• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.161-171
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• 1999

Aerodynamic sensitivity analysis codes are developed via the hand-differentiation using a direct differentiation method and an adjoint method respectively from discrete two-dimensional compressible Navier-Stokes equations. Unlike previous other researches, Baldwin-Lomax algebraic turbulence model is also differentiated by hand to obtain design sensitivities with respect to design variables of interest in turbulent flows. Discrete direct sensitivity equations and adjoint equations are efficiently solved by the same time integration scheme adopted in the flow solver routine. The required memory for the adjoint sensitivity code is greatly reduced at the cost of the computational time by allowing the large banded flux jacobian matrix unassembled. Direct sensitivity code results are found to be exactly coincident with sensitivity derivatives obtained by the finite difference. Adjoint code results of a turbulent flow case show slight deviations from the exact results due to the limitation of the algebraic turbulence model in implementing the adjoint formulation. However, current adjoint sensitivity code yields much more accurate sensitivity derivatives than the adjoint code with the turbulence eddy viscosity being kept constant, which is a usual assumption for the prior researches.

• Research in Mathematical Education
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• v.8 no.1
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• pp.19-30
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• 2004

This research applies the discursive approach to investigate the social transformation of students' conceptual model of differential equations. The analysis focuses on the students' use of metaphor in class in order to find kinds of metaphor used, their characteristics, and a pattern in the use of metaphor. Based on the analysis, it is concluded that the students' conceptual model of differential equations gradually becomes transformed with respect to the historical and cultural structure of the communal practice of mathematics. The findings suggest that through participating in the daily practice of mathematics as a historical and cultural product, a learner becomes socially transformed to a certain kind of a cultural being with historicity. This implies that mathematics education is concerned with the formation of historical and cultural identity at a fundamental level.

• Interaction and multiscale mechanics
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• v.1 no.1
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• pp.53-81
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• 2008

The theory of microlocal analysis of hyperbolic partial differential equations shows that the energy density associated to their high-frequency solutions satisfies transport equations, or radiative transfer equations for randomly heterogeneous materials with correlation lengths comparable to the (small) wavelength. The main limitation to the existing developments is the consideration of boundary or interface conditions for the energy and power flow densities. This paper deals with the high-frequency transport regime in coupled heterogeneous structures. An analytical model for the derivation of high-frequency power flow reflection/transmission coefficients at a beam or a plate junction is proposed. These results may be used in subsequent computations to solve numerically the transport equations for coupled systems, including interface conditions. Applications of this research concern the prediction of the transient response of slender structures impacted by acoustic or mechanical shocks.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.749-756
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• 2006

Because of the orthotropic elastic properties and significant two-way bending action, orthotropic plate theory may be suitable for describing the behavior of concrete filled grid bridge decks. Current AASHTO LRFD Bridge Design Specification(2004) has live load moment equations considering flexural rigidity ratio between longitudinal and transverse direction, but the Korea highway bridge design specification(2005) doesn't. The Korea highway bridge standard specification LRFD(1996) considers an orthotropic plate model with a single load to estimate live load moments in concrete filled grid bridge decks, which may not be conservative. This paper presents live load moment equations for truck and passenger car, based on orthotropic plate theory. The equations of truck model use multiple presence factor, impact factor, design truck and design tandem of the Korea highway bridge standard specification LRFD(1996). The estimated moments are verified through finite-element analyses.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.05a
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• pp.878-883
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• 2003

To modify some problems of ACI shear provisions, ultimate shear strength equation considering size effect and arch action to compute shear strength in high-strength concrete beams without stirrups is presented in this research. Three basic equations, namely size reduction factor, rho factor, and arch action factor, are derived from crack band model of fracture mechanics, analysis of previous some shear equations for longitudinal reinforcement ratio, and concrete strut described as linear function in deep beams. Constants of basic equations are determined using statistical analysis of previous shear testing data. To verify proposed shear equation for each variable, namely d, , ρ, f/sub c/' and aid, about 250 experimental data are used and proposed shear equation is compared with ACI 318-99 code, CEB-FIP Model code, Kim & Park's equation and Zsutty's equation. While proposed shear equation is simpler than other shear equations, it is shown to be economical predictions and reasonable safety margin. Hence proposed shear strength equation is expected to be applied to practice shear design.

• Macromolecular Research
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• v.9 no.3
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• pp.164-170
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• 2001

Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the pom-pom equations have been derived by McLeish and Larson on the basis of the reptation dynamics with simplified branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for the simplified differential version of these constitutive equations. It is proved that they are globally Hadamard stable except for the case of maximum constant backbone stretch (λ = q) with arm withdrawal s$\_$c/ neglected, as long as the orientation tensor remains positive definite or the smooth strain history in the now is previously given. However this model is dissipative unstable, since the steady shear How curves exhibit non-monotonic dependence on shear rate. This type of instability corresponds to the nonlinear instability in simple shear flow under finite amplitude disturbances. Additionally in the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady now curves, the constitutive equations will possibly violate the positive definiteness of the orientation tensor and thus become Hadamard unstable.

• Journal of the Society of Naval Architects of Korea
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• v.43 no.2 s.146
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• pp.147-155
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• 2006

Ice resistance estimation equations based on model tests and full-scale sea trial data from many previous research articles are studied. Measured ice resistance data and its empirical/semi-empirical estimation equations are summarized in common format and are compared with each other, considering three ship categories, i.e, icebreakers, tug/supply vessels, ice-strengthened cargo vessels. The most suitable estimation methods or prediction equations are recommended based on this ice resistance data analysis.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.127-146
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• 2016

We consider a coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two. We show temporal decay estimates of solutions with small initial data and obtain their asymptotic profiles as time tends to infinity.

• Current Optics and Photonics
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• v.4 no.5
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• pp.434-440
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• 2020

Based on single-mode rate equations, we present an improved equivalent-circuit model for distributed-feedback (DFB) lasers that accounts for the effects of parasitic parameters and nonradiative recombination. This equivalent-circuit model is composed of a parasitic circuit, an electrical circuit, an optical circuit, and a phase circuit, modeling the circuit equations transformed from the rate equations. The validity of the proposed circuit model is verified by comparing simulation results to measured results. The results show that the slope efficiency and threshold current of the model are 0.22 W/A and 13 mA respectively. It is also shown that increasing bias current results in the increase of the relaxation-oscillation frequency. Moreover, we show that the larger the bias current, the lower the frequency chirp, increasing the possibility of extending the transmission distance of an optical-fiber communication system. The results indicate that the proposed circuit model can accurately predict a DFB laser's static and dynamic characteristics.

• Magazine of the Korean Society of Agricultural Engineers
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• v.39 no.2
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• pp.97-103
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• 1997

DO concentration in the aquatic system is important for the water quality management perspective. Water quality model uses available reaeration coefficient (K2) estimation equations in calculating DO, however, they might include inevitable uncertainty that the model output can be less reliable. In this study, the calibrated QUAL2E model for the Passaic River in New Jersey, U.S., was used to examine the effect of K2 estimation equation on the output DO concentration of the river. The model was run with six commonly used equations separately with all the other conditions remained same. The result showed that the output DO concentration profiles varied widely with different equations, and maximum difference was 4.96 mg/L for the same location which is unacceptably large. It implies that the development of reliable equation is required for proper water quality management. The unreliable model output can lead to a wrong decision in water quality management such as unnecessarily high or too low treatment of wastewater, which will cause serious effect on the community economically and socially in either case. Generating more reliable model output with slight investment to develop a site specific K$_2$ equation can improve the decision making process significantly and is highly recommended.