Stability of outer planetary orbits around binary stars: A comparison of Hill's and Laplace's stability criteria

A comparison is made between the stability criteria of Hill and that of Laplace to determine the stability of outer planetary orbits encircling binary stars. The restricted, analytically determined results of Hill's method by Szebehely and co-workers and the general, numerically integrated results of Laplace's method by Graziani and Black are compared for varying values of the mass parameter =m ₂/(m ₁+m ₂). For 00.15, the closest orbit (lower limit of radius) an outer planet in a binary system can have and still remain stable is determined by Hill's stability criterion. For >0.15, the critical radius is determined by Laplace's stability criterion. It appears that the Graziani-Black stability criterion describes the critical orbit within a few percent for all values of .     

SOHM-4与MHM-2010氢原子频标的特点比较

基于对已投入国家授时中心守时运转的SOHM-4型与MHM-2010型氢原子频标的长期关注,对这两种氢原子频标的性能作了较详细的比较和分析。讨论了它们共同的优点、各自的特长和不足之处,还给出了稳定度的测试结果。     

Repeat Ground Track Orbits of the Earth Tesseral Problem as Bifurcations of the Equatorial Family of Periodic Orbits

Orbits repeating their ground track on the surface of the earth are found to be members of periodic-orbit families (in a synodic frame) of the tesseral problem of the Earth artificial satellite. Families of repeat ground track orbits appear as vertical bifurcations of the equatorial family of periodic orbits, and they evolve from retrograde to direct motion throughout the 180 degrees of inclination. These bifurcations are always close to the resonances of the Earth's rotation rate and the mean motion of the orbiter.     

Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field

We study the dynamics of a satellite (artificial or natural) orbiting an Earth-like planet at low altitude from an analytical point of view. The perturbation considered takes into account the gravity attraction of the planet and in particular it is caused by its inhomogeneous potential. We begin by truncating the equations of motion at second order, that is, incorporating the zonal and the tesseral harmonics up to order two. The system is formulated as an autonomous Hamiltonian and has three degrees of freedom. After three successive Lie transformations, the system is normalised with respect to two angular co-ordinates up to order five in a suitable small parameter given by the quotient between the angular velocity of the planet and the mean motion of the satellite. Our treatment is free of power expansions of the eccentricity and of truncated Fourier series in the anomalies. Once these transformations are performed, the truncated Hamiltonian defines a system of one degree of freedom which is rewritten as a function of two variables which generate a phase space which takes into account all of the symmetries of the problem. Next an analysis of the system is achieved obtaining up to six relative equilibria and three types of bifurcations. The connection with the original system is established concluding the existence of various families of invariant 3-tori of it, as well as quasiperiodic and periodic trajectories. This is achieved by using KAM theory techniques.     

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:

有限元强度折减法在边坡稳定性分析中的有效性及结果检验方法

有限元强度折减法的有效性及结果评价决定该方法是否能在工程上得到认可及推广的关键。本文基于有理论解的地基承载力问题和澳大利亚计算机应用协会（ACADS）边坡稳定性典型考题,通过计算值与理论解的对比以及塑性贯通区结果,对有限元强度折减法用于边坡稳定分析的有效性、失稳判据以及结果评价等问题进行了系统研究,提出了以塑性带宽度与长度之比检验计算结果的方法。结果发现,在足够且合理的网格密度下,有限元强度折减法分析边坡稳定性是有效的,不同类型的临界状态判据差异不大,而塑性区贯通判据最为客观;临界状态时塑性带的宽度与长度之比与安全系数的计算精度有很高的相关性,其值越小,精度越高,当塑性区相对宽度b/L小于0.05时,安全系数相对误差一般小于5%;对于强度折减法计算结果的精度评价,只要所得的等效塑性应变分布能确定滑动机制和大致的滑动面位置,其安全系数计算结果与更细密的网格的结果差异一般也在5%以内,精度就是足够的。     

Sequestration of CO2 in geological media: Criteria and approach for site selection in response to climate change

