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.     

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.     

Numerical investigation of motions of resonant asteroids in the three-dimensional space

Motions of asteroids in mean motion resonances with Jupiter are studied in three-dimensional space. Orbital changes of fictitious asteroids in the Kirkwood gaps are calculated by numerical integrations for 10⁵ – 10⁶ years. The main results are as follows: (1) There are various motions of resonant asteroids, and some of them are very complicated and chaotic and others are regular. (2) The eccentricity of some asteroids becomes very large, and the variation of the inclination is large while the eccentricity is large. (3) In the 3:1 resonance, there is a long periodic change in the variation of the inclination, when (7 : ) is a simple ratio (7: longitude of perihelion, : longitude of node). (4) In the 7:3 resonance, the variation of the inclination of some resonant asteroids is so large that prograde motion becomes retrograde. Some asteroids in the 7:3 resonance can collide with the Sun as well as with the inner planets.     

Resonance trapping and evolution of particles subject to poynting-robertson drag: Adiabatic and non-adiabatic approaches

The problem of resonance trapping for particles subject to Poynting-Robertson drag is approached initially from an adiabatic regime theory. A simplified Hamiltonian system is presented for simple eccentricity-type resonances up to order 3, and expressions related to the trapping process are deduced. The fast dissipation provoked by Poynting-Robertson leads to the employment of a numerical approach for the computation of resonance capture probabilities, for particles in the size range of practical importance. Some aspects of the dynamical evolution of a particle after capture are noticed from results of numerical integrations. Analytical methods are used in order to confirm the numerical results.     

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.     

基于不等式约束的磁共振信号T2谱多指数分解法及算法改进

磁共振地下水探测信号的弛豫时间T₂和振幅与地下岩石孔隙大小和地下水的含水量直接相关。目前,磁共振地下水探测方法中,信号的衰减特性由平均弛豫时间T^*₂来描述。然而,对于复杂的多孔介质组成的岩石结构,仅由T^*₂无法准确描述地下孔隙情况。详细研究了基于不等式约束的多指数分解法,进行了信号T₂谱的提取,并重新计算多指数形式下的信号初始振幅。结果表明：对比信号在不同采集时间下的T₂谱提取结果,延长信号的采集时间有助于T₂谱的准确提取;通过磁共振仿真信号计算并分析不同信噪比下的T₂谱提取结果,信噪比大于30 dB时相对误差平均值小于5%;进行算法改进,得到信噪比大于10 dB时相对误差平均值小于5%的结果,且幅值和T₂的相对误差平均值降低了约1/3。由此可知:采用多指数分解法能够获得磁共振信号的T₂谱,正则化技术和加权修正能够提高T₂谱的准确度和抗干扰能力;与单指数方式相比,采用多指数拟合能够更准确地恢复信号初始振幅。     

坐骨股骨撞击综合征的MRI表现

目的：总结坐骨股骨撞击综合征（IFIS）的MRI表现,提高对该病的认识。资料与方法：回顾性分析经我院确诊的IFIS 84个髋关节（病例组）及正常志愿者髋关节116个（对照组）的MRI图像,通过轴位T1WI序列测量两组人群坐骨股骨间隙（IFS）、股方肌间隙（QFS）、坐骨结节间距,并通过质子加权脂肪抑制序列观察股方肌形态及信号。结果：独立样本t检验分析表明对照组IFS及QFS （（2.36±0.47） cm、（1.58±0.39） cm）明显大于病例组（（1.56±0.42） cm、（0.89±0.24） cm）,对照组坐骨结节间距（（10.51±1.53） cm）小于病例组（（11.39±1.01） cm）,两组之间差异均有统计学意义（P<0.05）。Pearson相关分析表明髋关节IFS与QFS之间呈显著正相关,r=0.813,P<0.05;坐骨结节间距与IFS之间存在负相关关系,r=-0.263,P<0.05。在IFIS患者中,股方肌均有不同程度的变形及水肿。所测全部数据中,中青年组IFS、QFS宽度（（2.09±0.55） cm,（1.32±0.47） cm）均大于老年组（（1.90±0.58） cm,（1.19±0.39） cm）,两组之间差异有统计学意义（P<0.05）;而两组之间坐骨结节间距无显著性差异。结论：IFS和QFS变窄,同时股方肌出现变形、水肿,是坐骨股骨撞击综合征的典型MRI表现。     

Contribution of magnetic resonance sounding to aquifer characterization and recharge estimate in semiarid Niger

