• Nuclear Engineering and Technology
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• v.51 no.6
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• pp.1479-1486
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• 2019

The purpose of the present study is to develop the 3D static and noise simulator based on Galerkin Finite Element Method (GFEM) using the unstructured hexahedral elements. The 3D, 2G neutron diffusion and noise equations are discretized using the unstructured hexahedral by considering the linear approximation of the shape function in each element. The validation of the static calculation is performed via comparison between calculated results and reported data for the VVER-1000 benchmark problem. A sensitivity analysis of the calculation to the element type (unstructured hexahedral or tetrahedron elements) is done. Finally, the neutron noise calculation is performed for the neutron noise source of type of variable strength using the Green function technique. It is shown that the error reduction in the static calculation is considerable when the unstructured tetrahedron elements are replaced with the hexahedral ones. Since the neutron flux distribution and neutron multiplication factor are appeared in the neutron noise equation, the more accurate calculation of these parameters leads to obtaining the neutron noise distribution with high accuracy. The investigation of the changes of the neutron noise distribution in axial direction of the reactor core shows that the 3D neutron noise analysis is required instead of 2D.

• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.445-464
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• 2017

This study targeting 10 high school 3rd grade students who have studied space figures in natural sciences track analyzes the process of analogical discovery from the construction of inscribed and circumscribed circles of a triangle to that of inscribed and circumscribed spheres of a tetrahedron through the analytical method using Geogebra. The subjects are divided into two groups of five, the experimental group consisting of those who have experienced analytical method and the comparative group consisting of those who haven't. This research analyzing the process of constructing inscribed and circumscribed spheres of a tetrahedron. Although students of both groups all have an accurate preliminary knowledge of inscribed and circumscribed circles of a triangle, they have difficulty in constructing inscribed and circumscribed spheres of a tetrahedron. However, the students of experimental group who have studied the constructing process of inscribed and circumscribed circles of a triangle in reverse using analytical method and Geogebra can perform analogical discovery finding out the way to construct inscribed and circumscribed spheres of a tetrahedron using analogy by themselves. They can control and explore space figures by visualization. Also, they can immediately examine and provide feedback on the analogizing process of their own. In addition, the process affects the attitude of students toward mathematics positively as well as gives validity to the result of analogy.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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• pp.237-240
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• 1997

The casing oscillator is a construction equipment to clamp, oscillate and push a casing for foundation work. In case that the casing oscillator is operated on the slant ground, if another construction heavy equipment is not used, it is impossible to insert the casing in ground using only casing oscillator. So in this paper, we present the new casing oscillator that need not to level the ground for work of casing insertion. This mechanism can execute 4 DOF motion by actuating 5 single - rod hydraulic cylinders. The forward kinematics analysis of the casrng oscillator by tetrahedron geometry is performed so predict workspace, direction and poison of casing oscillatoer.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.83.4-83
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• 2001

The paper presents a new closed-form, not a polynomial-form, solution of the direct kinematics of the 3-6 (Stewart-Gough) Platform. Many research works have presented a single high-order polynomial equation of the direct kinematics. However the polynomial equation causes potential problems such as complicated formulation procedures and discrimination of the actual solution from all roots, which results in time-consuming task and heavy computational burden. Thus, to overcome these problems, we use a new formulation approach, based on the Tetrahedron Approach, to derive easily a closed-form nonlinear equation of the direct kinematics and use not the Newton-Raphson method, but the Secant method to obtain quickly the solution from ...

• Proceedings of the Korea Water Resources Association Conference
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• 2005.09a
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• pp.469-470
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• 2005

• School Mathematics
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• v.8 no.1
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• pp.27-43
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• 2006

The objective of this paper is to design teaching units to foster secondary pre-service teachers' mathematising abilities. In these teaching units we focus on generalizing area of a 2-dimensional triangle and volume of a 3-dimensional tetrahedron to n-volume of n-simplex In this process of generalizing, principle of the permanence of equivalent forms and Cavalieri's principle are applied. To find n-volume of n-simplex, we define n-orthogonal triangular prism, and inquire into n-volume of it. And we find n-volume of n-simplex by using vectors and determinants. Through these teaching units, secondary pre-service teachers can understand and inquire into n-simplex which is generalized from a triangle and a tetrahedron, and n-volume of n-simplex which is generalized from area of a triangle and volume of a tetrahedron. They can also promote natural connection between school mathematics and academic mathematics.

