• Journal of The Korean Astronomical Society
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• v.44 no.2
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• pp.59-65
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• 2011

A small number of active galactic nuclei are known to exhibit prominent double peak emission profiles that are well-fitted by a relativistic accretion disk model. We develop a Monte Carlo code to compute the linear polarization of a double peaked broad emission line arising from Thomson scattering. A Keplerian accretion disk is adopted for the double peak emission line region and the geometry is assumed to be Schwarzschild. Far from the accretion disk where flat Minkowski geometry is appropriate, we place an azimuthally symmetric scattering region in the shape of a spherical shell sliced with ${\Delta}{\mu}=0.1$. Adopting a Monte Carlo method we generate line photons in the accretion disk in arbitrary directions in the local rest frame and follow the geodesic paths of the photons until they hit the scattering region. The profile of the polarized flux is mainly determined by the relative location of the scattering region with respect to the emission source. When the scattering region is in the polar direction, the degree of linear polarization also shows a double peak structure. Under favorable conditions we show that up to 0.6% linear polarization may be obtained. We conclude that spectropolarimetry can be a powerful probe to reveal much information regarding the accretion disk geometry of these active galactic nuclei.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.03b
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• pp.14-17
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• 1999

The wrinkling behavior of a thin sheet with perfect geometry is a kind of compressive instability. The compressive instability is influenced by many factors such as stress state mechanical properties of the sheet material geometry of the body contact conditions and plastic anisotropy. The analysis of compressive instability in plastically deforming body is difficult considering all the factors because the effects of the factors are very complex and the instability behavior may show wide variation for small deviation of the factors. In this study the bifurcation theory is introduced for the finite element analysis of puckering initiation and growth of a thin sheet with perfect geometry. All the above mentioned analysis and the post-bifurcation behavior is analyzed by introducing the branching scheme proposed by Riks. The finite element formulation is based on the incremental deformation theory and elastic-plastic material modeling. in order to investigate the effect of plastic anisotropy on the compressive instability a square plate that is subjected to compression in one direction and tension in the other direction is analyzed by the above-mentionedfinite element analysis. The critical stress ratios above which the buckling does not take place are found for various plastic anisotropic modeling method and discussed. Finally the effect of plastic anisotropy on the puckering behavior in the spherical cup deep drawing process is investigated.

• Journal of Computational Design and Engineering
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• v.1 no.1
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• pp.27-36
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• 2014

Similar to the essential components of many mechanical systems, the geometrical properties of the teeth of spiral bevel gears greatly influence the kinematic and dynamic behaviors of mechanical systems. Logarithmic spiral bevel gears show a unique advantage in transmission due to their constant spiral angle property. However, a mathematical model suitable for accurate digital modeling, differential geometrical characteristics, and related contact analysis methods for tooth surfaces have not been deeply investigated, since such gears are not convenient in traditional cutting manufacturing in the gear industry. Accurate mathematical modeling of the tooth surface geometry for logarithmic spiral bevel gears is developed in this study, based on the basic gearing kinematics and spherical involute geometry along with the tangent planes geometry; actually, the tooth surface is a parametric surface defined on a parallelogrammic domain. Equivalence proof of the tooth surface geometry is then given in order to greatly simplify the mathematical model. As major factors affecting the lubrication, surface fatigue, contact stress, wear, and manufacturability of gear teeth, the differential geometrical characteristics of the tooth surface are summarized using classical fundamental forms. By using the geometrical properties mentioned, manufacturability (and its limitation in logarithmic spiral bevel gears) is analyzed using precision forging and multiaxis freeform milling, rather than classical cradle-type machine tool based milling or hobbing. Geometry and manufacturability analysis results show that logarithmic spiral gears have many application advantages, but many urgent issues such as contact tooth analysis for precision plastic forming and multiaxis freeform milling also need to be solved in a further study.

• Magazine of the Korean Society of Agricultural Engineers
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• v.40 no.3
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• pp.113-121
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• 1998

The widespread use of thin shell structures has created a need for a systematic method of analysis which can adequately account for arbitrary geometric form. Therefore, the stress analysis of thin shell has been one of the more challenging areas of structural mechanics. The analysis of axisymmetric spherical shell is almost an every day occurrence in many industrial applications. A reliable and accurate finite element analysis procedure for such structures was needed. In general, the shell structures designed according to quasi-static analysis may fail under conditions of dynamic loading. For a more realistic prediction on the load carrying capacity of these shell, in addition to the dynamic effect, consideration should also include other factors such as nonlinearities in both material and geometry since these factors, in different manner, may also affect the magnitude of this capacity. The objective of this paper is to demonstrate the dynamic characteristics of spherical Shell. For these purpose, the spherical shell subjected to uniformly distributed step load was analyzed for its large displacements elasto-viscoplastic dynamic response. The results for the dynamic characteristics of spherical shell in the cases under various conditions of base-radius/central height(a/H) and thickness/shell radius(t/R) were summarized as follows: 1. The dynamic characteristics with a/H, 1) As the a/H increases, the amplitude of displacement increased. 2) The values of displacement Dynamic Magnification Factor (DMF) range from 2.9 to 6.3 in the crown of shell and the values of factor in the mid-point of shell range from 1.8 to 2.6. 3) As the a/H increases, the values of DMF in the crown of shell is decreased rapidly but the values of DMF in mid-point of shell is increased gradually. 4) The values of DMF of hoop-stresses range from 3.6 to 6.8 in the crown of shell and the values of factor in the mid-point of shell range from 2.3 to 2.6, the values of DMF of stress were larger than that of displacement. 2. The dynamic characteristics with t/R, 1) With the decrease of thickness of shell decreses, the amplitude of the displacement and the period increased. 2) The values of DMF of the displacement were range from 2.8 to 3.6 in the crown of shell and the values of factor in the mid-point of shell were range from 2.1 to 2.2.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.8
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• pp.997-1009
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• 1999

