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.

Gamma - irradiation effect on polymethylmethacrylate (PMMA) samples has been studied using Positron Annihilation Lifetime (PAL) method. The orthopositronium (o-Ps) lifetime τ₃, hence the o-ps parameters, the volume hole size (V_h) and the free volume fraction (Ꞙ_h) in the irradiated samples were measured as a function of gamma-irradiation dose up to 28.05 kGy. It has been shown that τ ₃, V_h, and Ꞙ_h, are increasing in general with increasing gamma-dose, to reach a maximum percentage increment of 22.42% in τ₃, 60% in V_h and 29.5% in Ꞙ_h, at. 2.55 kGy, whereas τ₂ reaches maximum increment of 119. 7% at 7.65 kGy. The results s

     The nuclear ground-state structure of some Nickel (^58-66Ni) isotopes has been investigated within the framework of the mean field approach using the self-consist Hartree-Fock calculations (HF) including the effective interactions of Skyrme. The Skyrme parameterizations SKM, SKM*, SI, SIII, SKO, SKE, SLY4, SKxs15, SKxs20 and SKxs25 have been utilized with HF method to study the nuclear ground state charge, mass, neutron and proton densities with the corresponding root mean square radii, charge form factors, binding energies and neutron skin thickness. The deduced results led to specifying one set or more of Skyrme parameterizations that used to achieve the best agreement with the available experimental

The -multiple mixing ratios of γ-transitions from levels of populated in the are calculated in the present work by using the a2-ratio methods. We used the experimental coefficient (a2) for two γ-transitions from the same initial state, the statistical tensor, which is related to the a2-coefficient would be the same for the two transitions. This method was used in a previous work for pure transitions or which can be considered pure. In these cases the multiple mixing ratios for the second transition ( ) equal zero, but in our work we applied this method for mixed γ-transitions and then the multiple mixing ratio ( ) is known for one transition. Then we calculate the ( ) value and versareversa. The weight average of the -values calcu

Many objective optimizations (MaOO) algorithms that intends to solve problems with many objectives (MaOP) (i.e., the problem with more than three objectives) are widely used in various areas such as industrial manufacturing, transportation, sustainability, and even in the medical sector.  Various approaches of MaOO algorithms are available and employed to handle different MaOP cases. In contrast, the performance of the MaOO algorithms assesses based on the balance between the convergence and diversity of the non-dominated solutions measured using different evaluation criteria of the quality performance indicators. Although many evaluation criteria are available, yet most of the evaluation and benchmarking of the MaOO with state-of-art a

Journal of Physics: Conference Series PAPER • THE FOLLOWING ARTICLE ISOPEN ACCESS Estimate the Rate of Contamination in Baghdad Soils By Using Numerical Method Luma Naji Mohammed Tawfiq1, Nadia H Al-Noor2 and Taghreed H Al-Noor1 Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series, Volume 1294, Issue 3 Citation Luma Naji Mohammed Tawfiq et al 2019 J. Phys.: Conf. Ser. 1294 032020 DOI 10.1088/1742-6596/1294/3/032020 DownloadArticle PDF References Download PDF 135 Total downloads 88 total citations on Dimensions. Turn on MathJax Share this article Share this content via email Share on Facebook (opens new window) Share on Twitter (opens new window) Share on Mendeley (opens new window) Hide article and author

The -multiple mixing ratios of γ-transitions from levels of  populated in the  are calculated in the present work by using the a2-ratio methods.  We used the experimental coefficient (a2) for two γ -transitions from the same initial state, the statistical tensor, which is related to the a2-coefficient would be the same for the two transitions.  This method was used in a previous work for pure transitions or which can be considered pure. In these cases the multiple mixing ratios for the second transition ( ) equal zero, but in our work we applied this method for mixed γ-transitions and then the multiple mixing ratio ( ) is known for one transition. Then we calculate the ( ) value and versareversa.  The we

The aim of this paper is to evaluate the rate of contamination in soils by using accurate numerical method as a suitable tool to evaluate the concentration of heavy metals in soil. In particular, 2D –interpolation methods are applied in the models of the spread the metals in different direction.The paper illustrates the importance of the numerical method in different applications, especially nvironment contamination. Basically, there are many roles for approximating functions. Thus, the approximating of function namely the analytical expression may be expressed; the most common type being is polynomials, which are the easy implemented and simplest methods of approximation. In this paper the divided difference formula is used and extended