• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.173-185
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• 2014

In the present paper, we consider an anomalous diffusion problem in two dimensional space involving Caputo time and Riesz-Feller fractional derivatives and then solve it by using a series involving bilateral eigen-functions. Also, we obtain a numerical approximation formula of this problem and discuss some of its particular cases.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.683-693
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• 2008

In this paper, we study the asymptotic behavior of the residual empirical process from diffusion processes. For this task, adopting the discrete sampling scheme as in Florens-Zmirou [9], we calculate the residuals and construct the residual empirical process. It is shown that the residual empirical process converges weakly to a Brownian bridge.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1137-1146
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• 2010

In this paper, we study the divergence based goodness of fit test for partially observed sample from diffusion processes. In order to derive the limiting distribution of the test, we study the asymptotic behavior of the residual empirical process based on the observed sample. It is shown that the residual empirical process converges weakly to a Brownian bridge and the associated phi-divergence test has a chi-square limiting null distribution.

• Proceedings of the Korea Concrete Institute Conference
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• 2005.11a
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• pp.507-510
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• 2005

In winter, a large amount of de-icing salts such as $CaCl_2$, NaCl have been used on highways for road safety. They make concrete structures deteriorated. In this study, the chloride diffusion of concrete in presence of de-icing salt was investigated. The diffusion coefficient of chloride in presence of $CaCl_2$ solution was larger than in presence of NaCl solution. Therefore, it is necessary to assess chloride profile in presence of $CaCl_2$ by different way from the case in presence of NaCl solution or seawater.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.3-6
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• 2003

A nonlinear iterative filtering based on local statistics and anisotropic diffusion is introduced. Local statistics determines the diffusion coefficient at each iteration step. Anisotropic diffusion can be seen as estimates a piecewise smooth image from the noisy input image in the experimental section, our results are shown to suppress noise with preserving the edges. Therefore, it enhances the image and improves performance.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.377-380
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• 2003

A new color image segmentation scheme is presented in this paper. The proposed algorithm consists of image simplification, region labeling and color clustering. The vector-valued diffusion process is performed in the perceptually uniform LUV color space. We present a discrete 3-D diffusion model for easy implementation. The statistical characteristics of each labeled region are employed to estimate the number of total clusters and agglomerative hierarchical clustering is performed with the estimated number of clusters. Since the proposed clustering algorithm counts each region as a unit, it does not generate oversegmentation along region boundaries.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 1996.11a
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• pp.58-62
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• 1996

To check the variability of the effective diffusion coefficient in the unsaturated porous soil media. a Monte Carlo simulation was done for the equation suggested by Millington and Quirk(1961). The results shows that the probability density function of D$_{c}$/D$_{o}$ is positively skewed. It means the chance of having less effective diffusion coefficient values in the soil media than mean value is high. Also, the distribution types of D$_{c}$/D$_{o}$ are about same regardless of assumed distribution types of input parameters.ers.ers.

• Proceedings of the Korean Institute of Building Construction Conference
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• 2022.11a
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• pp.85-86
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• 2022

In this study, a simulation using Company A's COMSOL heat flow program was used to analyze the thermal diffusion simulation according to the depth of the high-temperature exposed cement paste. As a result of the analysis, it showed a similar relationship with the measured temperature as of 180 minutes.

• Membrane Journal
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• v.10 no.1
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• pp.19-29
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• 2000

To estimatc mutual diffusion coefficient for the analysis of mass transfer phenomena in polymer/solvent system, two models are proposed and the equations are derived. The estimates of mutual diffusion coefficients are obtained by two models suggested in this work and compared with and experimental data and Vrentas-Duda's. Vrentas-Duda's self diffusion coefficient was used for the mutual diffusion coefficient. Derivative of chemical potential on solvent was derived and used using original UNIFAC-FV and modified UNIFAC-FV. However, Vrentas-Duda's equation for mutual diffusion coefficient contains Flory-Huggins parameter x. For the derivative of chemical potential term, Vrentas-Duda assumed that parameter x was constant and independent of temperatures and concentrations The assumption is one of shortcoming in vrentas-Duda's mutual diffusion coefficient. New methods proposed in this work do not have such assumptions and simplifications. For the solvent of cyclohexane, n-pentane, and n-hexane in PIB(polyisolbutylene) and PMS-BR (poly(p-methylstyrene-co-isobutylene), new methods well correlate the experimental data at various temperatures and concentrations, and predicted the experimental data much better than Vrentas-Duda's for the PIB/toluene system. It is shown that new methods are excellent tools for correlating mutual diffusion coefficient data in polymer/solvent system over wide ranges of temperature and concentration without any assumptions or simplifications.

• Journal of Powder Materials
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• v.23 no.6
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• pp.432-436
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• 2016

We investigate the microstructural and magnetic property changes of $DyH_2$, $Cu+DyH_2$, and $Al+DyH_2$ diffusion-treated NdFeB sintered magnets with the post annealing (PA) temperature. The coercivity of all the diffusion-treated magnets increases with increasing heat treatment temperature except at $910^{\circ}C$, where it decreases slightly. Moreover, at $880^{\circ}C$, the coercivity increases by 3.8 kOe in Cu and 4.7 kOe in Al-mixed $DyH_2$-coated magnets, whereas this increase is relatively low (3.0 kOe) in the magnet coated with only $DyH_2$. Both Cu and Al have an almost similar effect on the coercivity improvement, particularly over the heat treatment temperature range of $790-880^{\circ}C$. The diffusivity and diffusion depth of Dy increases in those magnets that are treated with Cu or Al-mixed $DyH_2$, mainly because of the comparatively easy diffusion path provided by Cu and Al owing to their solubility in the Nd-rich grain boundary phase. The formation of a highly anisotropic $(Nd,\;Dy)_2Fe_{14}B$ phase layer, which acts as the shell in the core-shell-type structure so as to prevent the reverse domain movement, is the cause of enhanced coercivity of diffusion-treated Nd-Fe-B magnets.