• Geophysics and Geophysical Exploration
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• v.26 no.1
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• pp.1-7
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• 2023

This study derives the expressions of vector gravity and gravity gradient tensor due to an elliptical cylinder. The vector gravity for an arbitrary three-dimensional (3D) body is obtained by differentiating the gravitational potential, including the triple integral, according to the shape of the body in each axis direction. The vector gravity of the 3D body with axial symmetry is integrated along the axial direction and reduced to a double integral. The complex Green's theorem using complex conjugates subsequently converts the double integral into a one-dimensional (1D) closed-line integral. Finally, the vector gravity due to the elliptical cylinder is derived using 1D numerical integration by parameterizing a boundary of the elliptical cross-section as a closed line. Similarly, the gravity gradient tensor due to the elliptical cylinder is second-order differentiated from the gravitational potential, including the triple integral, and integrated along the vertical axis direction reducing it to a double integral. Consequently, all the components of the gravity gradient tensor due to an elliptical cylinder are derived using complex Green's theorem as used in the case of vector gravity.

• Geophysics and Geophysical Exploration
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• v.26 no.2
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• pp.77-83
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• 2023

In this study, the expressions of magnetic vector and magnetic gradient tensor due to an elliptical cylinder were derived. Igneous intrusions and kimberlite structures are often shaped like elliptical cylinders with axial symmetry and different radii in the strike and perpendicular directions. The expressions of magnetic fields due to this elliptical cylinder were derived from the Poisson relation, which includes the direction of magnetization in the gravity gradient tensor. The magnetic gradient tensor due to an elliptical cylinder is derived by differentiating the magnetic fields. This method involves obtaining a total of 10 triple derivative functions acquired by differentiating the gravitational potential of the elliptical cylinder three times in each axis direction. As the order of differentiation and integration can be exchanged, the magnetic gradient tensor was derived by differentiating the gravitational potential of the elliptical cylinder three times in each direction, followed by integration in the depth direction. The remaining double integration was converted to a complex line integral along the closed boundary curve of the elliptical cylinder in the complex plane. The expressions of the magnetic field and magnetic gradient tensor derived from the complex line integral in the complex plane were shown to be perfectly consistent with those of the circular cylinder derived by the Lipschitz-Hankel integral.

• Proceeding of EDISON Challenge
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• 2016.03a
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• pp.548-553
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• 2016

본 연구는 타원형 물체가 유체 중에서 침강할 때 물체의 형상과 밀도에 따른 침강특성을 분석하는 것이며, 이로 인해 종단속도에 미치는 영향을 평가하는 것이다. 복잡한 형태의 물체를 타원기둥으로 단순화하였고, 낮은 Reynolds 수(=0.5~100)에 대하여 연구를 진행하였다. 또한 침강형태가 종단속도에 미치는 영향을 연구하였다. 수치해석 검증을 통해 정확하고 효율적인 격자 크기를 결정하였다. 정확한 분석을 위해 단순히 종단속도의 변화를 본 것이 아니라 진동하지 않은 물체의 이론적 속도와 비교하여 이와 얼마나 차이가 있는지를 확인하였다. 수치해석 결과 장단축비에 따라 물체의 침강특성이 크게 변하였고 그 경향은 밀도비에 따라 다른 양상을 보였다. 또한 각의 진동에 대한 진폭과 진동수가 물체의 침강속도에 영향을 주는 것을 확인하고 그 원인에 대해서도 연구하였다.

