• Journal of the Society of Naval Architects of Korea
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• v.50 no.4
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• pp.224-231
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• 2013

The concept of the natural frequency is useful for understanding the characters of oscillating systems. However, when a circular cylinder floating horizontally on the water surface is heaving, due to the hydrodynamic forces, the system is not governed by the equation like that of the harmonic one. In this paper, in order to shed some lights on the more correct use of the concept of the natural frequency, a problem of the heaving circular cylinder is analyzed in the time domain. The equation of motion, an integro-differential equation, was derived following the fashion of Cummins (1962), and its coefficients including the retardation function were obtained using the numerical solution of Lee (2012). The equation was solved numerically, and the experiment was also carried out in the CNU flume. Using our numerical and experimental results, the natural frequency was defined as its average value given by the motion data excluding those of the initial stage. Our results were then compared with those of the existing investigations such as Maskell and Ursell (1970), Ito (1977) and Yeung (1982) as well as the newly obtained results of Lee (2012). Comparison showed that the natural frequency obtained here agrees well with that of Lee (2012), which was found through the frequency domain analysis. It was also shown that the approximation of heaving motion by a damped harmonic oscillation, which was regarded as suitable by most previous investigators, is not physically suitable for the reason that can be clearly shown through comparing the shape of MCFRs(Modulus of Complex Frequency Response). Furthermore, we found that although the previous approximations yield the damping ratio significantly different from our result the magnitude of natural frequency is not much different from our result.

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.231-249
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• 2020

We present an efficient and robust finite difference method for a two-asset jump diffusion model, which is a partial integro-differential equation (PIDE). To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. In addition, we use bilinear interpolation to solve integral term of PIDE. We can obtain more stable value by using the payoff-consistent extrapolation. We provide numerical experiments to demonstrate a performance of the proposed numerical method. The numerical results show the robustness and accuracy of the proposed method.

• The Pure and Applied Mathematics
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• v.22 no.2
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• pp.159-168
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• 2015

Abstract. We propose a fast and robust finite difference method for Merton's jump diffusion model, which is a partial integro-differential equation. To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. Also, we use non-uniform grids to increase efficiency. We present numerical experiments such as evaluation of the option prices and Greeks to demonstrate a performance of the proposed numerical method. The computational results are in good agreements with the exact solutions of the jump-diffusion model.

• Advances in aircraft and spacecraft science
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• v.11 no.1
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• pp.55-81
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• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.2
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• pp.87-94
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• 2014

In solid mechanics, the peridynamics theory has provided a suitable framework for material failure and damage propagation simulation. Peridynamics is computationally expensive since it is required to solve enormous nonlocal interactions based upon integro-differential equations. Thus, multiscale coupling methods with other local models are of interest for efficient and accurate implementations of peridynamics. In this study, peridynamic models are restricted to regions where discontinuities or stress concentrations are present. In the domains characterized by smooth displacements, classical local models can be employed. We introduce a recently developed blending scheme to concurrently couple bond-based peridynamic models and the Navier equation of classical elasticity. We demonstrate numerically that the proposed blended model is suitable for point loads and static fracture, suggesting an alternative framework for cases where peridynamic models are too expensive, while classical local models are not accurate enough.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.3
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• pp.47-58
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• 1994

Theoretical calculations are carried out for the estimation of linear maneuvering coefficients of a ship moving in shallow water region. Hydrodynamic forces and moments acting on a maneuvering ship are modelled based on a slender body theory, from which integro-differential equation for the unknown inner stream velocity is derived. Numerical algorithms fur solving this equation are described in detail. By considering water depth effects in the mathematical model, variations of maneuvering coefficients with water depth are studied. Programs are developed according to this method and calculations are done for Mariner, Series 60 and Wigley hull forms. For the verification of the programs, calculated results are compared with some analytic solutions and with published experimental results, which show good agreements in spite of many assumptions included in the mathematical model. It is expected that this method can be used as a preliminary tool for the estimation of maneuverability coefficients of a ship in shallow water region at its initial design stage.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.36D no.8
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• pp.45-53
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• 1999

