Volume 65, Issue 5

The primary and subharmonic resonances of a nonlinear single-degree-of-freedom system under feedback control with a time delay are studied by means of an asymptotic perturbation technique. Both external (forcing) and parametric excitations are included. By means of the averaging method and multiple scales method, two slow-flow equations for the amplitude and phase of the primary and subharmonic resonances and all other parameters are obtained. The steady state (fixed points) corresponding to a periodic motion of the starting system is investigated and frequency-response curves are shown. The stability of the fixed points is examined using the variational method. The effect of the feedback gains, the time-delay, the coefficient of cubic term, and the coefficients of external and parametric excitations on the steady-state responses are investigated and the results are presented as plots of the steady-state response amplitude versus the detuning parameter. The results obtained by two methods are in excellent agreement

In the present article, we have studied the effects of heat transfer on a peristaltic flow of a magnetohydrodynamic (MHD) Newtonian fluid in a porous concentric horizontal tube (an application of an endoscope). The problem under consideration is formulated under the assumptions of long wavelength and neglecting the wave number. A closed form of Adomian solutions and numerical solutions are presented which show a complete agreement with each other. The influence of pertinent parameters is analyzed through graphs

An analysis is performed for the slip effects on the exact solutions of flows in a generalized Burgers fluid. The flow modelling is based upon the magnetohydrodynamic (MHD) nature of the fluid and modified Darcy law in a porous space. Two illustrative examples of oscillatory flows are considered. The results obtained are compared with several limiting cases. It has been shown here that the derived results hold for all values of frequencies including the resonant frequency.

This paper deals with a Cauchy problem for the coupled system of nonlinear viscoelastic equations with damping and source terms. We prove a new finite time blow-up result for compactly supported initial data with non-positive initial energy as well as positive initial energy by using the modified energy method and the compact support technique.

This article looks at the heat and mass transfer characteristics in mixed convection boundary layer flow about a linearly stretching vertical surface. An incompressible Maxwell fluid occupying the porous space takes into account the diffusion-thermo (Dufour) and thermal-diffusion (Soret) effects. The governing partial differential equations are transformed into a set of coupled ordinary differential equations, by invoking similarity transformations. The involved nonlinear differential system is solved analytically using the homotopy analysis method (HAM) to determine the convergent series expressions of velocity, temperature, and concentration. The physical interpretation to these expressions is assigned through graphs and tables for the Nusselt number θ '(0) and the Sherwood number φ '(0). The dependence of suction parameter S, mixed convection parameter λ, Lewis number Le, Prandtl number Pr, Deborah number β , concentration buoyancy parameter N, porosity parameter γ , Dufour number Df, and Soret number Sr is seen on the flow quantities.

In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation u tt −u xx −u yy −(u 2 ) xx −u xxxx = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation u xt −6u x 2 +6uu xx −u xxxx −u yy −u zz = 0. By using this method, an explicit numerical solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method numerical results are derived by using the calculated components of the homotopy perturbation series. The numerical solutions are compared with the known analytical solutions. Results derived from our method are shown graphically.

In this paper, an application of He’s variational iteration method is applied to solve nonlinear integro-differential equations. Some examples are given to illustrate the effectiveness of the method. The results show that the method provides a straightforward and powerful mathematical tool for solving various nonlinear integro-differential equations

The Green functions for Klein-Gordon and Dirac particles in a weak gravitational field are determined exactly by the path integral formalism. By using simple changes, it is shown that the classical trajectories play an important role in determining these Green functions

In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors’ knowledge, very little is known about the case, where twist conditions do not hold.

In many fields of the contemporary science and technology, systems with delaying links often appear. By a delay differential equation (DDE), we mean an evolutionary system in which the (current) rate of change of the state depends on the historical status of the system. Delay models play a relevant role in different fields such as biology, economy, control, and electrodynamics and hence have been attracted a lot of attention of the researchers in recent years. In this study, the numerical solution of a well-known delay differential equation, namely, the pantograph equation is investigated by means of the Adomian decomposition method and then a numerical evaluation is included to demonstrate the validity and applicability of this procedure

Lithium was electrochemically inserted from a 1 : 2 (v/v) mixed solution of ethylene carbonate (EC) and methylethyl carbonate (MEC) containing 1M LiClO 4 into liquid gallium to observe lithium isotope effects accompanying the insertion. It was observed that the lighter isotope 6 Li was preferentially fractionated into liquid gallium with the single-stage lithium isotope separation factors S, ranging from 1.005 to 1.031 at 50 °C and 1.003 to 1.024 at 25 °C. The lithium isotope effects estimated by molecular orbital calculations at the B3LYP/6-311G(d) level of theory agreed qualitatively with those of the experiments, but the quantitative agreement of the two was not satisfactory

The mechanical properties of medium-carbon steels with a carbon content ranging from 0.30 to 0.55 wt.% were investigated by tensile and microhardness tests at room temperature. It was observed that the higher carbon content results in an increase in yield stress and ultimate tensile stress, while the elongation remains essentially constant. The results were explained by the hindering of dislocation motion associated with solid solution hardening

Fluoranthenes are polycyclic conjugated molecules consisting of two benzenoid fragments, connected by two carbon-carbon bonds so as to form a five-membered ring. Fluoranthenes possessing Kekul´e structures are classified into three types, depending on the nature of the two carbon-carbon bonds connecting the two benzenoid fragments. Either both these bonds are essentially single (i. e., single in all Kekul´e structures), or both are essentially double (i. e., double in all Kekul´e structures), or one is essentially single and the other is essentially double. All Kekul´ean fluoranthenes have equal number of bonding and antibonding molecular orbitals (MO), and no non-bonding MO.