• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.15 no.4
• /
• pp.283-288
• /
• 2015

In this paper, we propose a dynamic mathematical model of love involving various external forces, in order to analyze the chaotic phenomena in a love model based on Romeo and Juliet. In addition, we investigate the nonlinear phenomena in a love model with external forces using time series and phase portraits. In order to describe nonlinear phenomena precisely using time series and phase portraits, we vary the type of external force, using models such as a sine wave, chopping wave, and square wave. We also apply various different parameters in the Romeo and Juliet model to acquire chaotic dynamics.

• Bulletin of the Korean Space Science Society
• /
• 2004.04a
• /
• pp.84-84
• /
• 2004

Using a one-dimensional MHD code of Total Variation Diminishing (TVD) scheme, we perform simulations of propagation of nonlinear magnetosonic waves. A magnetosonic wave is a longitudinal wave propagating perpendicularly to the magnetic field lines, and involves compression and rarefaction of the magnetic field lines and the plasma. We first confirm the theoretical solution of Lee and Kim (2000) for the evolution of nonlinear magnetosonic waves in the homogeneous space. (omitted)

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.9 no.6
• /
• pp.598-612
• /
• 2017

The recently developed Harmonic Polynomial Cell (HPC) method has been proved to be a promising choice for solving potential-flow Boundary Value Problem (BVP). In this paper, a flux method is proposed to consistently deal with the Neumann boundary condition of the original HPC method and enhance the accuracy. Moreover, fixed mesh algorithm with free surface immersed is developed to improve the computational efficiency. Finally, a two dimensional (2D) multi-block strategy coupling boundary-fitted mesh and fixed mesh is proposed. It limits the computational costs and preserves the accuracy. A fully nonlinear 2D numerical wave tank is developed using the improved HPC method as a verification.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.3
• /
• pp.261-267
• /
• 2007

We show the existence of the positive solution for the system of the following nonlinear wave equations with Dirichlet boundary conditions $$u_{tt}-u_{xx}+av^+=s{\phi}_{00}+f$$, $$v_{tt}-v_{xx}+bu^+=t{\phi}_{00}+g$$, $$u({\pm}\frac{\pi}{2},t)=v({\pm}\frac{\pi}{2},t)=0$$, where $u_+=max\{u,0\}$, s, $t{\in}R$, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}=1$ of the eigenvalue problem $u_{tt}-u_{xx}={\lambda}_{mn}u$ with $u({\pm}\frac{\pi}{2},t)=0$, $u(x,t+{\pi})=u(x,t)=u(-x,t)=u(x,-t)$ and f, g are ${\pi}$-periodic, even in x and t and bounded functions in $[-\frac{\pi}{2},\frac{\pi}{2}]{\times}[-\frac{\pi}{2},\frac{\pi}{2}]$ with $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}f{\phi}_{00}=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}g{\phi}_{00}=0$.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
• /
• 2006.11a
• /
• pp.382-385
• /
• 2006

A high-order spectral/boundary-element method is newly adapted as an efficient numerical tool. In this method, the velocity potential is expressed as the sum of surface potential and body potential. Then, surface potential is solved fly using the high-order spectral method and body potential is solved fly using the high-order boundary element method. Through the combination of these two methods, the wave-making problems fly a submerged sphere moving with the large amplitude oscillation are solved in time-domain. With the example calculations, nonlinear effects on free-surface profiles and hydrodynamic forces are shown and discussed.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.171-182
• /
• 2005

An analysis of the non-homogeneous term involved in the free surface condition for second order wave diffraction on a pair of cylinders is presented. In the computations of the nonlinear loads on offshore structures, the most challenging task is the computation of the free surface integral. The main contribution to this integrand is due to the non-homogeneous term present in the free surface condition for second order scattered potential. In this paper, the free surface condition for the second order scattered potential is derived. Under the assumption of large spacing between the two cylinders, waves scattered by one cylinder may be replaced in the vicinity of the other cylinder by equivalent plane waves together with non-planner correction terms. Then solving a complex matrix equation, the first order scattered potential is derived and since the free surface term for second order scattered potential can be expressed in terms of the first order potentials, the free surface term can be obtained using the knowledge of first order potentials only.

• Selected Papers of The Society of Naval Architects of Korea
• /
• v.1 no.1
• /
• pp.45-51
• /
• 1993

By using multiple-scale expansion techniques, the Mach reflection of sinusoidally- modulated nonlinear Stokes waves by a stationary thin wedge has been studied within the framework of potential theory. It is shown that the evolution of diffracted wave amplitude can be described by the Zakharov equation to the loading order and that It reduces to the cubic Schrodinger equation with an additional linear term in the case of stable modulations. Computations are made for the cubic Schrodinger equation for different values of nonlinear and dispersion parameters. Numerical results reflect the experimental findings in terms of the amplitude and width of generated stem waves. Based on the computations it is concluded that the nonlinearity dominates the wave field, while the dispersion does not significantly affect the wave evolution.

• Journal of Institute of Control, Robotics and Systems
• /
• v.7 no.3
• /
• pp.263-268
• /
• 2001

A new control scheme s proposed for the control of reactive batch distillation (RBD) column. A nonlinear wave model captures the essential dynamic behavior of the RBD process. The proposed control scheme is based on both Generic Model Control(GNC) and nonlinear wave model. The control scheme uses a profile position of the column as a controlled variable. Ethanol esterification process using RBD is chosen as an example process. Tight control of the distillate purity is obtained with the use of the proposed control scheme.

• 한국전산유체공학회:학술대회논문집
• /
• 1999.05a
• /
• pp.58-65
• /
• 1999

The two different approaches for solving the nonlinear ship wave problem are disscussed in the present paper. The first one is based on a panel method which neglects the viscous effects. Another one is based on a finite volume method which solves RANS equations. The present paper has been focused on the advantages/disadvantages of the above two methods. The developed methods are applied to calculating the flow around Wigley hull & Series 60 hull to validate the performance of the present nonlinear method, Although the two methods employ quite different numerical approaches, the calculated wave patterns from the both methods show good agreements with the experiments.

• Kyungpook Mathematical Journal
• /
• v.61 no.4
• /
• pp.859-888
• /
• 2021

This paper is devoted to the study of a nonlinear Kirchhoff-Carrier wave equation in an annulus associated with Robin-Dirichlet conditions. At first, by applying the Faedo-Galerkin method, we prove existence and uniqueness results. Then, by constructing a Lyapunov functional, we prove a blow up result for solutions with a negative initial energy and establish a sufficient condition to obtain the exponential decay of weak solutions.