• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.281-290
• /
• 2024

We consider the total scalar curvature functional, and show that if the second variation in the transverse traceless tensor direction is negative, then the metric is Einstein. We also find the relation between the second variation and the Lichnerowicz Laplacian.

• International Journal of CAD/CAM
• /
• v.6 no.1
• /
• pp.65-71
• /
• 2006

Based on the smoothness criterion of minimum curvature variation of the curve, tangent angle constraints guaranteeing an optimized geometric Hermite (OGH) curve both mathematically and geometrically smooth is given, and new methods for constructing composite optimized geometric Hermite (COH) curves are presented in this paper. The comparison of the new methods with Yong and Cheng's methods based on strain energy minimization is included.

• Transactions of Materials Processing
• /
• v.22 no.6
• /
• pp.310-316
• /
• 2013

Recently, numerical predictions of surface deflection based on curvature analysis have been developed. In the current study, a measure of surface deflection is proposed as the maximum variation of curvature difference between the panel and the tool in order to account for surfaces that have high curvature. The current study focused on the assessment of accuracy for the surface deflection prediction with the consideration of planar anisotropy. As an example, a shallow rectangular drawn part with rectangular embossing was considered. In terms of the proposed surface deflection measure, the maximum variation of curvature difference, the prediction with a planar anisotropic model shows better correspondence with experiment than the one using a normal anisotropic model.

• Journal of Korean Association for Spatial Structures
• /
• v.8 no.4
• /
• pp.57-64
• /
• 2008

In scissors deployable structure which could be easily removed by folding it, a method of curvature variation in the profile and the structural characteristics were examined. At first, the relation between the profile curvature and a eccentricity of joint in scissors members is presented by a formula and a graph. And then, the structural characters of scissors members with the curvature variation are presented by analysing a several models based on this relation. Also, a real modeling study is achieved in accordance with this composition method and the possibilities to be developed with the expected profile shape was examined.

• Journal of Industrial Technology
• /
• v.19
• /
• pp.261-268
• /
• 1999

It is a main object to find out the effect of curvature of pipe on the thermal flow field in copper pipe. the toroidal coordinate system is chosen for this project. 3-D numerical works are done by a commercial code, PHOENICS. The flow and temperature field are simulated and analysed on the view point of variation of pressure and temperature with Dean number. The results show that the strong recirculation phenomena and secondary flow are established and then a lot of pressure drop along main flow direction occurs at the curved portion of pipe and the temperature variation has a reversed trend of pressure variation along the axis of pipe.

• The Journal of Korea Robotics Society
• /
• v.18 no.1
• /
• pp.18-28
• /
• 2023

This study introduces a smart wrist band system with pressure measurements using wrist skin curvature variation due to finger motion. It is easy to wear and take off without pre-adaptation or surgery to use. By analyzing the depth variation of wrist skin curvature during each finger motion, we elaborated the most suitable location of each Force Sensitive Resistor (FSR) to be attached in the wristband with anatomical consideration. A 3D depth camera was used to investigate distinctive wrist locations, responsible for the anatomically de-coupled thumb, index, and middle finger, where the variations of wrist skin curvature appear independently. Then sensors within the wristband were attached correspondingly to measure the pressure change of those points and eventually the finger motion. The smart wrist band was validated for its practicality through two demonstrative applications, i.e., one for a real-time control of prosthetic robot hands and the other for natural human-computer interfacing. And hopefully other futuristic human-related applications would be benefited from the proposed smart wrist band system.

• Korean Journal of Mathematics
• /
• v.19 no.1
• /
• pp.25-32
• /
• 2011

This paper is a direct continuation of [1]. In this paper we investigate some properties of ES-curvature tensor of g - $ESX_n$, with main emphasis on the derivation of several useful generalized identities involving it. In this subsequent paper, we are concerned with contracted curvature tensors of g - $ESX_n$ and several generalized identities involving them. In particular, we prove the first variation of the generalized Bianchi's identity in g - $ESX_n$, which has a great deal of useful physical applications.

• Korean Journal of Mathematics
• /
• v.19 no.4
• /
• pp.381-390
• /
• 2011

This paper is a direct continuation of [1]. In this paper we derive tensorial representations of contracted ES curvature tensors of $g-ESX_n$ and prove several generalized identities involving them. In particular, a variation of the generalized Bianchi's identity in $g-ESX_n$, which has a great deal of useful physical applications, is proved in Theorem (2.9).

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.9 no.4
• /
• pp.1081-1085
• /
• 2008

To measure the curvature, in this paper, we investigate an optical curvature sensor based on the fiber Bragg gratings. We observed the variation of the Bragg resonant wavelength shift to measure the curvature change. From the experimental results, we knew that the Brags resonant wavelength shift was lineally increased with the increase of the curvature from $0\;m^{-1}$ to $10\;m^{-1}$. It's slope is about $8.8\;pm/m^{-1}$. On the other hand, the spectral reflection decreased with the increase of the curvature.

• Computers and Concrete
• /
• v.11 no.6
• /
• pp.515-529
• /
• 2013

The moment-curvature relation for simple bending is a well-studied subject and the classical moment-curvature diagram is commonly found in literature. The influence of axial forces has generally been considered as compression onto symmetrically reinforced cross-sections, thus strain at the reference fiber never has been an issue. However, when dealing with integral structures, which are usually statically indeterminate in different degrees, these concepts are not sufficient. Their horizontal elements are often completely restrained, which, under imposed deformations, leads to moderate compressive or tensile axial forces. The authors propose to analyze conventional beam cross-sections with moment-curvature diagrams considering asymmetrically reinforced cross-sections under combined influence of bending and moderate axial force. In addition a new diagram is introduced that expands the common moment-curvature relation onto the strain variation at the reference fiber. A parametric study presented in this article reveals the significant influence of selected cross-section parameters.