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 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... 

The effects of selected metal ions on the gas-phase acidity of weak organic acids have been explored using the DFT and Moller-Plesset Perturbation Theory (MP2) calculations. The three organic acids selected for this study were acetic acid (aliphatic), benzoic acid (aromatic), and glycine (amino acid). The acidities of these compounds are compared with the acidity of their Li +-, Na+-, and K+ -complexed species. The results indicate that upon complexation with Li+, Na+, and K+ at 298K, the gas-phase acidity of acetic acid, for example, varies from 345.3 to 218.8, 230.2, and 240.1 kcal/mol, respectively (i.e., its dissociation becomes much less endothermic). These values indicate that a weak... 

We present N-body simulations of unstable spiral modes in a dynamically cool collisionless disc. We show that spiral modes grow in a thin collisionless disk in accordance with the analytical perturbation theory. We use the particle-mesh code SUPERBOX with nested grids to follow the evolution of unstable spirals that emerge from an unstable equilibrium state. We use a large number of particles (up to N = 40 & 106) and high-resolution spatial grids in our simulations (1283 cells). These allow us to trace the dynamics of the unstable spiral modes until their wave amplitudes are saturated due to nonlinear effects. In general, the results of our simulations are in agreement with the analytical... 

The physical processes responsible for bubble formation in microchannels are not well understood and lack fundamental understanding. Experimental results are not exactly in agreement with each other and there are no definite theories to explain the possible effects of different parameters. Among different parameters the microchannel hydraulic diameter can affect the bubble formation mechanism in microchannels strongly. In this paper the effect of the time dependent pressure difference between inside and outside of the bubble on bubble dynamics in microchannels have been investigated. The source of this time dependency can be the emergence of bubble embryos which produces a density... 

In this paper, the large amplitude free vibration of a cantilever Timoshenko beam is considered. To this end, first Hamilton's principle is used in deriving the partial differential equation of the beam response under the mentioned conditions. Then, implementing the Galerkin's method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the natural frequency of the thick-cantilevered beam  

In this paper, the strain gradient theory, a non-classical continuum theory able to capture the size effect happening in micro-scale structures, is employed in order to investigate the size-dependent nonlinear forced vibration of Euler-Bernoulli microbeams. The nonlinearities are caused by mid-plane stretching and nonlinear external forces such as van-der-Waals force. The nonlinear governing equations of the microbeams are solved analytically utilizing the perturbation techniques. The primary, super-harmonic and sub-harmonic resonances of a microbeam are studied and the size-dependency of the frequency responses is assessed. The results indicate that the nonlinear forced vibration behavior... 

In this article, impedance control of a two link flexible link manipulators is addressed. The concept of impedance control of flexible link robots is rather new and is being addressed for the first time by the authors. Impedance Control provides a universal approach to the control of flexible robots, in both constrained and unconstrained maneuvers. The initial part of the paper concerns the use of Hamilton's principle to derive the mathematical equations governing the dynamics of joint angles, vibration of the flexible links and the constraining forces. The approximate elastic deformations are then derived by means of the Assumed-Mode-Method (AMM). Using the singular perturbation method, the... 

A novel approach for photonic crystals devices analysis, based on perturbation theory is reported. In this method the photonic crystal device is considered as the superposition of a parent lattice and a perturbing one. Then the solution is investigated in terms of the eigensolutions of the parent lattice. This way, one can easily obtain analytic expressions within the first order perturbation, describing the effects of different parameters on the eigensolutions of the structure. The perturbation theory employed in this work is typical of what is conventionally used in quantum mechanics literature. The proposed method is explicit, works fast, and does not involve complicated numerical... 

Supercavitation is known as the way of viscous drag reduction for the projectiles, moving in the liquid phase. In recent works, there is distinct investigation between cavitation flow and momentum transfer far away from the cavity surface. In fact such methodologies consider cavitation flow statically, rather than taking dynamic effects of overall flow into account. However, it seems that there is strong connection between overall flow and what takes place in the sheet cavity where a constant pressure distribution is assumed. Thereby, in order to configure the system conditions which may be cause of cavity perturbation and so system oscillation, we need to use proper methodologies in which... 

In this paper, the large amplitude tree vibration of a doubly clamped microbeam is considered. The effects of shear deformation and rotary inertia on the large amplitude vibration of the microbeam are investigated. To this end, first Hamilton's principle is used in deriving the partial differential equation of the microbeam response under the mentioned conditions. Then, implementing the Galerkin's method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the... 

