• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2012년도 춘계학술대회 논문집
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• pp.923-928
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• 2012

In this paper, static and oscillatory instability of a nanotube conveying fluid and modelled as a thin-walled beam is investigated. Analytically nonlocal effect, effects of boundary conditions, transverse shear and rotary inertia are incorporated in this study. The governing equations and the two different boundary conditions are derived through Hamilton's principle. Numerical analysis is performed by using extend Galerkin method which enables us to obtain more exact solutions compared with conventional Galerkin method. Variations of critical flow velocity for different boundary conditions of a nanotube with analytically nonlocal effect, partially nonlocal effect and local effect of a nanotube are investigated and pertinent conclusion is outlined.

• Korean Chemical Engineering Research
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• 제52권2호
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• pp.199-204
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• 2014

2성분 응고계에서 다공성 mush 층에서의 조성 대류는 생성되는 제품의 질에 영향을 준다. 본 연구에서는 일정한 속도로 응고되는 mush 층을 고려하였다. 선형 안정성 이론을 사용하여 mush 층에 대한 교란방정식을 유도하였고, 기본상태 온도장과 mush 층에서 기공률의 분포를 수치해법으로 조사하였다. 과열량이 클 때 mush 층의 두께는 열경계층의 두께에 비해 상대적으로 작았다. 과열량이 감소함에 따라 mush 층의 두께를 기준으로 한 Rayleigh 수는 증가하였고, mush 층은 조성 대류에 대해 안정해졌다. mush 층의 윗면에 등온조건을 적용한 경우보다 온도 및 열속의 연속조건을 액체-mush 계면에 적용한 경우에 임계 Rayleigh 수가 더 작게 얻어졌다.

• 열처리공학회지
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• 제5권1호
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• pp.13-22
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• 1992

The thermal stability of duplex high Mn-steel structure have been investigated using 15%Mn~1.0~2.4%C steels which are composed of ${\gamma}$-and ${\theta}$-phases in the range of temperature from 900 to $1100^{\circ}C$, and time from 50 to 300h. The results are as follows ; 1) The grain growth in single-phase region proceeds by grain boundary migration and the relation between mean radius $\bar{r}$ and annealing time t is described as follows ; $\bar{r}^2-{\bar{r}_0}^2=k_0{\cdot}t$ 2) The grain growth of duplex, (${\gamma}+{\theta}$), strucrure is slower than that single phase because the chemical composition of ${\gamma}$-and ${\theta}$-phases differs esch others. 3) The grain of (${\gamma}+{\theta}$) duplex structure grow slowly in a mode of Ostwald ripening. Because grain boundaries of ${\gamma}$-phase migrate under a restriction of pinning by ${\theta}$-phases. 4) In the duplex structures. the dispersed structures change to the dual-structures, as the volume fraction of the dispersed second-phase increase. Consequently, the growth-law, which is controlled by boundary-diffusion change to that of the volume diffusion-mechanism.

• 한국소음진동공학회논문집
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• 제18권10호
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• pp.1057-1064
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• 2008

In this paper, static and oscillatory instability of nanopipes conveying fluid and modelled as a thin-walled beam is investigated. Effects of boundary conditions and non-classical transverse shear and rotary inertia are incorporated in this study. The governing equations and the three different boundary conditions are derived through Hamilton's principle. Numerical analysis is performed by using extend Galerkin method which enables us to obtain more exact solutions compared with conventional Galerkin method. Variations of critical flow velocity for different boundary conditions of carbon nanopipes are investigated and pertinent conclusion is outlined.

