Radiation transfer in inhomogeneous dispersive media

Equations for the angular density of radiation, reflected and transmitted intensities associated with radiation scattered by inhomogeneous dispersive media are obtained. The Padé approximant technique is used to calculate these intensities in inhomogeneous and homogeneous media. The results for the [0/1] Padé approximant lead to numerical results that compared with the exact results.     

Radiative transfer in an infinite cylinder

The problem of radiation transfer in a cylinder with diffuse reflectivity and containing an energy source is connected with the source-free radiation transfer problem with isotropic boundary condition. Equation for the radiation heat flux is obtained for a polynomial source. In the special case of isotropic scattering, the radiation heat flux is given in terms of the albedo of the second problem. An expression is also given for the net radiation heat flux.     

Padé approximant calculations for the number of scattering during particle diffusion

The mean number of particle scattering in a semi-infinite and finite slab for arbitrary energy sources are calculated by Padé approximants. Uniform source distribution is considered for the finite slab. For the semi-infinite medium we calculatethe number of particles due external radiation and at a particular point in the medium. Numerical calculations and comparisons were performed.     

Discussion of “Interfacing the geographic information system,remote sensing,and the soil conservation service-curve number method to estimate curve number and runoff volume in the ASIR region of Saudi Arabia” by Fawzi S. Mohammad,Jan Adamowski

The soil conservation service curve number (SCS-CN) method is one of the most commonly used methods to compute the direct runoff from a rainfall event. Since the method was established, numerous researches were undertaken to improve the method through accurate estimation of its parameter and especially the curve number (CN). However, the essence of the SCS method, as an event-based Hortonian mechanism method, remained unchanged. The main assumption of the method related to the rainfall input is that the rainfall is continuous in time and uniform over the watershed. Mohammad and Adamowski (2015) paper apparently used the SCS method to estimate the annual runoff using the annual rainfall as one cumulative rainfall input value, which is a violation of the event-based principle of the method and of the assumption of the continuity of the rainfall event.To re-estimate the average annual runoff more realistically for the Asir region, Saudi Arabia, daily rainfall data from 14 rainfall stations are used for calculating the resulting runoff depths, on a daily event-by-event rainfall basis, throughout the whole simulation period. The resulting runoff depths are added for each year, and the total cumulative annual runoff values for each year are averaged to get the average annual runoff. The runoff values based on the previously mentioned procedure are an upper limit of the actual average annual runoff as the underlying SCS equations discard evaporation and similar long-term losses. Nevertheless, the average runoff values obtained in the discussion paper are an order of magnitude (at least five to tenfold) lower than the ones of the original paper. An equation is proposed to obtain a more realistic estimate of the average annual runoff, to be used with the average annual rainfall as an input, if the annual value is the only available rainfall information.     

Studying the impacts of groundwater evolution on the environment,west Qena city,Egypt

The current research has been conducted to evaluate groundwater aquifers qualitatively in the area located in the Western side of Qena city. The Quaternary aquifer represents the main groundwater source in the study area. It exists under unconfined to semiconfined conditions at depths varying between 4 m due North and 80 m in the South. The chemical analyses of the groundwater samples indicate that 77% of the total samples are fresh and 20% are brackish, while only 3% are saline. In addition, the iso-salinity contour map indicates that the salinity increases towards the central and northern parts of the study area. The total and permanent hardness increase as water salinity increases and vice versa in case of temporary hardness in the groundwater samples. The chemical water types and the ion ratios indicate meteoric origin of groundwater as well as the dissolution of terrestrial and marine salts. The contribution of recent recharge from the River Nile to a few groundwater wells in the study area varies from low to high. In addition, the most recharge sources are from the precipitation. Nitrate concentrations in groundwater increase towards the central and Northern areas significantly elevated in response to increasing anthropogenic land uses. Much of the solutes and physicochemical parameters in these waters are under the undesirable limits of World Health Organization (WHO) for drinking purpose, and a plot of sodium adsorption ratio versus EC shows that about 23% of the groundwater samples are good water quality, about 45% of groundwater samples are moderate quality, and 23% of the groundwater samples are intermediate water class, while the rest of samples (9%) are out of the range.     

Seismicity constraints on stress regimes along Sinai subplate boundaries

The relative movement between African, Arabian and Eurasian plates has significantly controlled the tectonic process of Sinai subplate region, although its kinematics and precise boundaries are still doubtful. The respective subplate bounded on both sides by the Aqaba-Dead Sea transform fault to the east and the Gulf of Suez, the only defined part, to the west. Seismicity parameters, moment magnitude relation and fault plane solutions were combined to determine the active tectonics along the aforementioned boundaries. Seven shallow seismogenic zones were defined by the heterogeneity in stress field orientations. Along the eastern boundary, the average fault plane solution obtained from the moment tensor summation (MTS) reveals a sinistral strike-slip faulting mechanism. The corresponding seismic strain rate tensor showed that the present tectonic stress producing earthquakes along the boundary is dominated by both NW-SE compression and NE-SW dilatation. Towards the north, the average focal mechanism showed a normal faulting mechanism of N185°E compression and an N94°E extension in the Carmel Fairi seismic zone. On the other hand, the active crustal deformation along the western boundary (Gulf of Suez region) showed a prevailing tensional stress regime of NE to ENE orientations; producing an average fault plane solution of normal faulting mechanism. The seismic strain rate tensor reveals a dominant stress regime of N58°E extension and N145°E compression in consistence with the general tectonic nature in northeastern Africa. Finally, the extensional to strike-slip stress regimes obtained in the present study emphasize that the deformation accommodated along the Sinai subplate boundaries are in consistence with the kinematics models along the plate boundaries representing the northern extremity part of the Red Sea region.     

