• Communications of Mathematical Education
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• v.35 no.2
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• pp.193-212
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• 2021

This study is to support the school's mathematics exploration activities. Mathematics exploration is a very important mathematical activity not only for mathematics teachers, but also for students. Looking at the development of mathematics, it has been extended from one mathematical fact to a new mathematical fact. Mathematics exploration activities are not unique to mathematicians, and opportunities are equally given to all ordinary people who are learning mathematics and teaching mathematics. Therefore, the purpose of this study is to develop a method of mathematics exploration activities that teachers and students can perform in schools, based on mathematics exploration activities based on one mathematical fact. Specifically, the cosine law was selected as one mathematical fact, and mathematical exploration activities were performed based on the cosine law. By analyzing the results of these mathematics exploration activities, we developed a method to explore school mathematics. Through the results of this study, it is expected that mathematics exploration activities will be conducted equally by students and teachers in the mathematics classroom.

• Journal of the Korean Society of Propulsion Engineers
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• v.25 no.5
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• pp.18-26
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• 2021

In this work, we have developed a 1D network model aimed at predicting eigenvalues for resonance frequency analysis in a lab-scale industrial gas turbine single nozzle combustion system. Modern industrial gas turbines generally adopt combustors with very complex geometry and flow path to meet various design requirements simultaneously. The current study has developed a network model for combustion systems with backflow at the same axial location. The modeling results of resonance frequencies and mode distributions for a given system using the network model were validated from comparisons with prediction results using a 3D Helmholtz solver.

• Nuclear Engineering and Technology
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• v.54 no.10
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• pp.3795-3802
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• 2022

NaI(Tl) scintillation materials are considered to be one of many materials that are used exclusively for γ-ray detection and spectroscopy. The gamma-ray spectrometer is not an easy-to-use device, and the accuracy of the numerical values must be carefully checked based on the rules of the calibration technique. Therefore, accurate information about the detection system and its effectiveness is of greater importance. The purpose of this study is to estimate, using an analytical-numerical formula (ANF), the purely geometric solid angle, geometric efficiency, and total efficiency of a cylindrical NaI(Tl) γ-ray detector with a side-through hole. This type of detector is ideal for scanning fuel rods and pipelines, as well as for performing radio-immunoassays. The study included the calculation of the complex solid angle, in combination with the use of various points like gamma sources, located axially and non-axially inside the through detector side hole, which can be applied in a hypothetical method for calibrating the facility. An extended γ-ray energy range, the detector, source dimensions, "source-to-detector" geometry inside the side-through hole, path lengths of γ-quanta photons crossing the facility, besides the photon average path length inside the detector medium itself, were studied and considered. This study is very important for an expanded future article where the radioactive point source can be replaced by a volume source located inside the side-trough hole of the detector, or by a radioactive pipeline passing through the well. The results provide a good and useful approach to a new generation of detectors that can be used for low-level radiation that needs to be measured efficiently.

• Structural Engineering and Mechanics
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• v.81 no.3
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• pp.349-365
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• 2022

Steel fibre-reinforced concrete (SFRC) is an emerging class of composite for construction. However, a reliable method to assess the flexural behaviour of SFRC structural member is in lack. An analytical technique is proposed for determining the moment-curvature response of concrete beams reinforced with steel fibres and longitudinal bars (R/SFRC members). The behaviour of the tensile zone of such members is highly complex due to the interaction between the residual (tension softening) stresses of SFRC and the tension stiffening stresses. The current study suggests a transparent and mechanically sound method to combine these two stress concepts. Tension stiffening is modelled by the reinforcement-related approach assuming that the corresponding stresses act in the area of tensile reinforcement. The effect is quantified based on the analogy between the R/SFRC member and the equivalent RC member having identical geometry and materials except fibres. It is assumed that the resultant tension stiffening force for the R/SFRC member can be calculated as for the equivalent RC member providing that the reinforcement strain in the cracked section of these members is the same. The resultant tension stiffening force can be defined from the moment-curvature relation of the equivalent RC member using an inverse technique. The residual stress is calculated using an existing model that eliminates the need for dedicated mechanical testing. The proposed analytical technique was validated against test data of R/SFRC beams and slabs.

