• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.5
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• pp.1308-1318
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• 1995

The influence of varying rotation speed of both crystal and crucible was numerically investigated for the Czochralski silicon-crystal growth. Based on a simplified model assuming flatness of free surfrae, the Navier-Stokes Boussinesq equations were employed to identify the flow pattern, temperature distribution as well as the shape of the melt/crystal interface. The present results showed that the interface shape was relatively convex with respect to the melt at lower pulling rate and tended to be concave as the pulling rate increased. In particular, the experimentally observed gull-winged shape of the interface was qualitatively in agreement with the predicted shape. The rotation of crystal alone little affected the growth system. When the rotation speed of the crucible was increased, there occurred inversion of the interface shape from convex to concave pattern. At rapid rotation of the crucible, an interesting channel formation was predictied primarily due to the assumption of laminar flow.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.2
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• pp.302-312
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• 1992

Three dimensional velocity measurements of a 35.deg. inclined jet issuing into turbulent boundary layer on both concave and convex surfaces have been conducted. To investigate solely the effect of each curvature on the flow field, streamwise pressure variations are minimized by adjusting the shape of the opposite wall in the curved region. From the measured velocity components, streamwise mean vorticities are calculated to determine jet-crossflow interface. The results on convex surface show that the injected jet is separated from the wall and the bound vortex maintains its structure far downstream. On concave surface, the secondary flow in the jet cross-sections are enhanced and in some downstream region from the jet exit, the flow on the concave surface has been developed to Taylor-Gortler vortices

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.11
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• pp.1003-1011
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• 2013

A new formulation of the MNDIF method is introduced to extract highly accurate eigenvalues of concave acoustic cavities. Since the MNDIF method, which was introduced by the author, can be applicable for only convex acoustic cavities, a new approach of dividing a concave cavity into two convex domains and formulating an algebraic eigenvalue problem is proposed in the paper. A system matrix equation, which gives eigenvalues, is obtained from boundary conditions for each domain and the condition of continuity in the interface between the two domains. The validity and accuracy of the proposed method are shown through example studies.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.10
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• pp.1069-1074
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• 2009

A sub-domain method for free vibration analysis of arbitrarily shaped, concave membranes with a deep groove is proposed in the paper. The proposed method divides the concave membrane of interest into two convex regions. The vibration displacement(approximate solution) of each convex region is assumed by linearly superposing plane waves generated at edges of the region. A sub-system matrix for each convex region is extracted by applying a provisional boundary condition to the approximate solution. Finally, a system matrix, which of the determinant gives eigenvalues of the concave membrane, is made by considering the fixed boundary condition(displacement zero condition) at edges and the compatibility condition(the condition of continuity in displacement and slope) at the interface between the two regions. Case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed are compared to those by NDIF method, FEM, or the exact method.

• The Journal of Korea Robotics Society
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• v.3 no.1
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• pp.58-67
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• 2008

This study developed a novel augmented reality interface for minimally invasive surgery. The augmented reality technique can alleviate the sensory feedback problem inherent to laparoscopic surgery. An augmented reality system merges real laparoscope image and reconstructed 3D patient model based on diagnostic medical image such as CT, MRI data. By using reconstructed 3D patient model, AR interface could express structure of patient body that is invisible outside visual field of laparoscope. Therefore, an augmented reality system improved sight information of limited laparoscope. In our augmented reality system, the laparoscopic view is located at the center of a wide-angle concave screen and reconstructed 3D patient model is displayed outside the laparoscope. By using a joystick, the laparoscopic view and the reconstructed 3D patient model view are changed concurrently. With our augmented reality system, the surgeon can see the peritoneal cavity from a wide angle of view, without having to move the laparoscope. Since the concave screen serves immersive environments, the surgeon can feel as if she is in the patient body. For these reasons, a surgeon can recognize easily depth information about inner parts of patient and position information of surgical instruments without laparoscope motion. It is possible for surgeon to manipulate surgical instruments more exact and fast. Therefore immersive augmented reality interface for minimally invasive surgery will reduce bodily, environmental load of a surgeon and increase efficiency of MIS.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.18 no.4
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• pp.140-145
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• 2008

