Lunisolar Apsidal Resonances at low Satellite Orbits

Eccentricity resonances between the secular motion of an Earth satellite's orbit and the longitudes of the Sun and the Moon are studied within a Hamiltonian framework. The problem is approximated in a traditional manner, with the Earth's potential including only the second zonal harmonic, and a Hill‐type approximation for perturbing bodies. For a family of 10 resonances, stable and unstable points are identified and libration widths are estimated. Numerical values are given for the maximum variation of eccentricity available at each resonance. The respective amplitudes of the perigee heights' librations range from 2 to 750 km. The resonances of the solar origin are generally stronger than their lunar counterparts. This revised version was published online in July 2006 with corrections to the Cover Date.     

Extended Fundamental Model of Resonance

Fundamental models are the simplest, one degree of freedom Hamiltonians that serve as a tool to understand the qualitative effects of various resonances. A new, extended fundamental model (EFM) is proposed in order to improve the classical, Andoyer type, second fundamental model (SFM). The EFM Hamiltonian differs from the SFM by the addition of a term with the third power of momentum; it depends on two free parameters. The new model is studied for the case of a first-order resonance, where up to five critical points can be present. Similarly, to the respective SFM, it admits only the saddle-node bifurcations of critical points, but its advantage lies in the capability of generating the separatrix bifurcations, known also as saddle connections. The reduction of parameters for the EFM has been performed in a way that allows the use of the model in the case of the so-called abnormal resonance.     

Scattering of Rayleigh waves by a shallow circular alluvial valley： High-frequency solution

Introduction The effect of local site conditions on wave propagation is one of the most attractive topics in engineering seismology. It may be resolved by either a numerical method or an analytical method. Numerical methods include the finite difference, finite element, boundary element method, etc. The analytical method is the wave function expansion method. The advantage of these numerical methods is that they can be applied to local inhomogeneity of arbitrary shapes, but analytical method …     

3-D rheologic model of earthquake prepa-ration (III): Precursor field

Introduction Based on the elastic theory of hard inclusion model proposed by Dobrovolskii (1991), we developed a rheologic inclusion model to study the spatial-temporal variation of earthquake pre-cursor by using the bulk-strain field resulted from rheologic inclusion model (SONG et al, 2000). Based on the elastic inclusion theory, the analytical expressions for the viscoelastic displacement field and strain field of rheologic inclusion model are derived (SONG et al, 2003, 2004). Further-m…     

Surface motion of a semi-cylindrical hill for incident plane SV waves： Analytical solution

Introduction Scattering of incident waves by local topographies is one of the most attractive topics in the field of engineering seismology. They can be resolved by either a numerical method or an analyti-cal method. The numerical methods include finite difference method, finite element method, boundary element method, etc. The analytical method is the wave function expansion method. Al-though numerical methods can be used for arbitrary-shaped topographies, the analytical solutions are still …     

On the origin of oriented rutile needles in garnet from UHP eclogites

Although oriented rutile needles in garnet have been reported from several ultrahigh‐pressure (UHP) rocks and considered to be important UHP indicators, their crystallographic features including growth habit and lattice correspondences with garnet host have never been properly characterized. This paper presents a detailed analytical electron microscopic (AEM) study on evenly distributed oriented rutile needles in garnet of two eclogitic rocks from Sulu. Some garnet in one UHP diamondiferous quartzofeldspathic rock from the Saxonian Erzgebirge, and in one high‐pressure (HP) felsic granulite from Bohemia also contain a few unevenly distributed oriented rutile needles. They have also been studied for the purpose of comparison. Despite different distribution patterns, AEM revealed that all rutile needles are oriented along the 〈111〉 directions of garnet with their lateral sides surrounded by the {110} planes of garnet, and that the growth directions of most needles are close to the normal of the {101} planes of rutile. No other specific crystallographic orientation relationships between rutile and garnet host were observed, and there is no pyroxene associated with rutile, as necessitated by the precipitation reaction of rutile in garnet as previously proposed. A simple solid‐state precipitation scenario for the formation of the rutile needles in garnet in these two eclogitic rocks is not justified. Three alternative mechanisms are considered for the formation of oriented rutile needles: (i) the rutile needles may be inherited from precursor minerals; (ii) the rutile needles may be formed by a dissolution–reprecipitation mechanism; and (iii) the rutile needles may be formed by cleaving and healing of garnet with rutile deposition. None of these mechanisms can fully explain the observations, although the first one is less likely and the third one is preferred. This study presents an example where the presence of oriented/aligned inclusions in minerals does not necessarily imply a precipitation origin.     

半球形沉积谷场地对入射平面Rayleigh波的三维散射解析解

把半球形沉积谷和周围半空间场地分别用具有不同弹性模量和不同半径的球坐标描述。利用Fourier-Bessel级数展开法,在频域内给出了半空间中半球形沉积谷场地在平面Rayleigh波入射下三维散射问题的解析解。利用这一解析解计算分析了入射波频率、场地软硬对场地内地表位移幅值的影响。     

Cosmological perturbation theory and the spherical collapse model — III. The velocity divergence field and the Ω dependence

Cosmological perturbation theory (PT) is a useful tool to study the cumulants of the density and velocity fields in the large-scale structure of the Universe. In Papers I and II of this series we saw that the spherical collapse (SC) model provides the exact solution to PT at tree-level and gives a good approximation to the loop corrections (next-to-leading orders), indicating negligible tidal effects. Here, we derive predictions for the (smoothed) cumulants of the velocity divergence field θ ≡ ▽ ⊙  v for an irrotational fluid in the SC model. By comparing these with the exact analytic results of Scoccimarro &38; Frieman, it is shown that, at least for the unsmoothed case, the loop corrections to the cumulants of θ are dominated by tidal effects. However, most of the tidal contribution seems to cancel out when computing the hierarchical ratios, T _J  = 〈θ ^J 〉 / 〈θ²〉  ^{J −1}. We also extend the work presented in Papers I and II to give predictions for the cumulants of the density and velocity divergence fields in non-flat spaces. In particular, we show the equivalence between the spherically symmetric solution to the equations of motion in the SC model (given in terms of the density) and that of the Lagrangian PT approach (given in terms of the displacement field). It is shown that the Ω dependence is very weak for both cosmic fields even at one loop (a 10 per cent effect at most), except for the overall factor f (Ω) that couples to the velocity divergence.     

An excursion set model for the distribution of dark matter and dark matter haloes

A model of the gravitationally evolved dark matter distribution, in the Eulerian space, is developed. It is a simple extension of the excursion set model that is commonly used to estimate the mass function of collapsed dark matter haloes. In addition to describing the evolution of the Eulerian space distribution of the haloes, the model allows one to describe the evolution of the dark matter itself. It can also be used to describe density profiles, on scales larger than the virial radius of these haloes, and to quantify the way in which matter flows in and out of Eulerian cells. When the initial Lagrangian space distribution is white noise Gaussian, the model suggests that the Inverse Gaussian distribution should provide a reasonably good approximation to the evolved Eulerian density field, in agreement with numerical simulations. Application of this model to clustering from more general Gaussian initial conditions is discussed at the end.