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.

This paper reports an experimental study of welding of dissimilar materials between transparent Polymethylmethacrylate (PMMA) and stainless steel 304 sheets using a pulsed mode Nd:YAG laser. The process was carried out for two cases; laser transmission joining (LTJ) and conduction joining (CJ). The former is achieved when the joint is irradiated from the polymer side and the latter when the joint is irradiated from the opposite side (metal side). The light and process parameters represented by the peak power (Pp), pulse duration (τ), pulse repetition rate (PRR), scanning speed (ν) and pulse shape have a significant effect on the joint strength (Fb), joint bead width (b), joint quality and appearance. The optimum parameters were determined

Flexure members such as reinforced concrete (RC) simply supported beams subjected to two-point loading were analyzed numerically. The Extended Finite Element Method (XFEM) was employed for the treatment the non-smooth h behaviour such as discontinuities and singularities. This method is a powerful technique used for the analysis of the fracture process and crack propagation in concrete. Concrete is a heterogeneous material that consists of coarse aggregate, cement mortar and air voids distributed in the cement paste. Numerical modeling of concrete comprises a two-scale model, using mesoscale and macroscale numerical models. The effectiveness and validity of the Meso-Scale Approach (MSA) in modeling of the reinforced concrete beams w

Continuous escalation of the cost of generating energy is preceded by the fact of scary depletion of the energy reserve of the fossil fuels and pollution of the environment as developed and developing countries burn these fuels. To meet the challenge of the impending energy crisis, renewable energy has been growing rapidly in the last decade. Among the renewable energy sources, solar energy is the most extensively available energy, has the least effect on the environment, and is very efficient in terms of energy conversion. Thus, solar energy has become one of the preferred sources of renewable energy. Flat-plate solar collectors are one of the extensively-used and well-known types of solar collectors. However, the effectiveness of the coll

                The characteristics of sulfur nanoparticles were studied by using atomic force microscope (AFM) analysis. The atomic force microscope (AFM) measurements showed that the average size of sulfur nanoparticles synthesized using thiosulfate sodium solution through the extract of cucurbita pepo extra was 93.62 nm. Protecting galvanized steel from corrosion in salt media was achieved by using sulfur nanoparticles in different temperatures. The obtained data of thermodynamic in the presence of sulfur nanoparticles referred to high value as compares to counterpart in the absence of sulfur nanoparticles, the high inhibition efficiency (%IE) and corrosion resistance were at high temperature, the corrosion rate or weig

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

Image is an important digital information that used in many internet of things (IoT) applications such as transport, healthcare, agriculture, military, vehicles and wildlife. etc. Also, any image has very important characteristic such as large size, strong correlation and huge redundancy, therefore, encrypting it by using single key Advanced Encryption Standard (AES) through IoT communication technologies makes it vulnerable to many threats, thus, the pixels that have the same values will be encrypted to another pixels that have same values when they use the same key. The contribution of this work is to increase the security of transferred image. This paper proposed multiple key AES algorithm (MECCAES) to improve the security of the tran

The Dirichlet process is an important fundamental object in nonparametric Bayesian modelling, applied to a wide range of problems in machine learning, statistics, and bioinformatics, among other fields. This flexible stochastic process models rich data structures with unknown or evolving number of clusters. It is a valuable tool for encoding the true complexity of real-world data in computer models. Our results show that the Dirichlet process improves, both in distribution density and in signal-to-noise ratio, with larger sample size; achieves slow decay rate to its base distribution; has improved convergence and stability; and thrives with a Gaussian base distribution, which is much better than the Gamma distribution. The performance depen