• Journal of the Korean Statistical Society
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• 제36권3호
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• pp.411-421
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• 2007

The recent work by the authors (see, Withers, 1999; Withers and McGavin, 2006; Withers and Nadarajah, 2006) provided new expressions for repeated upper tail integrals of the univariate normal density and so also for the general Hermite function. Here we derive new expressions for repeated lower tail integrals of the same. The calculations involve the use of Moran's L-function and the Airy function. In particular, the Hermite functions are expressed in terms of Moran's L-function and vice versa.

• Korea-Australia Rheology Journal
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• 제18권4호
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• pp.171-181
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• 2006

We present a short review for authors' previous work on direct numerical simulations for inertialess hard particle suspensions formulated either with a Newtonian fluid or with viscoelastic polymeric fluids to understand the microstructural evolution and the bulk material behavior. We employ two well-defined bi-periodic domain concepts such that a single cell problem with a small number of particles may represent a large number of repeated structures: one is the sliding bi-periodic frame for simple shear flow and the other is the extensional bi-periodic frame for planar elongational flow. For implicit treatment of hydrodynamic interaction between particle and fluid, we use the finite-element/fictitious-domain method similar to the distributed Lagrangian multiplier (DLM) method together with the rigid ring description. The bi-periodic boundary conditions can be effectively incorportated as constraint equations and implemented by Lagrangian multipliers. The bulk stress can be evaluated by simple boundary integrals of stresslets on the particle boundary in such formulations. Some 2-D example results are presented to show effects of the solid fraction and the particle configuration on the shear and elongational viscosity along with the micro-structural evolution for both particles and fluid. Effects of the fluid elasticity has been also presented.

• 공업화학
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• 제10권5호
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• pp.718-725
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• 1999

Inverse gas chromatography(IGC) 방법은 고분자-용매 계의 열역학적 특성을 신속하고 정확하게 결정할 수 있는 신뢰할 만한 방법 중 하나이다. 본 연구에서는 유한 농도에서의 IGC 방법을 사용하여 poly(dimethylsiloxane)(PDMS)과 물, 에탄올, 그리고 이소프로판올과의 상호작용을 정량적으로 결정하였다. 이를 위하여 고정상 내 용매의 체류시간으로부터 Flory-Huggins의 상호작용 계수를 산출하여 PDMS와 용매간의 소수성 상호작용을 의미하는 큰 양의 값(2$2.0{\times}10^{-3}mol/g$이었다. 또한 선형고분자에 대한 Kirkwood-Buff-Zimm(KBZ) 적분을 행하여 고분자와 용매의 분자분포 구조를 추정하였다. 이로부터 물분자는 PDMS에 대하여 용매화되지 않고 자체 분자끼리 부분적인 클러스트를 형성하며, 에탄올과 이소프로판올에서는 탄소수가 증가함에 따라 균일한 혼합에 가까운 분자분포의 구조적 성질을 추정할 수 있었다.

• 한국해양공학회지
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• 제24권5호
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• pp.16-21
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• 2010

During the loading/offloading operation of a liquefied natural gas carrier (LNGC) that is moored in a side-by-side configuration with an offshore plant, sloshing that occurs due to the partially filled LNG tank and the interactive effect between the two floating bodies are important factors that affect safety and operability. Therefore, a time-domain software program, called CHARM3D, was developed to consider the interactions between sloshing and the motion of a floating body, as well as the interactions between multiple bodies using the potential-viscous hybrid method. For the simulation of a floating body in the time domain, hydrodynamic coefficients and wave forces were calculated in the frequency domain using the 3D radiation/diffraction panel program based on potential theory. The calculated values were used for the simulation of a floating body in the time domain by convolution integrals. The liquid sloshing in the inner tanks is solved by the 3D-FDM Navier-Stokes solver that includes the consideration of free-surface non-linearity through the SURF scheme. The computed sloshing forces and moments were fed into the time integration of the ship's motion, and the updated motion was, in turn, used as the excitation force for liquid sloshing, which is repeated for the ensuing time steps. For comparison, a sloshing motion coupled analysis program based on linear potential theory in the frequency domain was developed. The computer programs that were developed were applied to the side-by-side offloading operation between the offshore plant and the LNGC. The frequency-domain results reproduced the coupling effects qualitatively, but, in general, the peaks were over-predicted compared to experimental and time-domain results. The interactive effects between the sloshing liquid and the motion of the vessel can be intensified further in the case of multiple floating bodies.