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.     

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。     

CARBON DYNAMICS OF WETLAND IN THE SANJIANG PLAIN

1INTRODUCTIONWetlandsplayanimportant roleintheprocessofcar-bonstorage.Thetotalcarbonstoredindifferentkindsofwetlandsisabout15%-35%ofthetotalcarboninthegloballandsoils(POSTetal.,1982;GORHAM,1991).Inaddition,wetlandsaresignificantnaturalsources fortheatmospheric CH4 (MOORE,1994).It isestimatedthatabout110×1012gCH4 originates fromanaerobicdecompositioninthenaturalwetlands,CH4 emission fromthenaturalwetlandsis15%-30%oftheglobalCH4 emission andtheCH4 emission from thepeat land at hi…     

Bond rolling resistance and its effect on yielding of bonded granulates by DEM analyses

A discrete element modelling of bonded granulates and investigation on the bond effect on their behaviour are very important to geomechanics. This paper presents a two‐dimensional (2‐D) discrete element theory for bonded granulates with bond rolling resistance and provides a numerical investigation into the effect of bond rolling resistance on the yielding of bonded granulates. The model consists of mechanical contact models and equations governing the motion of bonded particles. The key point of the theory is that the assumption in the original bond contact model previously proposed by the authors (55th CSCE‐ASCE Conference, Hamilton, Ont., Canada, 2002; 313–320; J. Eng. Mech. (ASCE) 2005; 131 (11):1209–1213) that bonded particles are in contact at discrete points, is here replaced by a more reliable assumption that bonded particles are in contact over a width. By making the idealization that the bond contact width is continuously distributed with the normal/tangential basic elements (BE) (each BE is composed of spring, dashpot, bond, slider or divider), we establish a bond rolling contact model together with bond normal/tangential contact models, and also relate the governing equations to local equilibrium. Only one physical parameter β needs to be introduced in the theory in comparison to the original bond discrete element model. The model has been implemented into a 2‐D distinct element method code, NS2D. Using the NS2D, a total of 86 1‐D, constant stress ratio, and biaxial compressions tests have been carried out on the bonded granular samples of different densities, bonding strengths and rolling resistances. The numerical results show that: (i) the new theory predicts a larger internal friction angle, a larger yielding stress, more brittle behaviour and larger final broken contact ratio than the original bond model; (ii) the yielding stress increases nonlinearly with the increasing value of β, and (iii) the first‐yield curve (initiation of bond breakage), which define a zone of none bond breakage and which shape and size are affected by the material density, is amplified by the bond rolling resistance in analogous to that predicted by the original bond model. Copyright © 2006 John Wiley & Sons, Ltd.     

格网DEM中基于坡度信息的粗差检测与剔除方法试验

提出了一种基于格网DEM的粗差检测及剔除方法,其基本思想是对每个表面上的点,在坡度上,高程或突变量引起的形状不连续,可能被怀疑有误差,通过坡度上每个点,应用坡度逼近或改变量来计算,考虑坡度变化的相对值,并以这些相对值计算一个统计值为判断该点合法性的阈值,使计算结果更为可靠。     

Damage identification method using harmonic excitation force considering both modelling and measurement errors

A method of structural damage identification using harmonic excitation force is presented. It considers the effects of both measurement and modelling errors in the baseline finite element model. Damage that accompanies changes in structural parameters can be estimated for a damaged structure from the change between measured vibration responses and ones calculated from the analytical model of the intact structure. In practice, modelling errors exist in the analytical model due to material and geometric uncertainties and a reduction in the degrees of freedom as well as measurement errors, making identification difficult. To surmount these problems, bootstrap hypothesis testing, which enables statistical judgment without information about these errors, was introduced. The method was validated by numerical simulation using a three‐dimensional frame structure and real vibration data for a three‐storey steel frame structure. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical prediction of blast‐induced stress wave from large‐scale underground explosion

This paper presents a numerical model for predicting the dynamic response of rock mass subjected to large‐scale underground explosion. The model is calibrated against data obtained from large‐scale field tests. The Hugoniot equation of state for rock mass is adopted to calculate the pressure as a function of mass density. A piecewise linear Drucker–Prager strength criterion including the strain rate effect is employed to model the rock mass behaviour subjected to blast loading. A double scalar damage model accounting for both the compression and tension damage is introduced to simulate the damage zone around the charge chamber caused by blast loading. The model is incorporated into Autodyn3D through its user subroutines. The numerical model is then used to predict the dynamic response of rock mass, in terms of the peak particle velocity (PPV) and peak particle acceleration (PPA) attenuation laws, the damage zone, the particle velocity time histories and their frequency contents for large‐scale underground explosion tests. The computed results are found in good agreement with the field measured data; hence, the proposed model is proven to be adequate for simulating the dynamic response of rock mass subjected to large‐scale underground explosion. Extended numerical analyses indicate that, apart from the charge loading density, the stress wave intensity is also affected, but to a lesser extent, by the charge weight and the charge chamber geometry for large‐scale underground explosions. Copyright © 2004 John Wiley & Sons, Ltd.