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.     

I(L)值完全诱导空间

作者引入 I(L)值完全下半连续映射 ,研究其性质。利用 I(L)值完全下半连续映射定义I(L)值完全诱导空间 ,给出 I(L)值完全诱导空间的拓扑基的表达形式 ,证得两个 I(L)值完全诱导空间的映射是连续映射的充分必要条件 ,并建立了乘积空间的 I(L)值完全诱导空间与 I(L)值完全诱导空间的乘积空间的联系     

The Contribution of Secondary Space to Benthic Taxon Richness of a Coral Reef: Colonisation of Dendrostrea frons (Mollusca)

Abstract. The reef‐dwelling oyster Dendrostrea frons occupied only a small proportion of space in coral reefs of the Quirimba Archipelago, Mozambique, but supported a disproportionately high variety of taxa. Assemblages on primary (substratum), secondary (dead coral heads) and ephemeral secondary space (D. frons shells) of similar area were compared across 5 depths (5, 10, 15, 20 and 25 m) and at four taxonomic levels (species, genus, class and phylum). Differences between the taxonomic richness of each type of space differed with both taxonomic level considered and depth. Of the three categories of space considered, ephemeral secondary space had the most taxa at all levels with the maximum at 10 – 15 m. Despite being small in space and time, animal externa, such as shells of D. frons, may provide important niches for particular organisms at many taxonomic levels.     

南麂列岛海洋自然保护区潮间带贝类资源时空分布

为了解南麂列岛海洋自然保护区潮间带贝类十多年来的动态变化,在1992年研究基础上,于2003年度再赴南麂列岛对岩、沙相贝类进行了研究.本次调查鉴定出贝类105种,其中岩相93种、沙相12种,6种为南麂列岛新记录种,对岩相、沙相贝类组合的生态特征进行了分析,岩相多样性和均匀度指数(1.25~2.20和0.54~0.70)高于沙相的(0.23~0.95和0.17~0.94).岩相贝类数量为3025.70g/m2和2660个/m2,生物量垂直分布为低潮区最高(6471.99g/m2),中潮区居中(3772.09g/m2),高潮区最小(78.35g/m2),栖息密度为中潮区最大(4245个/m2),低潮区居中(2973个/m2),高潮区最小(439个/m2).沙相贝类数量为16.81g/m2和11个/m2,低潮区(29.43g/m2和11个/m2)大于中潮区(14.01g/m2和10个/m2).通过与以往资料比对发现,岩礁贝类数量有所增加,沙滩贝类数量则明显下降,监控区贝类数量明显多于其他区域,对贝类资源变化产生影响的相关因子作了分析探讨.     

CA-AR模型在人口空间场属性变化模拟中的应用

本文结合CA(cellular automata)和AR(auto-regression)提出模拟人口空间场属性变化的CA-AR模型,以1991～2006年成都市各区、县市的人口统计数据和成都市行政区划图为基础,将行政单元转化为单元网格,分别建立成都市主城区各单元格的CA-AR模型。结果显示,模拟结果的绝对误差和相对误差都较小,模拟精度较高,模型的显著性水平都比较高,说明CA-AR模型用于模拟人口空间场的人口数量变化是可行的。