This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

Pure and Fe-doped zinc oxide nanocrystalline films were prepared
via a sol–gel method using -
C for 2 h.
The thin films were prepared and characterized by X-ray diffraction
(XRD), atomic force microscopy (AFM), field emission scanning
electron microscopy (FE-SEM) and UV- visible spectroscopy. The
XRD results showed that ZnO has hexagonal wurtzite structure and
the Fe ions were well incorporated into the ZnO structure. As the Fe
level increased from 2 wt% to 8 wt%, the crystallite size reduced in
comparison with the pure ZnO. The transmittance spectra were then
recorded at wavelengths ranging from 300 nm to 1000 nm. The
optical band gap energy of spin-coated films also decreased as Fe
doping concentra

The structural, optical properties of cupper indium gallium selenite (CuIn1-xGaxSe) have been studied. CuIn1-xGaxSe thin films for x=0.6 have been prepared by thermal evaporation technique, of 2000±20 nm thickness, with rate of deposition 2±0.1 nm/sec, on glass substrate at room temperature. Heat treatment has been carried out in the range (373-773) K for 1 hour. It demonstrated from the XRD method that all the as-deposited and annealed films have polycrystalline structure of multiphase. The optical measurement of the CIGS thin films conformed that they have, direct allowed energy gap equal to 1.7 eV. The values of some important optical parameters of the studied films such as (absorption coefficient, refractive index, extinction coeffici

 The effect of thermal annealing on some structural and optical  properties of ZnSe thin films was studied which prepared by thermal evaporation method with (550±20) nm thickness and annealing at (373,473)K for (2h), By using X-ray diffraction technique structural properties studied and showed that the films are crystalline nature and have ( cubic structure ) .From the observed results after heating treatment, We found that the annealing to perform decreases in grain size and increases in dislocation and observed the optical properties increase in absorption and decrease in transmission. From absorption spectra optical energy gap calculated about (2.66,2.68)eV which decreases value after heating treatment

CdSe alloy has been prepared successfully from its high purity elements. Thin films of this alloy with different thicknesses (300,700)nm have been grown on glass substrates at room temperature under very low pressure (10-5)Torr with rate of deposition (1.7)nm/sec by thermal evaporation technique, after that these thin films have been heat treated under low pressure (10-2)Torr at (473,673)K for one hour. X-ray patterns showed that both CdSe alloy and thin films are polycrystalline and have the hexagonal structure with preferential orientation in the [100] and [002] direction respectively. The optical measurements indicated that CdSe thin films have allowed direct optical energy band gap, and it increases from (1.77- 1.84) eV and from

CdSe alloy has been prepared successfully from its high purity elements. Thin films of this alloy with different thicknesses (300,700)nm have been grown on glass substrates at room temperature under very low pressure (10-5)Torr with rate of deposition (1.7)nm/sec by thermal evaporation technique, after that these thin films have been heat treated under low pressure (10-2)Torr at (473,673)K for one hour. X-ray patterns showed that both CdSe alloy and thin films are polycrystalline and have the hexagonal structure with preferential orientation in the [100] and [002] direction respectively. The optical measurements indicated that CdSe thin films have allowed direct optical energy band gap, and it increases from (1.771.84) eV and from (1.6-1

     The fabricated Photodetector n-CdO /-Si factory thin films Altboukaraharara spatial silicon multi- crystallization of the type (n-Type) the deposition of a thin film of cadmium and at room temperature (300K) and thickness (300 ± 20nm) and the time of deposition (1.25sec) was antioxidant thin films cadmium (Cd) record temperature (673k) for one hour to the presence of air and calculated energy gap optical transitions electronic direct ( allowed ) a function of the absorption coefficient and permeability and reflectivity by recording the spectrum absorbance and permeability of the membrane record within the wavelengths (300 1100nm). was used several the bias ranged between 1-5 Volts. The results showed that this

Abstract

  In this study, modified organic solvent (organosolv) method was applied to remove high lignin content in the date palm fronds (type Al-Zahdi) which was taken from the Iraqi gardens. In modified organosolv, lignocellulosic material is fractionated into its constituents (lignin, cellulose and hemicellulose). In this process, solvent (organic)-water is brought into contact with the lignocellulosic biomass at high temperature, using stainless steel reactor (digester). Therefor; most of hemicellulose will remove from the biomass, while the solid residue (mainly cellulose) can be used in various industrial fields. Three variables were studied in this process: temperature, ratio of ethano