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.

Soil stabilization with stone powder is a good solution for the construction of subgrade for road way and railway lines, especially under the platforms and mostly in transition zones between embankments and rigid structures, where the mechanical properties of supporting soils are very influential. Stone powder often has a unique composition which justifies the need for research to study the feasibility of using this stone powder type for ground improvement applications. This paper presents results from a comprehensive laboratory study carried out to investigate the feasibility of using stone powder for improvement of engineering properties of clays.

The stone powder contains bassanite (CaSO₄. ½ H

       The present study was performed to spotlight the potential role of soil bacteria in the Al-Rumaila oil field as a bioindicator of heavy metals pollution. For this purpose, nine soil samples were collected from different sites, with 20cm depth, to assess the pollution status depending on the total and available concentrations of heavy metals.  The result indicates pollution of the studied soils with the following metals: Cd, Cu, Fe, Zn, and Pb. The mean of total concentration for all studied metals was higher than the allowed maximum limit based on the international limit:(3.394, 3.994, 39.993, 8844.979,150.372, and 103.347 µg/g), respectively. While measuring the total Metal concentration is important in determining the de

In this study, gamma-ray spectrometry with an HPGe detector was used to measure the specific activity concentrations of ²²⁶Ra, ²³²Th, and ⁴⁰K in soil samples collected from IT1 oil reservoirs in Kirkuk city, northeast Iraq. The “spectral line Gp” gamma analysis software package was used to analyze the spectral data. ²²⁶Ra specific activity varies from 9  0.34 Bq.kg^-1 to 17  0.47 Bq.kg^-1. ²³²Th specific activity varies from 6.2  0.08 Bq.kg^-1 to 18  0.2 Bq.kg^-1. ⁴⁰K specific activity varies from 25  0.19 Bq.kg^-1 to 118  0.41 Bq.kg^-1. The radiological hazard due to the radiation emitted from natural r

Cantilever beams are used in many crucial applications in machinery and construction. For example, the airplane wing, the microscopic probe for atomic force measurement, the tower crane overhang and twin overhang folding bridge are typical examples of cantilever beams. The current research aims to develop an analytical solution for the free vibration problem of cantilever beams. The dynamic response of AISI 304 beam represented by the natural frequencies was determined under different working surrounding temperatures ((-100 ℃ to 400 ℃)). A Matlab code was developed to achieve the analytical solution results, considering the effect of some beam geometrical dimensions. The developed analytical solution has been verified successful

The art of preventing the detection of hidden information messages is the way that steganography work. Several algorithms have been proposed for steganographic techniques. A major portion of these algorithms is specified for image steganography because the image has a high level of redundancy. This paper proposed an image steganography technique using a dynamic threshold produced by the discrete cosine coefficient. After dividing the green and blue channel of the cover image into 1*3-pixel blocks, check if any bits of green channel block less or equal to threshold then start to store the secret bits in blue channel block, and to increase the security not all bits in the chosen block used to store the secret bits. Firstly, store in the cente

The gas sensing properties of Co₃O₄ and Co₃O₄:Y nano structures were investigated. The films were synthesized using the hydrothermal method on a seeded layer. The XRD, SEM analysis and gas sensing properties were investigated for Co₃O₄ and Co₃O₄:Y thin films. XRD analysis shows that all films are polycrystalline in nature, having a cubic structure, and the crystallite size is (11.7)nm for cobalt oxide and (9.3)nm for the Co₃O₄:10%Y. The SEM analysis of thin films obviously indicates that Co₃O₄ possesses a nanosphere-like structure and a flower-like structure for Co₃O₄:Y.

The sen