The influence of Casimir and van der Waals forces on the instability of vibratory micro and nano-bridge gyroscopes with proof mass attached to its midpoint is studied. The gyroscope subjected to the base rotation, Casimir and van der Waals attractions is actuated and detected by electrostatic methods. The system has two coupled bending motions actuated by the electrostatic and Coriolis forces. First a system of nonlinear equations for the flexural-flexural deflection of beam gyroscopes is derived using the extended Hamilton's principle. In modeling, the nonlinearities due to mid-plane stretching, electrostatic forces, including fringing field, Casimir and van der Waals attractions, are... 

In this paper, the strain gradient theory, a non-classical continuum theory able to capture the size effect happening in micro-scale structures, is employed in order to investigate the size-dependent nonlinear forced vibration of Euler-Bernoulli microbeams. The nonlinearities are caused by mid-plane stretching and nonlinear external forces such as van-der-Waals force. The nonlinear governing equations of the microbeams are solved analytically utilizing the perturbation techniques. The primary, super-harmonic and sub-harmonic resonances of a microbeam are studied and the size-dependency of the frequency responses is assessed. The results indicate that the nonlinear forced vibration behavior... 

Neutron noise induced by propagating thermal-hydraulic disturbances (propagation noise for short) in pressurized water reactors is investigated in this paper. A closed-loop neutron-kinetic/thermal-hydraulic noise simulator (named NOISIM) has been developed, with the capability of modeling the propagation noise in both Western-type and VVER-type pressurized water reactors. The neutron-kinetic/thermal-hydraulic noise equations are on the basis of the first-order perturbation theory. The spatial discretization among the neutron-kinetic noise equations is based on the box-scheme finite difference method (BSFDM) for rectangular-z, triangular-z and hexagonal-z geometries. Furthermore, the finite... 

We present a perturbation theory to find the response of an anisotropic DNA to the external tension. It is shown that the anisotropy has a nonzero but small contribution to the force-extension curve of the DNA. Thus an anisotropic DNA behaves like an isotropic one with an effective bending constant equal to the harmonic average of its soft and hard bending constants. © 2008 American Institute of Physics  

We have derived an analytical equation of state (EOS) based on the soft-core statistical mechanical perturbation theory for fluids, using the Weeks-Chandler-Andersen (WCA) theory recently developed by Ben-Amotz-Stell (BAS) for the choice of the hard-sphere diameter, but with a new algorithm for calculation of the pair and many-body interactions. We have used Carnahan-Starling expression with the Boltzmann factor criterion (BFC) as an effective hard-sphere diameter for the reference system, and also decomposed the perturbed pair potential to symmetric and asymmetric terms. The former term is due to the many-body interactions at high densities as was used in the linear isotherm regularity... 

The absolute free energy of solvation of methane (CH4) and its fluorinated forms (CH3F, CH2F2, CHF3 and CF4) have been computed via statistical perturbation theory (SPT) in the NPT ensemble at four thermodynamical states (whitin liquid and supercritical regions), in the context of Monte Carlo Simulations. Thermodynamical interpretation of the observed trend in the absolute free energy of solvation in different states reveals an exothermic solvation with ΔSslv < 0 (entropically unfavorable solvation) that the intermolecular interactions play an important role in the solvation process. The fluorinated methanes are confirmed to control the mutual arrangement of neighboring CO2 molecules and the... 

In this paper, the large amplitude free vibration of a doubly clamped microbeam is considered. The effects of shear deformation and rotary inertia on the large amplitude vibration of the microbeam are investigated. To this end, first Hamilton's principle is used in deriving the partial differential equation of the microbeam response under the mentioned conditions. Then, implementing the Galerkin's method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second-order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the... 

This paper is devoted to the analysis of nonlinear behavior of amplitude modulation (AM) and frequency modulation (FM) modes of atomic force microscopy. For this, the microcantilever (which forms the basis for the operation of AFM) is modeled as a single mode approximation and the interaction between the sample and cantilever is derived from a van der Waals potential. Using perturbation methods such as Averaging, and Fourier transform nonlinear equations of motion are analytically solved and the advantageous results are extracted from this nonlinear analysis. The results of the proposed techniques for AM-AFM, clearly depict the existence of two stable and one unstable (saddle) solutions for... 

A set of transforms (SVD transforms) were introduced in (Shahshahani and Tavakoli Targhi) for understanding images. These transforms have been applied to some problems in computer vision including segmentation, detection of objects in a texture environment, classification of textures, detection of cracks or other imperfections, etc. This technique is shown to be applicable to determination of the location of eyes in a facial image. This method makes no use of color cues, prior geometric knowledge or other assumptions and does not require training. It is also insensitive to local perturbations in lighting, change of orientation and pose, scaling, and complexity of the background including...