Silica particle formation and growth process including chemical reaction, coagulation and sintering was studied in a counterflow diffusion flame burner. The counterflow geometry provides a one dimensional flow field, along the stagnation point streamline, which greatly simplifies interpretation of the particle growth characteristics. $SiCl_4$ has been used as the source of silicon in hydrogen/oxygen/argon flames. The temperature profiles obtained by calculation showed a good agreement with experiment data. Using one and two dimensional sectional method, aerosol dynamics equation in a flame was solved, and these two results were compared. The two dimensional section method can consider sintering effect and growth of primary particle during synthesis, thus it showed evolution of morphology of non-spherical particles (aggregates) using surface fractal dimension. The effects of flame temperature and chemical loading on particle dynamics were studied. Geometric mean diameter based on surface area and total number concentration followed the trend of experiment results, especially, the change of diameters showed the sintering effect in high temperature environment.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.12
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• pp.212-219
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• 1998

During machining of dies and molds with sculptured surfaces. the cutter contact area changes continuously and results in cutting force variation. In order to implement cutting force prediction model into a CAM system, an effective and fast method is necessary. In this paper. a new method is proposed to predict mean cutting force. The cutter contact area in the spherical part of the cutter is obtained using Z-map, and expressed by the grids on the cutter plane orthogonal to the cutter axis. New empirical cutting parameters were defined to describe the cutting force in the spherical part of cutter. Before the mean cutting force calculation, the cutting force density in each grid is calculated and saved to force map on the cutter plane. The mean cutting force in an arbitrary cutter contact area can be easily calculated by summing up the cutting force density of the engaged grid of the force map. The proposed method was verifed through the slotting and slanted surface machining with various inclination angles. It was shown that the mean force can be calculated fast and effectively through the proposed method for any geometry including sculptured surfaces with cusp marks and holes.

• Journal for History of Mathematics
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• v.19 no.3
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• pp.95-112
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• 2006

The purpose of this paper is to investigate a classic mathematician and inventor Archimedes' work ${\ll}$On the Sphere and Cylinder${\gg}$. The propositions of this book which deals with three dimensional geometry are reviewed. Through the review this study tries to find out how Archimedes mastered spherical figures and how classical mathematics ideas are related to the modern concept of integration. The results of this study seems to help people understand deeply modern mathematics and to be good resources to develop new mathematical ideas.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.21 no.5
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• pp.773-777
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• 2012

Recently UV laser micromachining processes is widely introduced to meet the needs of advanced components of IT, BT and ET industries. Due to the characteristics of non-contact and high-speed laser processing, UV laser micromachining is applied to manufacture very thin substrate such as polymer, metals and composite. These minimum line width obtained by UV laser micromachining is generally determined from laser wavelength, optical lens and its numerical aperture. In this paper we will show the lens effect of water droplet on the surface of workpiece to reduce the line width when UV laser light is irradiated and focused through the water droplet. Because of the refraction effect generated by the semi-spherical or spherical shape of water droplet, we can find smaller line width. And water droplet could not only protect thermal deformation, but also carry away burr around micro dent. Firstly fundamental theory of minimum line width was derived from relationship between the geometry of water droplet and laser light trace, and then experimental and simulation results will be finally compared to verify the effectiveness of water droplet lens effect of UV laser micromachining process.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.706-710
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• 2008

The experiment of dome port cover under shock impact is performed with shock tube. The dome port cover blocked intake air duct up from the solid propellant during air breathing vehicle speed reach Mach 2.0. When the air breathing vehicle reach Mach 2.0, the inlet cover is removed and the dome port cover is broken to pieces by detonator or pressure of inlet air. Thus the dome port cover not only must stand the pressure of combustion chamber but also easy to break from the RAM pressure. In this study, a fracture evaluation on the $Al_2O_3$ ceramic spherical dome and circular plate port under impact has been presented. Ceramic were supported by the rigid body and a couple of O-ring. The Mooney-Rivlin model have been used to describe behaviors of both O-ring. And spherical dome and circular plate fracture results of the LS-DYNA code using Johnson-Holmquist(JH-2) constitutive equation was compared.

• Bulletin of the Korean Chemical Society
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• v.26 no.1
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• pp.107-114
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• 2005

Molecular aggregates of surfactant molecules consisting of one or more bilayers arranged in a hollow, closed, usually spherical geometry are termed “esicles”or “iposomes” In recent years it has been found that in certain systems the vesicular structure forms spontaneously and is long lived, and it has been suggested that these structures may in fact constitute the equilibrium state in these cases (as is true of micelles) This paper deals with the mixed CMC, vesicles, phase behavior, phase transition, geometrical structure, their formation and characterization in the aqueous solutions of mixed cationic/anionic surfactants systems. TEM micrographs revealed that the vesicles were of spherical shape and that their size was of around 180 nm. The zeta potentials are positive at CGS1-rich regions and negative at SLES-rich regions. In the region where SLES/CGS1 (6/4), the zeta potentials are very small, implying that the vesicles at this surfactant ratio may be less stable. At other surfactant ratios, the vesicles are thought to be stable, supported by large absolute values of zeta potentials and little change in UV absorbance for several months.