A second note on Hori-Lie perturbation technique

In this second note we show how to avoid the introduction of Hori's pseudo-time in analytical planetary theory in the case of the eight principal planets of our solar system excluding Pluto.     

The elimination of the 1:2 critical terms of a first order theory of Uranus perturbed by Neptune through Von Zeipel method

In this paper we eliminate in a first order U-N theory the 1 : 2 critical terms up to the third degree with respect to eccentricity — inclination in both parts, main and indirect of the U-N planetary Hamiltonian. We operate the Von Zeipel technique. We adopt, in this theory, the Jacobi-Radau coordinates, and the Poincaré canonical variables. We neglect powers higher than the third in the eccentricity-inclination. This paper is related to the two previous articles (Kamel, 1982; 1983).     

Expansion of the inverse of mutual distance between two bodies raised to any power

We calculate the expression forΔ ^-s in terms of true anomalies and classical orbital elements, referring to a common fixed plane and working up to power four of eccentricities and tangents of inclinations. We obtained two final results: the first wheny ^′>y, the second wheny>y ^′.     

Dielectric screening in the nonextensive Thomas-Fermi model

The dielectric screening process is revisited within the theoretical framework of the nonextensive Thomas-Fermi model with thermal effects. The nonextensive counterpart of the Fermion distribution function is used. It is found that the nonextensive corrections (which vanish in the zero-temperature limit) are more noticeable as the nonextensive character of the electrons becomes important. Our results should assist in interpreting the screening in dense stellar medium.     

Biodiesel synthesis from non-edible oils by transesterification using the activated carbon as heterogeneous catalyst

The need for renewable environmentally friendly energy resources is growing every day. Biodiesel is one of the most promising alternatives to the conventional non-renewable energy resources. Heterogeneous catalysts proved a high efficiency in the transesterification of oils to produce biodiesel. In this research, activated carbon was tested as a heterogeneous catalyst in the transesterification of two non-edible oils (waste cooking oil and Jatropha oil) with methanol to produce biodiesel. Activated carbon was characterized using X-ray diffraction, scanning electron microscope and Fourier transformed infrared. The effect of different operating parameters, namely operation time (30, 60, 120 and 180 min), alcohol-to-oil molar ratio (4:1, 6:1, 8:1 and 10:1), catalyst loading [0.5, 1, 2, 3 and 5% (w/w)] and rotational speed (100, 200, 300 and 400 rpm), was investigated. Results showed that increasing the operational time, the alcohol-to-oil molar ratio and the catalyst loading increases the conversion to biodiesel but only to some extent; increasing the stirring rate was found to be beneficial to the process. The optimum conditions were found to be 2 h of heating, 6:1 alcohol-to-oil ratio, 1 wt% catalyst loading and 400 rpm stirring. Under optimum conditions, the conversion to biodiesel reached 93.95 and 93.27% for the waste cooking oil and the Jatropha oil, respectively. The properties of the obtained biodiesel (density, viscosity, flash point, pour point and cloud point) were measured giving promising results.     

Intelligent methods for predicting nuclear magnetic resonance of porosity and permeability by conventional well-logs: a case study of Saharan field

In the well-log data processing, the principal advantage of the nuclear magnetic resonance (NMR) method is the measurement of fluid volume and pore size distribution without resorting to parameters such as rock resistivity. Preliminary processing of the well-log data allowed first to have the petrophysical parameters and then to evaluate the performances of the transverse relaxation time T ₂ NMR. Petrophysical parameters such as the porosity of the formation as well as the effective permeability can be estimated without having recourse the fluid type. The well-log data of five wells were completed during the construction of intelligent models in the Saharan oil field Oued Mya Basin in order to assess the reliability of the developed models. Data processing of NMR combined with conventional well data was performed by artificial intelligence. First, the support vector regression method was applied to a sandy clay reservoir with a model based on the prediction of porosity and permeability. NMR parameters estimated using intelligent systems, i.e., fuzzy logic (FL) model, back propagation neural network (BP-NN), and support vector machine, with conventional well-log data are combined with those of NMR, resulting in a good estimation of porosity and permeability. The results obtained during the processing are then compared to the FL and NN regression models performed by the regression method during the validation stage. They show that the correlation coefficients R ² estimated vary between 0.959 and 0.964, corresponding to the root mean square error values of 0.20 and 0.15.     