• 한국전산구조공학회논문집
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• 제12권2호
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• pp.223-231
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• 1999

본 연구는 복합하중을 받는 구조물에 있어서 구조물의 안정경계점을 계산하는 방법을 제시하고 있다. 여기에서는 우선 안정경계점에 놓여 있는 기지의 점에 대한 선형해를 일반역행열을 이용하여 선형 증분 평형방정식의 여해와 특이해의 선형결합으로 나타내었다. 다음으로 두 개의 하중계수를 구속하는 선형조건을 도입하고, 그 구속조건하에서 하중계수 비가 일정하게 되도록 반복계산을 수행하므로써, 안정경계점위의 다음 목표점이 얻어진다. 얻어진 이 점을 초기점으로 이용한다. 평형경로를 추적할 때, 본래의 두 개의 하중계수 문제는 하중계수의 비가 일정하다는 조건을 도입하여 단일 하중계수의 문제로 된다. 두 개의 예를 들어 수치해석을 행하였으며, 얻어진 결과로부터 본 연구에서 채택된 방법은 구조물의 경계안정점을 찾는 문제에 적합하며 더욱 개발할 여지가 있음을 보여주고 있다.

• 대한수학회논문집
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• 제30권3호
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• pp.297-311
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• 2015

We present a robust and accurate boundary condition for pricing financial options that is a hybrid combination of the payoff-consistent extrapolation and the Dirichlet boundary conditions. The payoff-consistent extrapolation is an extrapolation which is based on the payoff profile. We apply the new hybrid boundary condition to the multi-dimensional Black-Scholes equations with a high correlation. Correlation terms in mixed derivatives make it more difficult to get stable numerical solutions. However, the proposed new boundary treatments guarantee the stability of the numerical solution with high correlation. To verify the excellence of the new boundary condition, we have several numerical tests such as higher dimensional problem and exotic option with nonlinear payoff. The numerical results demonstrate the robustness and accuracy of the proposed numerical scheme.

• 한국강구조학회 논문집
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• 제12권2호통권45호
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• pp.221-230
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• 2000

자유단이 있는 비등방성 판의 안정성을 검토할 때, 기존의 해석적인 방법으로는 다양한 하중 조건 및 경계조건에 대해 좌굴하중 및 좌굴모드를 구할 수 없다. 이러한 단점을 해결하기 위해 수치해석 기법인 유한차분법을 사용하였다. 유한차분법을 적용할 때, 자유경계의 가상점 처리가 가장 난해하게 되므로 1변이 자유이고 3변이 고정인 경우와 마주보는 2변이 자유이고 다른 2변이 고정인 경우를 해석 모델로 삼아 좌굴해석을 수행하였다. 본 논문에서는 자유경계를 갖는 비등방성 판의 해석 기법으로 유한차분법을 제시하였으며, 다양한 수치해석을 통하여 자유경계의 좌굴하중 및 모드 특성을 규명하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권3호
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• pp.179-202
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• 2019

This paper presents second derivative generalized extended backward differentiation formulas (SDGEBDFs) based on the second derivative linear multi-step formulas of Cash [1]. This class of second derivative linear multistep formulas is implemented as boundary value methods on stiff problems. The order, error constant and the linear stability properties of the new methods are discussed.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.571-579
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• 2007

Finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with a periodic boundary condition, which is of the type $ut+\frac{{\partial}^2} {{\partial}x^2}\;g\;(u,\;u_x,\;u_{xx})=f(u,\;u_x,\;u_{xx})$. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Korean Chemical Engineering Research
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• 제57권1호
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• pp.142-147
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• 2019

The onset of buoyancy-driven convection in an initially isothermal and quiescent horizontal fluid layer was analyzed theoretically. It is well-known that at the critical Rayleigh number $Ra_c=669$ convective motion sets in with a constant-heat-flux cooling through the upper boundary. Here, based on the momentary instability concept, the dimensionless critical time ${\tau}_m$ to mark the onset of convective motion for Ra > 669 was analyzed theoretically. The energy method under the momentary stability concept was used to find the critical conditions as a function of the Rayleigh number Ra and the Prandtl number Pr. The predicted critical conditions were compared with the previous theoretical and experimental results. The momentary stability criterion gives more reasonable wavenumber than the conventional energy method.