The well-developed coal electricity generation and coal chemical industries have led to huge carbon dioxide (CO₂) emissions in the northeastern Ordos Basin. The geological storage of CO₂ in saline aquifers is an effective backup way to achieve carbon neutrality. In this case, the potential of saline aquifers for CO₂ storage serves as a critical basis for subsequent geological storage project. This study calculated the technical control capacities of CO₂ of the saline aquifers in the fifth member of the Shiqianfeng Formation (the Qian-5 member) based on the statistical analysis of the logging and the drilling and core data from more than 200 wells in the northeastern Ordos Basin, as well as the sedimentary facies, formation lithology, and saline aquifer development patterns of the Qian-5 member. The results show that (1) the reservoirs of saline aquifers in the Qian-5 member, which comprise distributary channel sand bodies of deltaic plains, feature low porosities and permeabilities; (2) The study area hosts three NNE-directed saline aquifer zones, where saline aquifers generally have a single-layer thickness of 3‒8 m and a cumulative thickness of 8‒24 m; (3) The saline aquifers of the Qian-5 member have a total technical control capacity of CO₂ of 119.25 × 10⁶ t. With the largest scale and the highest technical control capacity (accounting for 61% of the total technical control capacity), the Jinjie-Yulin saline aquifer zone is an important prospect area for the geological storage of CO₂ in the saline aquifers of the Qian-5 member in the study area.     

Estimation of Scalar Source/Sink Distributions in Plant Canopies Using Lagrangian Dispersion Analysis: Corrections for Atmospheric Stability and Comparison with a Multilayer Canopy Model

Source/sink distributions of heat, water vapour andCO₂ within a rice canopy were inferred using aninverse Lagrangian dispersion analysis and measuredmean profiles of temperature, specific humidity andCO₂ mixing ratio. Monin–Obukhov similarity theorywas used to account for the effects of atmosphericstability on _w(z), the standard deviation ofvertical velocity and _L(z), the Lagrangian timescale of the turbulence. Classical surface layer scaling was applied in the inertial sublayer (z > z_ruf)using the similarity parameter = (z - d)/L, where z is height above ground, d is the zero plane displacementheight for momentum, L is the Obukhov length,and z_ruf 2.3h_c, where h_c iscanopy height. A single length scale h_c, was usedfor the stability parameter 3 = h_c/L in the height range 0.25 < z/h_c < 2.5. This choice is justified by mixing layer theory, which shows that within the roughness sublayer there is one dominant turbulence length scaledetermined by the degree of inflection in the windprofile at the canopy top. In the absence of theoretical or experimental evidence for guidance,standard Monin–Obukhov similarity functions, with = h_c/L, were used to calculate the stabilitydependence of _w(z) and _L(z) in the roughness sublayer. For z/h_c < 0.25 the turbulence length and time scales are influenced by the presence of the lowersurface, and stability effects are minimal. With theseassumptions there was excellent agreement between eddycovariance flux measurements and deductions from theinverse Lagrangian analysis. Stability correctionswere particularly necessary for night time fluxes whenthe atmosphere was stably stratified.The inverse Lagrangian analysis provides a useful toolfor testing and refining multilayer canopy models usedto predict radiation absorption, energy partitioningand CO₂ exchanges within the canopy and at thesoil surface. Comparison of model predictions withsource strengths deduced from the inverse analysisgave good results. Observed discrepancies may be dueto incorrect specification of the turbulent timescales and vertical velocity fluctuations close to theground. Further investigation of turbulencecharacteristics within plant canopies is required toresolve these issues.     

Susceptibility assessment of earthquake-triggered landslides in El Salvador using logistic regression

This work has evaluated the probability of earthquake-triggered landslide occurrence in the whole of El Salvador, with a Geographic Information System (GIS) and a logistic regression model. Slope gradient, elevation, aspect, mean annual precipitation, lithology, land use, and terrain roughness are the predictor variables used to determine the dependent variable of occurrence or non-occurrence of landslides within an individual grid cell. The results illustrate the importance of terrain roughness and soil type as key factors within the model — using only these two variables the analysis returned a significance level of 89.4%. The results obtained from the model within the GIS were then used to produce a map of relative landslide susceptibility.     

Crack nucleation in saturated porous media

Crack nucleation has been the subject of important contributions in the last two last decades. However, it seems that few attention has been granted to the case of saturated porous media. This is the question addressed in the present paper which is devoted to nucleation in traction mode. From a physical point of view, nucleation is a sudden phenomenon, so that the material response is both adiabatic and undrained. In the spirit of the variational approach, the nucleated crack is viewed as the final state of a region of space in which the material undergoes a full damage process. In traction mode, the opening of a saturated crack in undrained condition induces a drop of fluid pressure. In case of low fluid compressibility, the presence of the fluid delays the brittle failure usually associated with nucleation, as long as the fluid pressure remains above the saturation vapor pressure. Nucleation is therefore possible only if a partial vaporization of the fluid takes place.