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Keywords = Wilcox expansion

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23 pages, 10120 KiB  
Article
Groundwater Quality Assessment Using Multi-Criteria GIS Modeling in Drylands: A Case Study at El-Farafra Oasis, Egyptian Western Desert
by Hanaa A. Megahed, Hossam M. GabAllah, Rasha H. Ramadan, Mohamed A. E. AbdelRahman, Paola D’Antonio, Antonio Scopa and Mahmoud H. Darwish
Water 2023, 15(7), 1376; https://doi.org/10.3390/w15071376 - 3 Apr 2023
Cited by 9 | Viewed by 3484
Abstract
The most critical issue that was the main research interest is its groundwater quality which is vital for public health concerns. Groundwater is a significant worldwide water supply for diverse communities, especially in dryland regions. Groundwater quality assessment in desert systems is largely [...] Read more.
The most critical issue that was the main research interest is its groundwater quality which is vital for public health concerns. Groundwater is a significant worldwide water supply for diverse communities, especially in dryland regions. Groundwater quality assessment in desert systems is largely hindered by the lack of hydrological data and the remote location of desert Oases. This study provides a preliminary understanding of the influences of climate, land usage, and population growth on the groundwater quality in El-Farafra Oasis in the Western Desert in Egypt from 2000 to now. Therefore, the study’s main objective was to determine the extent of change in temporal water quality and the factors causing it. The present study integrates chemical analyses and geospatial modeling better to assess groundwater quality in the study area. A chemical analysis of thirty-one groundwater samples from wells representing each study area was carried out during three time periods (2000, 2010, and 2022). Several chemical properties of groundwater samples gathered from wells in the research area were analyzed. Furthermore, the groundwater quality trend from 2000 to the present was identified using three approaches: Wilcox and Schoeller Diagram in Aq.QA software, interpolation in the ArcGIS software, and Ground Water Quality Index (GWQI). Moreover, the influence of changing land usage on groundwater quality was studied, and it was found that the increase in agriculture and urbanization areas is linked to groundwater quality degradation. The findings revealed that the barren area in 2000, 2010, and 2022 was 371.7, 362.0, and 343.2 km2, respectively, which indicates a substantial decrease of 6.2% within this research timeframe. In contrast, agriculture and human-made structures have expanded by 1.8%. Also, population growth has led to an increase in water consumption as the population has grown at a rate of 7.52% annually from 2000 to 2020. As the climatic condition increases from 2000 to 2022, these changes could extend to the water quality in shallow aquifers with increasing evaporation. Based on the water quality spatial model, it is found that, despite a declining tendency in the rate of precipitation and an expansion in agricultural areas and population growth, the water quality was still appropriate for human and farming consumption in large areas of the study area. The presented approach is applicable to the assessment of groundwater in desert regions in the Middle East area. Full article
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8 pages, 1854 KiB  
Article
Coronal Field Geometry and Solar Wind Speed
by Ivan Berezin and Andrey Tlatov
Universe 2022, 8(12), 646; https://doi.org/10.3390/universe8120646 - 5 Dec 2022
Cited by 7 | Viewed by 1988
Abstract
The Wang–Sheeley–Arge (WSA) solar wind (SW) model is based on the idea that weakly expanding coronal magnetic field tubes are associated with sources of fast SWs and vice versa. A parameter called the “flux tube expansion” (FTE) is used to determine the degree [...] Read more.
The Wang–Sheeley–Arge (WSA) solar wind (SW) model is based on the idea that weakly expanding coronal magnetic field tubes are associated with sources of fast SWs and vice versa. A parameter called the “flux tube expansion” (FTE) is used to determine the degree of expansion of magnetic tubes. The FTE is calculated based on the coronal magnetic field model, usually in the potential approximation. The second input parameter for the WSA model is the great circle distance from the base of the open magnetic field line in the photosphere to the boundary of the corresponding coronal hole (DCHB). These two coronal magnetic field parameters are related by an empirical relationship with the solar wind velocity near the Sun. The WSA model has shortcomings and does not fully explain the solar wind formation mechanisms. In the present work, we model various coronal magnetic field parameters in the potential-field source-surface (PFSS) approximation from a long series of magnetographic observations: the Solar Telescope-magnetograph for Operative Prognoses (STOP) (Kislovodsk Mountain Astronomical Station), the Helioseismic and magnetic imager (SDO/HMI), and data from the Wilcox Solar Observatory (WSO). Our main goal is to identify correlations between the coronal magnetic field parameters and the observed SW velocity in order to use them for modeling SW. We found that the SW velocity correlates relatively well with some geometric properties of the magnetic tubes, including the force line length, the latitude of the force line footpoints, and the DCHB. We propose a formula for calculating the SW velocity based on these parameters. The presented relationship does not use FTE and showed a better correlation with observations compared to the WSA model. Full article
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20 pages, 443 KiB  
Article
On a Novel Algorithmic Determination of Acoustic Low Frequency Coefficients for Arbitrary Impenetrable Scatterers
by Foteini Kariotou, Dimitris E. Sinikis and Maria Hadjinicolaou
Mathematics 2022, 10(23), 4487; https://doi.org/10.3390/math10234487 - 28 Nov 2022
Viewed by 1399
Abstract
The calculation of low frequency expansions for acoustic wave scattering has been under thorough investigation for many decades due to their utility in technological applications. In the present work, we revisit the acoustic Low Frequency Scattering theory, and we provide the theoretical framework [...] Read more.
The calculation of low frequency expansions for acoustic wave scattering has been under thorough investigation for many decades due to their utility in technological applications. In the present work, we revisit the acoustic Low Frequency Scattering theory, and we provide the theoretical framework of a new algorithmic procedure for deriving the scattering coefficients of the total pressure field, produced by a plane wave excitation of an arbitrary, convex impenetrable scatterer. The proposed semi-analytical procedure reduces the demands for computation time and errors significantly since it includes mainly algebraic and linear integral operators. Based on the Atkinson–Wilcox theorem, any order low frequency scattering coefficient can be calculated, in finite steps, through algebraic operators at all steps, except for the last one, where a regular Fredholm integral equation with a continuous and separable integral kernel is needed to be solved. Explicit, ready to use formulae are provided for the first three low frequency scattering coefficients, demonstrating the applicability of the algorithm. The validation of the obtained formulae is demonstrated through recovering of the well-known analytical results for the case of a radially symmetric scatterer. Full article
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21 pages, 627 KiB  
Article
A Unifying Framework for Perturbative Exponential Factorizations
by Ana Arnal, Fernando Casas, Cristina Chiralt and José Angel Oteo
Mathematics 2021, 9(6), 637; https://doi.org/10.3390/math9060637 - 17 Mar 2021
Cited by 2 | Viewed by 2171
Abstract
We propose a framework where Fer and Wilcox expansions for the solution of differential equations are derived from two particular choices for the initial transformation that seeds the product expansion. In this scheme, intermediate expansions can also be envisaged. Recurrence formulas are developed. [...] Read more.
We propose a framework where Fer and Wilcox expansions for the solution of differential equations are derived from two particular choices for the initial transformation that seeds the product expansion. In this scheme, intermediate expansions can also be envisaged. Recurrence formulas are developed. A new lower bound for the convergence of the Wilcox expansion is provided, as well as some applications of the results. In particular, two examples are worked out up to a high order of approximation to illustrate the behavior of the Wilcox expansion. Full article
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