Papers by Abdul Aziz Ismail
Mathematics
This paper focuses on the modification of the large parameter approach (LPA), a novelty procedure... more This paper focuses on the modification of the large parameter approach (LPA), a novelty procedure, for estimating the periodic solutions of two degrees-of-freedom (DOF) autonomous quasi-linear systems with a first integral. This strategy is crucial because it provides an effective approach to recognizing approximate solutions to problems for which it is impossible to obtain exact solutions. These problems arise in the fields of physics, engineering, aerospace, and astronomy. They can be solved analytically using several perturbation approaches that depend on a small parameter that can be recognized according to the initial conditions and the body parameters of each problem. Therefore, we propose a large parameter instead of a small one to solve the aforementioned 2DOF systems, as well as provide a comparison between the suggested procedure and the previous approaches.
The non-linear Schrödinger equation associated with the soliton surfaces in Minkowski 3-space
AIMS Mathematics
The quasi frame is more efficient than the Frenet frame in investigating surfaces, and it is rega... more The quasi frame is more efficient than the Frenet frame in investigating surfaces, and it is regarded a generalization frame of both the Frenet and Bishop frames. The geometry of quasi-Hasimoto surfaces in Minkowski 3-space $ \mathbb{E}_1^3 $ is investigated in this paper. For the three situations of non-lightlike curves, the geometric features of the quasi-Hasimoto surfaces in $ \mathbb{E}_1^3 $ are examined and the Gaussian and mean curvatures for each case are determined. The quasi-Hasimoto surfaces in $ \mathbb{E}_1^3 $ must satisfy a necessary and sufficient condition to be developable surfaces. As a result, the parameter curves of quasi-Hasimoto surfaces in $ \mathbb{E}_1^3 $ is described. Thus, the $ s $-parameter and $ t $-parameter curves of quasi-Hasimoto surfaces in $ \mathbb{E}_1^3 $ are said to be geodesics, asymptotic, and curvature lines under necessary and sufficient circumstances are proved. Finally, quasi curves and associated quasi-Hasimoto surface correspondences...
Evaluation of the stability of a two degrees-of-freedom dynamical system
Journal of Low Frequency Noise, Vibration and Active Control
This work studies a two degrees-of-freedom (DOF) dynamical system whose governing system is solve... more This work studies a two degrees-of-freedom (DOF) dynamical system whose governing system is solved analytically using the multiple scales approach (MSA). The solvability requirements are obtained in light of the elimination of secular terms. All resonance states are classified to understand the equilibrium of the dynamical system. Two of them are examined in parallel to get the associated equations for the system’s modulation. All probable fixed points are identified at the states of stability and instability using the criteria of Routh-Hurwitz (RH). The curves of resonance and the system’s behavior during the motion are plotted and analyzed. The numerical solutions (NS) of the governing system are obtained using the method of Runge-Kutta fourth-order, and they are compared with the analytical solutions (AS). The comparison reveals high consistency between them and proves the accuracy of the MSA. To determine the positive effects of different parameters on the motion, stability zone...
Research Paper, 2023
This work studies a two degrees-of-freedom (DOF) dynamical system whose governing system is solve... more This work studies a two degrees-of-freedom (DOF) dynamical system whose governing system is solved analytically using the multiple scales approach (MSA). The solvability requirements are obtained in light of the elimination of secular terms. All resonance states are classified to understand the equilibrium of the dynamical system. Two of them are examined in parallel to get the associated equations for the system's modulation. All probable fixed points are identified at the states of stability and instability using the criteria of Routh-Hurwitz (RH). The curves of resonance and the system's behavior during the motion are plotted and analyzed. The numerical solutions (NS) of the governing system are obtained using the method of Runge-Kutta fourth-order, and they are compared with the analytical solutions (AS). The comparison reveals high consistency between them and proves the accuracy of the MSA. To determine the positive effects of different parameters on the motion, stability zones are studied from the perspective of their graphs. The applications of such works are very important in our daily lives and were the reason for the development of several things, including protection from earthquakes, car shock absorbers, structure vibration, human walking, television towers, high buildings, and antennas.
