• 수산해양기술연구
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• 제23권3호
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• pp.111-116
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• 1987

이상으로부터 다음의 결론을 얻는다. 조파저항 이론의 전개에서 Michell 적분보다 더욱 정밀한 Neumann-Kelvin 문제가 복잡한 kernel 함수 때문에 많은 시간과 노력이 필요하지만, 원점 부근에서 Kelvin 소오스의 점근거동을 조사하여 세장체 근사를 행함으로 N-K 문제의 kernel 함수에 대한 근사와 동등하게 처리될 수 있었다. 조파저항의 계산 결과가 Michell 적분과 비슷한 경향을 보이나, 실험치와의 정확한 비교를 할 수 없었다. 그러나 세장선 이론을 적용함으로써 훨씬 복잡하고 지루한 작업을 들 수 있었다. 전진 속도를 갖는 경우에는 수정된 Green정리를 이용하면 될 것으로 기대된다.

• Journal of applied mathematics & informatics
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• 제34권5_6호
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• pp.495-508
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• 2016

A singularly perturbed reaction-diffusion fourth-order ordinary differential equation(ODE) with discontinuous source term is considered. Due to the discontinuity, interior layers also exist. The considered problem is converted into a system of weakly coupled system of two second-order ODEs, one without parameter and another with parameter ε multiplying highest derivatives and suitable boundary conditions. In this paper a computational method for solving this system is presented. A zero-order asymptotic approximation expansion is applied in the second equation. Then, the resulting equation is solved by the numerical method which is constructed. This involves non-overlapping Schwarz method using Shishkin mesh. The computation shows quick convergence and results presented numerically support the theoretical results.

• 대한수학회지
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• 제54권4호
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• pp.1175-1187
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• 2017

The spectral problem $$-y^{{\prime}{\prime}}+q(x)y={\lambda}y,\;0 < x < 1, \atop y(0)cos{\beta}=y^{\prime}(0)sin{\beta},\;0{\leq}{\beta}<{\pi};\;{\frac{y^{\prime}(1)}{y(1)}}=h({\lambda})$$ is considered, where ${\lambda}$ is a spectral parameter, q(x) is real-valued continuous function on [0, 1] and $$h({\lambda})=a{\lambda}+b-\sum\limits_{k=1}^{N}{\frac{b_k}{{\lambda}-c_k}},$$ with the real coefficients and $a{\geq}0$, $b_k$ > 0, $c_1$ < $c_2$ < ${\cdots}$ < $c_N$, $N{\geq}0$. The sharpened asymptotic formulae for eigenvalues and eigenfunctions of above-mentioned spectral problem are obtained and the uniform convergence of the spectral expansions of the continuous functions in terms of eigenfunctions are presented.

• 대한수학회논문집
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• 제12권2호
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• pp.479-490
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• 1997

We consider long nonlinear waves in the two-layer flow of an inviscid and incompressible fluid bounded above by a free surface and below by a rigid boundary. The flow is forced by a bump on the bottom. The derivation of the forced KdV equation fails when the density ratio h and the depth ratio $\rho$ yields a condition $1 + h\rho = (2-h)((1-h)^2 + 4\rho h)^{1/2}$. To overcome this difficulty we derive a forced modified KdV equation by a refined asymptotic method. Numerical solutions are given and hydraulic fall solution of a two layer fluid is expressed analytically in the case that derivation of the forced KdV (FKdV) equation fails.

