• Geophysics and Geophysical Exploration
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• v.27 no.1
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• pp.51-56
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• 2024

In this paper, the vector gravity and gravity gradient tensor of an elliptical disk are derived. The vector gravity of an elliptical disk is defined by differentiating the gravitational potential due to the elliptical disk expressed by a double integral with respect to each axial direction. The vector gravity defined by the double integral is then transformed into a line integral of a closed curve along the elliptical disk boundary using the complex Green's theorem. Finally, vector gravity due to the elliptical disk is derived by 1D parametric numerical integration along the elliptical disk boundary. The xz, yz, zz components of the gravity gradient tensor due to the elliptical disk are obtained by differentiating the vector gravity with respect to vertical direction. The xx, yy, xy components are derived by differentiating the horizontal components of the vector gravity in the form of a double integral with respect to horizontal directions and then using the complex Green's theorem.

• Geophysics and Geophysical Exploration
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• v.27 no.2
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• pp.108-118
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• 2024

In this study, expressions for the magnetic field and magnetic gradient tensor due to an elliptical disk were derived. Igneous intrusions and kimberlite structures often have elliptical cylinders with axial symmetry and elliptical cross sections. An elliptical cylinder with varying cross-sectional areas was approximated using stacks of elliptical disks. The magnetic fields of elliptical disks were derived using the Poisson relation, which includes the direction of magnetization in the gravity gradient tensor, as described in a previous study (Rim, 2024). The magnetic gradient tensor due to an elliptical disk is derived by differentiating the magnetic fields, which is equivalent to obtaining ten triple-derivative functions acquired by differentiating the gravitational potential of the elliptical disk three times in each axis direction. Because it is possible to exchange the order of differentiation, the magnetic gradient tensor is derived by differentiating the gravitational potential of the elliptical disk three times, which is then converted into a complex line integral along the closed boundary curve of the elliptical disk in the complex plane. The expressions for the magnetic field and magnetic gradient tensor derived from a complex line integral in complex plane are perfectly consistent with those of the circular disk derived from the Lipschitz-Hankel integral.

• 한국가시화정보학회:학술대회논문집
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• 2002.11a
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• pp.59-62
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• 2002

A study of three-dimensional unsteady incompressible flow past elliptic disk with aspect ratio 3 is presented. Numerical visualization using the vortex filament method was performed at Reynolds number of 20,000 on the basis of the minor diameter, the random walk method was used to calculate viscous diffusion effect. We suggest 3 stages about the wake development according to its structures, stability and motions and described the characteristics of each stages. The structure of the elliptic wake is more complicate and unstable than the wake behind a circular disk.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.05a
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• pp.41.2-41
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• 2004

본 발표에서는, 3차원 형상의 피스톤을 모방절삭이 아닌 CNC절삭을 행하기 위해 고속 이송계의 개발 사례를 다루었다. 여기서 다양한 고속 이송계의 구축형태와 적용 가능한 핵심요소 부품들을 비교하여 고속 이송 시스템으로서의 장단점을 검토하였다. 또한 타원형상의 가공물을 고속으로 처리하기 위한 소프트웨어와 제어보드에 대해 자세히 설명하였다. 비대칭 원형 절삭가공을 위한 장치개발이 공작기계 설계의 축소판이다.

• Composites Research
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• v.20 no.5
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• pp.56-63
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• 2007

An approach using complex potentials is presented for analysis of composite plate with an elliptical hole or a rectilinear crack. Composite structure is susceptible to encounter impact damages, which lead to considerable decrease in its residual strength. Such impact damages could be modeled as an equivalent elliptical hole or notch-like crack. Even though finite element method is widely used to analyze stresses or fracture mechanics parameters around such damage, it is tedious to make successive FE-modeling for damage tolerance assessment under fatigue loadings. In this point of view, the solutions based on complex potentials are very simple and easy to use. The computed results are also compared and discussed with those from FEA.

• 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.

• Korean Journal of Optics and Photonics
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• v.25 no.5
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• pp.262-272
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• 2014

Using an ellipsometer with dual rotating quarter-wave plates, we have analyzed the relationship between Fourier coefficients and Mueller matrices in the cases of an error-free optical system and of five systematic errors (alignment errors and retardation errors in the quarter-wave plates, and alignment error in the analyzer). In the case with five systematic errors, simulation results show that retardation errors cause more error in the diagonal elements of the Mueller matrix than do alignment errors. We have found that errors in the Mueller matrix caused by initial misalignment of the dual quarter-wave plates were the same. We have chosen the rotation rates of two quarter-wave plates such that the rotational frequencies ${\omega}_1$ and ${\omega}_2$ differ by a factor of 5, i.e. ${\omega}_2=5{\omega}_1$. The simulation results show 0.18% relative error in the diagonal elements ($m_{22}$ and $m_{33}$) and 200% relative error in the off-diagonal elements ($m_{23}$ and $m_{32}$), when we compare errors caused by misalignment of the analyzer to those caused by initial misalignment of the quarter-wave plates. We can use these results in measuring accurate Mueller matrices of optical materials.

• The Journal of the Korea institute of electronic communication sciences
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• v.12 no.6
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• pp.989-996
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• 2017

The proposed directional pencil beam antenna consists of a waveguide feeder with bended elliptical conductor plate feed and a parabolic curved reflector. Two rectangular apertures located at the broad wall near the end of the feed waveguide inserted from behind the reflector are located at the focus of the reflector and emit electromagnetic energy with bended elliptical conductor plate. This plate is designed to reflect electromagnetic energy primarily and to face the main reflector. The two rectangular apertures located at the waveguide end have inwardly protruding tabs for impedance matching of the antenna system, the shape of the tabs is a truncated oval. The proposed parabolic reflector antenna has a diameter of 400 mm and a focal length of 134.23 mm. The antenna gain is 33.68 dBi at the center frequency of 16.5 GHz, the beam width is $3.3^{\circ}$ and the reflection loss is -15 dB. Using the HFSS-IE, simulation results are performed to validate the proposed antennas.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.221-224
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• 2002

A technique of mixing enhancement in an underexpanded sonic round jet is studied with fully expanded jet Mach number 1.5. Tonal sound, jet screech can be produced at some underexpansion pressure ratio in a sonic jet. Since the jet screech excites the initial Jet shear layer to change the flow, a reflector which focuses the jet screech near the nozzle lip is designed. The reflector has an elliptic shape of which two foci are located near the nozzle lip and the jet screech source region. Jet screech tone near the nozzle lip increases with the elliptic reflector and spreading of the jet largely increases. It is concluded that mixing enhancement of the jet with the elliptic reflector is attributed to large scale structures which are initially excited by the increased jet screech.

• Korean Journal of Optics and Photonics
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• v.8 no.3
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• pp.223-229
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• 1997

A source code is developed on the basis of Berreman's 4$\times$4 matrix formalism for the analysis of polarization transmission characteristics of twisted nematic liquid crystal display. By using the program, the polarization transmission characteristics of liquid crystal cells and polarizers are analyzed. For a normally white twisted nematic liquid crystal cell, we obtained a family of iso-contrast contours which helps to understand the viewing angle characteristics of the liquid crystal display device by using the cell. The program also help us to understand the variation of the degree of polarization as well as the deviation of the state of polarization of the light transmitted through the polarizer commonly used in the LCD according to the change in incidence angle. This result suggests the contrast of the images appearing on the LCD can be limited by the characteristics of the polarizer in addition to the liquid crystal cell.