Electromagnetic scattering by finite number of conducting strips loaded on a grounded dielectric is considered for the TM polarization case from the viewpoints of transmitting(receiving) leaky wave antenna and grating coupler. An integro-differential equation whose unknowns are the induced currents over the strips is derived and solved by use of the method of moments. In order to construct the non-uniform leaky wave structures with specific source(current) distributions over the strips, distances between two adjacent strips and strip width are simultaneously varied along the structure. From some results for the current distributions over the strips and surface wave powers, it is observed that the maximum coupling efficiencies of the appropriately constructed non-uniform leaky wave structures from the viewpoints of both a receiving leaky wave antenna and a grating coupler amount upto 95%, which are about 15% improvements compared with those(80%) of the uniform structures.

• Nuclear Engineering and Technology
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• v.54 no.6
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• pp.2077-2083
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• 2022

In the unlikely event of core disruptive accident in sodium cooled fast reactors, the reactor containment building would be bottled up with sodium and fission product aerosols. The behavior of these aerosols is crucial to estimate the in-containment source term as a part of nuclear reactor safety analysis. In this work, the evolution of sodium aerosol characteristics (mass concentration and size) is simulated using HAARM-S code. The code is based on the method of moments to solve the integro-differential equation. The code is updated to FORTRAN-77 and run in Microsoft FORTRAN PowerStation 4.0 (on Desktop). The sodium aerosol characteristics simulated by HAARM-S code are compared with the measured values at Aerosol Test Facility. The maximum deviation between measured and simulated mass concentrations is 30% at initial period (up to 60 min) and around 50% in the later period. In addition, the influence of humidity on aerosol size growth for two different aerosol mass concentrations is studied. The measured and simulated growth factors of aerosol size (ratio of saturated size to initial size) are found to be matched at reasonable extent. Since sodium is highly reactive with atmospheric constituents, the aerosol growth factor depends on the hygroscopic growth, chemical transformation and density variations besides coagulation. Further, there is a scope for the improvement of the code to estimate the aerosol dynamics in confined environment.

• Journal of Korean Philosophical Society
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• v.105
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• pp.269-290
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• 2008

The purpose of this paper is to explore the possibility of backwards causation. For study, this paper was divided into four views as follows: The first view was sometimes suggested by the people such as M. Dummett who distinguished observers from behaviors. According to observers' view, backwards causation is impossible, whereas behaviors' view possible. However, in a real or genuine sense, it is incorrect for us to argue for impossibility of backwards causation from the observer aspect. The second view was supported by J. H. Schmidt. He analyzed the possibility of backwards causation in terms of macro and micro level analysis about the causal events. According to micro level analysis, backwards causation is possible, but macro level analysis impossible. Usually the latter makes the former something miraculous. Under the macro level analysis, backwards causation, at first, seems to be miraculous phenomena which belongs to the micro level analysis. The third view had to do with physical equation, and the fourth view physical phenomena, respectively. John Earman argued for the backwards causation by the transformation from Lorentz­-Dirac equation to a second-order integro-differential one in the field of electrodynamic acceleration. His argument was criticized because of his misunderstanding about the relationship between two equations. On the other hand, Phil Dowe defended a version of Reichenbach's own theory about the direction of causation founded on the fork asymmetrical causal relation. However his view was different from Reichenbach's because the former defended the backwards causation model of Bell phenomena in quantum mechanics. On the contrary, Reichenbach put stressed on the priority of cause in the causal process. Subjectivism has recently been defended by H. Price, under the label of perspectivism. According to him, in a certain sense causal asymmetry is not in the world, but is rather a product of our own asymmetric perspective on the world. He also suggested causal net, the symmetry of microphysics, and so on. As mentioned above, there are many kind of suggestions of backwards causation. However none of them replaced objectively the main streams of the direction of causal process. The main stream has been usually defended by pragmatical ground. That is, effects do not precede their causes although causes cannot be without their effects.