• Journal of the Korean Statistical Society
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• v.36 no.3
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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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• v.18 no.4
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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.

• Applied Chemistry for Engineering
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• v.10 no.5
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• pp.718-725
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• 1999

In order to investigate the interaction characteristics of poly(dimethylsiloxane) (PDMS) with various solvents such as water, ethanol, and iso-propanol, Inverse Gas Chromatography(IGC) at finite concentration, which is a very fast, accurate, and thus promising technique in thermodynamic study of polymer systems, is employed. By measuring the specific retention volumes of the probes, the interaction parameters are calculated by means of the Flory-Huggins equation. From the results, the interaction parameters of the probes are, as expected due to the hydrophobicity of the polymer, found to be of large positive values (2$2.0{\times}10^{-3}mol/g$. For the linear PDMS, interpretation of the space distribution of molecules is performed by the Kirkwood-Buff-Zimm(KBZ) integrals, which give intuitive information about physical properties. From the KBZ integrals, water does not show the tendency of preferential solvation with the PDMS but formed self-cluster. The larger solvent molecules show a stronger tendency to distribute more randomly in the mixture.

• Journal of Ocean Engineering and Technology
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• v.24 no.5
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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.