• Journal of radiological science and technology
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• v.40 no.1
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• pp.13-18
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• 2017

The purpose of this study was to investigate CTDI (computed tomography dose index at center) for various phantom shapes, sizes, and compositions by using GATE (geant4 application for tomographic emission) simulations. GATE simulations were performed for various phantom shapes (cylinder, elliptical, and hexagonal prism PMMA phantoms) and phantom compositions (water, PMMA, polyethylene, polyoxymethylene) with various diameters (1-50 cm) at various kVp and mAs levels. The $CTDI_{100center}$ values of cylinder, elliptical, and hexagonal prism phantom at 120 kVp, 200 mAs resulted in 11.1, 13.4, and 12.2 mGy, respectively. The volume is the same, but $CTDI_{100center}$ values are different depending on the type of phantom. The water, PMMA, and polyoxymethylene phantom $CTDI_{100center}$ values were relatively low as the material density increased. However, in the case of Polyethylene, the $CTDI_{100center}$ value was higher than that of PMMA at diameters exceeding 15 cm ($CTDI_{100center}$ : 35.0 mGy). And a diameter greater than 30 cm ($CTDI_{100center}$ : 17.7 mGy) showed more $CTDI_{100center}$ than Water. We have used limited phantoms to evaluate CT doses. In this study, $CTDI_{100center}$ values were estimated and simulated by GATE simulation according to the material and shape of the phantom. CT dosimetry can be estimated more accurately by using various materials and phantom shapes close to human body.

• 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.

• Progress in Medical Physics
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• v.19 no.4
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• pp.227-230
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• 2008

The purpose of this study was to design and construct an ultrasound phantom for volume calibration and evaluate the volume measurement accuracy of a 2 dimensional ultrasonic system. Ultrasound phantom was designed, constructed and tested. The phantom consisted of a background material and a target. The background was made by mixing agarose gel with water. A target, made with an elastic material, was filled with water to vary its volume and shape and inserted into background material. To evaluate accuracy of a 2 dimensional ultrasonic system (128XP, ACUSON), three different shapes of targets (a sphere, 2 ellipsoids and a triangular prism) were constructed. In case of ellipsoid shape, two targets, one with same size length and width (ellipsoid 1) and another with the length 2 times longer than width (ellipsoid 2) were examined. The target volumes of each shape were varied from 94cc to 450cc and measurement accuracy was examined. The volume difference between the real and measured target of the sphere shape ranged between 6.7 and 11%. For the ellipsoid targets, the differences ranged from 9.2 to 10.5% with ellipsoid 1 and 25.7% with ellipsoid 2. The volume difference of the triangular prism target ranged between 20.8 and 35%. An easy and simple method of constructing an ultrasound phantom was introduced and it was possible to check the volume measurement accuracy of an ultrasound system.

• Proceedings of the Korea Water Resources Association Conference
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• 2011.05a
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• pp.146-150
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• 2011

본 연구에서는 길이 35.6m, 폭 4m, 사행도 1.8의 2회 사행하는 복단면 사행하도의 상류 직선부와 만곡 정점부 6개 지점에 폭 0.4m, 길이 0.8m의 타원기둥 형태의 부유 구조물을 구성하여, 0.25m, 0.40m의 수심 조건으로 수치모의를 수행하였다. 수치모의 결과자료 중에서 부유 구조물 주변의 흐름특성을 국부적으로 분석해 본 결과 부유 구조물이 없을 때의 흐름과는 상당히 다른 흐름특성들이 발견되었는데, 특히 그 중에서도 부유 구조물 아래에서 작용하는 상승류와 부유 구조물로 인한 단면 이차류의 분리가 두드러졌다. 이와 함께 수로 유입부와 유출부 사이의 총 수두 값 변화도 수로 내 부유 구조물의 유무에 따라 다르게 나타났다. 그리고 이러한 결과들 모두 동일 측선 상에서라도 부유 구조물의 위치가 바뀌면 다른 양상으로 나타났다. 본 연구에서는 하도 내에 부유 구조물이 있을 때 부유 구조물의 위치에 따른 통수능 및 흐름특성의 변화를 3차원 수치모의 결과를 통하여 보여준다. 그리고 그 결과들은 하도 내 부유 구조물을 설치 할 때, 검토대상에 부유 구조물 뿐 아니라 하도형태 및 하천의 흐름특성도 함께 포함되어야 함을 뒷받침해준다.