• Korean Journal of Optics and Photonics
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• v.7 no.4
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• pp.403-413
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• 1996

We study the propagation of two pulses with orthogonal linear polarizations in a nonlinear periodic dielectric structure with $X^{(3)}$ nonlinearity. Using an envelope- function approach, we derive the coupled nonlinear Schrodinger equations governing the spatio-temporal evolutions of the two orthogonally polarized modes in a nonlinear periodic structure. We then find their solitary-wave solutions referred to as coupled gap solitons. We show that two orthogonally polarized pulses can co-propagate as a coupled gap soliton through a nonlinear periodic structure while each pulse alone will be strongly reflected due to the Bragg reflection. Based on the results, we present an all-optical switching scheme which has a novel architecture and principle. We also study the stability of coupled gap solitons to find the dragging phenomena in a nonlinear birefringent periodic medium.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.563-572
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• 2011

In this paper, the Lie symmetry analysis is performed on the three mixed second-order PDEs, which arise in fluid dynamics, nonlinear wave theory and plasma physics, etc. The symmetries and similarity reductions of the equations are obtained, and the exact solutions to the equations are investigated by the dynamical system and power series methods. Then, the exact solutions to the general types of PDEs are considered through a variable transformation. At last, the symmetry and integration method is employed for reducing the nonlinear ODEs.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.3
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• pp.281-289
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• 1994

An equation set of nonlinear model for regular/irregular waves presented in this study can be applied to waves travelling from deep water to shallow water, which is different from the Boussinesq equations. The presented equations completely satisfy the linear dispersion relationship and when expanded, they are proven to be consistent with the Boussinesq equation of several types. In addition, the position of averaged velocity below the still water level is estimated based on the linear wave theory.

• Journal of Ocean Engineering and Technology
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• v.37 no.2
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• pp.49-57
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• 2023

Since Chappelear developed a Fourier approximation method, considerable research efforts have been made. On the other hand, Fourier approximations are unsuitable for deep water waves. The purpose of this study is to provide a Fourier approximation suitable even for deep water waves and a numerical method to determine the Fourier coefficients and the wave properties. In addition, the convergence of the solution was tested in terms of its order. This paper presents a velocity potential satisfying the Laplace equation and the bottom boundary condition (BBC) with a truncated Fourier series. Two wave profiles were derived by applying the potential to the kinematic free surface boundary condition (KFSBC) and the dynamic free surface boundary condition (DFSBC). A set of nonlinear equations was represented to determine the Fourier coefficients, which were derived so that the two profiles are identical at specified phases. The set of equations was solved using Newton's method. This study proved that there is a limit to the series order, i.e., the maximum series order is N=12, and that there is a height limitation of this method which is slightly lower than the Michell theory. The reason why the other Fourier approximations are not suitable for deep water waves is discussed.

• Steel and Composite Structures
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• v.27 no.3
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• pp.255-271
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• 2018

This paper deals with the transient dynamic analysis and elastic wave propagation in a functionally graded graphene platelets (FGGPLs)-reinforced composite thick hollow cylinder, which is subjected to shock loading. A micromechanical model based on the Halpin-Tsai model and rule of mixture is modified for nonlinear functionally graded distributions of graphene platelets (GPLs) in polymer matrix of composites. The governing equations are derived for an axisymmetric FGGPLs-reinforced composite cylinder with a finite length and then solved using a hybrid meshless method based on the generalized finite difference (GFD) and Newmark finite difference methods. A numerical time discretization is performed for the dynamic problem using the Newmark method. The dynamic behaviors of the displacements and stresses are obtained and discussed in detail using the modified micromechanical model and meshless GFD method. The effects of the reinforcement of the composite cylinder by GPLs on the elastic wave propagations in both displacement and stress fields are obtained for various parameters. It is concluded that the proposed micromechanical model and also the meshless GFD method have a high capability to simulate the composite structures under shock loadings, which are reinforced by FGGPLs. It is shown that the modified micromechanical model and solution technique based on the meshless GFD method are accurate. Also, the time histories of the field variables are shown for various parameters.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2000.10a
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• pp.57-62
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• 2000

