• Journal of the korean academy of Pediatric Dentistry
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• v.30 no.4
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• pp.637-642
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• 2003

Morphology of primary root divergency and curvature determines the pattern of root resorption and periapical lesion, and affects successful root canal treatment. With the purpose of analysing the morphology of primary mandibular second molar roots and canals, the frequency, angle, radius, and start of curvature of the canal were measured. Fifty clinical radiographs were taken from $3{\sim}6$ years old children, followed by digitizing after scanning and analyzing by Scion image Beta 4.02TM(Scion Co. USA). The angle of curvature was determined by Schneider's method and the radius of curvature was determined by Schaefer's method. The results were as follows: 1. The angle of curvatures were $17.3^{\circ}{\pm}5.0$ (mesial), and $27.9^{\circ}{\pm}6.0$ (distal). Distal curvature was significantly larger than mesial.(p<0.05) 2. The radius of curvatures were $8.7mm{\pm}2.5$ (mesial), and $5.8\;mm{\pm}1.5$ (distal). Mesial curvature was significantly larger than distal.(p<0.05) 3. The start of curvatures were $4.1mm{\pm}0.6$ (mesial), and $4.2mm{\pm}0.6$ (distal). There were no difference between two groups. (P<0.05)

• Transactions of the Korean Society of Mechanical Engineers
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• v.6 no.4
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• pp.315-322
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• 1982

The slab analogy method was introduced in the 1920's for the first time as a new experimental stress analysis method. Notwithstanding its theoretical propriety, this method has not been recognized as efficient one because of its difficulty in practical measurement of the slab curvature. In this paper, aiming at experimental determination of two-dimensional stress intensity factors(S. I. F) of arbitrarily shaped cracks which had been regarded as almost impossible by conventional method, the slab analogy was reevaluated. Measuring of slab curvature was replaced by three simple measuring factors to overcome vital slab-analogy's shortcoming by joint use of the shadow-moire method. A determination formula was also derived from the theory of fracture mechanics. By this newly exploited method, it was found that the slab analogy still has its great advantage in determination of S.I.F. of arbitrarily shaped cracks with considerable accuracy compared with existent experimental methods.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.38 no.2
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• pp.199-207
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• 2001

In this paper, we suggest an edge-based surface segmentation algorithm of 3D image using curvature. For the first, in this proposed method, we approximate 3D depth data to second order curves by each scan line and decide splitting points of 3D edges by curvature of the approximated curves. And finally make a group as 3D surface with the region of input image by the 3D edges. In the conventional algorithms, there are some difficulties in detecting 3D edge with the separated processes for the jump edge and the crease edge and especially, in deciding the ambiguous discontinuity of surface directions about the crease edge. The proposed algorithm decides curvature discontinuity using curvature which is simply calculated by a geometrical approximation. Furthermore, the algorithm has a cooperated process to calculate the jump and crease edges. The results of computer simulations with several 3D images show that the proposed method yields better performance as comparing with the conventional methods.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1085-1100
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• 2023

For any given function f, we focus on the so-called prescribed mean curvature problem for the measure e^-f(|x|2)dx provided thate^-f(|x|2) ∈ L¹(ℝⁿ⁺¹). More precisely, we prove that there exists a smooth hypersurface M whose metric is ds² = dρ² + ρ²d𝜉² and whose mean curvature function is ${\frac{1}{n}}(\frac{u^p}{{\rho}^{\beta}})e^{f({\rho}^2)}{\psi}(\xi)$ for any given real constants p, β and functions f and ψ where u and ρ are the support function and radial function of M, respectively. Equivalently, we get the existence of a smooth solution to the following quasilinear equation on the unit sphere 𝕊ⁿ, $${\sum_{i,j}}({{\delta}_{ij}-{\frac{{\rho}_i{\rho}_j}{{\rho}^2+|{\nabla}{\rho}|^2}})(-{\rho}ji+{\frac{2}{{\rho}}}{\rho}j{\rho}i+{\rho}{\delta}_{ji})={\psi}{\frac{{\rho}^{2p+2-n-{\beta}}e^{f({\rho}^2)}}{({\rho}^2+|{\nabla}{\rho}|^2)^{\frac{p}{2}}}}$$ under some conditions. Our proof is based on the powerful method of continuity. In particular, if we take $f(t)={\frac{t}{2}}$, this may be prescribed mean curvature problem in Gauss measure space and it can be seen as an embedded result in Gauss measure space which will be needed in our forthcoming papers on the differential geometric analysis in Gauss measure space, such as Gauss-Bonnet-Chern theorem and its application on positive mass theorem and the Steiner-Weyl type formula, the Plateau problem and so on.

