• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.487-500
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• 1997

In this paper we introduce a multigrid method for solving the nonliear Urysohn integral equation. The algorithm is derived from a discrete resolvent equation which approximates the continuous resolvent equation of the nonlinear Urysohn integral equa-tion. The algorithm is mathematically equivalent to Atkinson's adap-tive twogrid iteration. But the two are different computationally. We show the convergence of the algorithm and its equivalence to Atkinson's adaptive twogrid iteration. in our numerical example we compare our algorithm to other multigrid methods for solving the nonliear Urysohn integral equation including the nonlinear multigrid nethod introduced by hackbush.

• 대한기계학회논문집A
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• 제26권5호
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• pp.952-959
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• 2002

The natural frequencies of a flexible spinning disk misaligned with the axis of rotation are studied in an analytic manner. The effects of misalignment on the natural frequency need to be investigated, because the misalignment between the axis of symmetry and the axis of relation cannot be avoided in the removable disks such as CD-R, CD-RW or DVD disks. Assuming that the in -plane displacements are in steady state and the out-of-plane displacement is in dynamic state, the equations of motion are derived for the misaligned spinning disk. After the exact solutions are obtained fur the steady -state in-plane displacements, they are plugged into the equation for the dynamic-state out-of-plane motion. The resultant equation is a linear equation for the out -of-plane displacement, which is discretized by the Galerkin method. Based on the discretized dquations, the effects of the misalignment are analyzed on the vibration characteristics of the spinning disk, i.e., the natural frequencies and the critical speed.

• 한국염색가공학회지
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• 제33권3호
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• pp.141-146
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• 2021

Supercritical fluid has excellent dissolving power for various materials based on low viscosity and high diffusion coefficient and is used as solvents in various chemical processes. However, its industrial application can be very tricky because the design, especially the size of the supercritical apparatus, should be carefully chosen to optimize the cost and the production of supercritical fluidic state. And the first step of the supercritical fluid apparatus design is to choose the appropriate size of the reactor vessel to produce supercritical fluid above its critical pressure and temperature. Therefore, this study aims to analyze thermodynamic behaviors of dichloromethane based on ideal gas, van der Waals, Redlich-Kwong, Soave-Redlich-Kwong, and Peng-Robinson equations of state. The correlation between the volume and pressure of dichloromethane at 200℃ was revealed and it can be used to design the optimized size of the supercritical apparatus for industrial production.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.817-825
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• 2001

The natural frequencies of a flexible spinning disk misaligned with the axis of rotation are studied in an analytic manner. The effects of misalignment on the natural frequency need to be investigated, because the misalignment between the axis of symmetry and the axis of rotation cannot be avoided in the removable disks such as CD-R, CD-RW or DVD disks. Assuming that the in-plane displacements are in steady state and the out-of-plane displacement is in dynamic state, the equations of motion are derived for the misaligned spinning disk. After the exact solutions are obtained for the steady-state in-plane displacements, they are plugged into the equation for the dynamic-state out-of-plane motion. The resultant equation is a linear equation for the out-of-plane displacement, which is discretized by the Galerkin method. Based on the discretized equations, the effects of the misalignment are analyzed on the vibration characteristics of the spinning disk, i.e., the natural frequencies and the critical speed

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권2호
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• pp.85-97
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• 2019

In this paper we introduce the reciprocal-negative Fermat's equation induced by the famous equation in the Fermat's Last Theorem, establish the general solution in the simplest cases and the differential solution to the equation, and investigate, then, the generalized Hyers-Ulam stability in a $quasi-{\beta}-normed$ space with both the direct estimation method and the fixed point approach.

• 화약ㆍ발파
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• 제34권2호
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• pp.31-38
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• 2016

유체 동역학 코드는 고속 충돌을 모델링하는 수치해석 툴로서 재료가 유체처럼 거동한다고 가정하며, 화약을 이용한 암반발파와 같은 충돌 문제를 푸는 데 광범위하게 사용된다. 암반발파를 현실적으로 모사하기 위해서는 화약을 수치해석적으로 모델링할 필요가 있으며, 이를 통해 암반과 화약의 상호작용 문제를 완전 연계된 방식으로 풀 수 있다. 화약을 수치 모델링하기 위해서는 특정 물리적 조건에서 재료의 상태를 나타내는 상태 방정식이 수립되어야 한다. 본 고에서는 발파 과정을 수치 모델링하기 위한 유체 동역학 코드, 화약의 상태 방정식과 관련 매개변수의 결정방법에 대해 소개하였다.

