Sharif Digital Repository

The method of multiple scales is one of the common perturbation techniques for exploring nonlinear ordinary differential equations. Sitnikov has presented a mathematics model of a negligible mass body oscillation perpendicular to a plane in which two heavy bodies with equal mass orbit on itself Keplerian ellipse. This problem is well known as the Sitnikov problem. In this investigation, the method of multiple scales is applied to the Sitnikov problem and it presented an analytical response that is consistent with numerical solution. At first step, the circular form of the Sitnikov equation is approximated by MMS and then the obtained dynamic model from first step is employed to investigate... 

In this paper, dynamic modeling and control problem for transfer of a sloshing liquid container suspended through rigid massless links from a team of quadrotors are investigated. By the proposed solution, pose of the slung container and fluid sloshing modes are stabilized appropriately. Dynamics of the container-liquid-quadrotors system is modeled by Euler-Lagrange method. Fluid slosh dynamics is included using multi-mass-spring model. According to derived model, a proper control law is designed for a system with three or more quadrotors. Implementing the proposed control law, quadrotors can control pose of the container, directions of the links and liquid sloshing modes simultaneously.... 

In this paper, nonlinear instability of an elliptical jet is investigated by considering the impacts of orifice geometry variations using regular perturbation method. In the breakup mechanisms, created disturbances on the jet interfaces will grow owing to the nonlinear dynamics of fluid. In this study, a scrutiny of nonlinear cylindrical jet breakup is done initially. Next, Cosserat equations as a low order form of Navies-Stokes equations are solved on the nonlinear form to exert the impacts of orifice deformation on various aspect ratios. These nonlinear equations, Cosserat equations, are linearly solved in the past papers. As a result, the dispersion equation is derived to find the most... 

Marton’s inner bound is the best known achievable rate region for a general two-receiver discrete memoryless broadcast channel. In this paper, we establish improved bounds on the cardinalities of the auxiliary random variables appearing in this inner bound to the true rate region. We combine a perturbation technique, along with a representation using concave envelopes of information-theoretic functions that involve the use of auxiliary random variables, to achieve this improvement. The new cardinality bounds lead to a proof that a randomized time-division strategy achieves every rate triple in Marton’s region for binary input broadcast channels. This extends the result by Hajek and Pursley... 

The general problem of impedance control is addressed for a robotic manipulator with a moving flexible base. Impedance control imposes a relation between force and displacement at the contact point with the environment. The concept of impedance control of flexible base moving manipulators (FBMMs) is rather new and is being considered. The dynamic of the manipulator is decomposed into slow and fast dynamics using the singular perturbation method. A new sliding mode impedance control (SMIC) method using an element on the end-effector is proposed for high-precision impedance control of FBMMs. The SMIC method as a robust impedance control law is derived for the slow dynamics. The asymptotic... 

Conceptual discussion on highly nonlinear Duffing type equation of surge motion of TLP gives a deep view on structural response under environmental loads with some simplifications. Such analytical response is a simple form that clarifies important points in behavior of the structure. This paper presents the dynamic motion responses of a TLP in regular sea waves obtained by applying three methods in time domain using MATLAB software. Surge motion equation of TLP is highly nonlinear because of large displacement and it should be solved with large perturbation parameter in time domain. In this paper, homotopy perturbation method (HPM) is used to solve highly nonlinear differential equation of... 

This paper presents the homotopy series solution of the Navier-Stokes and energy equations for non-Newtonian flows. Three different problems, Couette flow, Poiseuille flow and Couette-Poiseuille flow have been investigated. For all three cases, the nonlinear momentum and energy equations have been solved using the homotopy method and analytical approximations for the velocity and the temperature distribution have been obtained. The current results agree well with those obtained by the homotopy perturbation method derived by Siddiqui et al (2008 Chaos Solitons Fractals36 182-92). In addition to providing analytical solutions, this paper draws attention to interesting physical phenomena... 

One of the most important phenomena to affect the motion behaviour of Micro Resonators is their thermal dependency. This has recently received the attention of researchers widely. A thermal phenomenon has two main effects, the first is damping, due to internal friction, and the second is softening, due to Young's modulus-temperature relationship. In this research work, some theoretical and experimental reported results are used to make a proper model, including thermal phenomena. Two Lorentzian functions are used to describe the restoring and damping forces caused by thermal phenomena. In order to emphasize the thermal effects, a nonlinear model of the MEMS, considering capacitor... 

Experimental values for surface tension of single and mixed electrolyte solutions were correlated using the models based on the perturbation theory. The Mean Spherical Approximation (MSA) model, coupled with the Ghotbi-Vera (GV) and the Mansoori et al. (BMCSL) equations of state, were used to correlate the experimental values of the surface tension. The results showed that the models can favourably correlate the experimental values for single electrolyte solutions. However, it was observed that the GV-MSA model can more accurately predict the surface tension for single electrolytes, especially at higher concentrations. Two different expressions for concentration dependency of cation hydrated... 

This paper presents a coupled flap-lag-torsion aeroelastic stability analysis and response of a hingeless helicopter blade in the hovering flight condition. The boundary element method based on the wake eigenvalues is used for the prediction of unsteady airloads of the rotor blade. The aeroelastic equations of motion of the rotor blade are derived by Galerkin's method. To obtain the aeroelastic stability and response, the governing nonlinear equations of motion are linearized about the nonlinear steady equilibrium positions using small perturbation theory. The equilibrium deflections are calculated through the iterative Newton-Raphson method. Numerical results comprising steady equilibrium... 

