• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.227-234
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• 1996

Consider nonlinear autoregressive processes of order 1 defined by the random iteration $$ (1) X_{n + 1} = f(X_n) + \epsilon_{n + 1} (n \geq 0) $$ where f is real-valued Borel measurable functin on $R^1, {\epsilon_n : n \geq 1}$ is an i.i.d.sequence whose common distribution F has a non-zero absolutely continuous component with a positive density, $E$\mid$\epsilon_n$\mid$ < \infty$, and the initial $X_0$ is independent of ${\epsilon_n : n > \geq 1}$.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1149-1159
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• 2015

This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation $$-{\Delta}u_t+{\alpha}^2{\Delta}^2u_t+{\mu}{\Delta}^2u+{\bigtriangledown}{\cdot}{\vec{F}}(u)+B(u,u)={\epsilon}g(x,t)$$. Under some proper assumptions on the external force term g, the upper semicontinuity of pullback attractors is proved. More precisely, it is shown that the pullback attractor $\{A_{\epsilon}(t)\}_{t{\epsilon}{\mathbb{R}}}$ of the equation with ${\epsilon}>0$ converges to the global attractor A of the equation with ${\epsilon}=0$.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.8
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• pp.1444-1448
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• 2010

The ball and beam system is one of the most popular models for studying control systems because of its nonlinearity and several control techniques have been proposed. Sliding mode control is a popular robust control method which rejects the external disturbance. In this paper, we propose a robust controller using the ${\epsilon}$-sliding surface. On the ${\epsilon}$-sliding surface, the system robustness and convergence can be manipulated via a use of ${\epsilon}$. We show the stability analysis and convergence analysis on the ${\epsilon}$-sliding surface. In addition, the experimental results show the validity of the proposed controller.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.1
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• pp.212-218
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• 1995

Turbulent flow and heat transfer characteristics around staggered tube bundles were studied using a non-orthogonal boundary fitted coordinate system and the low Reynolds .kappa. - .epsilon. turbulence model suggested by Lam and Bremhorst. The predicted flow characteristics for two tube pitches and tube arrangement showed good agreement with the experimental data except the strongly curved region. The predicted Nusselt number was compared with measurements obtained in the staggered rough bundles and it revealed the similar trend to measurements, but the location of the maximum and minimum heat transfer differed somewhat from the measurements.

• 한국전산유체공학회:학술대회논문집
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• 2003.08a
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• pp.158-163
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• 2003

This paper assesses the two-equation turbulence models available in a commercial code, FLUENT, for heat transfer in a turbulent heated pipe flow. In case of flow under $Re_D=10,000$, Standard $\kappa-\epsilon$ and Realizable $\kappa-\epsilon$ models overpredict the Nusselt number about $20\%$ compared with the experimental correlation, and RNG $\kappa-\epsilon$ model overpredicts about $30\%$ when the two-layer zonal method is employed. When wall function method is adopted, all $\kappa-\epsilon$ models show better predictions. Standard $\kappa-\omega$ and SST $\kappa-\omega$ models have the dependency on the first grid point ($0.3). As Reynolds number becomes high, the predictions of all $\kappa-\epsilon$ and $\kappa-\omega$ models are in a good agreement with the experimental correlation.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.5
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• pp.685-697
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• 1998

Series of recent k-.epsilon. model modification have been carried out with the aid of DNS data to include the effect of near wall. Though these methods opened new way of turbulence modelings, newly developed turbulence models of its kind had yet shortcomings in prediction for the turbulent flows with various Reynolds numbers and various geometric conditions. As a remedy for these shortcomings, a new k-.epsilon. model proposed here by improving the dissipation rate equation and the damping function for eddy viscosity model. The new dissipation rate equation was modeled based on the energy spectrum and magnitude analysis. The damping function for eddy viscosity was also formulated on the ground of distribution of dissipation rate length scales near a wall and the DNS data. The new k-.epsilon. model was applied to the fully developed turbulent flows in a channel and a pipe with a wide range of Reynolds numbers. Prediction results showed that the present model represents properly the turbulence properties in all turbulent regions over a wide range of Reynolds numbers.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.7
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• pp.915-926
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• 1998

