• International Journal of CAD/CAM
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• v.7 no.1
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• pp.91-101
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• 2007

To understand the structure of molecules, various computational methodologies have been extensively investigated such as the Voronoi diagram of the centers of atoms in molecule and the power diagram for the weighted points where the weights are related to the radii of the atoms. For a more improved efficiency, constructs like an $\alpha$-shape or a weighted $\alpha$-shape have been developed and used frequently in a systematic analysis of the morphology of molecules. However, it has been recently shown that $\alpha$-shapes and weighted $\alpha$-shapes lack the fidelity to Euclidean distance for molecules with polysized spherical atoms. We present the theory as well as algorithms of $\beta$-shape and $\beta$-complex in $\mathbb{R}^3$ which reflects the size difference among atoms in their full Euclidean metric. We show that these new concepts are more natural for most applications and therefore will have a significant impact on applications based on particles, in particular in molecular biology. The theory will be equivalently useful for other application areas such as computer graphics, geometric modeling, chemistry, physics, and material science.

• Journal of Mechanical Science and Technology
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• v.20 no.1
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• pp.13-18
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• 2006

Ti-8Ta-3Nb, as a new biomaterial, was prepared by cast and swaging process. Their deformation behavior of Ti-8Ta-3Nb alloy has been characterized on the basis of its flow stress variation obtained from the true strain rate compression testing in the temperature of $700-900^{\circ}C$ and strain rate of $0.001-10\;s^{-1}$. At the strain rates lower than $0.1\;s^{-1}$ and the all temperature ranges which consist of two phase ${\alpha}+{\beta}$ as well as single ${\beta}$ phase fields, the flow curves show a small degree of flow softening behavior. In contrast, the shapes of the flow curves at other strain rates indicate unstable behavior. The shapes of the flow curves were similar in both as-cast and swaged specimen as well as in both ${\alpha}+{\beta}$ phase and ${\beta}$ phase. The flow stress data did not obey the kinetic rate equation over the entire regime of testing but a good fit has been obtained in the intermediate range of temperatures ($750-850^{\circ}C$). In this range, a stress exponent value of about 7.7 in as-cast specimens and about 6.2 in swaged specimens with an apparent activation energy of about 300 kJ/mol and about 206 kJ/mol respectively have been evaluated.

• Progress in Superconductivity
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• v.14 no.2
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• pp.87-91
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• 2012

Metallic magnetic calorimeters (MMCs) are one of the most competitive low temperature detector (LTD) readout sensors. They have the advantages of high time resolution, no heat dissipation, and a wide range of operating temperature. We apply MMCs to our neutrinoless double beta decay ($0v{\beta}{\beta}$) search experiment. A $CaMoO_4$ crystal was employed as both a source of $0v{\beta}{\beta}$ and an energy absorber. The crystal was thermally connected to a MMC sensor. We set a simple thermal model for this detector and measured pulse shapes are compared with a numerical solution of the thermal model.

• Journal of the Korean Ceramic Society
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• v.29 no.1
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• pp.74-82
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• 1992

Ultra-fine calcium phosphate powders were synthesized by the reaction of Ca(OH)2 suspension with various phosphoric aqueous solutions such as (NH4)2HPO4, H4P2O7 and H3PO4, and the characterization of powders was examined for each synthetic condition. When (NH4)2HPO4 and H3PO4 were used, hydroxyapatite powders with poor crystallinity were obtained. In the case of H4P2O7, amorphous calcium phosphate was obtained up to 0.3 mol/ι Ca(OH)2 suspension, but above the concentration, poor crystalline hydroxyapatite was produced. Crystalline phases of powders heat-treated at 80$0^{\circ}C$ were hydroxyapatite, $\beta$-tricalcium phosphate and $\beta$-tricalcium phosphate for the case of (NH4)2HPO4, H4P2O7 and H3PO4, respectively. SEM observation revealed that the shapes of synthesized powders were vigorously agglomerated spherical with the size below 100 nm, but TEM observation revealed that primary shapes of particles were rod for (NH4)2HPO4 and H3PO4 and were sphere for H4P2O7. There was no dependence of the concentration of Ca(OH)2 suspension. In the case that reaction temperature and pH of the suspension were raised, the inclination to the hydroxyapatite were remarkable. The amorphous calcium phosphate synthesized in this experiment contained water about 20% , and was crystallized to $\beta$-tricalcium phosphate at 69$0^{\circ}C$.

• Polymer(Korea)
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• v.34 no.4
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• pp.346-351
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• 2010

The mechanical properties of polypropylene (PP) composites, especially the effects of the filler shapes on the modulus were studied. The experimental results were investigated and compared with the theoretical approaches proposed by Lee and Paul and based on Eshelby's principle, which three dimensional ellipsoids were filled as filler and analyzed in terms of aspect ratio, ${\rho}_\alpha=a_1/a_3$ and ${\rho}_\beta=a_1/a_2$. The shapes of fillers were observed by SEM and aspect ratios were statistically calculated. Young's moduli in the longitudinal and transverse directions for barium sulfate whose shape was sphere ($\rho_\alpha=\rho_\beta=1$) had the same values, as predicted values. The modulus in the $x_1$ direction for a glass fibers increased as the filler content increased, while the modulus in the $x_3$ direction was increased relatively small. Furthermore, mica was also used to investigate the effects of the primary and secondary aspect ratios on the mechanical properties.

