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.

Abstract
A two electrode immersion electrostatic lens used in the design
of an electron gun, with small aberration, has been designed using
the finite element method (FEM). By choosing the appropriate
geometrical shape of there electrodes the potential V(r,z) and the
axial potential distribution have been computed using the FEM to
solve Laplace's equation.
The trajectory of the electron beam and the optical properties of
this lens combination of electrodes have been computed under
different magnification conditions (Zero and infinite magnification
conditions) from studying the properties of the designed electron
gun can be supplied with Abeam current of 5.7*10-6 A , electron
gun with half acceptance

Ag₂O (Silver Oxide) is an important p-type (in chasm to most oxides which were n-type), with a high conductivity semiconductor. From the optical absorbance data, the energy gap value of the Ag₂O thin films was 1.93 eV, where this value substantially depends on the production method, vacuum evaporation of silver, and optical properties of Ag₂O thin films are also affected by the precipitation conditions. The n-type and p-type silicon substrates were used  with porous silicon wafers to precipitate  ±125 nm, as thick Ag₂O thin film by thermal evaporation techniques in vacuum and via rapid thermal oxidation of 400^oC and oxidation time 95 s, then characterized by measurement of

A simplified theoretical comparison of the hydrogen chloride (HCl) and hydrogen fluoride (HF) chemical lasers is presented by using computer program. The program is able to predict quantitative variations of the laser characteristics as a function of rotational and vibrational quantum number. Lasing is assumed to occur in a Fabry-Perot cavity on vibration-rotation transitions between two vibrational levels of hypothetical diatomic molecule. This study include a comprehensive parametric analysis that indicates that the large rotational constant of HF laser in comparison with HCl laser makes it relatively easy to satisfy the partial inversion criterion. The results of this computer program proved their credibility when compared with th

Second harmonic generation (SHG) is a phenomenon observed in nonlinear optics that leads to frequency duplication for a high intensity laser incident on nonlinear crystal using BBO crystal. The SHG yield is achieved when the photons interact with a nonlinear optical material and effectively combine to form new photons with double frequency, and therefore double energy and half wavelength. This paper is concerned with the establishment of an SHG experiment to govern the process of producing half-wavelength laser beam from the input one. The theoretical effort was extended to compute the efficiency by using MATLAB software based on mathematical relationships. The values of the conversion maximum efficiencies, which were computed as a funct

Hyperpigmentation is the increase in the natural color of the skin. The purpose of this study is to evaluate the efficacy and safety of Q-Switched Nd:YAG (1064 & 532 nm) Laser in treatment of skin hyper pigmentation. This study was done in the research clinic of Institute of laser for postgraduate Studies/University of Baghdad from October 2008 to the end of January 2009. After clinical assessment of skin hyperpigmentation color, twenty six patients were divided according to their lesions. Eight Patients with freckles, seven patients with melasma, four patients with tattoo. Cases with tattoo, were subdivided into amateur tattoos two, professional tattoos one, and one traumatic tattoo. Four Patients with post inflammatory hyperpigment

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

Background: Cervical ectopy advanced to erosion is one of the common conditions in gynecological and pathological study. It is considered as a physiologic condition resulting from columnar epithelium migration from the cervical canal into the vaginal portion of the cervix, in which no treatment for asymptomatic cervical ectropion can be given. Treatment can be accomplished via thermal cauterization (Electro cautery), Cryosurgery. CO₂ laser therapy is another modality of treatment.

Objective: To study the effectiveness of CO₂ laser therapy and evaluate it as a biomedical tool for the treatment of cervical ectropion. The study was done at Laser Medicine Research Clinic at the