Neoproterozoic calc‐alkaline peraluminous granitoids of the Deleihimmi pluton,Central Eastern Desert,Egypt: implications for transition from late‐ to post‐collisional tectonomagmatic evolution in the northern Arabian–Nubian Shield

The widely distributed late‐collisional calc‐alkaline granitoids in the northern Arabian–Nubian Shield (ANS) have a geodynamic interest as they represent significant addition of material into the ANS juvenile crust in a short time interval (∼630–590 Ma). The Deleihimmi granitoids in the Egyptian Central Eastern Desert are, therefore, particularly interesting since they form a multiphase pluton composed largely of late‐collisional biotite granitoids enclosing granodiorite microgranular enclaves and intruded by leuco‐ and muscovite granites. Geochemically, different granitoid phases share some features and distinctly vary in others. They display slightly peraluminous (ASI = 1–1.16), non‐alkaline (calc‐alkaline and highly fractionated calc‐alkaline), I‐type affinities. Both biotite granitoids and leucogranites show similar rare earth element (REE) patterns [(La/Lu)_N = 3.04–2.92 and 1.9–1.14; Eu/Eu* = 0.26–0.19 and 0.11–0.08, respectively) and related most likely by closed system crystal fractionation of a common parent. On the other hand, the late phase muscovite granites have distinctive geochemical features typical of rare‐metal granites. They are remarkably depleted in Sr and Ba (4–35 and 13–18 ppm, respectively), and enriched in Rb (381–473 ppm) and many rare metals. Moreover, their REE patterns show a tetrad effect (TE_1,3 = 1.13 and 1.29) and pronounced negative Eu anomalies (Eu/Eu* = 0.07 and 0.08), implying extensive open system fractionation via fluid–rock interaction during the magmatic stage. Origin of the calc‐alkaline granitoids by high degree of partial melting of mafic lower crust with subsequent crystal fractionation is advocated. The broad distribution of late‐collisional calc‐alkaline granitoids in the northern ANS is related most likely to large areal and intensive lithospheric delamination subsequent to slab break‐off and crustal/mantle thickening. Such delamination caused both crustal uplift and partial melting of the remaining mantle lithosphere in response to asthenospheric uprise. The melts produced underplate the lower crust to promote its melting. The presence of microgranular enclaves, resulting from mingling of mantle‐derived mafic magma with felsic crustal‐derived liquid, favours this process. The derivation of the late‐phase rare‐metal granites by open system fractionation via fluid interaction is almost related to the onset of extension above the rising asthenosphere that results in mantle degassing during the switch to post‐collisional stage. Consequently, the switch from late‐ to post‐collisional stage of crustal evolution in the northern ANS could be potentially significant not only geodynamically but also economically. Copyright © 2011 John Wiley & Sons, Ltd.     

Compressibility and swelling characteristics of Al-Khobar Palygorskite, eastern Saudi Arabia

Expansive soils are found in different locations in eastern Saudi Arabia. The area is arid with high temperatures, highly variable humidity and an excessive rate of evaporation compared to the low precipitation. This resulted in the formation of water sensitive soils. In the present investigation, line valve buildings for a sweet water feeder (1118 mm in diameter) were constructed on a highly expansive material consisting mainly of brown palygorskite and gray palygorskite with thin sheets of gypsum and limestone. Block samples from both palygorskites were brought to the laboratory and cores as well as remolded samples were obtained from the blocks. The two palygorskites were found to be highly plastic and have a very high swelling potential. The liquid limit (LL) and plastic limit (PL) values for the brown palygorskite are 261% and 140%, respectively. The gray palygorskite has a LL of a 285% and a PL of 123%. The oedometer free swell tests for the two palygorskites produced an expansion ranging between 31.8% and 42.5% for the remolded samples. However, the expansion for cores ranges between 8.3% and 19.3%. The constant volume pressure tests produced a stress in excess of 4240 kPa. The swell potential reached a steady state after four days while the swelling pressure reached a steady state in about 3 h. The paper addresses the geology of the area, the characterization of the geomaterial including mineralogical composition using X-ray diffraction and SEM techniques and the swelling characteristics of the material.     

The effects of intermediate principle stress on the mechanical behavior of transversely isotropic rocks: Insights from DEM simulations

The discrete element method (DEM) is used to study the response of anisotropic rocks under true triaxial testing. Numerical samples of seven different bedding orientations (β = 0^o, 15^o, 30^o, 45^o, 60^o, 75^o, and 90^o) are created. Six series of test simulations (σ₃ = 0, 10, 30, 50, 70, and 100 MPa) are conducted on each sample, with five different σ₂ values, varied from σ₃ to σ₁. The effects of anisotropy and intermediate stress on the peak strength, brittle-ductile transition, and degree of anisotropy are subsequently explained through underlying micromechanics. Results show a “fan-shaped” variation of the peak strength with σ₂, displaying an ascending-then-descending trend. An increasing brittleness with σ₂ is observed at lower confining pressures for all, but medium anisotropy angles. For higher confining pressures, increasing ductility with σ₂ is seen for every anisotropy angle. A U-shaped variation of peak strength with anisotropy angles is noted that flattens under high intermediate stress. Hence, for numerical models of Posidonia shale under normalized σ₂ higher than 0.76, the anisotropy effect is found to be negligible. Micromechanical analyses reveal that the stress asymmetry, suppression of weak plane action as well as the localization and coalescence of microcracks in the intact rock matrix, due to σ₂, are the contributors towards the obtained trends. Since existing failure criteria do not weigh in these features in geotechnical assessments, this paper helps future studies by providing a deeper understanding of these effects and a comprehensive data set for the analyses of anisotropic rocks under polyaxial stress conditions.