• Bulletin of the Korean Chemical Society
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• v.23 no.5
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• pp.699-704
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• 2002

We characterized nanoelectrode arrays prepared from self-assembled monolayers (SAMs) by adsorption from a solution containing thiolated $\beta$-cyclodextrin ($\beta$-CD) and n-alkanethiol on the gold electrode surface, using electrochemical methods. While the framework, the n-hexadecanethiol SAM, effectively blocked electron transfer between the electrode surface and solution-phase redox probe molecules, the $\beta$-CD cavities isolated in the forests of n-hexadecanethiol molecules were shown to act as an ultramicroelectrode array. The shapes of cyclic voltammograms of probe molecules were related to the number densities of $\beta$-CD molecules within the monolayer films. Probe molecules that have the correct combination of physical and chemical characteristics were shown to effectively penetrate the framework through the $\beta$-CD pores and exchange electrons with the electrode surface.

• Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.79-87
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• 2014

Voronoi diagrams are powerful for solving spatial problems among particles and have been used in many disciplines of science and engineering. In particular, the Voronoi diagram of three-dimensional spheres, also called the additively-weighted Voronoi diagram, has proven its powerful capabilities for solving the spatial reasoning problems for the arrangement of atoms in both molecular biology and material sciences. In order to solve application problems, the dual structure, called the quasi-triangulation, and its derivative structure, called the beta-complex, are frequently used with the Voronoi diagram itself. However, the Voronoi diagram, the quasi-triangulation, and the beta-complexes are sometimes regarded as somewhat difficult for ordinary users to understand. This paper presents the two-dimensional counterparts of their definitions and introduce the BetaConcept program which implements the theory so that users can easily learn the powerful concept and capabilities of these constructs in a plane. The BetaConcept program was implemented in the standard C++ language with MFC and OpenGL and freely available at Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr).

• Journal of Powder Materials
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• v.5 no.1
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• pp.15-21
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• 1998

The effect of $\alpha$/$\beta$ phase on the mechanical properties and contact damage of silicon nitrides $Si_3N_4$) was investigated. Silicon nitride materials were prepared from two starting powders, at selective increasing hot-pressing temperatures to coarsen the microstructures: (i) from relatively coarse $\alpha$-phase powder, essentially equiaxed $\alpha$-$Si_3N_4$ grains, with limited, slow transformation to $\beta$-$Si_3N_4$ grain; (ii) from relatively fine $\alpha$-phase powder, a more rapid transformation to $\beta$-$Si_3N_4$, with attendant grain elongation. The resulting micro-structure thereby provided a spectrum of $\alpha$/$\beta$ phase ratios, grain sizes, and grain shapes. Fracture strength, hardness, and toughness were measured, and contact damage and strength degradation after indentation were investigated by Hertzian indentation using spherical indenter. A brittle to ductile transition in $Si_3N_4$ depended on $\alpha$/$\beta$ phase ratio as well as grain size. Silicon nitride with elongated $\beta$ grains showed a superior, contact damage resistance.

• Steel and Composite Structures
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• v.17 no.1
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• pp.1-19
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• 2014

Buckling and vibration characteristics of circular laminated plates under in-plane edge loads and resting on Winkler-type foundation are solved by the Ritz method. Inclusive numerical data are presented for the first three eigen-frequencies as a function of in-plane load for different classical edge conditions. Moreover, the effects of fiber orientation on the natural frequencies and critical buckling loads of laminated angle-ply plates with stacking sequence of $[({\beta}/-{\beta}/{\beta}/-{\beta})]_s$, are studied. Also, selected deformation mode shapes are illustrated. The correctness of results is established using finite element software as well as by comparison with the existing results in the literature.

• Journal of the Korean Ceramic Society
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• v.36 no.5
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• pp.547-554
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• 1999

The self-reinforced Si3N4 ceramics were prepared by pressureless-sintering using ${\beta}$-Si3N4 whiskers as a seed. Effects of ${\beta}$-Si3N4 whiskers on microstructure and mechanical properties and the ${\alpha}$ to ${\beta}$ phase transition of Si3N4 were investigated. The self-reinforced Si3N4 ceramics were densified(relative density$\geq$98%) by pressureless-sintering (1800$^{\circ}C$ 2h) using 8mol% Y2O3 and 6mol% Al2O3 as sintering aids and 5 vol% ${\beta}$-Si3N4 whiskers within self-reinforced Si3N4 ceramic seemed to hinder the densification owing to their acicular shapes but accelerated the ${\alpha}$ to ${\beta}$ phase transition because they acted as pre-existing nuclei. It was found that the more ${\beta}$-Si3N4 nucei the faster ${\alpha}$ to ${\beta}$ phase transition.