• Proceedings of the Korea Association of Crystal Growth Conference
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• 1996.06a
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• pp.139-156
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• 1996

The phase field model is becoming the model of choice for the theoretical study of the morphologies of crystals growth from the melt. This model provides an alternative approach to the solution of the classical (sharp interface) model of solidification by introducing a new variable, the phase field, Ø, to identify the phase. The variable Ø takes on constant values in the bulk phases and makes a continuous transition between these values over a thin transition layer that plays the role of the classically sharp interface. This results in Ø being governed by a new partial differential equation(in addition to the PDE's that govern the classical fields, such as temperature and composition) that guarantees (in the asymptotic limit of a suitably thin transition layer) that the appropriate boundary conditions at the crystal-melt interface are satisfied. Thus, one can proceed to solve coupled PDE's without the necessity of explicitly tracking the interface (free boundary) that would be necessary to solve the classical (sharp interface) model. Recent advances in supercomputing and algorithms now enable generation of interesting and valuable results that display most of the fundamental solidification phenomena and processes that are observed experimentally. These include morphological instability, solute trapping, cellular growth, dendritic growth (with anisotropic sidebranching, tip splitting, and coupling to periodic forcing), coarsening, recalescence, eutectic growth, faceting, and texture development. This talk will focus on the fundamental basis of the phase field model in terms of irreversible thermodynamics as well as it computational limitations and prognosis for future improvement. This work is supported by the National Science Foundation under grant DMR 9211276

• East Asian mathematical journal
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• v.18 no.2
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• pp.271-282
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• 2002

Let R be a ring with an endomorphism $\sigma$ and a derivation $\delta$. An ideal I of R is ($\sigma,\;\delta$)-ideal of R if $\sigma(I){\subseteq}I$ and $\delta(I){\subseteq}I$. An ideal P of R is a ($\sigma,\;\delta$)-prime ideal of R if P(${\neq}R$) is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideals I and J of R, $IJ{\subseteq}P$ implies that $I{\subseteq}P$ or $J{\subseteq}P$. An ideal Q of R is ($\sigma,\;\delta$)-semiprime ideal of R if Q is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideal I of R, $I^2{\subseteq}Q$ implies that $I{\subseteq}Q$. The ($\sigma,\;\delta$)-prime radical (resp. prime radical) is defined by the intersection of all ($\sigma,\;\delta$)-prime ideals (resp. prime ideals) of R and is denoted by $P_{(\sigma,\delta)}(R)$(resp. P(R)). In this paper, the following results are obtained: (1) $P_{(\sigma,\delta)}(R)$ is the smallest ($\sigma,\;\delta$)-semiprime ideal of R; (2) For every extended endomorphism $\bar{\sigma}$ of $\sigma$, the $\bar{\sigma}$-prime radical of an Ore extension $P(R[x;\sigma,\delta])$ is equal to $P_{\sigma,\delta}(R)[x;\sigma,\delta]$.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.7
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• pp.2464-2479
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• 2014

Multi-view video coding is an international encoding standard that attains good performance by fully utilizing temporal and inter-view correlations. However, it suffers from high computational complexity. This paper presents a fast encoder design to reduce the level of complexity. First, when the temporal correlation of a group of pictures is sufficiently strong, macroblock-based inter-view prediction is not employed for the non-anchor pictures of B-views. Second, when the disparity between two adjacent views is above some threshold, frame-based inter-view prediction is disabled. Third, inter-view prediction is not performed on boundary macroblocks in the auxiliary views, because the references for these blocks may not exist in neighboring views. Fourth, finer partitions of inter-view prediction are cancelled for macroblocks in static image areas. Finally, when estimating the disparity of a macroblock, the search range is adjusted according to the mode size distribution of the neighboring view. Compared with reference software, these techniques produce an average time reduction of 83.65%, while the bit-rate increase and peak signal-to-noise ratio loss are less than 0.54% and 0.05dB, respectively.

• Wind and Structures
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• v.29 no.6
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• pp.405-416
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• 2019

Aerodynamic characteristic of a small scale wind turbine under the influence of an incoming uniform wind field is studied using k-ω Shear Stress Transport turbulence model. Firstly, the lift and drag characteristics of the blade section consisting of S826 airfoil is studied using 2D simulations at a Reynolds number of 1×10⁵. After that, the full turbine including the rotational effects of the blade is simulated using Multiple Reference Frames (MRF) and Sliding Mesh Interface (SMI) numerical techniques. The differences between the two techniques are quantified. It is then followed by a detailed comparison of the turbine's power/thrust output and the associated wake development at three tip speeds ratios (λ = 3, 6, 10). The phenomenon of blockage effect and spatial features of the flow are explained and linked to the turbines power output. Validation of wake profiles patterns at multiple locations downstream is also performed at each λ. The present work aims to evaluate the potential of the numerical methods in reproducing wind tunnel experimental results such that the method can be applied to full-scale turbines operating under realistic conditions in which observation data is scarce or lacking.

