Volume 6, Issue 1

This research investigates the nonlinear behavior and stability of an elastic suspended cable system under combined parametric and external excitations, with an approach of higher accuracy and reliability. Geometric nonlinearity of the cable and its in-plane and out-of-plane vibrations are considered. Multiple solutions of the system are found existing, corresponding to a single frequency of external excitation. The nonlinear stability of the cable system is investigated with focus on the influence of different system parameters. With the newly developed Periodicity-Ratio (P-R) method, the influences of different external excitations on the nonlinear vibrations of the cable system are examined, and a periodic-nonperiodic-chaotic region diagram is created for quantitatively and graphically identifying the stability and nonlinear behavior of the system.

In this paper, the counter-current imbibition phenomenon in two phase fluid through fracture porous media is discussed and Adomian decomposition method is applied to find the saturation of wetting phase and the recovery rate of the reservoir. A simulation result is developed for the saturation of wetting phase in fracture matrix and in porous matrix for some interesting choices of parametric value to study the recovery rate of the oil reservoir with dimensionless time. This problem has a great importance in the oil recovery process.

The aim of this paper is to obtain the exact solutions of the strain wave equation applied for illustrating wave propagation in microstructured solids. The effective Kudryashov and functional variable methods along with the symbolic computation system have been used to accomplish the purpose.

Numerical investigation for the effect of thermal stratification on MHD flow and heat transfer of dusty fluid over a vertical stretching sheet embedded in a thermally stratified porous medium in the presence of uniform heat source and thermal radiation. The governing equations for the problem were reduced in to dimensionless ordinary differential equations using suitable similarity transformations. The transformed nonlinear ordinary differential equations are numerically solved by applying efficient RungeKutta Fehlberg-45 Method with shooting technique. The effects of various flow controlling parameters such as Prandtl number, heat source/sink parameter, fluid particle interaction parameter, heat source parameter, radiation parameter on velocity and temperature distributions of both fluid and dust phases are depicted graphically. Finally, the numerical results are compared and found to be in good agreement with previously published results under special cases. The results indicate that the fluid phase velocity is always greater than that of the particle phase and thermal stratification significantly affects the surface shear stress as well as the surface heat transfer.

In this article, entropy generation with combined effects of thermal radiation and chemical reaction on MHD boundary layer over a moving surface has been investigated. The governing flow comprises of linear momentum equation, energy, and concentration equations which are modified with the help of similarity variables. The reduced resulting nonlinear coupled ordinary differential equations are solved with the help of Successive linearization method (SLM) and Chebyshev spectral collocation method. The impact of all the physical parameters is demonstrated numerically and graphically. A detailed analysis have been given for all the pertinent parameters such as Hartmann number, porosity parameter, Prandtl number, radiation parameter, suction/injection parameter, moving parameter, Brinkmann number, Reynolds number, chemical reaction parameter and Schmidt number on velocity, temperature, concentration and entropy profile as well as the Skin friction coefficient, Nusselt number and Sherwood number are also conducted. The numerical comparison has also been given to the existing published literature.

Vulnerability of communication of digital images is an extremely important issue nowadays, particularly when the images are communicated through insecure channels. To improve communication security, many cryptosystems have been presented in the image encryption literature. This paper proposes a novel image encryption technique based on an algorithm that is faster than current methods. The proposed algorithm eliminates the step in which the secrete key is shared during the encryption process. It is formulated based on the symmetric encryption, asymmetric encryption and steganography theories. The image is encrypted using a symmetric algorithm, then, the secret key is encrypted by means of an asymmetrical algorithm and it is hidden in the ciphered image using a least significant bits steganographic scheme. The analysis results show that while enjoying the faster computation, our method performs close to optimal in terms of accuracy.

In this paper, a numerical θ scheme is proposed for solving nonlinear Burgers’ equation. By employing Hopf-Cole transformation, the nonlinear Burgers’ equation is linearized to the linear Heat equation. The resulting Heat equation is further solved by cubic B-splines. The time discretization of linear Heat equation is carried out using Crank-Nicolson scheme θ=12$\left( {\theta = {\textstyle{1 \over 2}}} \right)$ as well as backward Euler scheme (θ = 1). Accuracy in temporal direction is improved by using Richardson extrapolation. This method hence possesses fourth order accuracy both in space and time. The system of matrix which arises by using cubic splines is always diagonal. Therefore, working with splines has the advantage of reduced computational cost and easy implementation. Stability of the schemes have been discussed in detail and shown to be unconditionally stable. Three examples have been examined and the L 2 and L ∞ error norms have been calculated to establish the performance of the method. The numerical results obtained on applying this method have shown to give more accurate results than existing works of Kutluay et al . [1], Ozis et al . [2], Dag et al . [3], Salkuyeh et al . [4] and Korkmaz et al . [5].