K. Boubaker

Structural and Optothermal Properties of Iron Ditelluride Layered Structures in the Framework of the Lattice Compatibility Theory

This study concerns structural and optothermal properties of iron ditelluride layered structures which were fabricated via a low-cost protocol. The main precursors were FeCl3 · 6H2O and Fe2O3. After a heat treatment within a tellurium-rich medium at various temperatures (470°C, 500°C, and 530°C) during 24 h, classical analyses have been applied to the iron ditelluride layered structures. A good crystalline state with a preferential orientation of the crystallites along (111) direction has been recorded. Moreover, additional opto-thermal investigation and analyses within the framework of the Lattice Compatibility Theory gave plausible explanation for prompt temperature-dependent incorporation of tellurium element inside hematite elaborated matrices.

Effect of europium content on physical properties of In2O3 thin films for sensitivity and optoelectronic applications

In2O3 : Eu thin films were successfully grown by spray pyrolysis. XRD studies showed that the films had In2O3 cubic structure with (004) preferential orientation and best crystal properties at 1.5% Eu doping level. The optical band gap energy decreased with Eu content around 4.1 eV. Urbach energy was of the order of 278 meV, it decreased with Eu content which indicates a decrease in the defects by doping. The dispersion of the refractive index was discussed. Raman spectroscopy showed the band positions corresponding to In2O3 cubic phase with a small shift related to europium incorporation within In2O3 matrix. PL measurements showed a large band which was located at 410 nm and related to the band-to-band transitions and other bands related to impurity levels. Finally, the electric conductivity was investigated depending on the effect of temperature. Activation energy was found to range from 45 to 60 meV for films which were prepared with 1% Eu content.

Nonlinearities Distribution Homotopy Perturbation Method Applied to Solve Nonlinear Problems: Thomas-Fermi Equation as a Case Study

We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM). Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.

Analysis of Radiative Radial Fin with Temperature-Dependent Thermal Conductivity Using Nonlinear Differential Transformation Methods

Radiative radial fin with temperature-dependent thermal conductivity is analyzed. The calculations are carried out by using differential transformation method (DTM), which is a seminumerical-analytical solution technique that can be applied to various types of differential equations, as well as the Boubaker polynomials expansion scheme (BPES). By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related boundary conditions are transformed into a set of algebraic equations. The principle of differential transformation is briefly introduced and then applied to the aforementioned equations. Solutions are subsequently obtained by a process of inverse transformation. The current results are then compared with previously obtained results using variational iteration method (VIM), Adomian decomposition method (ADM), homotopy analysis method (HAM), and numerical solution (NS) in order to verify the accuracy of the proposed method. The findings reveal that both BPES and DTM can achieve suitable results in predicting the solution of such problems. After these verifications, we analyze fin efficiency and the effects of some physically applicable parameters in this problem such as radiation-conduction fin parameter, radiation sink temperature, heat generation, and thermal conductivity parameters.

Mathematical Models of Real Geometrical Factors in Restricted Blood Vessels for the Analysis of CAD (Coronary Artery Diseases) Using Legendre, Boubaker and Bessel Polynomials

Most cardiovascular emergencies are directly caused by coronary artery disease. Coronary arteries can become clogged or occluded, leading to damage to the heart muscle supplied by the artery. Modem cardiovascular medicine can certainly be improved by meticulous analysis of geometrical factors closely associated with the degenerative disease that results in narrowing of the coronary arteries. There are, however, inherent difficulties in developing this type of mathematical models to completely describe the real or ideal geometries that are very critical in plaque formation and thickening of the vessel wall. Neither the mathematical models of the blood vessels with arthrosclerosis generated by the heart and blood flow or the NMR/MRI data to construct them are available. In this study, a mathematical formulation for the geometrical factors that are very critical for the understanding of coronary artery disease is presented. Based on the Bloch NMR flow equations, we derive analytical expressions to describe in detail the NMR transverse magnetizations and signals as a function of some NMR flow and geometrical parameters which are invaluable for the analysis of blood flow in restricted blood vessels. The procedure would apply to the situations in which the geometry of the fatty deposits, (plague) on the interior walls of the coronary arteries is spherical. The boundary conditions are introduced based on Bessel, Boubaker and Legendre polynomials.

