• Title/Summary/Keyword: 회전 타원체

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Theory of Capillarity of Laplace and birth of Mathematical physics (라플라스 모세관이론과 수학물리학의 태동)

  • Lee, Ho-Joong
    • Journal for History of Mathematics
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    • v.21 no.3
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    • pp.1-30
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    • 2008
  • The success of Newton's Gravitational Theory has influenced the theory of capillarity, beginning in the early nineteenth century, by providing a major model of molecular attraction. He used the equation of the attraction of spheroids, which is expressed by second order partial differential equations, to utilize this analogy as the same kind of a particle's force, between gravitational, refractive force of light, and capillarity. The solution of the differential equation corresponds to the geometrical figure of the vessel and the contact angle which is made by the fluid. Unknown abstract functions $\varphi(f)$ represent interaction forces between molecules, giving their potential functions. By conducting several kinds of experimental conditions, it was found that the height of the ascending fluid in the tube is inversely proportional to the rayon of the tube or the distance of the plate. This model is an essential element in the theory of capillarity. Laplace has brought Newtonian mechanics to completion, which relates to the standard model of gravitational theory. Laplace-Young's equation of capillarity is applicable to minimal surfaces in mathematics, to surface tensional phenomena in physics, and to soap bubble experiments.

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Development of the Calibration Algorithm of 3 Axis Vector Sensor Using Ellipsoid (타원체를 이용한 3축 센서의 실시간 보정 알고리듬 개발)

  • Hwang, Jung Moon;Kim, Jung Han
    • Journal of the Korean Society for Precision Engineering
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    • v.32 no.7
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    • pp.643-651
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    • 2015
  • Multi-axis magnetic and accelerometer sensor are widely used in consumer product such as smart phones. The vector output of multi-axis sensors have errors on each axis such as offset error, scale error, non-orthogonality. These errors cause many problems on the performance of the applications. In this paper, we designed the effective inline compensation algorithm for calibrating of 3 axis sensors using ellipsoid for mass production of multi-axis sensors. The outputs with those kinds of errors can be modeled by ellipsoid, and the proposed algorithm makes sequential mappings of the virtual ellipsoid to perfect sphere which is calibrated function of the sensor on three-dimensional space. The proposed calibrating process composed of four main stages and is very straightforward and effective. In addition, another imperfection of the sensor such as the drift from temperature can be easily inserted in each mapping stage. Numerical simulation and experimental results shows great performance of the proposed compensation algorithm.

Nonlinear Dielectric Effect in Critical Solution (임계용액에서 비선형 유전체 효과)

  • Jo, Chang-Ho
    • The Journal of Natural Sciences
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    • v.3
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    • pp.1-10
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    • 1990
  • 임계 이중 연계혼합물인 nitroethane 과 cyclohexane 혼합물의 임계온도 근처에서 전기적 감수율 (electric susceptibility)을 전기용량의 온도에 대한 변화를 측정하여 얻었다. 비선형 효과를 관측하기 위하여 자기유도 타원편광축 회전에 의한 제3차 비선형 광학감수율을 측정하여 임계지수를 구하였다. 임계지수는 0.34 였다.

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Comparison between a spherical head model and a prolate spheroidal head model used in HRTF customization (맞춤형 머리전달함수에 사용될 수 있는 장구 회전타원체 형상 머리모델과 구형 머리모델 간의 비교)

  • Jo, Hyun;Park, Young-Jin;Park, Youn-Sik
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2007.11a
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    • pp.1009-1013
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    • 2007
  • To do a HRTF customization, researchers used a spherical head model for modeling the head block of structural modeling of HRTF, which is the one of the technique for HRTF customization, because of its simplicity. In this paper, an analytic spheroidal HRTF caused by an incident point source will be introduced. Using proposed spheroidal HRTF, near-field HRTF customization can be applicable through a structural modeling of HRTF. To see the necessity of sheroidal head model, comparison of two analytic solutions, which are classical spherical HRTF and proposed spheroidal HRTF, will be shown. On the view point of ITD, optimal head model which matches with the measured ITD of KEMAR HRTF can be obtained. ITD results show that there are only slight differences between spherical and spheroidal head model. Magnitude comparison is made by constructing head model using measured head size. Although magnitude comparison is not studied between optimal models, the results of 24 of 36 subjects are shown that spheroidal head model matches notch frequency pattern of measured HRTF better than those of spherical one, where the sound source is at contralateral position.

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A prolate spheroidal head modeling of head related transfer function based on ray tracing formula (선추적공식을 이용한 머리전달함수의 회전타원체 형상 모델링)

  • Jo, Hyun;Park, Young-Jin;Park, Youn-Sik
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2008.04a
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    • pp.934-938
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    • 2008
  • To customize individual characteristics of HRTF, a spherical model has been used for structural modeling technique. A pseudo-code of prolate spheroidal HRTF caused by incident acoustic point source is already developed, and it can be used a head shadow filter for structural modeling of HRTF. In this research, to see the necessity and efficiency of spheroidal head modeling, ITD optimization is performed on CIPIC HRTF database. From given cost function, ITD-optimized spheroidal head model, whose ITD information is the most matched version of measured ITD information, is found by varying head parameters subject by subject. By comparing results of ITD-optimized spheroids and ITD-optimized spheres, we concluded that a spherical head model is more efficient way of generating head shadow effect than a spheroidal head model does.

