Sharif Digital Repository

In this study, homotopy analysis method is used to derive analytic solutions to predict dynamic pull-in instability of electrostatically-actuated microsystems. The model considers midplane stretching, initial stress, distributed electrostatic force and fringing fields effect. Influences of different parameters on dynamic pull-in instability are investigated. Results are in good agreement with numerical and experimental findings. © 2009 Elsevier Ltd. All rights reserved  

With the rapid development of micro/nano-electro-mechanical systems (MEMS/NEMS), arch shaped resonators are becoming increasingly attractive for different applications. Nevertheless, the dynamics of bistable resonators is poorly understood, and the conditions for their appropriate performance are not well known. In this paper, an initially curved arch shaped MEMS resonator under combined DC and AC distributed electrostatic actuation is investigated. A reduced order model obtained from first mode Galerkin's decomposition method is used for numerical and analytical investigations. We have used the Homotopy Analysis Method (HAM) in order to derive analytical solutions both for the amplitude and... 

In this article, the homotopy analysis method has been applied to solve nonlinear differential equations of fractional order. The validity of this method has successfully been accomplished by applying it to find the solution of two nonlinear fractional equations. The results obtained by homotopy analysis method have been compared with those exact solutions. The results show that the solution of homotopy analysis method is good agreement with the exact solution. Crown  

In this study, the Volterra's prey and predator problem is investigated. Homotopy-Pade technique is utilized to find analytic solutions to the problem. Results show the accuracy of the method comparing with other methods. It is illustrated that homotopy-Pade technique can greatly enlarge the convergence region of the solution series  

In this article, we use an efficient analytical method called homotopy analysis method (HAM) to derive an approximate solution of nonlinear ion sound waves equation. Actually, we solved Korteweg-de Vries equation arises in a one-dimensional macroscopic plasma model describing the weakly nonlinear evolution of ion sound speed by the HAM. Unlike the perturbation method, the HAM does not require the addition of a small physically parameter to the differential equation. It is applica-ble to strongly and weakly nonlinear problems. Moreover, the HAM involves an auxiliary parameter, which renders the convergence param-eter of series solutions controllable, and increases the convergence, and... 

In this study, the homotopy analysis method is used to obtain an accurate analytical solution for fundamental non-linear natural frequency and corresponding displacement of tapered beams. Comparison between the obtained results and numerical solutions shows that the first-order approximation of present study leads to accurate solutions with a maximum relative error less than 0.5%  

In this work, we use a powerful analytical method called homotopy analysis method (HAM) to derive the frequency of a nonlinear oscillating system. Unlike the perturbation method, the HAM does not require the addition of a small physically parameter to the differential equation. It is applicable to strongly and weakly nonlinear problems. Moreover, the HAM involves an auxiliary parameter, h, which renders the convergence parameter of series solutions Controllable, and increases the convergence, and increases the convergence significantly. This article depicts that the HAM is an efficient and powerful method for solving oscillating systems  

We present high-precision photometry of two transit events of the extrasolar planetary system WASP-5, obtained with the Danish 1.54-m telescope at European Southern Obseratory La Silla. In order to minimize both random and flat-fielding errors, we defocused the telescope so its point spread function approximated an annulus of diameter 40 pixel (16 arcsec). Data reduction was undertaken using standard aperture photometry plus an algorithm for optimally combining the ensemble of comparison stars. The resulting light curves have point-to-point scatters of 0.50 mmag for the first transit and 0.59 mmag for the second. We construct detailed signal-to-noise ratio calculations for defocused... 

Purpose - The purpose of this paper is to study a two-dimensional steady convective flow of a micropolar fluid over a stretching sheet in the presence of radiation with constant temperature. Design/methodology/approach - The corresponding momentum, microrotation and energy equations are analytically solved using homotopy analysis method (HAM). Findings - To validate the method, investigate the accuracy and convergence of the results, a comparison with existing numerical and experimental results is done for several cases. Finally, by using the obtained analytical solution, for the skin-friction coefficient and the local Nusselt number as well as the temperature, velocity and angular velocity,... 

Vibrations of electrostatically-Actuated microbeams are investigated. Effects of electrostatic actuation, axial stress and midplane stretching are considered in the model. Galerkin's decomposition method is utilized to convert the governing nonlinear partial differential equation to a nonlinear ordinary differential equation. Homotopy perturbation method (i.e. a special and simpler case of homotopy analysis method) is utilized to find analytic expressions for natural frequencies of predeformed microbeam. Effects of increasing the voltage, midplane stretching, axial force and higher modes contribution on natural frequency are also studied. The anayltical results are in good agreement with the... 

In this study, the nonlinear free vibration of conservative two degrees of freedom systems is analyzed using the homotopy analysis method (HAM). The mathematical model of such systems is described by two second-order coupled differential equations with cubic nonlinearities. First, novel approximate analytical solutions for displacements and frequencies are established using HAM. Then, the homotopy Padé technique is applied to accelerate the convergence rate of the solutions. Comparison between the obtained results and those available in the literature shows that the first-order approximation of homotopy Padé technique leads to accurate solutions with a maximum relative error less than 0.068... 

In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtained using the Homotopy Analysis Method (HAM) and Homotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results and numerical solutions shows that only the first order approximation of the Homotopy Pade technique leads to accurate solution with a maximum relative error less than 0.4%. © 2008 Elsevier Ltd. All rights reserved  

Discussing the particularly long gravitational microlensing event OGLE-2014-BLG-1186 with a time-scale tE ∼ 300 d, we present a methodology for identifying the nature of localised deviations from single-lens point-source light curves, which ensures that (1) the claimed signal is substantially above the noise floor, (2) the inferred properties are robustly determined and their estimation is not subject to confusion with systematic noise in the photometry, (3) alternative viable solutions within the model framework are not missed. Annual parallax and binarity could be separated and robustly measured from the wing and the peak data, respectively. We find matching model light curves that involve... 

In this article, the homotopy analysis method has been applied to solve a coupled nonlinear diffusion-reaction equations. The validity of this method has been successful by applying it for these nonlinear equations. The results obtained by this method have a good agreement with one obtained by other methods. This work illustrates the validity of the homotopy analysis method for the nonlinear differential equations. The basic ideas of this approach can be widely employed to solve other strongly nonlinear problems. © 2008 Springer Science+Business Media B.V  

Aims. We report the discovery of a planet with a high planet-to-star mass ratio in the microlensing event MOA-2009-BLG-387, which exhibited pronounced deviations over a 12-day interval, one of the longest for any planetary event. The host is an M dwarf, with a mass in the range 0.07 M ⊙ < Mhost < 0.49 M1 at 90% confidence. The planet-star mass ratio q = 0.0132 ± 0.003 has been measured extremely well, so at the best-estimated host mass, the planet mass is mp = 2.6 Jupiter masses for the median host mass, M = 0.19 M ⊙. Methods. The host mass is determined from two "higher order" microlensing parameters. One of these, the angular Einstein radius θE = 0.31 ± 0.03 mas has been accurately...