Uncertainty propagation in orbital mechanics via tensor decomposition

Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker–Planck equation (FPE) is defined on a relatively high dimensional (6-D) state–space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the \(x-y-z\) subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors’ knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral (“super-fast”) convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations.     

Impact of ambient temperature on spring-based relative gravimeter measurements

In this paper, we investigate the impact of ambient temperature changes on the gravity reading of spring-based relative gravimeters. Controlled heating experiments using two Scintrex CG5 gravimeters allowed us to determine a linear correlation (R \(^{2}>\) 0.9) between ambient temperature and gravity variations. The relation is stable and constant for the two CG5 we used: ?5 nm/s\(^{2}/^\circ \)C. A linear relation is also seen between gravity and residual sensor temperature variations (R \(^{2}>\) 0.75), but contrary to ambient temperature, this relation is neither constant over time nor similar between the two instruments. The linear correction of ambient temperature on the controlled heating time series reduced the standard deviation at least by a factor of 2, to less than 10 nm/s\(^{2}\). The laboratory results allowed for reprocessing the data gathered on a field survey that originally aimed to characterize local hydrological heterogeneities on a karstic area. The correction of two years of monthly CG5 measurements from ambient temperature variations halved the standard deviation (from 62 to 32 nm/s\(^{2}\)) and led us to a better hydrological interpretation. Although the origin of this effect is uncertain, we suggest that an imperfect control of the sensor temperature may be involved, as well as a change of the properties of an electronic component.     

Paleo- and Neoproterozoic magmatic and tectonometamorphic evolution of the Isla Cristalina de Rivera (Nico Pérez Terrane, Uruguay)

The Isla Cristalina de Rivera crystalline complex in northeastern Uruguay underwent a multistage magmatic and metamorphic evolution. Based on SHRIMP U–Pb zircon, Th–U–Pb monazite (CHIME-EPMA method) and K–Ar age data from key units several events can be recognized: (1) multistage magmatism at 2,171–2,114?Ma, recorded on zircon of the granulitic orthogneisses and their 2,093–2,077?Ma overgrowths; (2) a distinct amphibolite facies metamorphism at ~1,980?Ma, recorded by monazite; (3) greenschist facies reworking and shearing at ca. 606?Ma (monazite and K–Ar on muscovite) along the Rivera Shear Zone, and finally (4) intrusion of the post-tectonic Sobresaliente and Las Flores granites at around 585?Ma. Lithological similarities, geographic proximity and coeval magmatic and metamorphic events indicate a similar tectonometamorphic evolution for the Isla Cristalina de Rivera, the Valentines Block in Uruguay and the Santa María Chico Granulitic Complex in southern Brazil, since at least 2.1?Ga.     

Monsoonal precipitation variation in the East Asia since A.D. 1840

Three tree-ring rainfall reconstructions from China and Korea are used in this paper to investigate the East Asian summer monsoon-related precipitation variation over the past 160 years. Statistically, there is no linear correlation on a year-by-year basis between Chinese and Korean monsoon rainfall, but region-wide synchronous variation on a decadal-scale was observed. More rainfall intervals were 1860–1890, 1910–1925, and 1940–1960, and dry or even drought periods were 1890–1910, 1925–1940, and 1960–present. Reconstructions also display that the East Asian summer monsoon precipitation suddenly changed from more into less around mid-1920. These tree-ring precipitation records were also confirmed by Chinese historical dryness/wetness index and Korean historical rain gauge data.     

注水诱发地震的成因及影响因素探讨

根据胜利油田东营凹陷深井注水所监测到的破裂信号特征分析,结合位于同一凹陷内的角7井注水诱发地震特征,对注水诱发地震的成因进行了探讨.注水过程中地层有无先存破裂面对所诱发的地震产生较大影响,认为诱发地震的震级与注采比和注水井的构造位置密切相关.     

An Analytical Solution for Mechanical Responses Induced by Temperature and Air Pressure in a Lined Rock Cavern for Underground Compressed Air Energy Storage

Mechanical responses induced by temperature and air pressure significantly affect the stability and durability of underground compressed air energy storage (CAES) in a lined rock cavern. An analytical solution for evaluating such responses is, thus, proposed in this paper. The lined cavern of interest consists of three layers, namely, a sealing layer, a concrete lining and the host rock. Governing equations for cavern temperature and air pressure, which involve heat transfer between the air and surrounding layers, are established first. Then, Laplace transform and superposition principle are applied to obtain the temperature around the lined cavern and the air pressure during the operational period. Afterwards, a thermo-elastic axisymmetrical model is used to analytically determine the stress and displacement variations induced by temperature and air pressure. The developments of temperature, displacement and stress during a typical operational cycle are discussed on the basis of the proposed approach. The approach is subsequently verified with a coupled compressed air and thermo-mechanical numerical simulation and by a previous study on temperature. Finally, the influence of temperature on total stress and displacement and the impact of the heat transfer coefficient are discussed. This paper shows that the temperature sharply fluctuates only on the sealing layer and the concrete lining. The resulting tensile hoop stresses on the sealing layer and concrete lining are considerably large in comparison with the initial air pressure. Moreover, temperature has a non-negligible effect on the lined cavern for underground compressed air storage. Meanwhile, temperature has a greater effect on hoop and longitudinal stress than on radial stress and displacement. In addition, the heat transfer coefficient affects the cavern stress to a higher degree than the displacement.     

Magma plumbing beneath Anak Krakatau volcano, Indonesia: evidence for multiple magma storage regions

Understanding magma plumbing is essential for predicting the behaviour of explosive volcanoes. We investigate magma plumbing at the highly active Anak Krakatau volcano (Indonesia), situated on the rim of the 1883 Krakatau caldera by employing a suite of thermobarometric models. These include clinopyroxene-melt thermobarometry, plagioclase-melt thermobarometry, clinopyroxene composition barometry and olivine-melt thermometry. Petrological studies have previously identified shallow magma storage in the region of 2–8 km beneath Krakatau, while existing seismic evidence points towards mid- to deep-crustal storage zone(s), at 9 and 22 km, respectively. Our results show that clinopyroxene in Anak Krakatau lavas crystallized at a depth of 7–12 km, while plagioclase records both shallow crustal (3–7 km) and sub-Moho (23–28 km) levels of crystallization. These magma storage regions coincide with well-constrained major lithological boundaries in the crust, implying that magma ascent and storage at Anak Krakatau is strongly controlled by crustal properties. A tandem seismic tomography survey independently identified a separate upper crustal (<7 km) and a lower to mid-crustal magma storage region (>7 km). Both petrological and seismic methods are sensitive in detecting magma bodies in the crust, but suffer from various limitations. Combined geophysical and petrological surveys, in turn, offer increased potential for a comprehensive characterization of magma plumbing at active volcanic complexes.     

代内公平、国际贸易与可持续发展

现阶段，不同国家或区域之间商品交流的种类与数量日益增大。由于发达国家与发展中国家在国际贸易中所扮演的角色不同，因此，在等经济价值交换规律的作用下，发展中国家的环境状况逐渐恶化。文章通过构建开放经济的物质流模型，探讨了物质交换行为对系统内部的自然环境的影响，并对1987年日本的物质流动状况进行了案例研究。分析表明，发达国家的经济发展水平在很大程度上依赖于其它国家内部自然资源与环境的支撑作用。     

试论世博会后昆明世博园的可持续发展

’99昆明世博会后，如何实现世博园的可持续发展，成为学术界和世博园管理者不可回避、急需解决的现实问题。文章在论述世博园的性质、现状、面临的问题、影响世博园持续发展的因素的基础上，初步提出出世博园可持续发展的对策。