• Journal of the Korean Ceramic Society
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• v.36 no.6
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• pp.655-661
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• 1999

${\beta}$-SiC formation mechanism in Si melt-C-SiC system with varying in size of carbon source was investigated. A continuous reaction sintering process using Si melt infiltration method was adopted to control the reaction sintering time effectively. It was found that ${\beta}$-SiC formation mechanism in Si melt-C-SiC system was directly affected by the size of carbon source. In the Si melt-C-SiC system with large carbon source ${\beta}$-SiC formation mechanism could be divided into two stages depending on the reaction sintering time: in early stage of reaction sintering carbon dissolution in Si melt and precipitation of ${\beta}$-SiC was occurred preferentially and then SIC nucleation and growth was controlled by diffusion of carbon throughy the ${\beta}$-SiC layer formed on graphite particle. Furthmore a dissolution rate of graphite particles in Si melt could be accelerated by the infiltration of Si melt through basal plane of graphite crystalline.

• Bulletin of the Korean Chemical Society
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• v.8 no.6
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• pp.444-449
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• 1987

Solvent effects on gas phase reactions of methoxide ion with substituted ethylenes, $CH_2$ = CHR where R = CN, CHO and $NO_2$, are investigated theoretically using the AM1 method. Results show that the methoxide approaches in-plane in all reactions, but subsequently rotate out-of-plane to form tetrahedral complexes in additon reactions. All reactions of a bare methoxide are found to be exothermic, the exothermicity being the greatest in the ${\beta}$-addition, in which the excess energy is forced to be contained within the ${\beta}$-adduct rendering extreme instability. However a part of the excess energy can be removed by a solvate molecule giving a stable complex prior to the product formation. The hydride transfer processes were found to be unfavorable due to the high activation barriers. The ${\alpha}-H^+$ abstraction process from acrylonitrile becomes endothermic as a result of monosolvation of the methoxide, in agreement with experimental results.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.21 no.5
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• pp.187-192
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• 2011

Tilt angle of r-plane wafer is a one of the important factors related with the quality of the GaN epi, so the fine control of the tilt angle is important for the growing of high quality non-polar a-GaN epi. We prepared the R-plane sapphire wafers with slight tilt angles for nonpolar a-plane GaN. The target tilt angles of ${\alpha}$ and ${\beta}$ were 0, -0.1, -0.15, -0.2, -0.4, $-0.6^{\circ}$ and -0.1, 0, $0.1^{\circ}$, respectively. The tilt angles of sliced R-plane sapphire wafers were measured by x-ray and the statistical evaluation of reliability of tilt angles of wafers were performed. The tolerance of the tilt angle was ${\pm}0.03^{\circ}$. R-plane sapphire wafers have relatively large distributions of BOW and TTV data than c-plane sapphire wafers due to the large anisotropy of R-plane. As the tilt angle ${\alpha}$ was increased from -0.1 to $-0.6^{\circ}$, the step widths and heights were decreased from 156 nm to 26 nm and 0.4 nm to 0.2 nm, respectively. The growth and qualities of GaN epi seems to be largely affected by the change of step structure of R-plane sapphire wafers with tilt angle.

• Journal of the korean society of oceanography
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• v.38 no.1
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• pp.11-16
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• 2003

The three dimensional structure of thermohaline circulation in a D-plane is investigated using a conceptual two layer model and a scaling argument. In this simple model, the water mass formation region is excluded. The upper layer represents the oceans above the main thermocline. The lower layer represents the deep ocean below the thermocline and is much thicker than the upper layer. In each layer, geostrophy and the linear vorticity balance are assumed. The cross interfacial velocity that compensates for the deep water mass formation balances downward heat diffusion from the top. From the above relations, we can determine the thickness of the upper layer, which is the same as thermocline depth. The results we get is basically the same as that we get for an f-plane ocean or the classical thermocline theory. Mass budget using the velocity scales from the scaling argument shows that western boundary and interior transports are much larger than the net meridional transport. Therefore in the thermohaline circulation, horizontal circulation is much stronger than the vertical circulation occuring on a meridional plane.

