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Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation 
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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
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Complex flows in heterogeneous confined and unconfined aquifers is a phenomenon that continues to present difficulties in flow mapping and modelling in the field, laboratory, and through numerical simulations. It is often the case with complicated phenomena that transformative scaling and reduction of the problem through symmetry is of great efficacy in the formation of predictive models in both the laboratory and computational settings. A detailed a study of the application of a broad class of Lie scaling transformations on a set of equations representing the groundwater flows in heterogeneous confined and unconfined aquifers has produced a set of scaling relationships between the spatial variables, hydrologic variables, and parameters. The set of scaling transformations preserve the structure of the equations in the sense that the scaling transformations leave the initial‐boundary value system representing the invariant groundwater flows. This theoretical approach elucidates not only the scaling relationships but also the properties that hydrologic variables and parameters must satisfy in order for calling to be possible. Validation of the theory developed is carried out through a series of four numerical simulations using the USGS modflow ‐2005 software package. The results of these experiments demonstrate that the derived scaling transformations can effectively form predictive models of large‐scale phenomena at small scales with negligible error in many cases. Comments on the limitations of the approach and directions for future research are made in the closing sections. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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In this review, the shifts in organic matter (OM) accumulation and C:N ratios in lake sediments to reconstruct paleoclimate and paleo-environmental changes since the early Holocene period are presented. The C:N proxy data of total OM reflect wet climatic conditions during early Holocene (10 to 8.2 kyrs BP) due to enhanced southwest monsoon. This was followed by intermittent arid conditions during the mid and late Holocene period (8.2 to 2.8 kyr BP). Enhanced values of C:N ratio during middle to late Holocene (7.8–2.3 kyrs B.P) indicate periods with lower lake levels and minimum precipitation, while decreased C:N ratio point to stronger SW monsoon and expansion of the lakes. Further, C:N and δ13C results from the lake sediments reveal a detailed and continuous paleo-environmental changes in the relative sources of OM (allochthonous vs autochthonous). Proxy records using such natural archives have also been utilized to reconstruct past extreme events and environmental changes around the lake systems, such as causes for lake desiccation, hydrographic changes, alternations between C3 and C4 vegetation and historical disturbances in the catchment area since the early-late Holocene period coupled with the Indian summer monsoon. 相似文献
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In this paper, a solution is presented for evolution of probability density function (PDF) of elastic–plastic stress–strain
relationship for material models with uncertain parameters. Developments in this paper are based on already derived general
formulation presented in the companion paper. The solution presented is then specialized to a specific Drucker–Prager elastic–plastic
material model. Three numerical problems are used to illustrate the developed solution. The stress–strain response (1D) is
given as a PDF of stress as a function of strain. The presentation of the stress–strain response through the PDF differs significantly
from the traditional presentation of such results, which are represented by a single, unique curve in stress–strain space.
In addition to that the numerical solutions are verified against closed form solutions where available (elastic). In cases
where the closed form solution does not exist (elastic–plastic), Monte Carlo simulations are used for verification. 相似文献
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Mehmet Levent Koç 《Ocean Engineering》2009,36(14):1060-1721
This paper proposes a preliminary investigation of possibility and evidence theories in a risk analysis of a vertical breakwater. The results obtained from both theories are presented and compared to the Monte Carlo simulations. This study indicates that the evidence theory approach is more flexible than the possibility theory approach and may provide a useful tool for a joint handling of variability and imprecision in the computation of risk. On the other hand, the possibility theory approach may have a good potential to be used for risk assessment of coastal structures, when sufficient data are not available. 相似文献
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Levent Altaş 《Solar physics》1994,151(1):169-176
The distribution of spotless flares (SFs) covering the time interval between 1947 and 1990 was investigated. The (11 – 20°)
latitude zone was found as the most prolific region for the occurrence of SFs. The longitudinal distribution of SFs occurred
most frequently at six or more places on the solar surface. In addition, the asymmetry of SF activity on the solar disk was
also studied in this paper. The variation of the asymmetry was compared with other solar activity manifestations. The existence
of secondary maxima of SFs appears to be an important result of our analysis. A one-year shift was found when the number of
events was plotted versus the year. 相似文献
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Acta Geotechnica - Experimental investigations on the expansion behavior of clayey soils are of great importance to correctly understand the response of the soil–foundation. In this context,... 相似文献
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There is not much information in the literature about the energy partitioning and micrometeorological features of sunn hemp. Therefore, in this study, the variations in the energy-balance components and plant characteristics such as aerodynamic and surface conductance, crop coefficient, albedo, short- and long wave down- and upward radiation have been measured and estimated for the time period from August to October 2004 over an irrigated sand field at the Arid Land Research Center in Tottori, Japan. The Bowen ratio energy-balance method was used to calculate the partitioning of heat fluxes of sunn hemp. The Bowen ratio values at the first growing stages in August were found to be higher than the Bowen ratio values at the latest growing stages in September and October because of the heavy rain and high soil-water content. The daytime averaged Bowen ratio was 0.19. During the measurement period, the daytime average net radiation, and soil, latent and sensible heat fluxes were approximately 231, 28, 164, and 39 W m–2, respectively. The net radiation and soil heat flux showed decreasing trends from the beginning to the end of the experiment period due to the atmospheric and crop growth conditions. The daytime averages of aerodynamic and surface conductance for sunn hemp were around 31 and 17 mm s–1, respectively. Also, the daytime average albedo of sunn hemp was around 19%. Finally, the high precipitation amount due to typhoons, high soil-water content, low available energy and low vapor-pressure deficit lead to decreasing trend of the energy fluxes during the generative phase of sunn hemp. 相似文献