• Communications of Mathematical Education
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• v.37 no.2
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• pp.299-327
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• 2023

In this study, we tried to find out the level of inductive reasoning ability and the aspects of visualization components shown in students in the class using exploratory software for the 'congruence and symmetry' unit in the second semester of the 5th grade of elementary school. To this end, classes using GeoGebra, one of the exploratory software, were conducted for a total of 19 students in one class of fifth graders in elementary school, and the results of the students' activities were analyzed. As a result of this study, the level of inductive reasoning ability of students remained at a similar level or developed, and it was shown that students inferred new properties of shapes using various functions of software inductively. In addition, in terms of visualization, students were able to quickly and easily draw shapes that met the conditions, and unlike the paper-and-pencil environment, using the 'measurement' and 'symmetry' functions, they transformed and manipulated complex yet precisely congruent and symmetrical external representations. Based on these analysis results, implications for the use of exploratory software in the area of figures were derived.

• Journal of the Korea Society of Computer and Information
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• v.28 no.12
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• pp.89-96
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• 2023

In this paper, we propose a GPU-based method for real-time processing of dynamic re-meshing required for tearing cloth. Thin shell materials are used in various fields such as physics-based simulation/animation, games, and virtual reality. Tearing the fabric requires dynamically updating the geometry and connectivity, making the process complex and computationally intensive. This process needs to be fast, especially when dealing with interactive content. Most methods perform re-meshing through low-resolution simulations to maintain real-time, or rely on an already segmented pattern, which is not considered dynamic re-meshing, and the quality of the torn pattern is low. In this paper, we propose a new GPU-optimized dynamic re-meshing algorithm that enables real-time processing of high-resolution fabric tears. The method proposed in this paper can be used for virtual surgical simulation and physics-based modeling in games and virtual environments that require real-time, as it allows dynamic re-meshing rather than pre-split meshes.

• The Journal of the Acoustical Society of Korea
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• v.43 no.4
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• pp.466-475
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• 2024

Matched-Field Processing (MFP) is a model-based approach that requires accurate knowledge of the ocean environment and array geometry (e.g., array tilt) to localize underwater acoustic sources. Consequently, it is inherently sensitive to model mismatches. In contrast, the waveguide invariant-based approach (also known as array invariant) offers a simple and robust means for source-range estimation in shallow waters. This approach solely exploits the beam angles and travel times of multiple arrivals separated in the beam-time domain, requiring no modeling of the acoustic fields, unlike MFP. This paper extends the waveguide invariant-based approach to shallow water environments featuring a shallow pit, where the waveguide invariant is not defined due to the complex bathymetry. An in-depth performance analysis is conducted using experimental data and numerical simulations.

• Geomechanics and Engineering
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• v.38 no.2
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• pp.107-123
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• 2024

The drilling angle of the well is an important factor that can affect the sand production process and make its destructive effects more severe or weaker. This study investigated the effect of different well angles on sand production for the Asmari Formation, located in one of the oil fields southwest of Iran. For this purpose, a finite difference model was developed for three types of vertical (90°), inclined (45°), and horizontal (0°) wells with casing and perforations in the direction of minimum and maximum horizontal stresses, then coupled with fluid flow. Here, finite element meshing was used, because the geometry of the model is so complex and the implementation of finite difference meshes is impossible or very difficult for such models. Using a combined FDM-FEM model with fluid flow, the sand production process in three different modes with different flow rates for the Asmari sandstone was investigated in this study. The results of numerical models show that the intensity of sand production is directly related to the in-situ stress state of the oil field and well drilling angle. Since the stress regime in the studied oil field is normal, the highest amount of produced sand was in inclined wells (especially wells drilled in the direction of minimum horizontal stress) and the lowest amount of sand production was related to vertical wellbore. Also, the Initiation time of sand production in inclined wells was much shorter than in other wellbores.