• Journal of the Korean Geotechnical Society
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• v.24 no.11
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• pp.111-120
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• 2008

The characteristic of induced anisotropy is investigated in this study for the Pohang mudstone involving the cut plane discontinuity. The uniaxial and triaxial compression tests are performed for anisotropic rocks with artificial joint to look into anisotropic strength characteristics. Both the uniaxial compressive strength and triaxial compressive strength show the lowest value at the angle of cut plane, ${\beta}=30^{\circ}$ and the shoulder type of anisotropy is obtained. Anisotropy ratio (Rc) in uniaxial compression measures 9.0, whereas Rc=1.29-1.98 in triaxial compression is appeared. A series of analyses are made with the test results to derive the suitable parameter values when it is applied to the Ramamurthy (1985) failure criterion. The result of uniaxial compression test is analyzed by introducing the n-index into Ramamurthy failure criterion. The result shows that, n=l is suitable for ${\beta}=0^{\circ}{\sim}30^{\circ}$ and n=3 is suitable for ${\beta}=30^{\circ}{\sim}90^{\circ}$. To analyze the result of triaxial compression test by Ramamurthy failure criterion, anisotropy ratio in uniaxial compression test is added to Ramamurthy's equation and material constants are estimated by modified Ramamurthy's equation. When these values are applied back to Ramamurthy failure criterion, the predicted values are well fitted to the test results. And strength anisotropy for failure criteria of Jaeger (1960), McLamore & Gray (1967) and Hoek & Brown (1980) are also investigated.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.367-379
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• 1996

Let $V = {(z, y) : f(z, y) = z^n + Ay^\alpha z^p + y^\beta z^q + y^k = 0}$ and $W = {(z, y) : g(z, y) = z^n + By^\gamma z^s + y^\delta z^t + y^k = 0}$ be germs of analytic irreducible subvarieties of a polydisc near the origin in $C^2$ with n < k and (n, k) = 1 where A and B are complex numbers. Assume that V and W are topologically equivalent near the origin.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.363-372
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• 2023

We consider Kuo problem of hydrodynamic stability which deals with incompressible, inviscid, parallel shear flows in the 𝛽-plane. For this problem, we derived instability region without any approximations and which intersects with Howard semi-circle region under certain condition. Also, we derived upper bound for growth rate and amplification factor of an unstable mode and proved Howard's conjecture.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.105-121
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• 2024

We consider incompressible, inviscid, stratified shear flows in β plane. First, we obtained an unbounded instability region intersect with semi-ellipse region. Second, we obtained a bounded instability regions depending on Coriolis, stratification parameters and basic velocity profile. Third, we obtained a criterion for wave stability. This has been illustrated with standard examples. Also, we obtained upper bound for growth rate.

• Journal of the Korean Vacuum Society
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• v.5 no.4
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• pp.301-308
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• 1996

The heat of desorption and the work function change induced by nitrogen adsorption on the slepped tungstein surface plants, W(210) and W(310), are measured using the Field Electron Emission Microscope(FEM). The adsoption sites are predicted from the Thermal Desortion Spectra(TDS). The wirk function change of both W(210) and W(310) planes increase as increasing the nitrogen dose and saturates at the nitrogen dose about 5 Langmuir to 0.29 eV and 0.20 eV respectively. We find three adsorption site on each plane for the low dose range. The TDS result shows that the intensity of $\alpha_1$ state on W(310) is much stronger than that of $\alpha_1$ state on W(210), and the direction of nitrogen dipole moment adsorbed on the sites correspond to $\alpha_1$ and $\beta_2$ state on W(210) and W(310) planes are in the opposite direction to that of the equivalent states on W(100) plane. From this observation we can predict the relative atomic position in the z-direction (perpendicular direction to the surface) of nitrogen molecules/atoms adsorbed on these sites.

• Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.79-87
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• 2014

Voronoi diagrams are powerful for solving spatial problems among particles and have been used in many disciplines of science and engineering. In particular, the Voronoi diagram of three-dimensional spheres, also called the additively-weighted Voronoi diagram, has proven its powerful capabilities for solving the spatial reasoning problems for the arrangement of atoms in both molecular biology and material sciences. In order to solve application problems, the dual structure, called the quasi-triangulation, and its derivative structure, called the beta-complex, are frequently used with the Voronoi diagram itself. However, the Voronoi diagram, the quasi-triangulation, and the beta-complexes are sometimes regarded as somewhat difficult for ordinary users to understand. This paper presents the two-dimensional counterparts of their definitions and introduce the BetaConcept program which implements the theory so that users can easily learn the powerful concept and capabilities of these constructs in a plane. The BetaConcept program was implemented in the standard C++ language with MFC and OpenGL and freely available at Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).