Silicon single crystals are grown by Czochralski (CZ) method in different growing conditions. The different shapes of the crystal-melt interface are obtained with various magnetic fields. Effects of zero-Gauss plane (ZGP) shape and magnetic intensity (MI) on the crystal-melt interface in the crystal experimentally are investigated. The shape of ZGP is not only flat but also parabolic, which is due to magnetic ratio (MR) of the lower to upper current densities in the configurations of the cusp-magnetic fields. As the MR increases, the crystal-melt interface becomes more concave. It means that the hot melt can be easily transported to the crystal-melt interface with increasing the MR. Effective shape of the crystal-melt interface is found to depend on the magnetic field in cusp-magnetic CZ method. The experimental results are compared with other studies and discussed.

• Journal of the Korean Ceramic Society
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• v.25 no.1
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• pp.78-82
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• 1988

Good quality LiNbO3 single crystals which can be applied to SAW devices, were grown by Czochralski method. It was observed that the gas-bubbles were concentrated in ring shape at the outer part of grown crystals, and this anomaly was illustrated by modeling the mechanism of gas-bubble entrapment according to the melt flow pattern in the crucible. And this mechanism was also encertained by observation of solid-liquid interface shape of grown crystals. The optimal condition for good quality crystals was known that the solid-liquid interface shape was slightly concave.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.9 no.4
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• pp.402-416
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• 1999

The thermal distributions near the growth interface of 150nm CZ crystals were measured by three thermocouples installed at the center, middle (half radius) and edge (10nm from surface) of the crystals. The results show that larger growth rates produced smaller thermal gradients. This contradicts the widely used heat flux balance equation. Using this fact, it is confirmed in CZ crystals that the type of point defects created is determined by the value of the thermal gradient(G) near the interface during growth, as already reported for FZ crystals. Although depending on the growth systems the effective length of the thermal gradient for defect generation are varied, we defined the effective length as 10n,\m from th interface in this experiment. If the G is roughly smaller than 20C/cm, vacancy rich CZ crystals are produced. If G is larger than 25C/cm, the species of point defects changes dramatically from vacancies to interstitials. The experimental results after detaching FZ and CZ crystals from the melt show that growth interfaces are filled with vacancies. We propose that large G produces shrunk lattice spacing and in order to relax such lattice excess interstitials are necessary. Such interstitials recombine with vacancies which were generated at the growth interface, nest occupy interstitial sites and residuals aggregate themselves to make stacking faults and dislocation loops during cooling. The shape of the growth interface is also determined by te distributions of G across the interface. That is, the small G and the large G in the center induce concave and convex interfaces to the melts, respectively.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.281-292
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• 2009

The solution of the interface problem or Poisson problem with concave corner has singular perturbation at the interface corners or singular corners. The decoupled dual singular function method (DDSFM) which exploits the singular representations of the solutions was suggested in [3, 9] and estimated optimal accuracy in [10]. The convergence rates consist with theoretical results even for the problems with very strong singularity, with the efficiency depending on parameters used in the methods. Furthermore the errors in $L^2$ and $L^\infty$-spaces display some oscillation, in the cases with meshsize not small enough. In this paper, we present an answer to remove the oscillation via numerical experiments. We observe the effects of parameters in DDSFM, and show the consisting efficiency of the method over the strong singularity.

• Journal of the Korean Ceramic Society
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• v.27 no.5
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• pp.698-701
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• 1990

The necessary conditions for the growth of high quality Bi12SiO20 single crystals by the Czochralski method have been determined. The interface of melt and crystal was transformed convex to concave above 7 rpm. For growth <001> and <111> directions, facet morphology exhibited 4-fold and 6-fold symmetry. When the crystal of <001> growth direction was broadened, minor facet {110} was developed outstandingly.