• Coupled systems mechanics
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• v.4 no.1
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• pp.67-98
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• 2015

Numerical prediction of dynamic behavior of fully coupled saturated porous media is of great importance in many engineering problems. Specifically, static and dynamic response of soils - porous media with pores filled with fluid, such as air, water, etc. - can only be modeled properly using fully coupled approaches. Modeling and simulation of static and dynamic behavior of soils require significant Verification and Validation (V&V) procedures in order to build credibility and increase confidence in numerical results. By definition, Verification is essentially a mathematics issue and it provides evidence that the model is solved correctly, while Validation, being a physics issue, provides evidence that the right model is solved. This paper focuses on Verification procedure for fully coupled modeling and simulation of porous media. Therefore, a complete Solution Verification suite has been developed consisting of analytical solutions for both static and dynamic problems of porous media, in time domain. Verification for fully coupled modeling and simulation of porous media has been performed through comparison of the numerical solutions with the analytical ones. Modeling and simulation is based on the so called, u-p-U formulation. Of particular interest are numerical dispersion effects which determine the level of numerical accuracy. These effects are investigated in detail, in an effort to suggest a compromise between numerical error and computational cost.

• ETRI Journal
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• v.33 no.4
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• pp.621-628
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• 2011

The redactable signature scheme was introduced by Johnson and others in 2002 as a mechanism to support disclosing verifiable subdocuments of a signed document. In their paper, a redactable signature based on RSA was presented. In 2009, Nojima and others presented a redactable signature scheme based on RSA. Both schemes are very efficient in terms of storage. However, the schemes need mechanisms to share random prime numbers, which causes huge time consuming computation. Moreover, the public key in the scheme of Johnson and others is designed to be used only once. In this paper, we improve the computational efficiency of these schemes by eliminating the use of a random prime sharing mechanism while sustaining the storage efficiency of them. The size of our signature scheme is the same as that of the standard RSA signature scheme plus the size of the security parameter. In our scheme, the public key can be used multiple times, and more efficient key management than the scheme of Johnson and others is possible. We also prove that the security of our scheme is reduced to the security of the full domain RSA signature scheme.

• Structural Engineering and Mechanics
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• v.66 no.1
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• pp.61-73
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• 2018

In this article, a higher shear deformation theory (HSDT) is improved to consider the influence of thickness stretching in functionally graded (FG) plates. The proposed HSDT has fewer numbers of variables and equations of motion than the first-order shear deformation theory (FSDT), but considers the transverse shear deformation influences without requiring shear correction coefficients. The kinematic of the present improved HSDT is modified by considering undetermined integral terms in in-plane displacements and a parabolic distribution of the vertical displacement within the thickness, and consequently, the thickness stretching influence is taken into account. Analytical solutions of simply supported FG plates are found, and the computed results are compared with 3D solutions and those generated by other HSDTs. Verification examples demonstrate that the developed theory is not only more accurate than the refined plate theory, but also comparable with the HSDTs which use more number of variables.

• Journal of the Korean Society for Aviation and Aeronautics
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• v.14 no.3
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• pp.7-15
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• 2006

Aerodynamic analysis of an airfoil in the transonic region was automated in order to enable parametric study by using the journal file of the commercial analysis code FLUENT, pre/post process Gambit and computational mathematics code MATLAB. The automated capability was illustrated via NACA 0012 and RAE 2822 airfoils. This analysis was carried out at Mach numbers ranged from 0.70 to 0.80, angles of attack; 1$^{\circ}$, 2$^{\circ}$ and 4$^{\circ}$, Reynolds numbers; 4.0${\times}$106, 6.5${\times}$106. The analysis results of a pressure coefficient were verified by comparing with the experimental data which were measured in terms of chord length because the pressure coefficient of an airfoil surface is a good estimator of flow characteristics. The results of two airfoils show that this analysis code is useful enough to be used in the design optimization of airfoil.

• The Mathematical Education
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• v.48 no.3
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• pp.235-263
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• 2009

The purpose of the study was to investigate the influence of children's understanding of fractions in mathematics problem solving. Kieren has claimed that the concept of fractions is not a single construct, but consists of several interrelated subconstructs(i.e., part-whole, ratio, operator, quotient and measure). Later on, in the early 1980s, Behr et al. built on Kieren's conceptualization and suggested a theoretical model linking the five subconstructs of fractions to the operations of fractions, fraction equivalence and problem solving. In the present study we utilized this theoretical model as a reference to investigate children's understanding of fractions. The case study has been conducted with 6 children consisted of 4th to 5th graders to detect how they understand factions, and how their understanding influence problem solving of subconstructs, operations of fractions and equivalence. Children's understanding of fractions was categorized into "part-whole", "ratio", "operator", "quotient", "measure" and "result of operations". Most children solved the problems based on their conceptual structure of fractions. However, we could not find the particular relationships between children's understanding of fractions and fraction operations or fraction equivalence, while children's understanding of fractions significantly influences their solutions to the problems of five subconstructs of fractions. We suggested that the focus of teaching should be on the concept of fractions and the meaning of each operations of fractions rather than computational algorithm of fractions.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.679-690
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• 2001

Doubly stochastic matrices are n$\times$n nonnegative ma-trices whose row and column sums are all 1. Convex polytope $\Omega$$_{n}$ of doubly stochastic matrices and more generally (R,S), so called transportation polytopes, are important since they form the domains for the transportation problems. A theorem by Birkhoff classifies the extremal matrices of , $\Omega$$_{n}$ and extremal matrices of transporta-tion polytopes (R,S) were all classified combinatorially. In this article, we consider signed version of $\Omega$$_{n}$ and (R.S), obtain signed Birkhoff theorem; we define a new class of convex polytopes (R,S), calculate their dimensions, and classify their extremal matrices, Moreover, we suggest an algorithm to express a matrix in (R,S) as a convex combination of txtremal matrices. We also give an example that a polytope of signed matrices is used as a domain for a decision problem. In this context of finite reflection(Coxeter) group theory, our generalization may also be considered as a generalization from type $A_{*}$ n/ to type B$_{n}$ D$_{n}$. n/.