Effect of Water and Leachate on Hydraulic Behavior of Compacted Bentonite,Calcareous Sand and Tuff Mixtures for Use as Landfill Liners

Compacted soil–bentonite liners, consisting of a sandy soil mixed with bentonite as backfill, are used extensively as engineered barriers for contaminant containment. This paper studies the valorization of local materials containing calcareous sand, tuff obtained from Laghouat region (in the South Algeria), to associate with bentonite in order to improve their hydraulic characteristics for use as landfill liner material. Firstly, a geotechnical characterization of mixtures chooses from a fixed percentage to 10% bentonite and different percentages of calcareous sand and tuff so that they are complementary to 90% by not 10%. Thereafter, the determination of saturated hydraulic conductivity at falling-head permeability (K_v) and oedometer (K_id, indirect Measure) tests of all compacted mixtures at Optimum Normal Proctor have been carried out using both permeates by tap water and a landfill leachate in order to simulate long-term conditions. The results showed that the saturated hydraulic conductivity of tap water is relatively lower than the one saturated by leachate in the falling-head test, unlike the oedometer test. The B₁₀CS₂₀T₇₀ mixture has satisfied the hydraulic conductivity criterion of bottom barriers (i.e. water permeated: k_v20° = 1.97 × 10^?9 and k_id from 7 × 10^?9 to 1.83 × 10^?10 < 10^?9m/s; leachate permeated: k_v20° = 2.91 × 10^?9 and k_id from 7 × 10^?9 at 1.44 × 10^?10 < 10^?9 m/s). Finally, a comparison between direct measurements of the saturated hydraulic conductivity by triaxial (K_d) test and oedometer test (K_id) in the range of effective stress applied 100–800 kPa led to propose equations of correlations between these two methods. In conclusion, adopted formulation B₁₀CS₂₀T₇₀ perfectly meets the regulatory requirements in force and constitutes an economic product based on available local materials for engineers barriers.     

Flow exchange between the deep and shallow groundwaters in the Sbeϊtla synclinal basin (Tunisia): an isotopic approach

Stable (¹⁸O, ² H) and radiogenic (³H, ¹⁴C) isotopes of water have been used to constrain the source, origin, age, migration pathway and mixing processes in the Sbeïtla (Tunisia) system. The system is composed of an upper unconfined Middle Miocene aquifer with a variable thickness from 10–300 m, an intermediate confined/unconfined Lower Miocene aquifer about 100 m thick and a deeper confined Lower Cretaceous aquifer about 150 m thick separated by a thin clay layer. A total of 53 groundwater samples from the three aquifers and spring samples were collected during February and March 2000 and isotopically analysed using conventional methods. The stable isotopes composition of waters establishes that the deep groundwater (depleted as compared to present corresponding local rainfall) is ancient water recharged probably during the late Pleistocene and the early Holocene periods. The relatively recent water in the superficial aquifer is composed of mixed waters resulting presumably from upward leakage from the deeper groundwater. The radiogenic (³H, ¹⁴C) isotopes data confirm that the recent water, with a tritium content between 6.5 and 19 TU, represents post-nuclear recharge and the ancient groundwater with low carbon-14 contents between 7 and 26 pmC infiltrated between 8,000 to 20,000 years ago. When used in conjunction with the stable isotopes data, the mixing process can be clearly identified, especially in the Sbeïtla sill area. Groundwater of the upper aquifer exhibits isotopic signatures of both the old and recent waters. By using isotopic mass balance, the computed contribution of the deep groundwater in recharging the upper aquifer is up to 94%.     

A second order Jupiter-Saturn planetary theory

We complete by this part II the establishment of a second order secular Jupiter-Saturn theory. This is achieved by taking into consideration the influence of the indirect part of the planetary disturbing function, and expressing the second order secular Hamiltonian in terms of Poincaré's canonical variables.     

Application of Hori's technique in general planetary theory

In this part we present the complete solution of the planetary canonical equations of motion by the method of G. Hori through successive changes of canonical variables using the Lie series. Thus, we can eliminate the long or critical terms of the planetary perturbing function, in our general planetary theory. In our formulas, we neglect perturbation terms of order higher than the third with respect to planetary masses.