• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.453-464
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• 2007

A computationally efficient numerical scheme is presented for the phase-field model of two-phase systems for anisotropic interfacial energy. The scheme is solved by using a nonlinear multigrid method. When the coefficient for the anisotropic interfacial energy is sufficiently high, the interface of the system shows corners or missing crystallographic orientations. Numerical simulations with high and low anisotropic coefficients show excellent agreement with exact equilibrium shapes. We also present spinodal decomposition, which shows the robustness of the pro-posed scheme.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.637-648
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• 2001

An n-dimensional ME-manifold ME $X_{n}$ is a general-ized Riemannian manifold connected by the ME-connection which is both Einstein and of the form (2.13). The purpose of this paper is to study the properties of the ME-curvature tensors, the con-tracted ME-curvature tensors and the field equations in ME $X_{n}$)n)

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1131-1145
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• 2021

In this article, we study the Klein-Gordon-Maxwell equations arising from a semilocal gauge field model. This model describes the interaction of two complex scalar fields and one gauge field, and generalizes the classical Klein-Gordon equation coupled with the Maxwell electrodynamics. We prove that there exist infinitely many standing wave solutions for p ∈ (2, 6) which are radially symmetric. Here, p comes from the exponent of the potential of scalar fields. We also prove the nonexistence of nontrivial solutions for the critical case p = 6.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.23 no.2
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• pp.169-173
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• 2010

Because of power consumption increase, global warming, and limitation of installation, not only high reliability and interruption capability but also compact and light power apparatuses are needed. In this paper, E field calculation and experiment were processed to identify the influence of the shape of end shield and gap distance. It is expected that the results of FEM simulation and experiments could be the basic data to develop VI. the results of FEM simulation and experiments are as following. Firstly, maximum E fields were compared by means of finite element method as a function of the shape of end shield. 3 types of models were used to analyze maximum E field of each model and the influence of shape of shield could be identified. As a result, proposed L type shield could reduce the maximum E field by 20%. Secondly, the influence of the gap distance between end shields on E field was analyzed. As the gap distance become short the gap distance between inner walls of ceramic also become short. And the maximum E field concentrated on inner wall of ceramic finally increased. Thirdly, the experiment was conducted by fabricating each prototype. As a result, no creepage occurred in shieldless model. In other words, creepage occurred in the shield-installed models. And creepage inception voltages were different from each other because of the difference of maximum E field. Fourthly, The equation that shows relation between calculated E field and measured creepage inception voltage was proposed as a result of FEM analysis and experiment. It is concluded that when designing VI this equation could be important data to reduce time and cost by identifying indirectly the optimal gap distance and the shape of shield required to prevent creepage.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.179-188
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• 2013

In this paper, we study the number of solutions to the equation $(x+1)^d=x^d+1$. This equation gives the value of the third power sum equation in case of Niho type exponents and is helpful in finding the distribution of the values $C_d({\tau})$. We provide the number of the solutions using the new method.

• Journal of Ocean Engineering and Technology
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• v.15 no.3
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• pp.9-19
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• 2001

In this paper we present the aspect of inertial oscillation typically observed in the spin-up of fluids at low Rossby numbers in a circular cylinder. Numerical computations for the quasi three-dimensional equation as well as one-dimensional equation are performed to estimate the predictability of the one-dimensional equation with Ekman pumping/suction models. It is assumed that the discrepancy between the two results may be attributed to the inertial oscillation The detailed analysis to the numerical results reveals that the axial plane is dominated by a comparatively strong oscillatory flows caused by the inertial oscillation. In view of the fact that the time-averaged flow field however agrees to the Taylor-Proudman theorem, it is recommended that further analysis is needed to obtain an improved one-dimensional model like the Reynolds-averaged Navier-Stokes equation for turbulent flows.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.4
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• pp.201-210
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• 2010

We propose a new robust and accurate method for the numerical solution of medical image segmentation. The modified Allen-Cahn equation is used to model the boundaries of the image regions. Its numerical algorithm is based on operator splitting techniques. In the first step of the splitting scheme, we implicitly solve the heat equation with the variable diffusive coefficient and a source term. Then, in the second step, using a closed-form solution for the nonlinear equation, we get an analytic solution. We overcome the time step constraint associated with most numerical implementations of geometric active contours. We demonstrate performance of the proposed image segmentation algorithm on several artificial as well as real image examples.

• Magazine of the Korean Society of Agricultural Engineers
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• v.34 no.4
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• pp.97-105
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• 1992

The main purpose of this paper is to present the buckling loads of tapered columns due to dynamic concept. The ordinary differential equation governing the bucking loads for tapered columns is derived on the basis of dynamic concept. Three kinds of cross sectional shape are considered in the governing equation. The Improved Euler method and Determinant Search method are used to perform the integration of the differential equation and to determine the buckling loads, respectively. The hinged-hinged, hinged-clamped, clamped-clamped and free-clamped end constraints are applied in numerical examples. The buckling loads are reported as the function of section ratio, and the effects of cross-sectional shapes are investigated. The buckling load equation, which are fitted by numerical data, are proposed as a function of section ratio. It is expected that these equations can be utilized in structural engineering field.

• Structural Engineering and Mechanics
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• v.64 no.6
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• pp.695-701
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• 2017

This paper investigates some general properties in the degenerate scale problem of antiplane elasticity or Laplace equation. For a given configuration, the degenerate scale problem is solved by using conformal mapping technique, or by using the null field BIE (boundary integral equation) numerically. After solving the problem, we can define and evaluate the degenerate area which is defined by the area enclosed by the contour in the degenerate configuration. It is found that the degenerate area is an important parameter in the problem. After using the conformal mapping, the degenerate area can be easily evaluated. The degenerate area for many configurations, from triangle, quadrilles and N-gon configuration are evaluated numerically. Most properties studied can only be found by numerical computation. The investigated properties provide a deeper understanding for the degenerate scale problem.

• 한국연소학회:학술대회논문집
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• 2000.05a
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• pp.189-196
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• 2000

A numerical simulation was conducted to analyze the interaction of flame and vortices. The characteristic scales of flame and vortices were limited in the thin laminar flamelet regime. Within this regime, flame is assumed as discontinuity surface and its motion in flow field was described by G-equation instead of full governing equations. Additional approximations include distribution of line volume sources on flame surface to simulate effect of volume expansion. Contrast to previous calculations, current study employed vortex transport equation to evaluate attenuation and smearing of vortices. Two extreme conditions of frozen vortex and frozen flame were considered to validate the current method. Comparison with direct numerical simulation resulted in satisfactory quantitative agreement with higher computational efficiency which warrants the usefulness of the present model in more complex situation.