• Macromolecular Research
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• 제9권3호
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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.

• 대한수학회논문집
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• 제37권3호
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• pp.939-955
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• 2022

In this paper, we study a first-order non-linear singularly perturbed Volterra integro-differential equation (SPVIDE). We discretize the problem by a uniform difference scheme on a Bakhvalov-Shishkin mesh. The scheme is constructed by the method of integral identities with exponential basis functions and integral terms are handled with interpolating quadrature rules with remainder terms. An effective quasi-linearization technique is employed for the algorithm. We establish the error estimates and demonstrate that the scheme on Bakhvalov-Shishkin mesh is O(N^-1) uniformly convergent, where N is the mesh parameter. The numerical results on a couple of examples are also provided to confirm the theoretical analysis.

• Structural Engineering and Mechanics
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• 제86권3호
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• pp.361-371
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• 2023

Boundary condition is an important factor affecting the vibration characteristics of structures, under different boundary conditions, structures will exhibit different vibration behaviors. On the basis of the previous work, this paper extends to the nonlinear resonance behavior of axially moving graphene platelets reinforced metal foams (GPLRMF) plates with geometric imperfection under different boundary conditions. Based on nonlinear Kirchhoff plate theory, the motion equations are derived. Considering three boundary conditions, including four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS), the nonlinear ordinary differential equation system is obtained by Galerkin method, and then the equation system is solved to obtain the nonlinear ordinary differential control equation which only including transverse displacement. Subsequently, the resonance response of GPLRMF plates is obtained by perturbation method. Finally, the effects of different boundary conditions, material properties (including the GPLs patterns, foams distribution, porosity coefficient and GPLs weight fraction), geometric imperfection, and axial velocity on the resonance of GPLRMF plates are investigated.

• 한국가시화정보학회:학술대회논문집
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• 한국가시화정보학회 2001년도 Proceedings of 2001 Korea-Japan Joint Seminar on Particle Image Velocimetry
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• pp.62-74
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• 2001

Present paper describes the principles of PIV measurement approaching from the analytical view, which enables to explain the general form of principles covering all the PIV measurement, and that gives theoretical basis for its higher measurement performances. The explanation of the measurement principles started from the definition of governing equation in differential form as same as the gradient method, and the integral along the particle path line was executed to show the principle of the correlation method with same basis. The integral processes clearly shows the analytical reason why the correlation peak gives the terminal point of path line, and how the effects of deformation and rotation of fluid appears in the correlation map. These results have no differences from our experiences and understandings of the conventional PIV measurement definition in final form. However, the analytical approach enable to understand those facts a priori, and it makes easy to achieve the innovative higher performances of measurement. Analytical explanation clearly shows the behavior of the residual errors caused by the fluid motion, and it enables to analyze the measurement uncertainty theoretically.

• Wind and Structures
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• 제1권3호
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• pp.243-253
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• 1998

The paper deals with numerical analysis of interference galloping of two elastically supported circular cylinders of equal diameters. The basis of the analysis is quasi-steady model of this phenomenon. The model assumes that both cylinders participate in process of interference galloping and they have two degrees of freedom. The movement of the cylinders is written as a set of four nonlinear differential equations. On the basis of numerical solutions of this equations the authors evaluate the correctness of this quasi-steady model. Then they estimate the dependence of a critical reduced velocity on the Scruton number, turbulence intensity and arrangements of the cylinders.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권3호
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• pp.93-106
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• 2021

In this paper, an efficient hybrid numerical method for solving two-asset option pricing problem is presented based on the Crank-Nicolson and the radial basis function methods. For this purpose, the two-asset Black-Scholes partial differential equation is considered. Also, the convergence of the proposed method are proved and implementation of the proposed hybrid method is specifically studied on Exchange and Call on maximum Rainbow options. In addition, this method is compared to the explicit finite difference method as the benchmark and the results show that the proposed method can achieve a noticeably higher accuracy than the benchmark method at a similar computational time. Furthermore, the stability of the proposed hybrid method is numerically proved by considering the effect of the time step size to the computational accuracy in solving these problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권2호
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• pp.121-137
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• 2022

In this paper, we investigate an efficient hybrid method for solving two-asset time fractional Black-Scholes partial differential equations. The proposed method is based on the Crank-Nicolson the radial basis functions methods. We show that, this method is convergent and we obtain good approximations for solution of our problems. The numerical results show high accuracy of the proposed method without needing high computational cost.

• 한국지반환경공학회 논문집
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• 제8권5호
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• pp.31-38
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• 2007

현재 실무에서 사용되고 있는 샌드매트의 설계법에서는 주로 수평배수층의 배수거리, 침하속도, 투수성 등을 설계 인자로 사용하고 있으며, 현장 시공 시에는 성토체 하부에 동일한 두께로 시공하고 있다. 그러나 하부 연약지반의 변형에 따라 성토 중앙부와 양단에서 부등침하가 발생하게 되어 샌드매트 두께산정에 있어 과소평가될 가능성과 배수지연을 유발할 우려가 있음이 지적되어왔다. 본 연구에서는 연약지반의 변형으로 인해 생기는 부등침하의 발생이 배수지연 및 샌드매트의 두께산정에 어떠한 영향을 미칠 수 있는지 여부를 수치해석을 통해 분석하였다. 해석 결과 부등침하로 인하여 실질 유로두께의 감소를 확인할 수 있었으며, 새로운 위치수두의 차가 발생하여 배수지연 현상을 유발할 가능성이 있음이 확인되었다. 이에 대한 대응책으로 본 연구에서는 사전에 부등침하를 예측하여 성토 중앙부의 샌드매트 두께를 증가시킨 마운드형 샌드매트의 적용성에 대하여 검토하였으며, 압밀의 진행에 따라 변형이 크게 발생하여도 소정의 실질 유로두께를 유지하고 있음을 확인하였다. 특히, 마운드형 샌드매트는 연약지반 성토와 같이 변형의 분포가 위치에 따라 다른 경우의 건설공사에 매우 유효하리라 판단하며, 경제적이고 합리적인 수평배수재로서 적용이 가능할 것으로 판단되었다. 또한, 마운드형 샌드매트의 설계를 위해서는 성토단계별로 압밀속도, 배수거리나 투수성뿐만 아니라 연약지반의 침하특성을 정확하게 예측하는 것이 필수적이라고 사료된다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2007년도 추계학술대회 논문집 전력기술부문
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• pp.75-77
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• 2007

Current percentage differential relaying has been recognized as the principal basis of main protection for stator windings of AC generator. The DWT has merit of obtaining frequency characteristics in time domain. In order to compensate for DFT's defects, we proposed fault detection algorithm using DWT. This paper describes a comparative analysis about conventional DFT-based DFR and advanced DWT-based relaying.

• Journal of the Korean Statistical Society
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• 제29권4호
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• pp.489-499
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• 2000

We propose a new instrumental variable estimator of the complex parameter of a class of univariate complex-valued diffusion processes defined by the possibly non-stationary and/or nonlinear stochastic differential equations. On the basis of the exact finite sample distribution of the pivotal quantity, we construct the exact confidence intervals and the exact tests for the parameter. Monte-Carlo simulation suggests that the new estimator seems to provide a viable alternative to the maximum likelihood estimator (MLE) for nonlinear and/or non-stationary processes.