• East Asian mathematical journal
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• v.35 no.1
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• pp.99-108
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• 2019

In this paper, we introduce a numerical approach to solve heat-diffusion equation with discontinuous diffusion coefficients in the three dimensional rectangular domain. First, we study the support operator method and suggest a new method, the continuous velocity method. Further, we apply both methods to a diffusion process for neurotransmitter release in an individual synapse and compare their results.

• Bulletin of the Korean Chemical Society
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• v.32 no.6
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• pp.1970-1974
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• 2011

The effects of convection on the measurement of the diffusion coefficients of liquids by the pulsed gradient spin echo (PGSE) NMR method at low temperature are discussed. To examine the generation of convective flows, we used four different types of sample tubes in the diffusion measurements with temperature variation; a normal 5 mm NMR tube, a Shigemi tube, an ELISE type tube, and a capillary tube. Below room temperature, the calculated diffusion coefficients of chloroform in 5 mm o.d. type tubes increased with decreasing temperature, while those in the capillary tube decreased linearly. The convective flow was found to be significant even at low temperature and it seemed to be mainly induced by the transverse temperature gradient. It was also found that the capillary tube was most appropriate to measure the diffusion coefficients, since its small diameter is effective in suppressing the convective flows at both high and low temperatures.

• Polymer(Korea)
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• v.24 no.2
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• pp.194-200
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• 2000

The diffusion coefficients in polyimide/N-methyl-2-pyrrolidone (NMP) systems were proposed using tile Vrentas-Duda's hole free volume theory. Several free volume parameters included in the diffusion coefficients were obtained from the fundamental physical properties of polyimide and NMP and group contribution theory, and the pre-exponential diffusion coefficient, D$_{0}$ was also determined from the dynamic swelling behavior of polyimide in NMP solution. The experimental swelling behavior of polyimide films in NMP was well described by the theoretical one using the proposed diffusion coefficient.t.

• Proceedings of the Membrane Society of Korea Conference
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• 1997.10a
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• pp.27-30
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• 1997

1. Introduction : Molecular diffusion of small molecules in polymers plays an important role in many areas where polymers are acting as barriers, and in separation processes, such as selective diffusion. Different applications of polymers have different requirements on their transport properties. Therefore, reliable predictions of diffusion coefficients for small molecules in polymeric materials could be a useful tool to design appropriate materials. For many years, the theories based on free-volume concepts have been widely used to correlate and predict diffusion behavior in polymer/solvent systems. In the theory derived by Vrentas and Duda, the empty space between molecules that is available for molecular transport, referred to as hole free-volume, is being redistributed. Molecular transport will occur only when a free-volume of sufficient size appears adjacent to a molecule and the molecule has enough energy to jump into this void. The diffusive jump is considered complete when the void left behind is closed before the molecule returns to its original position. In this paper, the Vrentas-Duda free-volume theory is presented and the methods to estimate free-volume parameters for predicting polymer/ solvent diffusion coefficients are described in detail.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1584-1589
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• 2003

This work applies the equilibrium molecular dynamics simulation method to study a Lennard-Jones liquid thin film suspended in the vapor and calculates diffusion coefficients by Green-Kubo equation derived from Einstein relationship. As a preliminary test, the diffusion coefficients of the pure argon fluid are calculated by equilibrium molecular dynamics simulation. It is found that the diffusion coefficients increase with decreasing the density and increasing the temperature. When both argon liquid and vapor phases are present, the effects of the system temperature on the diffusion coefficient are investigated. It can be seen that the diffusion coefficient significantly increases with the temperature of the system.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.837-845
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• 1998

In this work, we consider Euler approxiamtion for one-dimensional jump-diffusion processes under Yamada-Watanabe type conditions on the coefficients which turns out to converge to the strong solution in uniform $L^1$-sense.

• Proceedings of the Korea Concrete Institute Conference
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• 1999.10a
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• pp.747-750
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• 1999

Chloride ions are considered to be the major cause of steel corrosion in concrete structures exposed to seashore environments. Thus, estimating chloride ion concentrations by ages is needed to predict service life of seashore structures. Experimentally measured chloride profiles were used in this study for estimating chloride diffusion coefficients, and a relationship between mixing properties and chloride diffusion coefficients is proposed for predicting chloride penetrations.

• Journal of the Korean Ceramic Society
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• v.31 no.12
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• pp.1459-1466
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• 1994

A novel technique for determining the oxygen tracer diffusion coefficients in oxides was developed. After the 16O-18O solid-gas exchange reactions between 16O in the oxides and 18O in the ambient gas, Raman spectra of the cross sections of oxide samples were measured in a spatial resolution of 5 ${\mu}{\textrm}{m}$. From thus obtained Raman spectra, depth profiles of 18O concentration in the oxide samples were calculated. The oxygen tracer diffusion coefficients and the surface exchange coefficients were determined under the assumptions that samples are semi-infinite slab and that the surface exchange reactionsare not negligible. The oxygen tracer diffusion coefficient of 2.8 mol% Y2O3-containing tetragonal ZrO2 polycrystals, 8 mol% Y2O3-containing ZrO2 polycrystals, and 10 mol% Y2O3-containing cubic ZrO2 single crystals (along the a axis) are as follows.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.21-24
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• 2008

This study proposes a optimized shape of diffuser profile through investigating the scattering and diffusion characteristics of diffusers. The scattering coefficient according to ISO 17497-1 evaluates uniformity of reverberant sound field of late reflections, while the diffusion coefficient according to AES-4id-2001 evaluates polar response of early reflections. Thus both scattering and diffusion characteristics should contribute to design shape of diffusers to maximize physical performance. To find out design method, the previous results on hemisphere diffusers are reviewed. The frequency characteristics of scattering coefficients depended on the structural height of the diffusers, while amount of scattering coefficients depended on the surface coverage density of the diffusers. However absorptive properties also increased with augment of surface coverage density, thus optimum coverage density should be considered. For the directional diffuser, three types of 2D-diffusers are proposed; semicylinder of h=5mm, semi-truncated cone of h=5-25mm and semicylinder of h=25mm. As results, diffusers with the maximum height of 25mm show the highest scattering coefficients, while diffuser of h=5mm shows high scattering coefficients only at the high-frequency bands. Diffusion coefficient will be investigated for diffusive properties of the early reflection.

• Bulletin of the Korean Chemical Society
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• v.5 no.6
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• pp.249-253
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• 1984

Mutual diffusion coefficients of choline chloride were determined by using the diaphragm cell method in aqueous solutions of chondroitin sulfate A at $25^{\circ}C$. The diffusion coefficients of choline chloride in 0.1g/100ml, 0.5g/100ml and 1g/100ml respectively of chondroitin sulfate solutions were compared with those of binary systems of water-choline chloride. At low concentrations, the diffusion coefficients of the choline chloride in the presence of chondroitin sulfate were significantly smaller than the values obtained in the absence of chondroitin sulfate, indicating a strong interaction between these solutes. The effect of this interaction on the diffusion of choline ion is largest at higher chondroitin sulfate concentrations and at lower choline chloride concentrations. The influence of chondroitin sulfate is overcome at higher choline chloride concentrations. Self-diffusion coefficients of choline ion in the presence of chondroitin sulfate are also obtained. Excellent agreements were obtained between the experimental data and the calculated values obtained by using the Manning's equations. These observations suggest that the interaction between choline chloride and chondroitin sulfate involves primarily a long range electrostatic effect and there is no appreciable "condensation" or binding of choline ion to the chondroitin sulfate.