To improve the knowledge of the regionally important Continental Terminal 3 (CT3) aquifer in south-western Niger, fifteen magnetic resonance soundings (MRS) were carried out in December 2005 in the vicinity of wells and boreholes. The output MRS geophysical parameters, i.e. water content and decay constants versus depth, were compared to hydrogeological characteristics, i.e. water table depth, total porosity, specific yield and transmissivity estimated from direct measurements, pumping tests and transient groundwater modelling. The MRS-determined parameters were then used to estimate the rates of groundwater recharge.Contained in poorly consolidated Tertiary sandstones, the CT3 aquifer's water table has continuously risen by 4 m in total over the past four decades. Additionally, a significant portion of this increase has occurred in the past decade alone, with an annual rise now ranging between 0.1 and 0.3 m depending on the monitored well. Increase in groundwater recharge due to land clearance and deforestation explains this situation. According to previous estimations, the pre-clearing recharge ranged from 1 to 5 mm per year in 1950–60 s, while more recent recharge rates (1990s–2000s) range from 20 to 50 mm per year. These recharge values are directly affected by estimated aquifer specific yield value, while the spatial variation of rates of water table rise can be attributed to large scale hydrodynamic heterogeneities in the aquifer. However, few field measurements were available to confirm these assumptions.The main results of this study are: (1) The water table depth and aquifer transmissivity are estimated from MRS output parameters with an average accuracy of ± 10% and ± 9% respectively. (2) The MRS-determined water content is linked to both the total porosity and the specific yield of the aquifer, but no quantitative formulation can be proposed as yet. (3) Using the average MRS-determined water content over the investigated area, i.e. 13%, the groundwater recharge rates can be estimated to be ~ 2 mm per year in the 1950–1960s (pre-clearing period), and ~ 23 mm per year for the last decade. (4) The variations in specific yield and transmissivity cannot explain by themselves the spatial variability of the rise of the water table. (5) The ranges in transmissivity and water content obtained from MRS are more realistic than the groundwater modelling outputs. Therefore, MRS could be used to better constrain the aquifer parameters in groundwater modelling with a dense site network.Finally, this work illustrates how MRS can successfully improve characterisation and transient multi-year groundwater balance of commonly found sedimentary aquifers, particularly when integrated with well observations and pumping tests.     

海潮负荷对自由核章动参数拟合的影响

基于武汉基准台超导重力仪重力潮汐观测资料 ,利用根据不同海潮模型获得的负荷重力改正值对观测数据作海潮改正 ,拟合了地球自由核章动 ( FCN)共振参数。结果表明 FCN的本征周期为 435 .2恒星日 ,品质因子为 4730 ,复共振强度为 ( - 6.34× 1 0 - 4,- 0 .0 9× 1 0 - 4)°/h。不同的海潮模型对 FCN本征周期和共振强度实部计算结果的影响很小 ,差异分别不超过± 1 .6%和± 7.7% ,对品质因子 Q值和共振强度虚部拟合结果的影响非常显著。基于 Ori96全球海潮模型得到的重力改正值可以很好地解释武汉基准台周日重力潮汐观测残差。     

2D magnetic resonance tomography applied to karstic conduit imaging

Karstic conduits play a crucial role for water supply in many parts of the world. However, the imaging of such targets is generally a difficult task for most geophysical methods. Magnetic Resonance Sounding (MRS) is a geophysical method designed for imaging of water bearing structures. Initially, MRS was developed for characterizing horizontally stratified aquifers. However, when applying a 1D MRS measuring setup to the imaging of 2D–3D targets, the size of which may be much smaller than the loop, the accuracy and the lateral resolution may not be sufficient. We have studied the possibility of simultaneously processing several MRS aligned along a profile to perform a Magnetic Resonance Tomography (MRT). This work emphasizes the gain of resolution for 2D–3D imagery of MRT versus the interpolation of 1D inversion results of MRS along the same profile. Numerical modelling results show that the MRT response is sensitive to the size and location of the 2D target in the subsurface. Sensitivity studies reveal that by using the coincident transmitting/receiving (TX/RX) setup and shifting the loop around the anomaly area, the depth, section and position of a single karstic conduit with a size smaller than the MRS loop size can be resolved. The accuracy of the results depends on the noise level and signal level, the latter parameter being linked to the depth and volume of the karstic conduit and the water content in the limestone matrix. It was shown that when applying MRT to the localization of 2D anomalies such as karstic conduits, the inclination of the geomagnetic field, the orientation of the MRT profile and the angle of crossover of the conduit by the MRT profile must be taken into account. Otherwise additional errors in interpretation should be expected. A 2D inversion scheme was developed and tested. Both numerical and experimental results confirm the efficiency of the developed approach.