Approximation for transient of nonlinear circuits using RHPM and BPES methods

The microelectronics area constantly demands better and improved circuit simulation tools. Therefore, in this paper, rational homotopy perturbation method and Boubaker Polynomials Expansion Scheme are applied to a differential equation from a nonlinear circuit. Comparing the results obtained by both techniques revealed that they are effective and convenient.

AMLOUK–BOUBAKER EXPANSIVITY: A BPES-RELATED PARAMETER FOR OPTIMIZING PV–T HYBRID SOLAR CELL FUNCTIONAL MATERIALS

In this study, we define a synthetic parameter, optothermal expansivity, as a quantitative guide to evaluating and optimizing PV–T functional materials in both thermal and optical performance. This parameter, ψAB (or Amlouk–Boubaker expansivity), is calculated using both the thermal diffusivity and the optical effective absorptivity of the material. The values of this parameter, which seems to be a characteristic one, correspond to the total volume that contains a fixed amount of heat per unit time (m3s-1) and can be considered, for future use, as a 3D velocity of the transmitted heat inside the material.

Homotopy-based direct current analysis with formal stop criterion

Circuit simulation aids to predict and improve analog circuits performance. Direct current (DC) simulation highlights as a key tool to analyse linear and nonlinear circuits. Then, during the recent decades homotopy continuation methods (HCM) have been proposed as replacement for Newton-Raphson method (NR) to obtain operating points (OP) of nonlinear circuits. HCM has the ability to find multiple OP with global convergence, whilst NR method can only find one OP due to its characteristic of local convergence. Nonetheless, HCM lacks of a formal stop criterion to end DC simulations. Therefore, in this work, we propose a new double bounded homotopy (DBH) as a tool to find multiple OP of nonlinear circuits with a reliable mathematical stop criterion based on its property of forming closed trajectories. This kind of homotopy joins the other two reported DBH. Hence, we will show a performance comparison between the proposed method and the other two existent DBH; resulting in a better performance by the proposed HCM for a benchmark study case circuit having nine OP and containing bipolar transistors as nonlinear elements.

Quantum Effects of Indium/Ytterbium Doping on ZnO-Like Nano-Condensed Matter in terms of Urbach-Martienssen and Wemple-DiDomenico Single-Oscillator Models Parameters

Conducting and transparent optical ZnO thin films were deposited on glass substrates by a simple mini spray technique. Alternatively, some of the obtained films were doped with indium and ytterbium at the molar rates of: 1, 2, and 3% (In) and 100, 200, and 300 ppm (Yb). In addition to the classical structural investigations including XRD, microhardness vickers (Hv), and optothermal techniques, thorough optical measurements have been carried out for comparison purposes. The refractive indices and the extinction coefficients of the differently doped layers have been deduced from their transmission-reflection spectra over an extended wavelength range. Analysis of the refractive index data through Wemple-DiDomenico single oscillator model yielded quantum characteristics along with the values of long-wavelength dielectric constant, average oscillator wavelength, average oscillator strength, average oscillator energy and dispersion energy. Real and imaginary parts of dielectric constant have also been used to calculate free carrier plasma resonance frequency, optical relaxation time, and free carriers concentration-to-effective mass ratio. Finally, analysis of Urbach-Martienssen model parameters allowed proposing nanoscale explanations to the divergence about doping-related evolution of Urbach tails, this intriguing item having been intensively discussed in the literature in the last decades.

An efficient numerical method for computation of the number of complex zeros of real polynomials inside the open unit disk

Abstract In this paper, a simple and efficient numerical method is proposed for computing the number of complex zeros of a real polynomial lying inside the unit disk. The proposed protocol uses the Boubaker polynomial expansion scheme (BPES) to build sequence of polynomials based on the concept of Sturm sequences. The method is used in a direct way without using any restrictions in reference to other existing methods. The protocol is applied to some example polynomials of different orders and utility of the algorithm is noticed.