The integrable cases of the general spatial three-body problem at third-order resonance

For the general three-body problem at third-order resonance an analytical solution is obtained by the use of the Weierstrass functions.     

Assessing the Vibrational Frequencies of the Holweide Hospital in the City of Cologne (Germany) by Means of Ambient Seismic Noise Analysis and FE modelling

Ambient seismic noise measurements were conducted inside the Holweide Hospital (Cologne) for checking whether its frequencies of vibration fall into the range where soil amplification is expected. If this is the case, damage might increase in case of an earthquake due to an amplified structural response of the building. Two different techniques were used: the ratio between the horizontal and vertical components of the spectra recorded at stations located inside the building and the ratio between the corresponding components of the spectra recorded simultaneously inside the building and at a reference station placed outside. While the former method might be preferred because of less equipment involved, the latter has the advantage of producing more stable results and deleting automatically the influence of the sedimentary cover, which might obscure some eigenfrequencies of vibration of the building. An independently performed finite-element analysis of the hospital showed a good correlation between measured and calculated eigenmodes.     

A web of secondary resonances for large <Emphasis Type="Italic">A</Emphasis>/<Emphasis Type="Italic">m</Emphasis> geostationary debris

The dynamics of space debris with very high A/m near the geostationary orbit is dominated by the gravitational coefficient C ₂₂ and the solar radiation pressure. An analysis of the stability of the orbits by the chaos indicator MEGNO and frequency analysis map FAM shows chaotic layers around the separatrix and reveals a web of sub-structures associated to resonances with the annual period of the Sun. This succession of stable thin islands and chaotic layers can be reproduced and explained by a quite simple toy model, based on a pendulum approach, perturbed, through the eccentricity, by the external (Sun) frequency. The use of suitable action-angle variables in the circulation and libration regions of the pendulum allows to point out new resonances between the geostationary libration angle and the Sun’s longitude. They correspond very well (positions, shape, width) to the structures visible on the FAM representations.     

Polarization of resonance lines in the case of a Voigt absorption profile

Multiple resonance scattering of radiation in a spectral line is considered in the case of a Voigt absorption profile. The scattering is assumed to take place in a nonmagnetic semi-infinite atmosphere with uniformly distributed sources of unpolarized radiation. Polarization characteristics have been obtained for the emergent radiation by numerically solving the Ambartsumian-Chandrasekhar matrix integral equation.     

The librations, shape, and icy shell of Europa

Europa, the smallest of the Galilean satellites, has a young icy surface and most likely contains an internal ocean. The primary objective of possible future missions to Europa is the unambiguous detection and characterization of a subsurface ocean. The thickness of the overlying icy shell provides important information on the thermal evolution of the satellite and on the interaction between the ocean and the surface, the latter being fundamental for astrobiology. However, the thickness is not well known, and estimates range from several hundred of meters to some ten of kilometers. Here, we investigate the use of libration (rotation variation) observations to study the interior structure of Europa and in particular its icy shell. A dynamical libration model is developed, which includes gravitational coupling between the icy shell and the heavy solid interior. The amplitude of the main libration signal at 3.55 days (the orbital period) is shown to depend on Europa's shape and structure. Models of the interior structure of Europa are constructed and the equatorial flattening of the internal layers, which are key parameters for the libration, are calculated by assuming that Europa is in hydrostatic equilibrium. Europa's flattened shape is assumed to be due to rotation and permanent tides, and we extend the classical Radau equation for rotationally flattened bodies to include also tidal deformation. We show that the presence of an ocean increases the amplitude of libration by about 10%, depending mainly on the thickness of the icy shell. Therefore, libration observations offer possibility of detection of a subsurface ocean in Europa and estimation of the thickness of its overlying icy shell.     

