Volume 14, Issue 3-4

In this paper, the approximate solution of delay differential equations is obtained by a reliable algorithm based on an adaptation of the classical variational iteration method (VIM), which is called the multi-stage variational iteration method (MSVIM). Examples are carried out and numerical results with comparison to exact solutions, VIM and MATLAB dde23 solver are given. The comparison reveals that the MSVIM is a promising tool to solve delay differential equations.

In this article we investigate the viscous dissipation effects on mixed convection three-dimensional flow of Jeffery fluid over a vertical stretching surface. Hall and ion effects are also taken into account. The problem is first formulated and then non-dimensionalized by employing the suitable similarity transformations. Homotopy analysis method (HAM) has been employed for the computations of solutions of velocity and temperature fields. The convergence of derived series solutions is shown. The velocity components and temperature have been examined for several important parameters of interest. Numerical computations for skin friction coefficients and Nusselt number are displayed and discussed.

In this communication, we mainly focus our attention on the global dynamical behavior of forced and nonlinearly damped pendulum. We consider the nonlinear damping term proportional to the power of velocity ( v | v | p −1 ). Analytically we obtain the threshold condition for the occurrence of homoclinic bifurcation using Melnikov technique. We carry out the bifurcation analysis to identify the route to chaos for various cases of damping (p = 1, 2 and 3) and analyze the topological shape and fractalness of phase space attractor by computing Kaplan-Yorke dimension and Correlation dimension. We identify the regions of 2D parameter space (consists of external forcing amplitude and damping coefficient) corresponding to various types of asymptotic dynamics through extensive Lyapunov exponent calculation and analyze the fragileness and globalness of chaos in the parameter space with the introduction of nonlinear damping. We also analyze the complexity of basin of attraction for all three cases (p = 1, 2 and 3) and compute the correlation dimension to quantify the fractalness of basin boundaries.

In this paper, exponential stabilization and synchronization of complex-variable chaotic system are investigated. Periodically intermittent controllers are designed and applied to achieve the stabilization and synchronization. Based on the differential inequality method and the analysis technique, several simple and useful synchronization criteria are derived. Simulated examples are provided to verify the effectiveness of the proposed method.

The unsteady oscillatory magneto-hydrodynamic flow of blood in small diameter arteries with mild constriction is analyzed, blood being modelled as a Herschel-Bulkley fluid. Finite difference method is employed for solving the associated initial boundary value problem. Explicit finite difference schemes for velocity distribution, flow rate, skin friction and longitudinal impedance to the flow are obtained. The effects of pressure gradient, yield stress, magnetic field, power law index and maximum depth of the stenosis on the aforesaid flow quantities are discussed through appropriate graphs. It is found that the velocity and flow rate decrease and the skin friction and longitudinal impedance to flow increase with the increase of the magnetic field parameter. It was recorded that the flow rate increases and the skin friction decreases with the increase of the phase angle. It was also noted the skin friction and longitudinal impedance to flow that increase almost linearly with the increase of maximum depth of the stenosis. The estimates of the increase in the longitudinal impedance to flow and skin friction are increased considerably by the presence of the magnetic field.

Because of electromechanical coupled properties and anisotropy of piezoelectric materials, it is quite a challenge to obtain analytical solution and numerical solution. In the paper, the dual form of the generalized VPs for piezoelectricity are established using the variational integral method and form the Hamilton symplectic dual system for piezoelectricity. These then provide the theoretical foundation of the finite element method for piezoelectricity.

A fractal structure is introduced to Jordan-von Neumann-Wigner procedure and Jordan algebra, and some composition algebras are discussed from the point of view of a related fractal structure. Our approach aims at modifying and simplifying the Onsager-Zhang procedure of analyzing simple orthorhombic Ising lattices.

A bilinear cohesive law analyzes the in-plane nominal strength of Quasi-brittle material containing a single hole in which damage around the open hole is represented by a line crack loaded on its faces. This analysis of quasi-brittle structures has been done by taking into account the geometry and length of fracture processing zone and the shape of the cohesive law. The nominal strength based on size effect is analyzed for similarly shape specimen geometry. Simple design tables for the bilinear cohesive law have been developed respect to the specimen types offering a very useful for engineering designers.

In the present paper we study the complex dynamics of non-linear cobweb models of real estate markets in discrete time. Our model incorporates two sub-markets, land and housing, interacting with each other. We start by outlining the basic model, which assumes that land prices determine housing supply. This provides the foundations for the development of the more refined and complicated models that follow. These explore the dynamics of the real estate system, when land supply is affected by housing prices. Two forms of this relation are examined: linear and quotient, in order to investigate the dynamics of the system and the qualities and behaviour of the solutions. Stability analysis is obtained in order to investigate the stability properties of the fixed points. Various numerical simulation tools are used in order to study the complex dynamics of the systems. Finally, a global bifurcation occurring in the nonlinear case (quotient) is investigated, which changes the asymptotic behaviour of the system leading from a situation of bistability (cycle of period 2) to chaotic behaviour.