• East Asian mathematical journal
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• v.24 no.4
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• pp.407-414
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• 2008

Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations with damping and convection terms, which describe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1247-1256
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• 2009

Finite difference schemes are considered for a nonlinear $Ca^{2+}$ diffusion equations with stationary and mobile buffers. The scheme inherits mass conservation as for the classical solution. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained. using the extended Lax-Richtmyer equivalence theorem.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.299-306
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• 2008

Finite difference schemes are considered for a $Ca^{2+}$ diffusion equations, which discribe $Ca^{2+}$ buffering by using stationary and mobile buffers. Stability and $L^\infty$ error estimates of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem.

• Progress in Superconductivity and Cryogenics
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• v.5 no.2
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• pp.66-70
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• 2003

Transient magnetic diffusion process in a melt-cast Bi2Sr2CaCu20X(Bi-2212) tube was studied by experimental and numerical analyses. The transient diffusion partial differential equation is transformed into an ordinary differential equation by integral method. The penetration depth of magnetic field into a superconducting tube is obtained by solving the differential equation numerically. The results show that the penetration depth as a function of time which is somewhat different from the results by Bean's critical state model. The reason of the difference between the present results and that of Bean's model is discussed and compared in this paper. This experiment measure the magnetic flux density in the supercondutor after supply direct-current of Bi-2212 rounded by copper coil. This study was discussed of valid of a previous numerical solution which is compared by the penetrate time and the magnetic flux density difference of between the present results and the numerical solution.

• Journal of the Korea Concrete Institute
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• v.22 no.2
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• pp.209-217
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• 2010

Recently, some mathematical models for the prediction on progress of carbonation of concrete were reported. These models take account for $CO_2$ diffusion and chemical reaction between $Ca(OH)_2$ and $CO_2$. Based on the assumption that $CO_2$ diffuses in the carbonation zone and reacts with $Ca(OH)_2$ at the outer face of carbonation zone and non-carbonation zone. In this study, a mathematical model to predict the progress of carbonation of concrete has been established based on the reducing concentration of $Ca(OH)_2$ in the carbonation progress zone, where $Ca(OH)_2$ reacts with $CO_2$ and $Ca(OH)_2$ and $CaCO_3$ coexist. Also, the prediction model of carbonation progress rate of concrete using the air permeability coefficient regarding to $CO_2$ diffusion is developed. As a result of this study, an expression, the model equation is obtained for the prediction of carbonation based on the time and interaction velocity between $CO_2$ and Ca(OH)$_2$ dependent air permeability coefficient. The prediction by the model satisfied the experimental data of the accelerated carbonation for painted concrete. Consequently, the model can predict the rate of carbonation and the potential service life of concrete structure exposed to atmosphere.

• Korean Chemical Engineering Research
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• v.50 no.6
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• pp.939-944
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• 2012

The electrochemical behavior of magnesium ions was examined by cyclic voltammetry in a molten $MgCl_2-CaCl_2$-NaCl salt. The reduction potential of magnesium ions was measured and those values were estimated with the variation of the concentration of $MgCl_2$ and the temperature of molten salts. The diffusion coefficient of the $Mg^{2+}$ ions has been determined at 660, 680, 700, 720 and $740^{\circ}C$. The values were $8.79{\times}10^{-6}$, $9.56{\times}10^{-6}$, $1.17{\times}10^{-5}$, $1.4{\times}10^{-5}$ and $1.77{\times}10^{-5}\;cm^2\;s^{-1}$. The activation energy for the diffusion processes of $Mg^{2+}$ ions was found to be $70.28\;kJ\;mol^{-1}$ by using the Arrhenius equation.

• The Journal of Engineering Research
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• v.3 no.1
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• pp.223-233
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• 1998

The kinetic and mechanism of the hydrothermal reaction between lime and quartz used solid state reaction equations have been investigated. Hydrothermal reaction on the starting materials was carried out in an autoclave that quartz mixed with calcium hydroxide in CaO/$SiO_2$ ratio of 0.8-1.0 for 0.5-8 hour at saturated steam pressure of $180-200^{\circ}C$. The rate of reaction was given from the ratio of uncombined lime and quartz content to the total lime and quartz content. The rate of reaction was obtained the results by the Jander's equation $[1-(1-\alpha)^{1/3}]^N=Kt$. The reaction of lime is controlled mainly by the dissolution such as N=1, and the reaction of quartz is controlled mostly by the diffusion such as $N\risingdotseq2$. The rate of hydrothermal reaction in the calcium silicate hydrates system is suggested to be determined generally by the mass transfer through the product laver formed around the reactant particles. The rate equation for whole hydrothermal reaction is shown that it is converted into the rate determining step by the diffusion from the boundary reaction such as approximately $N=1-2$.

• Proceedings of the Korea Concrete Institute Conference
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• 2010.05a
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• pp.221-222
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• 2010

In this study an expression is obtained the model equation for the prediction of carbonation based on the time and interaction velocity between $CO_2$ and $Ca(OH)_2$ diffusion coefficient.

• Journal of the Korean Ceramic Society
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• v.40 no.3
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• pp.234-240
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• 2003

Hardened cement pastes of OPC which contains 10 wt% CSA type expansive additives were immersed in aqueous solution of 10 wt% MgS $O_4$.7$H_2O$ and then investigated by compressive strength, XRD. SEM and DSC etc.. According to the results including the hydration products and the microstructure of the hardened paste, the case of CSA type expansive additives［No. 6(C/(equation omitted) : 2.29, A/(equation omitted) : 0.16)] prepared from raw materials increased the resistance to $Mg^{2＋}$, S $O_4$$^{2-}$ ion diffusion than that of OPC paste due to the densification by the formation of fine ettringite in the first stage and the hydrates according to $\beta$-C$_2$S hydration in the late period.

• KSBB Journal
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• v.4 no.2
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• pp.110-117
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• 1989

The fiffusion characteristics of substrate of varing biomass concentrations into and from Ca- alginate gel beads in well-stirred solutions were investigated. Ca-alginate gel beads were immobilized by Zymomonas mobilis or free from cells. The values of the diffusion coefficient of substrate were calculated by means of the method of Least squares and Random pore model. Reaction rates are expressed by the Michaelis-Menten type equation, and the results are compared with experimental data. Intraparticle effective diffusivity of substrate resistance on reaction by using immobilized Z.mobilis entrapped by Ca-alginated gel seemed to be restricted by cell density. The experimental data also indicated relationship between the effective diffusivity and the cell concentration used in the gel preparation.