• Journal of Digital Contents Society
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• v.16 no.6
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• pp.909-916
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• 2015

This paper presents a method to display the 3D vector fields by analyzing phase space. This method is based on the connections between ordinary differential equations and the topology of vector fields. The phase space analysis should be geometric interpolation of an autonomous system of equation in the form of the phase space. Every solution of it system of equations corresponds not to a curve in a space, but the motion of a point along the curve. This analysis is the basis of this paper. This new method is required to decompose the hexahedral cell into five or six tetrahedral cells for 3D vector fields. The critical points can be easily found by solving a simple linear system for each tetrahedron. The tangent curves can be integrated by finding the intersection points of an integral curve traced out by the general solution of each tetrahedron and plane containing a face of the tetrahedron.

• Journal of the Mineralogical Society of Korea
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• v.13 no.4
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• pp.186-195
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• 2000

To study phosphate adsorption on kaolinite, $^{31}$ P MAS NMR(magic angle spinning nuclear magnetic resonance spectroscopy)has been used for kaolinite reacted in 0.1 M phosphate solutions at pH’s from 3 to 11. There are at least 3 different forms of phosphate on kaolinite. One is the phosphate physically adsorbed on kaolinite surface (outer-sphere complexes) or species left after vacuum-filtering. The second is the phosphate adsorbed by ligand exchange (inner-sphere complexes), and the third is Al-phosphate precipitates which are pH dependent. Most of the inner-spherer complexes and surface precipitates are mainly on hydroxided Al(aluminol) rather than hydroxided Si(silanol). These are pertinent with the results obtained from the phosphate adsorption experiments on silica gel and ${\gamma}$-Al$_2$O$_3$ as model compounds, respectively. The two peaks with more negative chemical shifts(more shielded) than the ortho-phosphate peak (positive chemical shift) are assigned to be the inner-sphere complexes and surface precipitates. The $^{31}$ P chemical shifts of the Al-phosphate precipitates are more negative than those of inner-sphere complexes at a given pH due to the larger number of P-O-Al linkages per tetrahedron. The chemical shifts of both the inner-sphere complexes and surface precipitates are more negative than those of inner-sphere complexes at a given pH due to the larger number of P-O-Al linkages per tetrahedron. The chemical shifts of both the inner-sphere complexes and surface precipitates become progressively less shielded with increasing pH. For the inner-sphere complexes, decreasing phosphate protonation combined with peak averaging by rapid proton exchange among phosphate tetrahedra with different numbers of protons is though to be the reason for the peak change. The decreasing shielding with increasing pH for surface precipitates is probably due to the decreasing average number of P-O-Al linkages per tetrahedron combined with decreasing protonation like inner-sphere complexes.

• Corrosion Science and Technology
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• v.22 no.1
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• pp.44-54
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• 2023

The rupture disk corrosion test (RDCT) method was recently developed to evaluate stress corrosion cracking (SCC) and was found to have great potential for the real-time detection of SCC initiation in a high temperature and pressure environment, simulating the primary water coolant of pressurized water reactors. However, it is difficult to directly measure the stress applied to a disk specimen, which is an essential factor in SCC initiation. In this work, finite element analysis (FEA) was performed using ABAQUS^TM to calculate the stress and deformation of a disk specimen. To determine the best mesh design for a thin disk specimen, hexahedron, hex-dominated, and tetrahedron models were used in FEA. All models revealed similar dome-shaped deformation behavior of the disk specimen. However, there was a considerable difference in stress distribution in the disk specimens. In the hex-dominated model, the applied stress was calculated to be the maximum at the dome center, whereas the stress was calculated to be the maximum at the dome edge in the hexahedron and tetrahedron models. From a comparison of the FEA results with deformation behavior and SCC location on the disk specimen after RDCT, the most proper FE model was found to be the tetrahedron model.

• Korean Journal of Crystallography
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• v.16 no.2
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• pp.102-106
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• 2005

The crystal structure of the title compound has been analyzed by single crystal X-ray diffraction method. The compound crystallized in the triclinic space group $P\bar{1}$ with a=11.300(6) ${\AA}$, c=18.716(10) ${\AA}$, ${\alpha}=82.833(10)^{\circ}$, ${\beta}=83.042(11)^{\circ}$, ${\gamma}=66.139(10)^{\circ}$, $V=2162(2)\;{\AA}^{3}$, Z=2 and R1=0.661 for 10578 unique reflections. The four $C_{5}Me_{5}$ planar groups from a tetrahedron with a mean dihedral angle $70.92(9)^{\circ}$ among them and the $Ti_{4}O_{6}$ cage sits at the center of the tetrahedron. Each Ti atom in the $Ti_{4}O_{6}$ cage is bonded by three bridging oxygen atoms and coordinated by a $C_{5}Me_{5}$ ligand with a mean distance $2.067{\AA}$ from Ti atoms to the centroids of the four five-membered rings. Two oxygen atoms facing each other in $Ti_{4}O_{6}$ cage are $4.051(3){\AA}$ away in average.