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.     

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。     

Effect of metamorphism and partial melting of host rocks on zircons

Abstract Zircons have been studied from different layers of migmatites (from Arvika, western Sweden and Nelaug, southern Norway) and from a paragneiss (from Arvika) associated with one of the migmatites. The main purpose of the investigation is to establish whether or not information about zircons can help in the elucidation of the parentage and rock-forming processes of migmatites.
The elongation ratio of zircons from all layers is small and characteristic of sedimentary zircons. Further, the absence of characteristic colours and the growth trends of the zircons (indicated by the reduced major axes) observed in the various samples both support a sedimentary parentage for these rocks. The zircons of all layers exhibit secondary growth (overgrowth, outgrowth and multiple growth) due to metamorphism. Compared with the zircons from the paragneiss, those of the migmatite layers are more clouded and less rounded, some of them becoming opaque or even skeletal; this is especially true of the zircons from the leucosomes. These observations indicate an alteration of the original sedimentary zircons in the migmatite, especially in the leucosomes, in response to the migmatization process, previously interpreted as partial melting.     

Microboudin structures of piemontite along the Sambagawa metamorphic belt, Japan: implications for lateral variation of differential stress during regional metamorphism

Evidence is presented of a lateral variation in differential stress during metamorphism along a regional metamorphic belt on the basis of the proportion of microboudinaged piemontite grains (p) in a quartz matrix in metacherts. It is proposed that p is a practical indicator of relative differential stress. Analysis of 123 metacherts from the 800 km long Sambagawa metamorphic belt, Japan, reveals that p‐values range from < 0.01 to 0.7 in this region. Most samples from Wakayama in the mid‐belt area have p‐values of 0.4–0.6, whereas those from western Shikoku have p‐values of < 0.1. This difference cannot be explained by variations in metamorphic temperature, and is instead attributed to a regional, lateral variation in differential stress during metamorphism.     

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.     

Infiltration at the Tai rain forest (Ivory Coast): Measurements and modelling

Infiltration experiments have been performed at three sites along a well-known catena under virgin tropical rain forest using a portable sprinkling infiltrometer. Experimentally determined infiltration curves are presented. Infiltration curves are also simulated on the basis of the Mein-Larson equation. The parameters for this model have been obtained from the infiltration curves (saturated conductivity) and simple soil moisture determinations (fillable porosity). The agreement between experimentally determined and modelled infiltration is reasonable, provided (a) saturated conductivity as derived from the experimental data is corrected, (b) a storage parameter, also derived from the experimental data, is added to the Mein-Larson model, and (c) the decline in soil porosity with depth is either small or occurs abruptly at shallow depth. Comparison of observed infiltration rates with rainfall intensity shows that Horton Overland Flow has to occur naturally at least on the middle and lower section of the catena. Despite the fact that most parameters can be estimated in principle from basic soil data, it remains advisable to obtain sprinkling infiltrometer field measurements, because of soil variability due to dynamic surface conditions, macroporosity, air entrapment, and irregularity of the wetting front.     

Partial crustal melting beneath the Betic Cordillera (SE Spain): The case study of Mar Menor volcanic suite

The Neogene Volcanic Province (NVP) within the Betic Cordillera (SE Spain) consists of three main metapelitic enclave suites (from SW to NE: El Hoyazo, Mazarrón and Mar Menor). Since the NVP represents a singular place in the world where crustal enclaves were immediately quenched after melting, their microstructures provide a “photograph” of the conditions at depth just after the moment of the melting.

The thermobarometric information provided by the different microstructural assemblages has been integrated with the geophysical and geodynamical published data into a model of the petrologic evolution of the Mar Menor enclaves. They were equilibrated at 2–3 kbar, 850–900 °C, and followed a sequence of heating melt producing reactions. A local cooling event evidenced by minor melt crystallization preceded the eruption.

The lower crustal studies presented in this work contribute to the knowledge of: (i) the partial melting event beneath the Mar Menor volcanic suite through a petrologic detailed study of the enclaves; (ii) how the microstructures of fast cooled anatectic rocks play an important role in tracing the magma evolution in a chamber up to the eruption, and how they can be used as pseudothermobarometers; (iii) the past and current evolution of the Alborán Domain (Betic Cordillera) and Mediterranean Sea, and how the base of a metapelitic crust has melted within an active geodynamic setting.