• Advances in nano research
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• v.17 no.2
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• pp.181-195
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• 2024

This study introduces a novel functionally graded material model, termed the "Coated Functionally Graded Graphene-Reinforced Composite (FG GRC)" model, for investigating the free vibration response of plates, highlighting its potential to advance the understanding and application of material property variations in structural engineering. Two types of coated FG GRC plates are examined: Hardcore and Softcore, and five distribution patterns are proposed, namely FG-A, FG-B, FG-C, FG-D, and FG-E. A modified displacement field is proposed based on the higher-order shear deformation theory, effectively reducing the number of variables from five to four while accurately accounting for shear deformation effects. To solve the equations of motion, an analytical solution based on the Galerkin approach was developed for FG GRC plates resting on a viscoelastic Winkler/Pasternak foundation, applicable to various boundary conditions. A comprehensive parametric analysis elucidates the impact of multiple factors on the fundamental frequencies. These factors encompass the types and distribution patterns of the coated FG GRC plates, gradient material distribution, porosities, nonlocal length scale parameter, gradient material scale parameter, nanoplate geometry, and variations in the elastic foundation. Our theoretical research aims to overcome the inherent challenges in modeling structures, providing a robust alternative to experimental analyses of the mechanical behavior of complex structures.

• Bulletin of the Korean Chemical Society
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• v.33 no.5
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• pp.1581-1585
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• 2012

Two pyridinecarboxamide dicyanidecobalt(III) building blocks and two mononuclear seven-coordinated macrocycle manganese(II) compounds have been rationally selected to assemble cyanide-bridged heterobimetallic complexes, resulting in three cyanide-bridged $Co^{III}-Mn^{II}$ complexes. Single X-ray diffraction analysis show that these complexes $\{[Mn(L^1)][Co(bpb)]\}ClO_4{\cdot}CH_3OH{\cdot}0.5H_2O$ ($\mathbf{1}$), $\{[Mn(L^2)][Co(bpb)]\}ClO_4{\cdot}0.5CH_3OH$ ($\mathbf{2}$) and ${[Mn(L^1)][Co(bpb)]\}ClO_4{\cdot}H_2O$ ($\mathbf{3}$) ($L^1$ = 3,6-diazaoctane-1,8-diamine, $L^2$ = 3,6-dioxaoctano-1,8-diamine; $bpb2^{2-}$ = 1,2-bis(pyridine-2-carboxamido)benzenate, $bpmb2^{2-}$ = 1,2-bis(pyridine-2-carboxamido)-4-methyl-benzenate) all present predictable one-dimensional single chain structures. The molecular structures of these one-dimensional complexes consists of alternating units of $[Mn(L)]^{2+}$ ($L=L^1$ or $L^2$) and $[Co(L^{\prime})(CN)2]^-$ ($L^{\prime}=bpb2^{2-}$, or $bpmb2^{2-}$), forming a cyanide-bridged cationic polymeric chain with free $ClO_4{^-}$ as the balance anion. The coordination geometry of manganese(II) ion in the three one-dimensional complexes is a slightly distorted pentagonal-bipyrimidal with two cyanide nitrogen atoms at the trans positions and $N_5$ or $N_3O_2$ coordinating mode at the equatorial plane from ligand $L^1$ or $L^2$. Investigation over magnetic properties of these complexes reveals that the very weak magnetic coupling between neighboring Mn(II) ions connected by the diamagnetic dicyanidecobalt(III) building block. A best-fit to the magnetic susceptibility of complex ${\mathbf}{1}$ leads to the magnetic coupling constants $J=-0.084(3)cm^{-1}$.