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1.
The groundwater divide is a key feature of river basins and significantly influenced by subsurface hydrological processes. For an unconfined aquifer between two parallel rivers or ditches, it has long been defined as the top of the water table based on the Dupuit–Forchheimer approximation. However, the exact groundwater divide is subject to the interface between two local flow systems transporting groundwater to rivers from the infiltration recharge. This study contributes a new analytical model for two-dimensional groundwater flow between rivers of different water levels. The flownet is delineated in the model to identify groundwater flow systems and the exact groundwater divide. Formulas with two dimensionless parameters are derived to determine the distributed hydraulic head, the top of the water table and the groundwater divide. The locations of the groundwater divide and the top of the water table are not the same. The distance between them in horizontal can reach up to 8.9% of the distance between rivers. Numerical verifications indicate that simplifications in the analytical model do not significantly cause misestimates in the location of the groundwater divide. In contrast, the Dupuit–Forchheimer approximation yields an incorrect water table shape. The new analytical model is applied to investigate groundwater divides in the Loess Plateau, China, with a Monte Carlo simulation process taking into account the uncertainties in the parameters. 相似文献
2.
Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation 下载免费PDF全文
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
3.
Janis Britals 《Celestial Mechanics and Dynamical Astronomy》1992,54(4):305-316
It is shown in this paper how to build a canonical transformation of variables, so that the eccentric anomaly becomes the new independent variable. In the case of eccentric elliptical orbits it changes the equations of motion so, that they can be integrated analytically to any order of approximation comparatively easy. 相似文献
4.
本文对Osherovich的黑子返回磁通量模型作了适当的修改,使用黑子中心作为边界条件,用五种观测结果,导出了理论模型所需的五个主要参量,用半经验方法求得了黑子静力学模型的磁场、压力和温度等物理量.将此模型应用于一个中等大小的圆形对称黑子,可得到一个特解,结果发现我们的模型既能满足黑子的磁性质,同时又能满足合理的热力学量分布. 相似文献
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George Saklatvala Michael P. Hobson Stafford Withington 《Monthly notices of the Royal Astronomical Society》2006,367(3):1194-1200
We describe a procedure for the numerical modelling of astronomical interferometers, with particular relevance to far-infrared and submillimetre wavelengths. The scheme is based on identifying a set of modes that carry power from the sky to the detector. The procedure is extremely general, and can be used to model scalar or vector fields, in any state of coherence and polarization, the only limitation being that the propagation of a coherent field through the system be described by an integral transform, a constraint that is in practise always met.
We present simulations of ideal, multimode two-dimensional interferometers, and show that the modal theory reproduces the correct behaviour of both Michelson and Fizeau interferometers. We calculate simulated visibility data for a multimode bolometric Michelson interferometer, with a synthesized source, and produce a dirty map, recovering the original source with the usual artefacts associated with interferometers. 相似文献
We present simulations of ideal, multimode two-dimensional interferometers, and show that the modal theory reproduces the correct behaviour of both Michelson and Fizeau interferometers. We calculate simulated visibility data for a multimode bolometric Michelson interferometer, with a synthesized source, and produce a dirty map, recovering the original source with the usual artefacts associated with interferometers. 相似文献
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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。 相似文献
9.
乐茂华 《广东海洋大学学报》2004,24(4):47-48
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。 相似文献
10.