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.

Background: Maxillary first premolar with wide MOD cavity more susceptible to fracture. The aim of this study was to assess the influence of cavity design for cusp coverage on the fracture resistance of weakened maxillary first premolar restored with CAD/CAM hybrid ceramic versus nanohybide composite. Materials and Methods: Fifty six intact maxillary first premolars of approximately comparable sizes were divided into seven groups eight for each: Group A: Intact teeth (control group); Group B: teeth prepared for MOD inlay; Group C: teeth prepared for MOD onlay covering the lingual cusp; Group D: teeth prepared for MOD covering buccal and lingual cusps ,the previous three groups indirectly restored with nanohybrid composite (3M ESPE Z 250 X

Background: Restoration of the gingival margin of Class II cavities with composite resin continues to be problematic, especially where no enamel exists for bonding to the gingival margin. The aim of study is to evaluate the marginal leakage at enamel and cementum margin of class II MOD cavities using amalgam restoration and modern composite restorations Filtek™ P90, Filtek™ Z250 XT (Nano Hybrid Universal Restorative) and SDR bulk fill with different restoratives techniques. Materials and method: Eighty sound maxillary first premolar teeth were collected and divided into two main groups, enamel group and cementum group (40 teeth) for each group. The enamel group was prepared with standardized Class II MOD cavity with gingival margin (1 m

Object tracking is one of the most important topics in the fields of image processing and computer vision. Object tracking is the process of finding interesting moving objects and following them from frame to frame. In this research, Active models–based object tracking algorithm is introduced. Active models are curves placed in an image domain and can evolve to segment the object of interest. Adaptive Diffusion Flow Active Model (ADFAM) is one the most famous types of Active Models. It overcomes the drawbacks of all previous versions of the Active Models specially the leakage problem, noise sensitivity, and long narrow hols or concavities. The ADFAM is well known for its very good capabilities in the segmentation process. In this

The flow measurements have increased importance in the last decades due to the shortage of water resources resulting from climate changes that request high control of the available water needed for different uses. The classical technique of open channel flow measurement by the integrating-float method was needed for measuring flow in different locations when there were no available modern devices for different reasons, such as the cost of devices. So, the use of classical techniques was taken place to solve the problem. The present study examines the integrating float method and defines the parameters affecting the acceleration of floating spheres in flowing water that was analyzed using experimental measurements. The me

This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.

       Finally, all algori

Due to wind wave actions, ships impacts, high-speed vehicles and others resources of loading, structures such as high buildings rise bridge and electric transmission towers undergo significant coupled moment loads. In this study, the effect of increasing the value of coupled moment and increasing the rigidity of raft footing on the horizontal deflection by using 3-D finite element using ABAQUS program. The results showed that the increasing the coupled moment value leads to an increase in lateral deflection and increase in the rotational angle (α◦). The rotational angle increases from (0.014, 0.15 to 0.19) at coupled moment (120 kN.m), (0.29, 0.31 and 0.49) at coupled moment (240 kN.m) and (0.57, 0.63 and 1.03) at cou

The aim of this study is to investigate the sedimentation environments and diagenetic processes of the Ibrahim Formation (Oligocene-early Miocene) in Zurbatiya, eastern Iraq. The Ibrahim Formation is comprised mostly of clayey micrite and skeletal grains composed of planktonic foraminifera, calcispheres, radiolaria, and benthic foraminifera. Glauconite and pyrite were documented in some restricted zones of this formation; they reflect quiet and reducing conditions. Radiolaria were identified in Late-Oligocene which was not known previously at this age regionally in carbonate formations of the Arabian Plate (AP). Mudstone, wackestone, and planktonic foraminiferal wackepackstone are the main microfacies that are affected by dissolutio

The BEK family of flows have many important practical applications such as centrifugal pumps, steam turbines, turbo-machinery and rotor-stator devices. The Bödewadt, Ekman and von Kármán flows are particular cases within this family. The convective instability of the BEK family of rotating boundary-layer flows has been considered for generalised Newtonian fluids, power-law and Carreau fluids. A linear stability analysis is conducted using a Chebyshev collocation method in order to investigate the effect of shear-thinning and shear-thickening fluids for generalised Newtonian fluids on the convective Type I (inviscid crossflow) and Type II (viscous streamline curvature) modes of instability. The results reveal that shear-thinning power-law

Efficiency of Pisum sativum plants in using tricalcium super phosphate (TSP) in presence and absence of mycorrhizal fungi was evaluated in the field experiment in College of Science / Al-Mustansiriyah University. The experiment comprised of (6) treatments prepared from the interaction of two levels of inoculation [non-inoculation with fungus F0 and inoculation with Glomus mosseae fungus (F1)]. And three levels of phosphorus: 0,20,40 Kg P/ha. The experimental size was (1x2)m. Irrigation and hand-weeding were done when needed. The following plant measurements were recorded: (Shoots dry weight, concentration of N and P% in addition to percentage of root infection with mycorrhizal fungi at flowering 50% of plants. The re