• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.6 s.177
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• pp.1520-1528
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• 2000

This study presents a method for determining bearing stiffness and damping coefficients of air-lubricated slider bearing, and shows influences of air-bearing surface geometry(recess depth, crown an d pivot location) on flying attitude and dynamic characteristics. To derive the dynamic lubrication equation, the perturbation method is applied to the generalized lubrication equation which based on linearized Boltzmann equation. The generalized lubrication equation and the dynamic lubrication equation are converted to a control volume formulation, and then, the static and dynamic pressure distributions are calculated by finite difference method. The recess depth and crown of the slider show significantly influence on flying attitude and dynamic characteristics comparing with those of pivot location.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1999.06a
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• pp.291-296
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• 1999

This study presents a method for determining stiffness and damping coefficients of 30% U slider-air bearings by using perturbation method, and shows that this method is more accurate than steady state method according to the comparison of those with the modal analysis method. Through a generalized lubrication equation, which based on linealized Boltzmann equation, the static and dynamic pressure distributions are calculated by finite volume method.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.749-762
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• 2018

In this paper, the new optimal perturbation iteration method has been applied to solve the generalized regularized long wave equation. Comparing the new analytic approximate solutions with the known exact solutions reveals that the proposed technique is extremely accurate and effective in solving nonlinear wave equations. We also show that,unlike many other methods in literature, this method converges rapidly to exact solutions at lower order of approximations.

• 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 Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.261-267
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• 2006

A local convergence analysis of Newton's method for perturbed generalized equations is provided in a Banach space setting. Using center Lipschitzian conditions which are actually needed instead of Lipschitzian hypotheses on the $Fr\'{e}chet$-derivative of the operator involved and more precise estimates under less computational cost we provide a finer convergence analysis of Newton's method than before [5]-[7].

• Nuclear Engineering and Technology
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• v.52 no.3
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• pp.461-468
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• 2020

The improvements of the DeCART/MUSAD code system for uncertainty analysis of HTGR neutronic parameters are presented in this paper. The function for quantifying an uncertainty of critical-spectrumweighted few group cross section was implemented using the generalized adjoint B₁ equation solver. Though the changes between the infinite and critical spectra cause a considerable difference in the contribution by the graphite scattering cross section, it does not significantly affect the total uncertainty. To reduce the number of iterations of the generalized adjoint transport equation solver, the generalized adjoint B₁ solution was used as the initial value for it and the number of iterations decreased to 50%. To reflect the implicit uncertainty, the correction factor was derived with the resonance integral. Moreover, an additional correction factor for the double heterogeneity was derived with the effective cross section of the DH region and it reduces the difference from the complete uncertainty. The code system was examined with the MHTGR-350 Ex.II-2 3D core benchmark. The k_eff uncertainty for Ex.II-2a with only the fresh fuel block was similar to that of the block and the uncertainty for Ex.II-2b with the fresh fuel and the burnt fuel blocks was smaller than that of the fresh fuel block.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2004.11a
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• pp.143-148
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• 2004

The numerical analysis of the hard disk drive slider is presented. The pressure distribution was calculated using the finite element method. The generalized Reynolds equation was applied in order to include the gas rarefaction effect. The balance of the air bearing force and preload force was considered. The characteristics of the small vibrations near the equilibrium were studied using the perturbation method. Triangular mesh with variable element size was employed to model the two-rail slider. The flying height, pitching angle, rolling angle, stiffness and damping of the two-rail slider were calculated for radial position changing from the inner radius to the outer radius and for a wide range of the slider crown values. It was found that the flying height, pitching angle and rolling angle were increased with radial position while the stiffness and damping coefficients were decreased. The higher values of crown resulted in increased flying height, pitching angle and damping and decreased stiffness.

• Geophysics and Geophysical Exploration
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• v.13 no.4
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• pp.315-322
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• 2010

The phase-screen and the split-step Fourier migrations, which are implemented in both the frequency-wavenumber and frequency-space domains by using one-way scalar wave equation, allow imaging in laterally heterogeneous media with less computing time and efficiency. The generalized-screen migration employs the series expansion of the exponential, unlike the phase-screen and the split-step Fourier migrations which assume the vertical propagation in frequency-wavenumber domain. In addition, since the generalized-screen migration generalizes the series expansion of the vertical slowness, it can utilize higher-order terms of that series expansion. As a result, the generalized-screen migration has higher accuracy in computing the propagation with wide angles than the phase-screen and split-step Fourier migrations for media with large and rapid lateral velocity variations. In this study, we developed a 2D prestack generalized-screen migration module for imaging a complex subsurface efficiently, which includes various dips and large lateral variations. We compared the generalized-screen propagator with the phase-screen propagator for a constant perturbation model and the SEG/EAGE salt dome model. The generalized-screen propagator was more accurate than the phase-screen propagator in computing the propagation with wide angles. Furthermore, the more the higher-order terms were added for the generalized-screen propagator, the more the accuracy was increased. Finally, we compared the results of the generalizedscreen migration with those of the phase-screen migration for a model which included various dips and large lateral velocity variations and the synthetic data of the SEG/EAGE salt dome model. In the generalized-screen migration section, reflectors were positioned more accurately than in the phase-screen migration section.

• Nuclear Engineering and Technology
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• v.55 no.6
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• pp.2172-2194
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• 2023

A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (k_eff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2-3.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.3
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• pp.191-197
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• 1993

Mathematical models of nonlinear waves due to disturbances moving with the near critical velocity in a basin of variable depth are discussed. A two-dimensional model for waves of arbitrary amplitude is developed. In the case of small perturbation it is shown that nonlinear ray method can be applied to obtain the generalized forced Korteweg-de Vries equation.