Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.     

The response of an elastic half‐space under a momentary shear line impulse

The response of an ideal elastic half‐space to a line‐concentrated impulsive vector shear force applied momentarily is obtained by an analytical–numerical computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. The shear force is concentrated along an infinite line, drawn on the surface of the half‐space, while being normal to that line as well as to the axis of symmetry of the half‐space. An exact loading model is introduced and built into the computational method for this shear force. With this model, a compatibility exists among the prescribed applied force, the geometric decay of the shear stress component at the precursor shear wave, and the boundary conditions of the half‐space; in this sense, the source configuration is exact. For the transient boundary‐value problem described above, a wave characteristics formulation is presented, where its differential equations are extended to allow for strong discontinuities which occur in the material motion of the half‐space. A numerical integration of these extended differential equations is then carried out in a three‐dimensional spatiotemporal wavegrid formed by the Cartesian bicharacteristic curves of the wave characteristics formulation. This work is devoted to the construction of the computational method and to the concepts involved therein, whereas the interpretation of the resultant transient deformation of the half‐space is presented in a subsequent paper. Copyright © 2003 John Wiley & Sons, Ltd.     

Human spaceflight in the UK: the cost of non-participation

Human space exploration is not considered a strategic priority in the United Kingdom at present. However the UK would benefit from participating in human spaceflight, for both scientific and social reasons. From the point of view of medical science there are many parallels between the physiology of spaceflight and terrestrial disease processes, and studies of the response of astronauts to long-duration spaceflight can therefore help in the development of therapeutic strategies on Earth. On the social side, human spaceflight is an attractive vehicle for stimulating the interest of young people in science and engineering, something that must be of value for an aspiring ‘knowledge-based’ economy.     

The 550-au Mission: a critical discussion

We have studied the science rationale, goals and requirements for a mission aimed at using the gravitational lensing from the Sun as a way of achieving high angular resolution and high signal amplification. We find that such a mission concept is compromised by several practical problems. Most severe are the effects due to the plasma in the solar atmosphere which cause refraction and scattering of the propagating rays. These effects either limit the frequencies that can be observed to those above ∼1 THz, or they move the optical point outwards beyond the vacuum value of ≥550 au. (Thus for observing frequency of 300 GHz the optical point is moved outwards to ∼ 680 au.) Density fluctuations in the inner solar atmosphere will further cause random pathlength differences for different rays. The corrections for the radiation from the Sun itself will also be a major challenge at any wavelength used, but could be mitigated with coronographic techniques. Given reasonable constraints on the spacecraft (particularly in terms of size and propulsion), source selection as well as severe navigational constraints further add to the difficulties for a potential mission. Nevertheless, unbiased surveys of small-scale structure on the sky at short wavelengths might be the most promising application of such a mission.     

概率赋范空间的S-凸和K-凸

文献[1][2]认为M－PN空间是局部凸的。通过定理说明这个结论对t-模T（a,b)≥min(a,b)时成立。又通过反例表明，当t-模型T（a,b)=max(a b-1,0）时无论邻域Nθ（ε，λ）概率有界还是概率半有界结论均不成立。还讨论了Takahashi凸性并对S－凸和K－凸作了比较。     

Elastic solutions for stresses in a transversely isotropic half‐space subjected to three‐dimensional buried parabolic rectangular loads

In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half‐space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half‐space, induced by three‐dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian co‐ordinate system for a transversely isotropic half‐space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half‐spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. Copyright © 2002 John Wiley & Sons, Ltd.     

彭州市立体农业气候资源的研究(一)降水资源分析

分析了彭州市境内位于不同海拔高度的4个观测站的降水资料，结果表明，彭州市雨量充沛，但降水量的年际变化显著，雨季起、止时间和雨季长、短的年际变化很大，降水的时间分配极不均匀，因为这4个站具有相同的气候背景、，降水量的年、季、月变化呈现基本一致的规律和趋势，但因为海拔高度不同等气候背的差异，4站的降水特点又显著不同。降水量随海拔高度的升高而增加，降水变幅和雨日也阴海拔高度的升高而增加，大降水过程具有明显的局地性，不同海拔高度的旱、涝情况亦有差异，降水的空间分布表现出明显的立体性特征。     

Occurrence and evolution of the Xiaotangshan hot spring in Beijing, China

Thermal groundwater occurs in bedrock aquifers consisting of the dolomite of the Wumishan Group of the Jixianin System and the Cambrian carbonate in the Xiaotangshan geothermal field near the northern margin of the North China Plain, China. The hot water in the geothermal field of basin-type discharges partly in the form of the Xiaotangshan hot spring under natural conditions. The hot water has TDS of less than 600 mg/L and is of Na·Ca-HCO₃ type. The geothermal water receives recharge from precipitation in the mountain area with elevation of about 500 m above sea level to the north of the spring. Thermal groundwater flows slowly south and southeast through a deep circulation with a residence time of 224 years estimated with the Ra–Rn method. The Xiaotangshan hot spring dried up in the middle of the 1980s owing to the increasing withdrawal of the hot water in the geothermal field in the past decades. The water level of the geothermal system still falls continually at an annual average rate of about 2 m, although water temperature changes very little, indicating that the recharge of such a geothermal system of basin-type is limited. Over-exploitation has a dramatic impact on the geothermal system, and reduction in exploitation and reinjection are required for the sustainable usage of the hot water.     

Application of MODFLOW and geographic information system to groundwater flow simulation in North China Plain, China

MODFLOW is a groundwater modeling program. It can be compiled and remedied according to the practical applications. Because of its structure and fixed data format, MODFLOW can be integrated with Geographic Information Systems (GIS) technology for water resource management. The North China Plain (NCP), which is the politic, economic and cultural center of China, is facing with water resources shortage and water pollution. Groundwater is the main water resource for industrial, agricultural and domestic usage. It is necessary to evaluate the groundwater resources of the NCP as an entire aquifer system. With the development of computer and internet information technology it is also necessary to integrate the groundwater model with the GIS technology. Because the geological and hydrogeological data in the NCP was mainly in MAPGIS format, the powerful function of GIS of disposing of and analyzing spatial data and computer languages such as Visual C and Visual Basic were used to define the relationship between the original data and model data. After analyzing the geological and hydrogeological conditions of the NCP, the groundwater flow numerical simulation modeling was constructed with MODFLOW. On the basis of GIS, a dynamic evaluation system for groundwater resources under the internet circumstance was completed. During the process of constructing the groundwater model, a water budget was analyzed, which showed a negative budget in the NCP. The simulation period was from 1 January 2002 to 31 December 2003. During this period, the total recharge of the groundwater system was 49,374 × 10⁶ m³ and the total discharge was 56,530 × 10⁶ m³ the budget deficit was −7,156 × 10⁶ m³. In this integrated system, the original data including graphs and attribution data could be stored in the database. When the process of evaluating and predicting groundwater flow was started, these data were transformed into files that the core program of MODFLOW could read. The calculated water level and drawdown could be displayed and reviewed online.     

气举反循环采矿方法单井试验及应用探讨

湖南道县一个矿区,铁锰矿体储量约2200万t。由于复杂的水文地质和工程地质条件,从20世纪70年代发现后,一直没有开采。笔者通过多年大直径工程井的实践经验,查阅国内外资料后,提出了钻井-气举反循环法试开采的方法,并在现场进行了单孔开采试验,获得了比较满意的效果。以该矿体Ⅱ号矿为例,介绍了钻井-气举反循环法采矿的适用条件、工艺过程以及试采情况,并就以后大面积开采提出了若干技术措施。