Sharif Digital Repository

A very common phenomena in car-traffic system is investigated in this article. The problem is one-dimensional. We try to find the wave equation of the traffic and then, we'll talk more about the simulation of the system using Matlab7.6  

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 article, a new general approach has been presented for exact and efficient extraction of eigenpolarizations in anisotropic electromagnetic media with arbitrary constitutive relations. It is shown that the plane wave propagation eigenpolarizations in a linear homogeneous time-independent anisotropic media without free sources, can be obtained through extremizing the difference between stored electric and magnetic energies as a variational functional. It is demonstrated that at these stationary points the wave equation is satisfied by showing that each of the Maxwell curl equations may be obtained by using the other equation as a constraint. Furthermore, it is proven that the theorem... 

Identification of existing instability modes from experimental pressure measurements of rocket engines is difficult, specially when steep waves are present. Actual pressure waves are often non-linear and include steep shocks followed by gradual expansions. It is generally believed that interaction of these non-linear waves is difficult to analyze. A method of mode identification is introduced. After presumption of constituent modes, they are superposed by using a standard finite difference scheme for solution of the classical wave equation. Waves are numerically produced at each end of the combustion tube with different wavelengths, amplitudes, and phases with respect to each other. Pressure... 

The travel time of subsurface flow in complex hillslopes (hillslopes with different plan shape and profile curvature) is an important parameter in predicting the subsurface flow in catchments. This time depends on the hillslopes geometry (plan shape and profile curvature), soil properties and climate conditions. The saturation capacity of hillslopes affect the travel time of subsurface flow. The saturation capacity, and subsurface travel time of compound hillslopes depend on parameters such as soil depth, porosity, soil hydraulic conductivity, plan shape (convergent, parallel or divergent), hillslope length, profile curvature (concave, straight or convex) and recharge rate to the groundwater... 

At the present research, a new analytical model is developed for the impact of a deformable blunt projectile to metallic targets using the plastic stress wave propagation theory and the momentum equations. At this model, the deformation of the projectile is considered, too. Also, the effects of dishing and plugging phenomena on failure of the target are investigated. All of the obtained results are compared with the experimental and other available analytical results where good agreement has been observed. The other outcome of this research is a new definition for the penetration stages which includes 9 ones. Motion equations are derived for each of these stages, accordingly  

In this paper, the effects of ion-pair formation on the gain dynamics of multi cavity optical automatic gain control erbium doped fiber amplifier is modelled. The inhomogeneous Cabezas simple model is used to write the rate and propagation equations for the active medium. The solution of the governing equations shows that in high concentration of the erbium ions, depending on the pumping rate, the relaxation oscillations are converted to nT-Periodic or even to chaotic behavior. Although the high concentration erbium ion in the optical amplifiers decreases the conversion efficiency and increases the threshold pump power, amplitude of the transient effects is reduced in the multi feedback-loop... 

In spite of numerous attempts which have been made during the last decade to optimize pulse tube refrigerators, still theoretical and analytical realization of this device needs to be thoroughly explained. In this paper, in addition to the oscillatory flow analysis in the pulse tube refrigerator through a simple analytical model, the performance of the alternate tube section of this device is analyzed using a generalized efficiency, based on the entropy generation rate. In this model, in order to extract the entropy generation rate and the dissipative terms caused by fluid friction and heat flow in alternate tube, simplified momentum and energy equations are solved analytically and velocity... 

A new analytical method for finding the general solution of the nth-order linear differential equation with variable coefficients is given based on generalizing the idea of differential transfer matrix method already proposed for solving the second order Helmholtz equation. Our generalization has two aspects. First, the given formulation copes with the nth-order linear differential equations, rather than the special case of second order wave equations. Second, the proposed approach is generalized in several different ways each yielding different types of differential transfer matrices with correspondingly different numerical accuracies. The presented methods can be applied to problems such... 

In this note we extend the Differential Transfer Matrix Method (DTMM) for a second-order linear ordinary differential equation to the complex plane. This is achieved by separation of real and imaginary parts, and then forming a system of equations having a rank twice the size of the real-valued problem. The method discussed in this paper also successfully removes the problem of dealing with essential singularities, which was present in the earlier formulations. Then we simplify the result for real-valued problems and obtain a new set of basis functions, which may be used instead of the WKB solutions. These basis functions not only satisfy the initial conditions perfectly, but also, may... 

