A novel coupled FDM-DEM modelling method for flexible membrane boundary in laboratory tests

Difficulties are involved in discrete element method (DEM) modelling of the flexible boundary, that is, the membranes covering the soil sample, which can be commonly found in contemporary laboratory soil tests. In this paper, a novel method is proposed wherein the finite difference method (FDM) and DEM are coupled to simulate the rubber membrane and soil body, respectively. Numerical plane strain and triaxial tests, served by the flexible membrane, are implemented and analysed later. The effect of the membrane modulus on the measurement accuracy is considered, with analytical formulae derived to judge the significance of this effect. Based on an analysis of stress-strain responses and the grain rotation field, the mechanical performances produced by the flexible and rigid lateral boundaries are compared for the plane strain test. The results show that (1) the effect of the membrane on the test result becomes more significant at larger strain level because the membrane applies additional lateral confining pressure to the soil body; (2) the tested models reproduce typical stress and volumetric paths for specimens with shear bands; (3) for the plane strain test, the rigid lateral boundary derives a much higher peak strength and larger bulk dilatation, but a similar residual strength, compared with the flexible boundary. The latter produces a more uniform (or ‘diffuse') rotation field and more mobilised local kinematics than does the former. All simulations show that the proposed FDM-DEM coupling method is able to simulate laboratory tests with a flexible boundary membrane.     

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 Upper Devonian Kellwasser event recorded in a regressive sequence from inner shelf to lagoonal pond,Catalan Coastal Ranges,Spain

This study, conducted in the Catalan Coastal Ranges, north‐east Spain, describes the Upper Devonian Kellwasser event in a shallowing‐upward sequence of black shales, siltstones and quartz arenites. This sequence was deposited in a progradational and regressive coastal system where the sedimentary environment evolved from the inner shelf to a lagoonal pond located landward of the shoreline. Three anomalous succeeding steps have been identified by geochemical analysis. The first one, detected on the inner shelf, was characterized by oxygen depletion and high organic productivity. The second, detected in the nearshore, was caused by hydrothermal activity occurring under normal oxic conditions. The third and most intense step was identified in the muds of the lagoonal pond and has been linked to strong anoxic conditions, elevated clastic input derived from changes in the weathering regime at the source area and moderate hydrothermal activity. The Kellwasser event is thus defined in the study area as stepwise and multi‐causal. This is the first time that the Kellwasser event has been identified in a sedimentary environment behind the shoreline. It is also the first time that it has been reported in the Catalan Coastal Ranges.     

有关边界层问题中一类奇异积分方程新的存在性结果

对边界层理论新结果中出现的一类奇异积分方程w（t）=∫1 t（1-s）（λ＋λs＋s）/w（s）ds＋（1-t）∫t 0s/w（s）ds,t∈（0,1）进行讨论，并得出了上述方程在λ∈（-1/2,0）上正解存在性的新结果。     

关于Diophantine方程的解

对于正整数a ,设S(a)是Smarandache函数。证明了 :方程S(1·2 ) +S(2·3) +… +S(x(x +1) ) =S(x(x +1) (x +2 ) /3)仅有正整数解x =1。     

用比电导法研究活性炭的吸附特性

用比电导法研究两种活性炭自稀水溶液中吸附强电解质硫酸铬和硫酸铜的吸附平衡特性。结果表明,在本文的研究条件下,两种活性炭对硫酸铬和硫酸铜都有吸附作用。同时,活性炭吸附硫酸铜的吸附平衡特性可以用 Freundlich 方程式来描述。研究的结果对固体在溶液中的吸附基础理论以及处理工业废水具有一定的意义。     

Boundary curves for families of planar orbits

For monoparametric familiesf(x,y)=c of planar orbits, created by a planar potentialV(x,y), we introduce the notion of the family boundary curves (FBC). All members of the familyf(x,y)=c are traced in an allowable region of thexy plane, defined by the corresponding FBC, with total energyE=E(c) varying along the family. Family boundary curves are also found for two-parametric familiesf(x,y,b)=c. The relation of equilibrium points and asymptotic orbits, possibly possessed by the potentialV(x,y), to be FBC is studied.     

山西省石炭系与二叠系界线

１８８２年李希霍芬在太原西山建立石炭系的太原系含煤建造以来，石炭系与二叠系的分界意见，归纳起来有三：①以Ｐｓｅｕｄｏｓｃｈｗａｇｅｒｉｎａ（ｓ．１）带之底为界，下面为石炭系，上面为二叠系；②以晋东南的灰白色“佳祥砂岩”与太原西山黄绿色“骆驼脖子砂岩”对比，砂岩底面为石炭系与二叠系的分界线，下面是石炭系山西组，上面是二叠系石盒子组，山西组的地层时代定为晚石炭世；③以晋东南灰白色第三砂岩（陵川砂岩）与太原西山“北岔沟砂岩”对比，砂岩底面为石炭系与二叠系的分界线，下面是石炭系太原组，上面是二叠系山西组，山西组的地层时代为早二叠世。笔者认为石炭系与二叠系的划分，以第③方案较适宜。