• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.275-281
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• 1996

In order to examine the validity of an asymptotic solution obtained from the method of multiple scales, we investigate a third-order subharmonic resonance response of a bar constrained by a nonlinear spring to a harmonic excitation. The motion of the bar is governed by a linear partial differential equation with a nonlinear boundary condition. The nonlinear boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution.

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.997-1008
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• 2012

This work provides an alternative derivation of third order response functions in four wave mixing spectroscopy of multichromophoric macromolecular systems considering only single exciton states. For the case of harmonic oscillator bath linearly and diagonally coupled to exciton states, closed form expressions showing all the explicit time dependences are derived. These expressions can provide more solid physical basis for understanding 2-dimensional electronic spectroscopy signals. For more general cases of system-bath coupling, the quantum master equation (QME) approach is employed for the derivation of multistep time evolution equations for Green function-like operators. Solution of these equations is feasible at the level of 2nd order non-Markovian QME, and the new approach can account for inter-exciton coupling, dephasing, relaxation, and non-Markovian effects in a consistent manner.

• 한국전산유체공학회:학술대회논문집
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• 2000.05a
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• pp.78-83
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• 2000

An iterative time marching procedure for solving incompressible internal flow has been applied to the flow around a rotor-stator. This procedure solves three-dimensional incompressible Reynolds-averaged Navier-Stokes equation on a moving, time-deforming, non-orthogonal body-fitted grid using second-order accurate schemes for the time derivatives and third/second-order accurate schemes for the spatial derivatives. To handle rotationg geometry, the multiblock technique is applied and the overall flow domain is subdivided into two blocks. In each block, a grid is generated and flowfield is solved independently of the other blocks. The boundary data for each block is provided by the neighboring blocks using bilinear interpolation technique.

• Journal of Mechanical Science and Technology
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• v.15 no.6
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• pp.788-795
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• 2001

The effects of nonequilibrium condensation on the shock boundary layer interaction over a transonic bump model were investigated experimentally and numerically. An experiment was conducted using a supersonic indraft wind tunnel. A droplet growth equation was incorporated into two-dimensional Navier-Stokes equation systems. Computations were carried out using a third-order MUSCL type TVD finite-difference scheme with a second-order fractional time step. Computation compared with the experimental results. Nonequilibirum condensation suppressed the boundary layer separation and the pressure fluctuations due to the shock boundary layer interaction. Especially the nonequilbrium condensation was helpful to suppress the high frequency components of the pressure fluctuations.

• Proceedings of the KSME Conference
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• 2000.11b
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• pp.544-549
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• 2000

The effects of nonequilibrium condensation on the shock boundary layer interaction over a transonic bump model were investigated experimentally and numerically. An experiment was conducted using a supersonic indraft wind tunnel. A droplet growth equation was incorporated into two-dimensional Navier-Stokes equation systems. Computations were carried out using a third-order MUSCL type TVD finite-difference scheme with a second-order fractional time step. Computations compared with the experimental results. Nonequilibirum condensation suppressed the boundary layer separation and the pressure fluctuations due to the shock boundary layer interaction. Especially the nonequilibrium condensation was helpful to suppress the high frequency components of the pressure fluctuations.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.229-244
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• 2005

In this paper, we study the third order ordinary differential equation : $$x'(t)=f(t,x(t),x'(t),x'(t)),t{\in}(0,1)$$ subject to the boundary value conditions: $$x'(0)=x'(\xi),x'(1)=^{m-3}{\Sigma}_{i=1}{{\beta}x'({\eta}i),x'(1)=0}$$. Here ${\beta}_{i}{\in}R,\;^{m-3}{\Sigma}_{i=1}\;{\beta}_{i}\;=\;1,\;0<{\eta}_1<{\eta}_2<{\cdots}<{\eta}_{m-3}<1,\;0<\xi<1$. This is the case dimKer L = 2. When the ${\beta}_i$ have different signs, we prove some existence results for the m-point boundary value problem at resonance by use of the coincidence degree theory of Mawhin [12, 13]. Since all the existence results obtained in previous papers are for the case dimKerL = 1, our work is new.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.4
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• pp.865-875
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• 1988

A two-dimensional stepped wall jet was numerically investigated by applying three different models : One is the standard k-.epsilon. and the other is the modified k-.epsilon. model which takes account of the streamline curvature effect by modifying the Reynolds shear stress and a source term in the dissipation equation, and a third is curvature dependent third-order correlation model. In order to test the influences of the numerical result, both the upwind scheme and the skew-upwind scheme were sued for the computations. By comparing the numerical results with available experiments, it was found that the modified k-.epsilon. model gives best overall prediction accuracy only when the numerical diffusion is eliminated by using the skew-upwind scheme. The numerical scheme was found to have more pronounced effect on the accuracy of the turbulence computation than the turbulence models.

• Geomechanics and Engineering
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• v.29 no.6
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• pp.667-681
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• 2022

This paper presents a thermoelastic analysis of variable thickness plates made of functionally graded materials (FGM) subjected to mechanical and thermal loads. The thermal load is applied to the plate as a temperature difference between the top and bottom surfaces. Temperature distribution in the plate is obtained using the steady-state heat equation. Except for Poisson's ratio, all mechanical properties of the plate are assumed to vary linearly along the thickness direction based on the volume fractions of ceramic and metal. The plate is resting on an elastic foundation modeled based on the Winkler foundation model. The governing equations are derived based on the third-order shear deformation theory (TSDT) and are solved numerically for various boundary conditions using the differential quadrature method (DQM). The effects of various parameters on the stress distribution and deflection of the plate are investigated such as the value of thermal and mechanical loads, volume fractions of ceramic and metal, and the stiffness coefficients of the foundation.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.845-852
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• 2010

A nonlinear algebraic equation f(x) = 0 is considered to find a root with integer multiplicity $m{\geq}1$. A variant of Newton-secant method for a multiple root is proposed below: for n = 0, 1, $2{\cdots}$ $$x_{n+1}=x_n-\frac{f(x_n)^2}{f^{\prime}(x_n)\{f(x_n)-{\lambda}f(x_n-\frac{f(x_n)}{f^{\prime}(x_n)})\}$$, $$\lambda=\{_{1,\;if\;m=1.}^{(\frac{m}{m-1})^{m-1},\;if\;m{\geq}2$$ It is shown that the method has third-order convergence and its asymptotic error constant is expressed in terms of m. Numerical examples successfully verified the proposed scheme with high-precision Mathematica programming.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2004.10a
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• pp.369-374
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• 2004

Web-based analysis programs for reliability assessment of machine tools were developed in this study. First, the reliability data analysis program was developed to search for failure rate using failure data and reliability test data of mechanical part. Second, failure mode analysis was developed through performance tests like circular movement test vibration test for machine tools. This analysis program shows correlation between failure mode and performance test result. Third, tool life was predicted by correlation between flank wear and cutting time, using the extended Taylor tool life equation in turning data and the equivalently converted equation in order to apply ball endmill data to Taylor tool life equation in milling data. All the information related to input and result data can be stored in theses programs.