This research paper performs a numerical investigation on Nano-fluid’s laminar flow and the effec... more This research paper performs a numerical investigation on Nano-fluid’s laminar flow and the effect of their thermo-physical characteristics on convective heat transfer. Thus, Ag-Al2O3/H2O hybrid Nano-fluid was chosen based on its excellent properties and a magneto-hydrodynamic flow analysis inside of a modified trapezoidal porous enclosure has been conducted. Using the Darcy-Forchheimer-Brinkmann model and the finite element method to resolve the non-dimension equations, the exploitation was carried out by altering Rayleigh, Darcy, Hartmann, and the volume fraction of the hybrid Nano-fluid. The outcomes revealed intriguing results, supporting the augmentation of Ra, Da, and
to improve the average Nusselt and boost thermal transfer, and recommending that Ha should be decremented. Furthermore, the findings of this study evaluated the geometrical features of the trapezoid and indicated that decreasing the aspect ratio of the enclosure, the undulation number of the wall, and raising the inclination angle of the side walls are critical for prolonged thermal efficiency and heat transmission.
MDPI, 2023
This paper focuses on the modification of the large parameter approach (LPA), a novelty procedure... more This paper focuses on the modification of the large parameter approach (LPA), a novelty procedure, for estimating the periodic solutions of two degrees-of-freedom (DOF) autonomous quasi-linear systems with a first integral. This strategy is crucial because it provides an effective approach to recognizing approximate solutions to problems for which it is impossible to obtain exact solutions. These problems arise in the fields of physics, engineering, aerospace, and astronomy. They can be solved analytically using several perturbation approaches that depend on a small parameter that can be recognized according to the initial conditions and the body parameters of each problem. Therefore, we propose a large parameter instead of a small one to solve the aforementioned 2DOF systems, as well as provide a comparison between the suggested procedure and the previous approaches.
Complexity, 2022
In the present paper, we introduce new models of pendulum motions for two cases: the first model ... more In the present paper, we introduce new models of pendulum motions for two cases: the first model consists of a pendulum with mass M moving at the end of a string with a suspended point moving on an ellipse and the second one consists of a pendulum with mass M moving at the end of a spring with a suspended point on an ellipse. In both models, we use the Lagrangian functions for deriving the equations of motions. The derived equations are reduced to a quasilinear system of the second order. We use a new mathematical technique named a large parameter method for solving both models’ systems. The analytical solutions are obtained in terms of the generalized coordinates. We use the numerical techniques represented by the fourth-order Runge–Kutta method to solve the autonomous system for both cases. The stabilities of the obtained solutions are studied using the phase diagram procedure. The obtained numerical solutions and analytical ones are compared to examine the accuracy of the mathema...
Hindawi, 2022
In the present paper, we introduce new models of pendulum motions for two cases: the first model ... more In the present paper, we introduce new models of pendulum motions for two cases: the first model consists of a pendulum with mass M moving at the end of a string with a suspended point moving on an ellipse and the second one consists of a pendulum with mass M moving at the end of a spring with a suspended point on an ellipse. In both models, we use the Lagrangian functions for deriving the equations of motions. e derived equations are reduced to a quasilinear system of the second order. We use a new mathematical technique named a large parameter method for solving both models' systems. e analytical solutions are obtained in terms of the generalized coordinates. We use the numerical techniques represented by the fourth-order Runge-Kutta method to solve the autonomous system for both cases. e stabilities of the obtained solutions are studied using the phase diagram procedure. e obtained numerical solutions and analytical ones are compared to examine the accuracy of the mathematical and numerical techniques. e large parameter technique gives us the advantage to obtain the solutions at infinity in opposite with the famous Poincare's (small parameters) method which was used by many outstanding scientists in the last two centuries.
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Papers by Abdul Aziz Ismail
to improve the average Nusselt and boost thermal transfer, and recommending that Ha should be decremented. Furthermore, the findings of this study evaluated the geometrical features of the trapezoid and indicated that decreasing the aspect ratio of the enclosure, the undulation number of the wall, and raising the inclination angle of the side walls are critical for prolonged thermal efficiency and heat transmission.