This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a wide time frame. Two examples are provided for showing the ability and advantages of the proposed method to approximate the solution of the power law nonlinearity of NLSEs. For pictorial representation, graphical inputs are included to represent the solution and show the precision as well as the validity of the MMRDTM.
Abstract
All central air conditioning systems contain piping system with various components, sizes, material, and layouts. If such systems in operating mode, the flow in piping system and its component such as valves can produce severe vibration due to some flow phenomenon’s. In this research, experimental measurements and numerical simulation are used to study the flow-induced vibration in valves. Computational fluid dynamics (CFD) concepts are included with one-way and two-way fluid-structure interaction concepts by using finite element software Package (ANSYS 14.57). Detection analysis is performed on flow characteristics under operation conditions and relations with structural vibration. Most of
... Show MoreVisualization of water flow around different bluff bodies at different Reynolds number ranging (1505 - 2492) was realized by designing and building a test rig which contains an open channel capable to ensure water velocity range (4-8cm/s) in this channel. Hydrogen bubbles generated from the ionized water using DC power supply are visualized by a light source and photographed by a digital camera. Flow pattern around a circular disk of (3.6cm) diameter and (3mm) thickness, a sphere of (3.8cm) diameter and a cylinder of
(3.2cm) diameter and (10cm) length are studied qualitatively. Parameters of the vortex ring generated in the wake region of the disk and the separation angle of water stream lines from the surface of the sphere are plott
In this paper, a national grid-connected photovoltaic (PV) system is proposed. It extracts the maximum power point (MPP) using three-incremental-steps perturb and observe (TISP&O) maximum power point tracking (MPPT) method. It improves the classic P&O by using three incremental duty ratio (ΔD) instead of a single one in the conventional P and O MPPT method. Therefore, the system's performance is improved to a higher speed and less power fluctuation around the MPP. The Boost converter controls the MPPT and then is connected to a three-phase voltage source inverter (VSI). This type of inverter needs a high and constant input voltage. A second-order low pass (LC) filter is connected to the output of VSI to reduce t
... Show MoreThe preparation and spectral characterization of complexes for Co(II), Ni(II), Cu(II), Cd(II), Zn(II) and Hg(II) ions with new organic heterocyclic azo imidazole dye as ligand 2-[(2`-cyano phenyl) azo ]-4,5-diphenyl imidazole ) (2-CyBAI) were prepared by reacting a dizonium salt solution of 2-cyano aniline with 4,5-diphenyl imidazole in alkaline ethanolic solution .These complexes were characterized spectroscopically by infrared and electronic spectra along with elemental analysis‚ molar conductance and magnetic susceptibility measurements. The data show that the ligand behaves a bidantate and coordinates to the metal ion via nitrogen atom of azo and with imidazole N3 atom. Octahedral environment is suggested for all metal complex
... Show MoreThe reaction oisolated and characterized by elemental analysis (C,H,N) , 1H-NMR, mass spectra and Fourier transform (Ft-IR). The reaction of the (L-AZD) with: [VO(II), Cr(III), Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg(II)], has been investigated and was isolated as tri nuclear cluster and characterized by: Ft-IR, U. v- Visible, electrical conductivity, magnetic susceptibilities at 25 Co, atomic absorption and molar ratio. Spectroscopic evidence showed that the binding of metal ions were through azide and carbonyl moieties resulting in a six- coordinating metal ions in [Cr (III), Mn (II), Co (II) and Ni (II)]. The Vo (II), Cu (II), Zn (II), Cd (II) and Hg (II) were coordinated through azide group only forming square pyramidal
... Show MoreTwo simple methods for the determination of eugenol were developed. The first depends on the oxidative coupling of eugenol with p-amino-N,N-dimethylaniline (PADA) in the presence of K3[Fe(CN)6]. A linear regression calibration plot for eugenol was constructed at 600 nm, within a concentration range of 0.25-2.50 μg.mL–1 and a correlation coefficient (r) value of 0.9988. The limits of detection (LOD) and quantitation (LOQ) were 0.086 and 0.284 μg.mL–1, respectively. The second method is based on the dispersive liquid-liquid microextraction of the derivatized oxidative coupling product of eugenol with PADA. Under the optimized extraction procedure, the extracted colored product was determined spectrophotometrically at 618 nm. A l
... Show MoreThe goal of this research is to develop a numerical model that can be used to simulate the sedimentation process under two scenarios: first, the flocculation unit is on duty, and second, the flocculation unit is out of commission. The general equation of flow and sediment transport were solved using the finite difference method, then coded using Matlab software. The result of this study was: the difference in removal efficiency between the coded model and operational model for each particle size dataset was very close, with a difference value of +3.01%, indicating that the model can be used to predict the removal efficiency of a rectangular sedimentation basin. The study also revealed
Nanosilica was extracted from rice husk, which was locally collected from the Iraqi mill at Al-Mishikhab district in Najaf Governorate, Iraq. The precipitation method was used to prepared Nanosilica powder from rice husk ash, after treating it thermally at 700°C, followed by dissolving the silica in the alkaline solution and getting a sodium silicate solution. Two samples of the final solution were collected to study the effect of filtration on the purity of the sample by X-ray fluorescence spectrometry (XRF). The result shows that the filtered samples have purity above while the non-filtered sample purity was around The structure analysis investigated by the X-ray diffraction (XRD), found that the Nanosilica powder has an amorphous
... Show MoreOur research comes to shed light on Iraqi literature as literature that arose in special circumstances alongside foreign literature. Using comparative research methods, we chose to highlight two distinguished writers, who have their mark in the world of literature. The first is the Iraqi writer Maysaloun Hadi, who is considered an icon of Iraqi feminist literature, and the second is the French writer Le Clézieu, who won the Nobel in 2008. We will see through the research how the two authors expressed their views of modernity and urbanism. And how each of them separately portrayed the psychological and moral projections that formed the essence of man today.
Résumé
Notre recherche abord un des points inc
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