Prof. Dr. Ibrahim A. Abbas

Professor - Department of Mathematics

Faculty of science

Address: Sohag University, Egypt.



Publications Which contain the keyword: analytical solution

2018-11-30 14:29:55 Keywords analytical solution, qubits, rotating wave approximation,
Analytical solution and applications of three qubits in three coupled modes without rotating wave approximation
We study the dynamics of the three-qubit system interacting with multi-mode without rotating wave approximation (RWA). A physical realization of the system without direct qubits interactions with dephasing bath is proposed. It is shown that non-Markovian characters of the purity of the three qubits and the coupling strength of modes are stronger enough the RWA is no longer valid. The ... Read more

2018-12-03 15:38:11 Keywords analytical solution, Quantum Rabi Model,
Analytical Solution of The Two-Qubit Quantum Rabi Model
In this paper, an analytical solution of the two-qubit Rabi model for the general case is presented. Furthermore, a comparison between the information entropies and the Von Neumann entropy $(\rho_{A})$ is given for some special values of the qubit-photon coupling constants in case of the detuning parameters. It is demonstrated that oscillations of the occupation probabilities $\rho_{11}, \rho_{22}, \rho_{33}$ and ... Read more

Analytical approximations to nonlinear oscillation of nanoelectro-mechanical resonators
Abstract. We introduce a new analytical-approximate method based on the global residue harmonic balance method (GRHBM) to study the oscillation of nonlinear nanoelectromechanical resonators. The proposed method is efficiently implemented and evaluated numerically. An illustrative example demonstrates the validity and applicability of the method, further discussed in detail. A highly remarkable agreement found between the approximated solution obtained with the ... Read more

2018-10-25 07:56:57 Keywords Strongly nonlinear oscillator, analytical solution,
An analytical coupled homotopy-variational approach for solving strongly nonlinear differential equation
In the present paper, a novel technique combining the homotopy concept with variational formula has been presented to find accurate analytical solution for nonlinear differential equation with inertia and static non-linearity. The obtained results are compared with other analytical and exact solutions to confirm the excellent accuracy and correctness of the approximate analytical technique. The results of the present paper ... Read more

Analytical solution of magnetothermoelastic interaction in a fiber-reinforced anisotropic material
The present paper is concerned with the investigation of the analytical solution of a fiber-reinforced anisotropic material under generalized magnetothermoelastic theory using the eigenvalue approach. Based on the Lord-Shulman theory, the formulation is applied to generalized magnetothermoelasticity with one relaxation time. Based on eigenvalue approach, exponential Fourier transform and Laplace techniques, the analytical solutions has been obtained. The inverses of ... Read more

2018-10-08 19:23:18 Keywords Thermoelastic, analytical solution, eigenvalue approach,
Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating
In this article, we consider the problem of a two-dimensional thermoelastic half-space in the context of generalized thermoelastic theory with one relaxation time. The surface of the half-space is taken to be traction free and thermally insulated. The solution of the considered physical quantity can be broken down in terms of normal modes. The nonhomogeneous basic equations have been written ... Read more

2018-10-02 21:35:59 Keywords laser pulse, analytical solution, Thermoelastic,
Analytical solution of a two-dimensional thermoelastic problem subjected to laser pulse
In this article, the problem of a two-dimensional thermoelastic half-space are studied using mathematical methods under the purview of the generalized thermoelastic theory with one relaxation time is studied. The surface of the half-space is taken to be thermally insulated and traction free. Accordingly, the variations of physical quantities due to by laser pulse given by the heat input. The ... Read more

Analytical Solution of Thermoelastic Damping in a Nanoscale Beam using the Fractional Order Theory of Thermoelasticity
In this paper, we study the generalized thermoelastic vibration of a bounded nano-beam resonator under fractional order theory of thermoelasticity. The theory of generalized thermoelasticity with one relaxation time can be established in the limit as the special cases of the present model. The effect of fractional parameter is investigated on the nano-beam resonator for beams with clamped ends. Analytical ... Read more

Analytical Solution for a Free Vibration of a Thermoelastic Hollow Sphere
For a free vibration problem of a thermoelastic hollow sphere into the context of the generalized thermoelasticity theory with one relaxation time, exact analytic solutions are obtained with the use of eigenvalue approach. Both the inner and outer curved surfaces of the sphere are considered stress-free and isothermal surfaces. The dispersion relations for the existence of various types of possible ... Read more