大气中粘性效应对三维地形波及其波动阻力的影响

采用两层大气模式, 通过引入瑞利摩擦系数来定性描述大气中粘性机制, 讨论了粘性效应对三维简单地形波及其波动阻力的影响。结果表明,无论低层大气为稳定层结还是不稳定层结, 大气中粘性的存在将减弱地形波的强度, 减小其产生的波动阻力     

GD—DTPA脊髓造影磁共振扫描技术应用的研究

本文目的,通过将ＧＤ－ＤＴＰＡ直接注入蛛网膜下腔后进行脊髓造影ＭＲ扫描,探索一种新的ＭＲ检查方法,材料方法：对１１例患者进行ＧＤ－ＤＴＰＡ蛛网膜腔直接注射脊髓造影前后ＭＲ扫描,保持扫描序列不变。造影剂量为０．５～１．０ｍｌ,结果：所有患者脊髓造影后即刻扫描显示脑脊液信号反转,Ｔ１Ｗ高信号。Ｔ２Ｗ低信与,结论：小剂量ＧＤ－ＤＴＰＡ直接蛛网膜注射脊髓造影ＭＲ扫描是一种安全可靠的检查方法。对观察脑脊液动     

基于稀疏表示的地面磁共振信号提取方法

在多孔隙含水层中地面磁共振（surface nuclear magnetic resonance,SNMR）信号呈现多弛豫衰减特性,常规盲源分离方法和单指数拟合方法引起信号严重失真和信息缺失等问题.本文提出了基于稀疏表示的随机噪声背景下多弛豫SNMR信号的提取方法.根据SNMR信号的衰减特征,设计了精确刻画SNMR信号且与随机噪声不相关的离散衰减余弦冗余字典.其次,针对多弛豫SNMR信号稀疏度未知的问题,通过设置合理的残差比阈值控制迭代次数,改进了广义正交匹配追踪（generalized orthogonal matching pursuit,gOMP）算法,使得该方法应用于SNMR信号的提取时,具有更好的自适应性和普适性.再次,鉴于SNMR测量数据为多次独立重复采集的结果,提出了基于数据流的SNMR信号提取策略,在提高算法鲁棒性的同时,保证了信号提取结果的唯一性.最后,通过仿真和实测数据证明了基于gOMP算法的稀疏表示方法可以显著地提升多弛豫SNMR信号的提取质量,降低随机噪声对含水层反演结果的影响,提高SNMR探测能力.     

地下核磁共振小尺寸线圈设计和实验

很多国家在进行隧道挖掘、地下矿体开采时,经常会遇到突水涌泥事故.核磁共振方法(Magnetic Resonance Sounding,MRS)作为目前唯一一种直接找水的地球物理技术,在探测诱发灾害的水体方面具有明显的优势.本文首先给出了多匝分离式线圈的MRS信号响应和核函数的计算公式,分析了线圈的匝数、边长和含水层位置对MRS信号响应的影响.分析表明,在限定空间内,利用多匝分离式线圈的设计方法可以提高小尺寸线圈的探测能力.同时,对高匝数线圈给探测系统带来的不利因素进行了分析和改进.最后,为了验证本研究所采用的方法,利用6 m边长的方形线圈和改进型MRS探测系统在中国温州一处在建隧道内的地下场地进行实地探测,探测结果与瞬变电磁方法结果对比表明,6 m边长的方形线圈可以对地下30 m内的含水层进行有效探测.     

Measuring hydrological connectivity inside a soil by low field nuclear magnetic resonance relaxometry

Hydrological connectivity inside the soil is related to the spatial patterns inside the soil (i.e., the structural connectivity). This, in turn, is directly associated with the physical and the chemical processes at a molecular level (i.e., the functional connectivity). Nuclear magnetic resonance (NMR) relaxometry can be successfully applied to reveal both structural and functional components of soil hydrological connectivity. In the present study, the low field NMR relaxometry was applied on water suspended soils sampled at the upstream‐ and downstream‐end of three different length plots. Also the sediments collected from the storage tanks at the end of each plot were water suspended and monitored by NMR relaxometry. The results from the NMR investigations were elaborated by using a mathematical approach in order to quantify both the functional and structural connectivity components. In particular, following integration of the T₁ distribution curve, an S‐shaped curve was obtained. It revealed two plateaus corresponding to the shortest (low component) and the longest (high component) intervals of relaxation times, respectively. According to relaxometry theory, the two T₁ intervals, associated to the different plateaus, were attributed to micro and macro soil pores, respectively. The two T₁ intervals were used to define a functional connectivity index, while the central part of the S‐shaped distribution was used to define a structural connectivity index. Here we provide the physical meaning of the our mathematical approach, thereby revealing that functional connectivity index increases with plot length, as a result of a selective eroded particle transport. Moreover, the relationship structural connectivity index versus plot length resulted quasi‐independent of grainsize distribution, whereas the values of the structural connectivity index for the sediment samples resulted lower than those obtained for the corresponding soils.