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Derivation of a Confidence Matrix for Orientation Components in the ICP Algorithm (ICP 알고리즘의 회전 성분 신뢰도 행렬 유도)

  • Lee, Byung-Uk;Kim, Chul-Min;Park, Rae-Hong
    • Journal of the Korean Institute of Telematics and Electronics S
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    • v.35S no.12
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    • pp.69-76
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    • 1998
  • This paper proposes a matrix which represents the confidence in the rotation components of the Iterative Closest Point (ICP) algorithm is image registratiion, The reliability of the ICP algorithm depends on the shape of the object. For example, an object with more complex features shows higher reliablility than the one with rotation symmetry such as a cylinder. We show that the reliablity of the ICP algorithm can be estimated when the input range data has additive noise. Finally, we demonstrate that the proposed reliability formula is in good agreement with the computer simulation.

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Nonlinear optical behavior of binary mixture protein and water near the phase separation temperature (상분리 온도 근방에서 섞임체 단백질-물의 비선형 광학적 특성)

  • 조창호;김태균;서영석
    • Korean Journal of Optics and Photonics
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    • v.8 no.6
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    • pp.461-465
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    • 1997
  • The 3rd order nonlinear optical susceptibility was measured through the self-induced ellipse rotation. The phase separation temperature increases with the increase of salt and it decreases with the increase of glycerol.

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NUMERICAL SIMULATION OF THREE-DIMENSIONAL INTERNAL WAVES USING THE FDS SCHEME ON THE HCIB METHOD (FDS 기법과 HCIB법을 이용한 3차원 내면파 수치 모사)

  • Shin, Sang-Mook
    • Journal of computational fluids engineering
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    • v.17 no.1
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    • pp.8-15
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    • 2012
  • A code developed using the flux-difference splitting scheme on the hybrid Cartesian/immersed boundary method is applied to simulate three-dimensional internal waves. The material interface is regarded as a moving contact discontinuity and is captured on the basis of mass conservation without any additional treatment across the interface. Inviscid fluxes are estimated using the flux-difference splitting scheme for incompressible fluids of different density. The hybrid Cartesian/immersed boundary method is used to enforce the boundary condition for a moving three-dimensional body. Immersed boundary nodes are identified within an instantaneous fluid domain on the basis of edges crossing a boundary. The dependent variables are reconstructed at the immersed boundary nodes along local normal lines to provide the boundary condition for a discretized flow problem. The internal waves are simulated, which are generated by an pitching ellipsoid near an material interface. The effects of density ratio and location of the ellipsoid on internal waves are compared.

Palaeomagnetism of the Okchon Belt, Korea : Anisotropy of Magnetic Susceptibility (AMS) and Deformation of the Hwanggangri Formation in Chumgju-Suanbo Area (옥천대에 대한 고자기 연구:충주-수안보 일원 황강리층의 변형과 대자율 비등방성(AMS))

  • Son, Moon;Kim, In-Soo;Kang, Hee-Cheol
    • Economic and Environmental Geology
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    • v.34 no.1
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    • pp.133-146
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    • 2001
  • We report the results of structural field observation and measurement of anisotropy of magnetic susceptibility (AMS) of the diamictitic Hwanggangri Formation distributed in Chungju-Suanbo area of the Okchon Belt, Korea. The outcrops of the Hwanggangri Formation show two types of cleavage in general: slaty cleavage (SI) and crenulation cleavage (5z). 5] cleavage is, however, well observable only in the notheastem (NE) part of study area, while overwhelmed by 52 cleavage in the southwestern (5W) part, indicating stronger later deformation in 5W part of the study area. This partitioning of the study area is corroborated by both IRM and AMS parameters: NE part of the study area is characterized by higher IRM intensity, higher bulk magnetic susceptibility, higher AM5 degree, and by oblate shape of magnetic susceptibility ellipsoid. Their values become drastically lowered toward southwest, and reach to a stable minimum in the whole 5W part of the study area. In addition, degree of both metamorphism and deformation tends to increase gradually from northeast toward southwest and also from northwest toward southeast in the study area. Based on the distribution pattern of the principal axes ( $k_1, k_2, k_3$ axes) of magnetic anisotropy ellipsoids revealed in the NE part of the study area, three episodes of deformation ( $D_1, D_2, D_3$ ) are recognized: D_1$ deformation produced $S_2$ cleavage with NE-5W trend, which is caused by a strong NW-SE tlattening of a coaxial pure shear. $D_2$ deformation produced 5z cleavage characterized by a non-coaxial deformation. It was caused by a ductile or semi-ductile thrusting toward NW and concurrent sinistral shearing along $S_2$ cleavage plane. Lastly, $D_3$ deformation produced tlexural folding of all previous structures with a nearly horizontal NE fold axis. Distribution pattern of the principal axes of magnetic anisotropy ellipsoid from the SW part of the study area, on the other hand, does not show any coherency among sites or samples. We interpret that this dispersed pattern of $k_1, k_2, k_3$ axes together with lower anisotropy strength indicates that magnetic fabrics in the SW part have been disturbed either by a superposition of strong deformation/metamorphism or by a kind of reciprocal strain due to an overlapping of $D_1$ and $D_2$ or by both processes.

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