Nonlinear ultrasound modeling is finding an increasing number of applications in both medical and industrial areas where due to high pressure amplitudes the effects of nonlinear propagation are no longer negligible. Taking nonlinear effects into account makes the ultrasound beam analysis more accurate in these applications. One of the most widely used nonlinear models for propagation of 3D diffractive sound beams in dissipative media is the KZK (Khokhlov, Kuznetsov, Zabolotskaya) parabolic nonlinear wave equation. Various numerical algorithms have been developed to solve the KZK equation. Generally, these algorithms fall into one of three main categories: frequency domain, time domain and... 

A new method which is a combination of the harmonic balance and finite difference techniques (HBFD) is proposed for complete time-harmonic solution of the nonlinear wave equation. All interactions between different harmonics up to an arbitrary order can be incorporated. The effect of higher order harmonics on two important nonlinear optical phenomena, namely, the second harmonic generation (SHG) and frequency mixing is investigated by this method and the results are compared with well-known analytical solutions. The method is quite general and can be used to study wave propagation in all nonlinear media  

Extended Boussinesq-type water wave equations are derived in two horizontal dimensions to capture the nonlinearity effects and frequency dispersion of wave in a high accuracy order. A multi-parameter perturbation analysis is applied in several steps to extend the previous second order Boussinesq-type equations in to 6th order for frequency dispersion and consequential order for nonlinearity terms. The presented high-order Boussinesq-type equation is applied in a numerical model to simulate the wave field transformation due to physical processes such as shoaling, refraction and diffraction. The models results are compared with available experimental data which obtained in a laboratory wave... 

Laboratory investigations have been performed on the submarine landslide generated waves by performing 120 laboratory tests. Both rigid and deforming-slide masses are considered. The effects of bed slope angle, initial submergence, slide geometry, shape and deformation on impulse wave characteristics have been inspected. Impulse wave amplitude, period, energy and nonlinearity are studied in this work. The effects of bed slope angle on energy conversion from slide into wave are also investigated. Laboratory-based prediction equations are presented for impulse wave amplitude and period in near and far-field and are successfully verified using the available data in previous laboratory and... 

This paper presents an analytical method in computational aeroelasticity for an airfoil considering two degrees of freedom (heaving and pitching) based on the Wagner integral function. In the obtained aeroelastic equations of motion, there are some integral parts that give an integro-differential system of equations. Using appropriate approximation for the Wagner function, a new form of equations can be obtained by derivation from mentioned equations. These equations are in the form of ordinary differential equations. Using the obtained equations, the flutter speed is predicted for a given airfoil and the results are compared with the results of other investigators. Also, the dynamic... 

Based on the quantum mechanics principles and classically calculated dressed potential surfaces by using field assisted dissociation model the dissociation probability for CH4 + molecule exposed with a 100 femtosecond 8 Jcm-2 Ti:sapphire laser pulses is calculated. Using the gradient optimization method two tailored rectangular laser pulses for controlling the dissociation of C-H bond of CH4 + molecule along laser pulse direction is found. In the proposed optimization method, the complicacy of solving Schrodinger wave equation is reduced by using classical method and in contrast to the usual controlling and pulse shaping methods of chemical reactions, the experimental data is not needed and... 

In this paper an effective numerical technique is presented to model turbulent motion of a standing surface wave in a tank. The equations of motion for turbulent boundary layers at the solid surfaces are coupled with the potential flow in the bulk of the fluid, and a mixed BEM-finite difference technique is used to obtain the wave and boundary layer characteristics. A mixing-length theory is used for turbulence modeling. The results are compared with previous experimental data. Although the technique is presented for a standing surface wave, it can be easily applied to other free surface problems. Copyright © 2008 by ASME  

Axial-torsional vibrations of rotating pretwisted thin-walled composite box beams exhibiting primary and secondary warping are investigated. Considering the nonlinear strain-displacement relations, the coupled nonlinear axial-torsional equations of motion are derived using Hamilton's principle. Ignoring the axial inertia term leads to differential equation of motion in terms of elastic torsion in the case of axially immovable beams. Centrifugal load in the presence of material anisotropy and pretwist angle leads to an induced static torque. The nonlinear equation should be linearized about the corresponding equilibrium state to obtain the linear differential equation of motion. Extended... 

The aim of this study is to carry out the numerical computation of nonlinear normal modes for rotating pretwisted composite thin-walled beam in axial-torsional vibrations. The structural model considered here, incorporates a number of non-classical effects such as primary and secondary warping, non-uniform torsional model, rotary inertia and pretwist angle. Ignoring the axial inertia term leads to differential equation of motion in terms of angle of twist in the case of axially immovable beam ends. The governing differential equations of motion are derived using Hamilton's principle and the reduced model around the static equilibrium position is obtained using 2-mode Galerkin discretization...