The very large flcating structure which am be used for as airport may be as large as several kilomet wide. The first order wave forces as well as wave drift forces are very important forces on such a very large floating In the present studv, the time simulation of motion responses with dolphin-moored VLFS in waves is presented The coeffcients and wave forces involved in the equations are obtained from a three-dimensionul panel method in the frequc The horizontal drift forces and mooring forces for dolphin systems are taken into account. As for numerical example, analyses are carried out for a VLFS in irregular wave condition

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.611-624
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• 2010

A Numerical scheme based on collocation method using quartic B-spline functions is designed for the numerical solution of one-dimensional modified equal width wave (MEW) wave equation. Using Von-Neumann approach the scheme is shown to be unconditionally stable. Performance of the method is validated through test problems including single wave, interaction of two waves and use of Maxwellian initial condition. Using error norms $L_2$ and $L_{\infty}$ and conservative properties of mass, momentum and energy, accuracy and efficiency of the suggested method is established through comparison with the existing numerical techniques.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.34 no.9
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• pp.361-367
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• 1985

A new injection method is proposed for active power filters to eliminate AC harmonics in ac input current of nonlinear loads such as rectifiers. By injecting the PWM current determined by the proposed injection method, all the harmonics up to order nn can be eliminated to exactly zero. This PWM injection current can be generated by sampling total harmonic wave at the rate of M and the sampled values are converted into the proposed PWM wave with N pulse-width variables and adjustable current magnitude Im. These variables are deetermined by solving a set of N nonlinear harmonic equations and the harmonic-elimination characteristics of the new injection are investigated through digital computer sinmulation. Also by comparing between the simulated results and the ones synthesized by data stored in EPROM, the possibility of the suggested injection method can be shown.

• Journal of the Society of Naval Architects of Korea
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• v.41 no.1
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• pp.8-14
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• 2004

As the number of offshore structure is glowing in deep waters, there have been increased damages of it. These floating structures in offshore locations exposed to harsh environmental conditions. In recent years, there has been a slowing attention around damages on bow and deck on FPSO caused by waves in steep storm condition. This paper describes a study of the water on deck due to the dynamic behavior of a FPSO with turret mooring system. The nonlinear motions of the FPSO are simulated under external forces due to wave, current, wind, and mooring forces in the time domain. The direct integration method is employed to estimate low frequency drift wave forces. The current forces are calculated by using slow motion maneuvering equations in the horizontal plane. The coefficients of a model for wind forces are calculated from Isherwood's experimental data and the variation of wind speed is estimated by wind spectrum according to the guidelines of API-RP2A.

• Ocean Systems Engineering
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• v.11 no.1
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• pp.1-16
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• 2021

Experimental and numerical investigations were conducted to study the performance of a surface-fixed horizontal porous wave barrier in regular waves. The characteristics of the reflection and transmission coefficients, energy dissipation, and vertical wave force were examined versus different porosities of the barrier. Numerical simulations based on 3D Reynolds Averaged Navier-Stokes equations with standard low-Re k-ε turbulent closure and volume of fluid approach were accomplished and compared with the experimental results conducted in a 2D wave tank. Experimental measurements and numerical simulations were shown to be in satisfactory agreement. The qualitative wave behavior propagating over a horizontal porous barrier such as wave run-up, wave breaking, air entrapment, jet flow, and vortex generation was reproduced by CFD computation. Through the discrete harmonic decomposition of the vertical wave force on a wave barrier, the nonlinear characteristics were revealed quantitatively. It was concluded that the surface-fixed horizontal barrier is more effective in dissipating wave energy in the short wave period region and more energy conversion was observed from the first harmonic to higher harmonics with the increase of porosity. The present numerical approach will provide a predictive tool for an accurate and efficient design of the surface-fixed horizontal porous wave barrier.