Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation          下载免费PDF全文

Tongbi Tu  Ali Ercan  M. Levent Kavvas 《水文研究》2018,32(10):1406-1419

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.  相似文献   

Developing constitutive models from EPR‐based self‐learning finite element analysis          下载免费PDF全文

Ali Nassr  Akbar Javadi  Asaad Faramarzi 《国际地质力学数值与分析法杂志》2018,42(3):401-417

A constitutive model that captures the material behavior under a wide range of loading conditions is essential for simulating complex boundary value problems. In recent years, some attempts have been made to develop constitutive models for finite element analysis using self‐learning simulation (SelfSim). Self‐learning simulation is an inverse analysis technique that extracts material behavior from some boundary measurements (eg, load and displacement). In the heart of the self‐learning framework is a neural network which is used to train and develop a constitutive model that represents the material behavior. It is generally known that neural networks suffer from a number of drawbacks. This paper utilizes evolutionary polynomial regression (EPR) in the framework of SelfSim within an automation process which is coded in Matlab environment. EPR is a hybrid data mining technique that uses a combination of a genetic algorithm and the least square method to search for mathematical equations to represent the behavior of a system. Two strategies of material modeling have been considered in the SelfSim‐based finite element analysis. These include a total stress‐strain strategy applied to analysis of a truss structure using synthetic measurement data and an incremental stress‐strain strategy applied to simulation of triaxial tests using experimental data. The results show that effective and accurate constitutive models can be developed from the proposed EPR‐based self‐learning finite element method. The EPR‐based self‐learning FEM can provide accurate predictions to engineering problems. The main advantages of using EPR over neural network are highlighted.  相似文献   

Is the age problem resolved?     

Ali Akbar Navabi  Nematollah Riazi 《Journal of Astrophysics and Astronomy》2003,24(1-2):3-10

The cosmological, astrophysical, and nucleocosmochronological methods for estimating the age of the universe and the corresponding uncertainties are comparatively studied in the present paper. We are led to the conclusion that the new measurements of cosmological parameters, and the recent estimates of the age of globular clusters have led to the gradual disappearance of the age problem from the arena of modern cosmology.  相似文献   

Nonlinear impact monitoring: line of variation searches for impactors     

Andrea Milani  Steven R. Chesley  Giacomo Tommei 《Icarus》2005,173(2):362-384

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Fault movements and tectonics of eastern Iran: boundaries of the Lut plate     

Ali A. Nowroozi  A. Mohajer-Ashjai 《Geophysical Journal International》1985,83(1):215-237

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Integration error over very long time spans     

Andrea Milani  Anna M. Nobili 《Celestial Mechanics and Dynamical Astronomy》1987,43(1-4):1-34

The main limit to the time span of a numerical integration of the planetary orbits is no longer set by the availability of computer resources, but rather by the accumulation of the integration error. By the latter we mean the difference between the computed orbit and the dynamical behaviour of the real physical system, whatever the causes. The analysis of these causes requires an interdisciplinary effort: there are physical model and parameters errors, algorithm and discretisation errors, rounding off errors and reliability problems in the computer hardware and system software, as well as instabilities in the dynamical system. We list all the sources of integration error we are aware of and discuss their relevance in determining the present limit to the time span of a meaningful integration of the orbit of the planets. At present this limit is of the order of 10⁸ years for the outer planets. We discuss in more detail the truncation error of multistep algorithms (when applied to eccentric orbits), the coefficient error, the method of Encke and the associated coordinate change error, the procedures used to test the numerical integration software and their limitations. Many problems remain open, including the one of a realistic statistical model of the rounding off error; at present, the latter can only be described by a semiempirical model based upon the simpleN ² formula (N=number of steps, =machine accuracy), with an unknown numerical coefficient which is determined only a posteriori.  相似文献   

The shape of the small satellites of Saturn: Gravitational equilibrium vs solid-state strength     

P. Farinella  A. Milani  A. M. Nobili  P. Paolicchi  V. Zappala' 《Earth, Moon, and Planets》1983,28(3):251-258

In the set of small satellites of Saturn recently imaged by the Voyager probes, we can observe the transition from irregularly-shaped, strength-dominated objects to larger, gravity-dominated bodies with shapes roughly fitting the theoretical equilibrium figures. The transition occurs for a radius of 100±50 km, corresponding to a typical material strength of the order of 10⁷ dynes cm^?2. We discuss briefly the cases of Mimas, Enceladus, Hyperion, Phoebe and the small coorbital and F-ring shepherding moons, showing that an analysis of the shape data can often provide interesting results on the physical properties, origin and collisional history of these objects.  相似文献   