Based on the first-order shear deformation plate theory with von Karman non-linearity, the non-linear axisymmetric and asymmetric behavior of functionally graded circular plates under transverse mechanical loading are investigated. Introducing a stress function and a potential function, the governing equations are uncoupled to form equations describing the interior and edge-zone problems of FG plates. This uncoupling is then used to conveniently present an analytical solution for the non-linear asymmetric deformation of an FG circular plate. A perturbation technique, in conjunction with Fourier series method to model the problem asymmetries, is used to obtain the solution for various clamped... 

We propose a perturbation method for time division multiplexed (TDM) pumping fiber Raman amplifier (FRA). The method is based on the solution of Raman partial differential equations (PDEs) by a closed integral form. Taking the signals and pumps power as the interim solution and updating their values in an iterative process, Raman gain and pump/signal evolution can be calculated in any order of accuracy. In the first order of perturbation, some analytical formulas for the FRA dynamic control are obtained. Analytical formulas are employed for gain ripple minimization and also the gain clamping problem under channel reconfiguration. © 2009 Elsevier Inc. All rights reserved  

In this paper, some commonly used model reduction methods for integer-order systems are employed to approximate commensurate fractional-order linear systems. In comparison with the original system, the approximating model possesses a smaller inner dimension, while its fractional order is the same as that of the original system. The applied methods fall into the global reduction category, such as direct truncation and singular perturbation methods, and into the local reduction category, such as Pade approximation, partial realization, shifted Pade approximation, and rational interpolation methods. The applicability of these methods is illustrated by approximating a sample high-dimensional,... 

This paper applies the homotopy perturbation method to the simulation of the static response of nano-switches to electrostatic actuation and intermolecular surface forces. The model accounts for the electric force nonlinearity of the excitation and for the fringing field effect. Using a mode approximation in the Galerkin projection method, the nonlinear boundary value differential equation describing the statical behavior of nano-switch is reduced to a nonlinear algebraic equation which is solved using the homotopy perturbation method. The number of included terms in the perturbation expansion for achieving a reasonable response has been investigated. Three cases have been specifically... 

In this study, nonlinear bending of functionally graded (FG) circular sector plates with simply supported radial edges subjected to transverse mechanical loading has been investigated. Based on the first-order shear deformation plate theory with von Karman strain-displacement relations, the nonlinear equilibrium equations of sector plates are obtained. Introducing a stress function and a potential function, the governing equations which are five non-linear coupled equations with total order of ten are reformulated into three uncoupled ones including one linear edge-zone equation and two nonlinear interior equations with total order of ten. The uncoupling makes it possible to present... 

In this paper, we consider the problem of minimizing the uplink delays of users in a 5G cellular network. Such cellular network is based on a Cloud Radio Access Network (CRAN) architecture with limited fronthaul capacity, where our goal is to minimize delays of all users through an optimal resource allocation. Earlier works minimize average delay of each user assuming same transmit power for all users. Combining Pareto optimization and Markov Decision Process (MDP), we show that every desired balance in the trade-off among infinite-horizon average-reward delays, is achievable by minimizing a properly weighted sum delays. In addition, we solve the problem in two realistic scenarios;... 

Siligraphene belonging to the family of two-dimensional (2D) materials has great potential in optoelectronics due to its considerable excitonic effects. In this study, the strain effects on the electronic structure and the real-space exciton wave functions of g - SiC 7 are investigated using the first-principles calculations based on the ab initio many-body perturbation theory. Alongside the increase (decrease) of the bandgap with compressive (tensile) strain, our results show that the exciton in the siligraphene monolayer under in-plane biaxial compressive strains is much more localized than that in the case of tensile one, leading to the higher and lower exciton binding energies,... 

Marton's inner bound is the best known achievable rate region for a general two-receiver discrete memoryless broadcast channel. In this paper, we establish improved bounds on the cardinalities of the auxiliary random variables appearing in this inner bound to the true rate region. We combine a perturbation technique, along with a representation using concave envelopes of information-theoretic functions that involve the use of auxiliary random variables, to achieve this improvement. The new cardinality bounds lead to a proof that a randomized-time-division strategy achieves every rate triple in Marton's region for binary input broadcast channels. This extends the result by Hajek and Pursley... 

The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system are solved by means of a multiple scales method considering the first three liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The fixed points of the gyroscopic type of governing differential equations are determined and their stability is investigated employing the perturbation method. The obtained results reveal an increase in the stability region for a single-mode... 

In the binary alloy with composition AxB1-x of two atoms with ionic energy scales ±Δ, an apparent Anderson insulator (AI) is obtained as a result of randomness in the position of atoms. Using our recently developed technique that combines the local self-energy from strong-coupling perturbation theory with the transfer matrix method, we are able to address the problem of adding a Hubbard U to the binary-alloy problem for millions of lattice sites on the honeycomb lattice. By adding the Hubbard interaction U, the resulting AI phase will become metallic, which in our formulation can be manifestly attributed to the screening of disorder by Hubbard U. Upon further increase in U, again the AI...