• International Journal of Aeronautical and Space Sciences
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• 제3권1호
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• pp.95-104
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• 2002

Numerical solution of the full Navier-Stokes equation as well as the energy equation has been obtained for the unsteady natural convection in a rectangular enclosure. One side wall was maintained at very high temperature simulating fires. Especially the effect of surface radiation was taken into account. While the enclosed air was assumed to be transparent, the internal walls directly interacted one another through the surface radiation. Due to a significant temperature difference in the flow field, the equation of state was used instead of the Boussinesq approximation. It was found that the rapid heating of the adiabatic ceiling and floor by the incoming radiation from the hot wall made the evolution at thermo-fluid field highly unstable in the initial period. Therefore, the secondary cells brought about at the floor region greatly affected the heat transfer mechanism inside the enclosure. The heat transfer rate was augmented by the radiation, resulting in requiring less time for the flow to reach the steady state. At the steady state neglecting radiation two internal hydraulic jumps were clearly observed in upper/left as well as in lower/right comer. However, the hydraulic jump in the lower/right comer could not be observed for the case including radiation due to its high momentum flow over the bottom wall. Radiation resulted in a faster establishment of the steady state phenomena.

• 한국항공우주학회지
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• 제36권12호
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• pp.1152-1162
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• 2008

본 논문은 헬리콥터 비선형 제어기 설계를 위한 State-Dependent Riccati Equation (SDRE) 기법을 다루었다. SDRE 제어기법은 비선형 운동방정식에 대해 선형 시스템과 같은 구조를 갖는 방정식을 필요하기 때문에 State-Dependent Coefficient (SDC) factorization 기법을 개발하여 비선형 운동방정식으로부터 이러한 구조의 방정식을 유도하였다. SDRE제어기를 온라인상에서 설계하는데 필요한 대수 Riccati 방정식의 효율적인 수치해법을 연구하였다. 본 연구에서 제안된 수치기법을 헬리콥터의 경로추종문제로 적용하였으며, 고 신뢰도의 헬리콥터 수학적 모델을 적용하여 실시간으로 SDRE 제어기를 설계할 수 있는 방안을 제안하였다.

• 한국추진공학회지
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• 제26권5호
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• pp.24-34
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• 2022

초임계 영역에서 작동하는 탄화수소 연료를 사용하는 재생냉각채널의 냉각성능을 예측하기 위해서는 타당한 물성 예측이 필수이다. 본 연구는 고분자 탄화수소의 임계 압축인자에 따라 밀도와 비열을 적절하게 예측하기 위해 2-파라미터 상태방정식인 SRK(Soave-Redlich-Kwong) 및 PR(Peng-Robinson) 상태방정식과 이를 합한 3-파라미터 상태방정식인 RK-PR 상태방정식에 대한 비교 분석을 수행하였다. 대표적으로 낮은 임계압축 인자를 갖는 n-dodecane 연료와 높은 임계압축 인자를 갖는 JP-10 연료를 선정하여 두 연료의 열역학적 물성을 예측할 때 적합한 상태방정식을 제시하였다. 마지막으로 밀도와 비열의 예측 결과를 NIST REFPROP 데이터와 비교하여 검증하였다.

• 설비공학논문집
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• 제11권1호
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• pp.91-99
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• 1999

Vapor-liquid equilibrium apparatus is designed and set up. The equilibrium data of two binary systems, HFC-32/143a and HFC-143a/134a, are measured. Fifteen equilibrium data for HFC-32/143a and HFC-143a/134a systems are measured over the temperature range 263.15~283.15K at 10K interval and the composition range 0.10~0.80, respectively. And vapor-liquid equilibrium data are calculated using equation of state and correlation of activity coefficient and compared with the present data. Equation of state is used CSD and RKS equations and correlation of activity coefficient is used Margules' and Van Ness and Abbott's correlations. Real behavior of HFC-32/143a system has very large deviation with Raoult's rule which is ideal behavior. But real behavior of HFC-143a/134a system is similar to ideal behavior. The calculated data from CSD equation are compared with the data in the open literatures and the calculated data from REFPROP. In the results for REFPROP, the relative deviations of bubble point pressure for HFC-32/143a system are within -2.16~0.84% for CSD equation and within -0.20~1.10% for RKS equation. And the relative deviations of bubble point pressure for HFC-143a/134a system are within -0.45~0.12% and -0.20~2.8% for CSD and RKS equations, respectively.