Velocity fields of near turbulent was behind a porous wind fence were measured using the 2-frame PTV method in a circulating water channel. The fences used in this study had different geometric porosity(.epsilon.) of 0, 20, 40 and 65%. The fence was embedded in a thin laminar boundary layer, i.e., .delta./H ~ = 0.1. Reynolds number based on the fence height H and free stream velocity(U$\_$o/) was about 8,400. As a result, a recirculating flow region was formed behind the fence for the .epsilon.=0% and 20% wind fence. For the wind fences having porosity larger than .epsilon.=40%, it was difficult to see separation bubbles behind the fence. The .epsilon.=20% porous fence reveals the maximum velocity reduction, however, the turbulent intensity and Reynolds shear stress are much greater than those of .epsilon.=40% fence. Among the wind fence tested in this study, the porous wind fence of .epsilon.=40% porosity is the most effective for abating wind erosion.

• Korean Journal of Optics and Photonics
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• v.25 no.1
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• pp.29-37
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• 2014

We have studied and demonstrated general, systematic error-correction methods for a dual rotating quarter-wave plate ellipsometer. To estimate and correct 5 systematic error sources (three offset angles and two unexpected retarder phase delays), we used 11 of the 25 Fourier components of the ellipsometry signal obtained in the absence of an optical sample. Using these 11 Fourier components, we can determine the errors from the 5 sources with nonlinear optimization methods. We found systematic errors ${\epsilon}_3$, ${\epsilon}_4$, ${\epsilon}_5$) are more sensitive to the inverted Mueller matrix than retarder phase delay errors (${\epsilon}_1$, ${\epsilon}_2$) because of their small condition numbers. To correct these systematic errors we have found that error of any variety must be less than 0.05 rad. Finally, we can use the magnitudes of these errors to correct the Mueller matrix of optical components. From our experimental ellipsometry signals, we can measure phase delay and the rotational angular position of its fast axis for a half-wave plate.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.10
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• pp.1940-1954
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• 1992

Fine grid computations were attempted to analyze the turbulent flows in the near wall low Reynolds number region and the numerical analyses were incorporated by a finite-volume discretization with full find grid system and low Reynolds number k-.epsilon. model was employed in this region. For the improvement of low Reynolds number k-.epsilon. model, modification coefficient of eddy viscosity $f_{\mu}$ was derived as a function of turbulent Reynolds number $R_{+}$ and nondimensional length $y^{+}$ from the concept of two length scales of dissipation rate of turbulent kinetic energy. The modification coefficient $f_{\epsilon}$ in .epsilon. transport equation was also derived theoretically. In the turbulent kinetic energy equation, pressure diffusion term was added in order to consider low Reynolds number region effect. The main characteristics of this low Reynolds number k-.epsilon. model were founded as : (1) In high Reynolds number region, the present model has limiting behavior which approaches to the high Reynolds number model. (2) Present low Reynolds number k-.epsilon. model dose not need additional empirical constants for the transport equations of turbulent kinetic energy and dissipation of turbulent kinetic energy in order to consider wall effect. Present low Reynolds number turbulence model was tested in the pipe flow and obtained improved results in velocity profiles and Reynolds stress distributions compared with those from other k-.epsilon. models.s.s.

• The Journal of the Acoustical Society of Korea
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• v.16 no.3
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• pp.99-105
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• 1997

This paper analyzes DLL(Delay lock loop) under the multipath fading effects. The evaluated performance measures include the steady-state timing error probability density function (PDF) and the mean-time-to-lose-lock (MTLL) under multipath fading effects. The discriminator characteristic S(${\epsilon}$) is shown to be zero at the point of timing error ${\epsilon}_{0}$ that is not zero, and the MTLL decreases as the delayed signal power $g_{2}$ and delayed time ${\tau}_{d}$ increase. We approximate the steady-state timing error PDF linearly with these variables and evaluate the steady-state timing error PDF and MTLL. The severe multipath fading effects result lower MTLL, in this case we make MTLL larger by increasing the early-late discriminator offset ${\Delta}$. First, we calculate the timing error point ${\epsilon}_{0}$, and present the performance of DLL under multipath fading. The timing error PDF, MTLL and the performance of DLL with ${\Delta}$ are also investigated. And we conclude that the larger ${\Delta}$ makes a higher MTLL and a better performance of DLL under multipath fading effects.