• Journal of the Society of Naval Architects of Korea
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• v.52 no.4
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• pp.338-348
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• 2015

In this study, the added resistance of ships in short waves is systematically studied by using two different numerical methods - Rankine panel method and Cartesian grid method – and existing asymptotic and empirical formulae. Analysis of added resistance in short waves has been preconceived as a shortcoming of numerical computation. This study aims to observe such preconception by comparing the computational results, particularly based on two representative three-dimensional methods, and with the existing formulae and experimental data. In the Rankine panel method, a near-field method based on direct pressure integration is adopted. In the Cartesian grid method, the wave-body interaction problem is considered as a multiphase problem, and volume fraction functions are defined in order to identify each phase in a Cartesian grid. The computational results of added resistance in short waves using the two methods are systematically compared with experimental data for several ship models, including S175 containership, KVLCC2 and Series 60 hulls (C_B = 0.7, 0.8). The present study includes the comparison with the established asymptotic and empirical formulae in short waves.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.11
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• pp.1500-1508
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• 2001

This paper represents the importance of dependent variables in non-orthogonal curvilinear coordinates just as the importance of those variables of convective scheme and turbulence model in computational fluid dynamics. Each of Cartesian, physical covariant and physical contravariant velocity components was tested as the dependent variables of momentum equations in the staggered grid system. In the flow past a circular cylinder, the results were computed to use each of three variables and compared to experimental data. In the skewed driven cavity flow, the results were computed to check the grid dependency of the variables. The results used in Cartesian and physical contravariant components of velocity in cylinder flow show the nearly same accuracy. In the case of Cartesian and contravariant component, the same number of vortex was predicted in the skewed driven cavity flow. Vortex strength of Cartesian component case has about 30% lower value than that of the other two cases.

• Journal of computational fluids engineering
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• v.15 no.2
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• pp.14-20
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• 2010

Shock-focusing concave reflectors can have parabolic, circular or elliptic cross-sections. They produce effectively a very high pressure at the focusing point. In the past, many optical images have been obtained on shock focusing via experiments. Measurement of field variables is, however, difficult in the experiment. Using the wave propagation algorithm and the Cartesian embedded boundary method, we have successfully obtained numerical Schlieren images that appear very much like the experimental results. In addition, we obtained the detailed field variables such as pressure, velocity, density and vorticity in the unsteady domain. The present numerical results have made it possible to understand the shock focusing phenomenon in more detail than before.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.2
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• pp.206-218
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• 2014

The wave attenuation by floating breakwaters in high amplitude waves, which can lead to wave overtopping and breaking, is examined by numerical simulations. The governing equations, the Navier-Stokes equations and the continuity equation, are calculated in a fixed Cartesian grid system. The body boundaries are defined by the line segment connecting the points where the grid line and body surface meet. No-slip and divergence free conditions are satisfied at the body boundary cell. The nonlinear waves near the moving body is defined using the modified marker-density method. To verify the present numerical method, vortex induced vibration on an elastically mounted cylinder and free roll decay are numerically simulated and the results are compared with those reported in the literature. Using the present numerical method, the wave attenuations by three kinds of floating breakwaters are simulated numerically in a regular wave to compare the performance.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1820-1823
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• 1997

For the Cartesian space position controlled robot, it is required to have the accurate mapping from the Cartesian space to the joint space in order to command the desired joint trajectories correctly. since the actual mapping from Cartesian space to joint space is obtained at the joint coordinate not at the actuator coordinate, uncertainty in Jacobian can be present. In this paper, two feasible neural network schemes are proposed to compensate for the kinematic Jacobian uncertainties. Uncertainties in Jacobian can be compensated by identifying either actuator Jacobian off-line or the inverse of that in on-line fashion. the case study of the stenciling robot is examined.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.783-790
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• 2014

Most distance functions, including taxicab distance, are defined on Cartesian plane, and recent studies on distance functions have been mainly focused on Cartesian plane. However, most streets in cities include not only straight lines but also curves. Therefore, there is a significant need for a distance function to be defined on a curvilinear coordinate system. In this paper, we define a new function named polar taxicab distance, using polar coordinates. We prove that this function satisfies the conditions of distance function. We also investigate the geometric properties and classifications of circles in the plane with polar taxicab distance.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.894-897
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• 2004

In this paper, we address a position control scheme for a stage system, which is levitated and driven by electric magnetic actuators. This consists of a levitating object (called platen) with 4 permanent magnetic linear synchronous motors in parallel. Each motor generates vertical force for suspension against gravity and propulsion force horizontally as well. This stage can generate six degrees of freedom motion by the vertical and horizontal forces. Dynamic equations of the stage system are derived based on Newton-Euler method and its special Jacobian matrix describing a relation between the Joint velocity and platen velocity is done. There are proposed two control schemes for positioning, which are Cartesian space controller and Joint space controller. The control performance of the Cartesian space controller is better than the Joint space controller in task space trajectory while the Joint space controller is simpler than the Cartesian space controller in controller realization.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.765-778
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• 2017

Finding an initial feasible solution on the central path is the main difficulty of feasible interior-point methods. Although, some algorithms have been suggested to remedy this difficulty, many practical implementations often do not use perfectly centered starting points. Therefore, it is worth to analyze the case that the starting point is not exactly on the central path. In this paper, we propose a weighted-path following interior-point algorithm for solving the Cartesian $P_{\ast}({\kappa})$-linear complementarity problems (LCPs) over symmetric cones. The convergence analysis of the algorithm is shown and it is proved that the algorithm terminates after at most $O\((1+4{\kappa}){\sqrt{r}}{\log}{\frac{x^0{\diamond}s^0}{\varepsilon}}\)$ iterations.

• Research in Mathematical Education
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• v.20 no.1
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• pp.39-49
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• 2016

The History of Mathematics (HOM) was integrated in teaching the Cartesian Coordinate Plane (CCP) to Grade Seven learners of Moonwalk National High School using Lesson Study. After the lesson was taught, there were three valuable issues emerged: (1) HOM is a Springboard and/or a Medium of Motivation in Teaching CCP; (2) The History of CCP Opened a Wider Perspective about Its Real-life Application in the Modern World (3) Integration of History Developed a Sense of Purpose and an Appreciation of Mathematics Among Learners. Feedbacks solicited from the learners showed that they have understanding of the importance of studying Mathematics after they learned the life and contributions of Rene Descartes to Mathematics. Hence, integration of history plays a vital role in developing positive attitudes among learners towards Math.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.91-94
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• 2002

It is important to develop new effective technologies for increasing the interruption capacity and reducing the size of a GCB (Gas Circuit Breaker). It is not easy to test the real GCB model in practice as in theory. Therefore, a simulation tool based on a CFD (Computational Fluid Dynamics) algorithm has been developed to facilitate an optimization of the interrupter. But the choice of grid is not at all trivial in the complicated geometries like a GCB. In this paper, we have applied a CFD-CAD integration using Cartesian cut-cell method, which is one of the grid generation techniques for dealing with complex and multi-component geometries.