as to the truncation of accretion disks through stellar jet acceleration.     

On bridges B(pL, qS) around triangular libration points

When μ is smaller than Routh’s critical value μ ₁ = 0.03852 . . . , two planar Lyapunov families around triangular libration points exist, with the names of long and short period families. There are periodic families which we call bridges connecting these two Lyapunov families. With μ increasing from 0 to 1, how these bridges evolve was studied. The interval (0,1) was divided into six subintervals (0, μ ₅), (μ ₅, μ ₄), (μ ₄, μ ₃), (μ ₃, μ ₂), (μ ₂, μ ₁), (μ ₁, 1), and in each subinterval the families B(pL, qS) were studied, along with the families B(qS, qS′). Especially in the interval (μ ₂, μ ₁), the conclusion that the bridges B(qS, qS′) do not exist was obtained. Connections between the short period family and the bridges B(kS, (k + 1)S) were also studied. With these studies, the structure of the web of periodic families around triangular libration points was enriched.     

New doubly-symmetric families of comet-like periodic orbits in the spatial restricted (N + 1)-body problem

For any positive integer N ≥ 2 we prove the existence of a new family of periodic solutions for the spatial restricted (N +1)-body problem. In these solutions the infinitesimal particle is very far from the primaries. They have large inclinations and some symmetries. In fact we extend results of Howison and Meyer (J. Diff. Equ. 163:174–197, 2000) from N = 2 to any positive integer N ≥ 2.      

地电场架设中需要注意的问题以及干扰的排除

通过对全疆大地电场仪器的架设和观测资料的分析,发现了很多我们需要注意的问题及排除干扰的方法,例如在架设过程中测线的接法,挖极坑的时候需要注意的事项,以及筛选电极时需要注意的问题,等等,如果这些问题不慎重解决,就直接影响到以后观测资料的好坏。另外,在观测中遇到一些干扰问题,如磁暴、雷电、附加电场等,分析了这些干扰出现的规律性。     

卫星测高混合边值问题的球谐级数解法

研究了球界面下卫星测高问题的解法,利用有限逼近方法得到了下列结论：若陆地部分是球冠,则卫星测高问题的解可以转换成关于球谐级数位系数的线性方程组,并且位系数的阶和次是以分离形式出现的,从而确保该解法具有实用意义. 利用重力场360阶模型进行模拟计算的结果表明：该解法得到的位系数的相对精度达到了10－１１. 同时证明了常用的Stokes问题、Dirichlet问题、Neumann问题可以看成卫星测高问题的特殊情况.     

澜沧江某冰水堆积体演化过程及工程地质问题探讨

第四纪冰期大型山岳冰川运动遗留下的大型冰水堆积体是我国西南高山峡谷地区一类重要的第四系堆积物.本世纪以来,随着该地区大型基础工程的陆续上马,这种大型冰水堆积体的存在常常成为工程建设必须面临的工程地质问题,这些冰水堆积体因其形成演化过程的特殊性,使得其在结构、物质组成、力学特性、水理特性等诸多方面与一般松散堆积体存在显著差别,因而研究其结构特征、形成演化过程以及带来的工程地质问题具有重要意义.以澜沧江某电站坝前冰水堆积体为例,在调查分析其结构特征的基础上,对冰水堆积体的形成演化过程进行分析和研究,并对冰水堆积体的工程特性,以及带来的工程地质问题进行了探讨,认为该冰水堆积体的工程特性明显好于其他第四系松散堆积体,电站蓄水后整体失稳的可能性较小,但其前缘仍存在局部失稳的可能.     

Robustness and the Paradox of Bridging Organizations: The Exit Problem in Regional Water Governance Networks in Central America

Bridging organizations facilitate a range of governance processes, including cooperation and social learning, and are theorized to be a key component of robust governance systems. In this article, we use node removal simulations to test structural hypotheses of robustness in a regional water governance network in Central America. We investigate the response of network measures supporting core governance processes to the targeted removal of bridging organizations and other actors, which we compare to random and centrality-based simulations. The results indicate removing bridging organizations has a greater impact on the network than any other type of actor, suggesting bridging organizations are critical to the robustness of the governance system. Furthermore, network structures supporting cooperation may be less robust than structures facilitating social learning. We conclude with policy implications of the research findings as they relate to the exit problem in governance systems with a large presence of international development actors.     

Economic‐Development Stakeholder Perspectives on Boomtown Dynamics in the Eagle Ford Shale,Texas

Unconventional oil and gas production in the United States reversed a decades‐old trend of rising oil imports, provided an argument for lifting the U.S. crude oil export ban and motivated the development of domestic natural gas export facilities. But the most visible impact of unconventional‐hydrocarbon extraction is the creation of boomtowns in rural regions. Despite widespread media coverage, scholarly analysis of boomtowns is restricted to regional econometric studies with little attention to how economic stakeholders understand and respond to booming economies. Here we analyze interviews with key economic stakeholders in the Eagle Ford Shale in Texas. Respondents consider their community's economic success relative to the price of oil and indicate concerns about the deterioration of roads, high housing demand, and skyrocketing wages. We also re‐examine John Gilmore's foundational work on boomtowns in the 1970s in the context of contemporary unconventional extraction.