SHRIMP zircon dating and Sm/Nd isotopic investigations of Neoproterozoic granitoids, Eastern Desert, Egypt   总被引：2，自引：0，他引：2  

Ewais M.M. Moussa  Robert J. Stern  William I. Manton  Kamal A. Ali 《Precambrian Research》2008,160(3-4):341-356

There is an increasing evidence for the involvement of pre-Neoproterozoic zircons in the Arabian–Nubian Shield, a Neoproterozoic crustal tract that is generally regarded to be juvenile. The source and significance of these xenocrystic zircons are not clear. In an effort to better understand this problem, older and younger granitoids from the Egyptian basement complex were analyzed for chemical composition, SHRIMP U–Pb zircon ages, and Sm–Nd isotopic compositions. Geochemically, the older granitoids are metaluminous and exhibit characteristics of I-type granites and most likely formed in a convergent margin (arc) tectonic environment. On the other hand, the younger granites are peraluminous and exhibit the characteristics of A-type granites; these are post-collisional granites. The U–Pb SHRIMP dating of zircons revealed the ages of magmatic crystallization as well as the presence of slightly older, presumably inherited zircon grains. The age determined for the older granodiorite is 652.5 ± 2.6 Ma, whereas the younger granitoids are 595–605 Ma. Xenocrystic zircons are found in most of the younger granitoid samples; the xenocrystic grains are all Neoproterozoic, but fall into three age ranges that correspond to the ages of other Eastern Desert igneous rocks, viz. 710–690, 675–650 and 635–610 Ma. The analyzed granitoids have (+3.8 to +6.5) and crystallization ages, which confirm previous indications that the Arabian–Nubian Shield is juvenile Neoproterozoic crust. These results nevertheless indicate that older Neoproterozoic crust contributed to the formation of especially the younger granite magmas.  相似文献   

Travel time based approach for the assessment of vulnerability of karst groundwater: the Transit Time Method     

Karolin Brosig  Tobias Geyer  Ali Subah  Martin Sauter 《Environmental Geology》2008,54(5):905-911

Karst aquifers represent important water resources in many parts of the world. Unfortunately, karst aquifers are characterised by high contamination risks. This paper presents a travel time based method for the estimation of karst groundwater vulnerability. It considers (1) physics-based lateral flow within the uppermost weathered zone (epikarst) in a limestone-dominated region and (2) high velocities of vertical infiltration at discrete infiltration points (e.g. sinkholes) or lines (e.g. dry valleys, faults). Consequently, the Transit Time Method honours the actual flow path within the unsaturated zone of a karst aquifer system. A test site in Northern Jordan was chosen for the demonstration of the assessment technique, i.e. the catchment area of the Qunayyah Spring north of the capital Amman. The results demonstrate that zones of highest vulnerability lie within valleys and nearby main fault zones. It also reveals that regions, categorised as protected areas by other methods due to thick unsaturated zones, contribute to a major degree to the total risk.  相似文献   

Impacts of at-site wastewater disposal systems on the groundwater aquifer in arid regions: case of Sfax City, Southern Tunisia     

Ibticem Chamtouri  Habib Abida  Hafedh Khanfir  Salem Bouri 《Environmental Geology》2008,55(5):1123-1133

Groundwater in Sfax City (Tunisia) has been known since the beginning of the century for its deterioration in quality, as a result of wastewater recharge into the aquifer. An average value of 12 × 10⁶ m³ of untreated wastewater reaches the groundwater aquifer each year. This would result not only in a chemical and biological contamination of the groundwater, but also in an increase of the aquifer piezometric level. Quantitative impacts were evaluated by examining the groundwater piezometric level at 57 surface wells and piezometers. The survey showed that, during the last two decades, the groundwater level was ever increasing in the urban area with values reaching 7 m in part; and decreasing in Sidi Abid (agricultural area) with values exceeding −3 m. Groundwater samples for chemical and microbial analysis were collected from 41 wells spread throughout the study area. Results showed significantly elevated levels of sodium, chlorides, nitrates and coliform bacteria all over the urban area. High levels (NO₃: 56–254 mg/l; Na >1,500 mg/l; Coliforms >30/100 ml) can be related to more densely populated areas with a higher density of pit latrine and recharge wells. Alternatively results showed a very variable chemical composition of groundwater, e.g. electrical conductivity ranges from 4,040 to19,620 μs/cm and the dry residual varies between 1.4 and 14 g/l with concentrations increasing downstream. Furthermore a softening of groundwater in Set Ezzit (highly populated sector) was observed.  相似文献