• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.97-111
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• 2002

We show that an analog of the age-Grayson-Hamilton Theorem for curves moving according to their mean curvature holds for the motion of quadrilaterals according to their Menger curvature.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.37-42
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• 2003

We study the asymptotic expansion in small time of the mean distance of Brownian motion on Riemannian manifolds. We compute the first four terms of the asymptotic expansion of the mean distance by using the decomposition of Laplacian into homogeneous components. This expansion can he expressed in terms of the scalar valued curvature invariants of order 2, 4, 6.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.45-48
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• 2002

Consider the mean distance of Brownian motion on Riemannian manifolds. We obtain the first three terms of the asymptotic expansion of the mean distance by means of Stochastic Differential Equation(SDE) for Brownian motion on Riemannian manifold. This method proves to be much simpler for further expansion than the methods developed by Liao and Zheng(1995). Our expansion gives the same characterizations as the mean exit time from a small geodesic ball with regard to Euclidean space and the rank 1 symmetric spaces.

• Restorative Dentistry and Endodontics
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• v.30 no.4
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• pp.327-334
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• 2005

This study investigated the effect of anticurvature filing method on preparation of the curved root canal using ProFile. Thirty six resin blocks were divided equally into three groups by instrumentation motions: anticurvature filing motion. circumferential filing motion and straight up-and-down motion. Each resin block was sectioned at 8mm level from the apex and at the greatest curvature of the canal and reassembled in metal mold by a modified Bramante technique. All groups were instrumented with the ProFile system. At each levels. image of sectioned surface were taken using CCD camera under a stereomicroscope at $\times40$ magnification and stored. Distances of transportation at the inner and outer area of curvature and the centering ratio were determined and compared by statistical analysis. along with the assessment of the increase of root canal cross-sectional area. The results were as follows; 1. In all groups. there was no statistical difference in the mean increase of root canal cross-sectional area. the centering ratio. and the mean distances of transportation at the inner area of curvature at each level. 2. At 8mm level from the apex. the mean distances of transportation at the outer area of curvature decreases in following order anticurvature filing motion. circumferential filing motion. straight up-and­down motion but. no significant difference at the greatest curvature of the canal among three groups. Effect of anticurvature filing motion using ProFile does not seem to be different from other instrumentation motions at the inner area of curvature in curved root canal.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.819-824
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• 2001

Mean velocity and Reynolds stress components of the developing turbulent flows in a rotating 90 degree bend with square cross-section were measured by a hot-wire anemometer. Effects of the centrifugal and Coriolis forces generated by the curvature and rotation of bend on the mean motion and turbulence structures are investigated experimentally. Results show that the Coriolis force associated with the rotation of the bend may act both through the mean motion and turbulent structures, thereby changing the pressure fields, mean and turbulent velocities distributions.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1077-1100
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• 2016

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.9
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• pp.2223-2236
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• 1995

0The fields of turbomachinery and electrical generators provide many examples of flow through rotating internal passages. At the practicing Reynolds number, most of the flow motion is three dimensional and highly turbulent. The proper understanding for the characteristics of these turbulent flow is necessary for the design of thermo-fluid machinery of a good efficiency. The flow characteristics in the rotating duct with curvature are very complex in practice due to the curvature and rotational effect of the duct. The understanding of the effect of the curvature on the structure and rotational effect of the duct. The understanding of the effect of the curvature on the structure of turbulence in the curved passage and the characteristics of the flow in a rotating radial straight channel have been well studied separately by many workers. But the combined effects of curvature and rotation on the flow have not been well understood inspite of the importance of the phenomena in the practical design process. In this study, the characteristics of a developing turbulent flow in a square sectioned 90.deg. bend rotating at a constant angular velocity are measured by using hot-wire anemometer to seize the rotational effects on the flow characteristics. As the results of this study, centrifugal forces associated with the curvature of the bend and Coriolis forces and centripetal forces associated with the rotational affect directly both the mean motion and the turbulent fluctuations.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.31-36
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• 2003

Using a short time expansion of the fundamental solution of heat equation by analysis of Wiener functional with the help of Malliavin calculus, we obtain the asymptotic expansion of the mean distance of Brownian motion on Riemannian manifolds.

• Journal of Biomedical Engineering Research
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• v.21 no.3 s.61
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• pp.261-271
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• 2000

The present study investigated flow dynamics of a two-dimensional abdominal aortic bifurcation model under sinusoidal flow conditions considering wall motion. impedance phase angle(time delay between pressure and flow waveforms), and non-Newtonian fluid using computational fluid dynamics. The wall shear stress showed large variations in the bifurcated region and the wall motion reduced amplitude of wall shear stress significantly. As the impedance phase angle was changed to more negative values, the mean wall shear stress (time-averaged) decreased while the amplitude (oscillatory) of wall shear stress increased. At the curvature site on the outer wall where the mean wall shear stress approached zero. influence of the phase angle was relatively large. The mean wall shear stress decreased by $50\%$ in the $-90^{\circ}$ phase angle (flow wave advanced pressure wave by a quarter period) compared to the $0^{\circ}$ phase angle while the amplitude of wall shear stress increased by $15\%$. Therefore, hypertensive patients who tend to have large negative phase angles become more vulnerable to atherosclerosis according to the low and oscillatory shear stress theory because of the reduced mean and the increased oscillatory wall shear stresses. Non-Newtonian characteristics of fluid substantially increased the mean wall shear stress resulting in a less vulnerable state to atherosclerosis.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.10 s.103
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• pp.1186-1194
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• 2005

In this paper, we have systematically formulated the equations concerned to the in-plane and out-of-plane motions and deformations of a thick circular beam by using the kinetic and strain energies in order to analyse natural frequencies of a thick ring. The effects of variation of radius of curvature across the cross-section and also the effects of bending shear, extension and twist are considered. The equations of motion for natural vibration analysis of a ring are obtained utilizing the cyclic symmetry of vibration modes of the ring. The frequencies calculated using thick ring model and thin ring model are compared and discussed with the ones obtained from finite element analysis using the method of cyclic symmetry with 20-node hexahedral solid elements for rings with the different ratio of radial thickness to mean radius.