In this paper, a least squares group finite element method for solving coupled Burgers' problem in   2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved.  The theoretical results  show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the effic

The semiempirical (PM3) and DFT quantum mechanical methods were used to investigate the theoretical degradation of Indigo dye. The chemical reactivity of the Indigo dye was evaluated by comparing the potential energy stability of the mean bonds. Seven transition states were suggested and studied to estimate the actually starting step of the degradation reaction. The bond length and bond angle calculations indicate that the best active site in the Indigo dye molecule is at C10=C11.  The most possible transition states are examined for all suggested paths of Indigo dye degradation predicated on zero-point energy and imaginary frequency. The first starting step of the reaction mechanism is proposed. The change in enthalpy, Gibbs free energ

This work aims to optimize surface roughness, wall angle deviation, and average wall thickness as output responses of ALuminium-1050 alloy cone formed by the single point incremental sheet metal forming process. The experiments are accomplished based on the use of a mixed level Taguchi experimental design with an L18 orthogonal array. Six levels of step depth, three levels of tool diameter, feed rate, and tool rotational speed have been considered as input process parameters. The analyses of variance (ANOVA) have been used to investigate the significance of parameters and the effect of their levels for minimum surface roughness, minimum wall angle deviation, and maximum average wall thickness. The results indicate that step depth and tool r

In the context of normed space, Banach's fixed point theorem for mapping is studied in this paper. This idea is generalized in Banach's classical fixed-point theory. Fixed point theory explains many situations where maps provide great answers through an amazing combination of mathematical analysis. Picard- Lendell's theorem, Picard's theorem, implicit function theorem, and other results are created by other mathematicians later using this fixed-point theorem. We have come up with ideas that Banach's theorem can be used to easily deduce many well-known fixed-point theorems. Extending the Banach contraction principle to include metric space with modular spaces has been included in some recent research, the aim of study proves some pro

The propagation of laser beam in the underdense deuterium plasma has been studied via computer simulation using the fluid model. An appropriate computer code “HEATER” has been modified and is used for this purpose. The propagation is taken to be in a cylindrical symmetric medium. Different laser wavelengths (1 = 10.6 m, 2 = 1.06 m, and 3 = 0.53 m) with a Gaussian pulse type and 15 ns pulse widths have been considered. Absorption energy and laser flux have been calculated for different plasma and laser parameters. The absorbed laser energy showed maximum for  = 0.53 m. This high absorbitivity was inferred to the effect of the pondermotive force.

   In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the  traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit

Background: Tap waters play an important role in fulfilling the people needs for drinking and domestic purposes. Contaminate the tap water with different pollutants has become an issue of great concern for 90% of people who are depended on the tap water as the main source of drinking. Pollutants can make their way easily into the delivering pipes which suffer from the leaking resulting in decreasing the quality of water. Objective: Therefore, assess the water quality for drinking purpose by calculating the water quality index is an important tool to ascertain whether the water is suitable for human consumption or not. Methods: In the present work, the water quality of the Al-Salam, western region of Baghdad city, Iraq was investigated for 7

Given the importance of increasing economic openness transport companies’ face various issues arising at present time, this required importing different types of goods with different means of transport. Therefore, these companies pay great attention to reducing total costs of transporting commodities by using numbers means of transport methods from their sources to the destinations. The majority of private companies do not acquire the knowledge of using operations research methods, especially transport models, through which the total costs can be reduced, resulting in the importance and need to solve such a problem. This research presents a proposed method for the sum of Total Costs (Tc) of rows and columns, in order to arrive at the init

Introduction: In recent decades, the endovascular treatment of cerebral arteriovenous malformations (AVMs) has advanced. However, it still carries risks of unanticipated complications. Coil migration is a reported complication of aneurysmal coiling procedures. Herein, we report a case of early intraprocedural coil migration during pressure cooker technique embolization of right thalamic AVM, discussing the management and potential explanations. The literature showed no report of coil migration after the pressure cooker technique in the form of coil-augmented Onyx injection technique (CAIT). Case description: An otherwise healthy 26-year-old female suddenly developed a severe headache with no loss of consciousness. Computed tomograp