• Journal of Biomedical Engineering Research
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• v.29 no.2
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• pp.146-150
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• 2008

In order to study cortical properties in human, it is necessary to obtain an accurate and explicit representation of the cortical surface in individual subjects. Among many approaches, surface-based method that reconstructs a 3-D model from contour lines on cross-section images is widely used. The conventional method detects match points of contours using the minimum straight distance between any pair of contour points which lie on different contours. Then, it generates a triangle strip. In general, however, it might yield small mismatches between contours in case of brain due to complex anatomical structures. In this paper, therefore, we present an improved method for tilting operation that uses the curvature values calculated from surface information. The usefulness of the proposed method has been verified using brain image.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.6
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• pp.1014-1019
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• 2003

A dynamic modeling method for beams undergoing overall rigid body motion is presented in this paper. Two special deformation variables are introduced to represent the stretching and the curvature and are approximated by the assumed mode method. Geometric constraint equations that relate the two special deformation variables and the cartesian deformation variables are incorporated into the modeling method. By using the special deformation variables, all natural as well as geometric boundary conditions can be satisfied. It is shown that the geometric nonlinear effects of stretching and curvature play important roles to accurately predict the dynamic response when overall rigid body motion is involved.

• Advances in aircraft and spacecraft science
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• v.4 no.6
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• pp.613-637
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• 2017

The development systems for the Structural Health Monitoring has attracted considerable interest from several engineering fields during the last decades and more specifically in the aerospace one. In fact, the introduction of those systems could allow the transition of the maintenance strategy from a scheduled basis to a condition-based approach providing cost benefits for the companies. The research presented in this paper consists of a definition and next comparison of four methods applied to numerical measurements for the extraction of damage features. The first method is based on the determination of the Structural Intensity field at the on-resonance condition in order to acquire information about the dissipation of vibrational energy throughout the structure. The Damage Quantification Indicator and the Average Integrated Global Amplitude Criterion methods need the evaluation of the Frequency Response Function for a healthy plate and a damaged one. The main difference between these two parameters is their mathematical definition and therefore the accuracy of the scalar values provided as output. The fourth and last method is based on the Mode-shape Curvature, a FRF-based technique which requires the application of particular finite-difference schemes for the derivation of the curvature of the plate. All the methods have been assessed for several damage conditions (the shape, the extension and the intensity of the damage) on two test plates: an isotropic (steel) plate and a 4-plies composite plate.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 1998.04a
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• pp.13-13
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• 1998

A simple model of the tip leakage flow models of the rotor downstream flow is developed, based on Lakshminarayana's theoretical concept on the tip clearance flow and the experimental data published in open literature. And new spanwise distribution models of deviation angle and pressure loss coefficient due to the tip leakage flow are formulated for use in association with the streamline curvature method as a through flow analysis. Combining these new models and previous deviation and loss models due to secondary flow, a robust streamline curvature method is established for flow analysis of single-stage, subsonic axial turbines with wide ranges of turning angle, aspect ratio and blading type. At the exit from rotor rows, the flow variables are mixed radially according to a spanwise transport equation. The proposed streamline curvature method is tested against a forced vortex type turbine as well as a free vortex type one. The results show that the spanwise variations of flow angle, axial velocity and loss coefficients at rotor exit are predicted with good accuracy, being comparable to a steady three-dimensional Navier-Stokes analysis. This simple and fast flow analysis is found to be very useful for the turbine design at the initial design phase.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.1
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• pp.95-104
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• 2002

A methods to calculate non-linear moment-curvature relations of high-strength PSC flexural members for numerical analysis has been proposed. The moment-curvature relations were calculated with assumptions of design codes and by the layer method. The results of the proposed procedures for moment-curvature relations and numerical analysis were compared with those of pre-existing tests. The absorption energy rate of the design codes was about 30% larger than that of the layer method. The ultimate load and the external work of the layer method were 90% and 85% of those of tests, respectively The ultimate load of the strength design method was 97% of that of tests, but the external work was over-estimated with 122%. The ultimate load and external work by the proposed equation of the CEB-FIP Model Code were 113% and 173% of those of tests, respectively. It show that the use of ultimate strain of 0.0035 should be over-estimated for high-strength concrete. The procedure of non-linear numerical analysis of this research could be stably simulated the behavior of concrete flexural members until the ultimate state, and calculate results of the load-deflection relation and cracking pattern were very similar with those of tests.

• 한국전산유체공학회:학술대회논문집
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• 2009.11a
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• pp.193-200
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• 2009

Recently, there have been efforts to construct hybrids among the existing methodologies for multiphase flow such as VOF, Level Set, and Front Tracking with the intention of facilitating simulations of general three-dimensional problems. As one of the hybrid method, we have developed the Level Contour Reconstruction Method (LCRM) for general three-dimensional multiphase flows including phase change. The main idea was focused on simplicity and a robust algorithm especially for the three-dimensional case. It combines characteristics of both Front Tracking and Level Set methods. While retaining an explicitly tracked interface using interfacial elements, the calculation of a vector distance function plays a crucial role in the periodic reconstruction of the interface elements in the LCRM method to maintain excellent mass conservation and interface fidelity. In addition, compact curvature formulation is incorporated for the calculation of the surface tension force thereby reducing parasitic currents to a negligible level.