• 대한수학회보
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• 제48권4호
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• pp.713-724
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• 2011

We study the dynamics of transcendental entire functions with Siegel disks whose singular values are just two points. One of the two singular values is not only a superattracting fixed point with multiplicity more than two but also an asymptotic value. Another one is a critical value with free dynamics under iterations. We prove that if the multiplicity of the superattracting fixed point is large enough, then the restriction of the transcendental entire function near the Siegel point is a quadratic-like map. Therefore the Siegel disk and its boundary correspond to those of some quadratic polynomial at the level of quasiconformality. As its applications, the logarithmic lift of the above transcendental entire function has a wandering domain whose shape looks like a Siegel disk of a quadratic polynomial.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.37-42
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• 2003

The problem of an orthotropic material with a central crack is studied. The material is subjected to uniform biaxial loading along its boundary. The normal stress ratio theory is applied to predict fracture strength behavior in cracked orthotropic material. The dependence of the critical stress with respect to the biaxial loading and the crack orientation is discussed. Our analysis shows significant effects of biaxial loading on the critical stress. The additional tenn in the asymptotic expansion of the crack tip stress field appears to provide more accurate critical stress prediction.

• 한국전산유체공학회지
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• 제2권1호
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• pp.129-137
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• 1997

We consider long nonlinear waves in the two-layer flow of an inviscid and incompressible fluid bounded above by a free surface and below by a rigid boundary. The flow is forced by a bump on the bottom. The derivation of the forced KdV equation fails when the density ratio h and the depth ratio ρ yields a condition 1＋hρ=(2-h)((1-h)²＋4ρh)/sup 1/2/. To overcome this difficulty we derive a forced modified KdV equation by a refined asymptotic method. Numerical solutions are given and hydraulic fall solution of a two layer fluid is expressed analytically in the case that derivation of the forced KdV(FKdV) equaition fails.

• Nuclear Engineering and Technology
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• 제41권3호
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• pp.279-286
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• 2009

Improving over a previous study [1], this paper provides a Monte Carlo method for the heat conduction analysis of problems with complicated geometry (such as a pebble with dispersed fuel particles). The method is based on the theoretical results of asymptotic analysis of neutron transport equation. The improved method uses an appropriate boundary layer correction (with extrapolation thickness) and a scaling factor, rendering the problem more diffusive and thus obtaining a heat conduction solution. Monte Carlo results are obtained for the randomly distributed fuel particles of a pebble, providing realistic temperature distributions (showing the kernel and graphite-matrix temperatures distinctly). The volumetric analytic solution commonly used in the literature is shown to predict lower temperatures than those of the Monte Carlo results provided in this paper.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 춘계학술대회논문집
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• pp.457-467
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• 2004

Wave Transmission analysis is one of methods for power transmission and reflection coefficients in coupled infinite structures. This paper focuses the wave transmission analysis of point coupled structures among semi-infinite beams and infinite thin plates considering all kinds of waves. It is supposed that the junction through the beams and plates is an identical spot and no point of contact exist except the spot. The boundary conditions are applied at the spot for continuities of 6 DOF displacements and 6 DOF force equilibriums, and then wave fields are obtained in the coupled structures. Since wave components in plate field are simplified using asymptotic expressions of Henkel functions, the displacements and forces at the plate junction can be simply expressed with magnitudes of the wave components. The wave fields according to incident waves gives the power transmission coefficients in beam/plate point coupled structures. For both coupled structures with a beam vertically and obliquely joined to a plate, power transmission analysis is performed and the analysis results are compared and examined.

• 수산해양기술연구
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• 제28권2호
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• pp.228-239
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• 1992

The purpose of the present research is to develop an efficient numerical method for the calculation of potential flow and predict the wave-making resistance for the application to ship design of tuna purse seiner. The paper deals with the numerical calculation of potential flow around the series 60 with forward velocity by the new slender ship theory. This new slender ship theory is based on the asymptotic expression of the Kelvin-source, distributed over the small matrix at each transverse section so as to satisfy the approximate hull boundary condition due to the assumption of slender body. Some numerical results for series 60, C sub(b) =0.6, hull are presented in this paper. The wave pattern and wave resistance are computed at two Froude numbers, 0.267 and 0.304. These results are better than those of Michell's thin ship theory in comparison with measured results. However, it costs much time to compute not only wave resistance but also wave pattern over some range of Froude numbers. More improvements are strongly desired in the numerical procedure.