• Applied Chemistry for Engineering
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• v.3 no.2
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• pp.349-359
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• 1992

Studies were carried out on the selective removal of inorganic salts such as NaCl and $Na_2SO_4$ from dye solution, using counter diffusion-reverse osmosis and nanofiltration, respectivey. For the dye solution used in the experiments, 1 to 30% of salts were removed by counter diffusion while the loss of dye molecules was less than 0.3%. The separation factors by one pass operation were 10-500 according to ionic species. In five successive operations, removals of anion($Cl^-$) increased but those of cation($Na^+$) decreased due to the Donnan effect. Effects of feed flow rate on removal efficiencies of various ions were also observed at constant flow rate of stripping water. Reverse osmosis of desalted dye solution by counter diffusion was conducted to prepare highly concentrated liquid dyes. The rejection efficiency of dye molecules was greater than 99%. For the rejection efficiency of chloride ion, experimental values were compared with theoretical ones based on solution-diffusion model. Two stage diafiltration was performed in nanofiltration. The rejection efficiency of chloride ion was continuously decreased due to the Donnan dialysis and even negative rejection was observed. The Donnan effect was more pronounced in the second diafiltration.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.27-41
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• 2014

In this paper, we present an efficient numerical method for multiphase image segmentation using a multiphase-field model. The method combines the vector-valued Allen-Cahn phase-field equation with initial data fitting terms containing prescribed interface width and fidelity constants. An efficient numerical solution is achieved using the recently developed hybrid operator splitting method for the vector-valued Allen-Cahn phase-field equation. We split the modified vector-valued Allen-Cahn equation into a nonlinear equation and a linear diffusion equation with a source term. The linear diffusion equation is discretized using an implicit scheme and the resulting implicit discrete system of equations is solved by a multigrid method. The nonlinear equation is solved semi-analytically using a closed-form solution. And by treating the source term of the linear diffusion equation explicitly, we solve the modified vector-valued Allen-Cahn equation in a decoupled way. By decoupling the governing equation, we can speed up the segmentation process with multiple phases. We perform some characteristic numerical experiments for multiphase image segmentation.

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.971-974
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• 2012

The facilitated diffusion effect on protein-DNA binding is studied. A rigorous theoretical approach is presented to deal with the coupling between one-dimensional and three-dimensional diffusive motions. For a simplified model, the present approach can provide numerically exact results, which are confirmed by the lattice-based Monte Carlo simulations.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.69-78
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• 2004

This paper treats the conditions for the existence of rotating wave solutions of a system modelling the behavior of students in graduate programs at neighbouring universities near each other which is a modified form of the model proposed by Scheurle and Seydel. We assume that both types of individuals are continuously distributed throughout a bounded two-dimension spatial domain of two types (circle and annulus), across whose boundaries there is no migration, and which simultaneously undergo simple (Fickian) diffusion. We will show that at a critical value of a system-parameter bifurcation takes place: a rotating wave solution arises.

• East Asian mathematical journal
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• v.32 no.3
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• pp.387-397
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• 2016

This paper is concerned with the optimal control problem for some reaction diusion model. That is, we show the existence of the global weak solution for the Field-Noyes model. We also show the existence of the optimal control.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.29-36
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• 2014

The limiting diffusion of special diploid model can be defined as a discrete generator for the rescaled Markov chain. Choi([2]) defined the operator of projection $S_t$ on limiting diffusion and new measure $dQ=S_tdP$. and showed the martingale property on this operator and measure. Let $P_{\rho}$ be the unique solution of the martingale problem for $\mathcal{L}_0$ starting at ${\rho}$ and ${\pi}_1,{\pi}_2,{\cdots},{\pi}_n$ the projection of $E^n$ on $x_1,x_2,{\cdots},x_n$. In this note we define $$dQ_{\rho}=S_tdP_{\rho}$$ and show that $Q_{\rho}$ solves the martingale problem for $\mathcal{L}_{\pi}$ starting at ${\rho}$.

• Computers and Concrete
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• v.15 no.5
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• pp.847-864
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• 2015

In this paper, a reaction-diffusion model of carbonation process in self-compacting concrete (SCC) was realized with a consideration of multi-field couplings. Various effects from environmental conditions, e.g. ambient temperature, relative humidity, carbonation reaction, were incorporated into a numerical simulation proposed by ANSYS. In addition, the carbonation process of SCC was experimentally investigated and compared with a conventionally vibrated concrete (CVC). It is found that SCC has a higher carbonation resistance than CVC with a comparable compressive strength. The numerical solution analysis agrees well with the test results, indicating that the proposed model is appropriate to calculate and predict the carbonation process in SCC. The parameters sensitivity analysis also shows that the carbon dioxide diffusion coefficient and moisture field are essentially crucial to the carbonation process in SCC.

• Computers and Concrete
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• v.13 no.2
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• pp.149-171
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• 2014

This study presents the mathematical model for predicting chloride penetration into saturated concrete under non-isothermal condition. The model considers not only diffusion mechanism but also migration process of chloride ions and other chemical species in concrete pore solution such as sodium, potassium, and hydroxyl ions. The coupled multi-ionic transport in concrete is described by the Nernst-Planck equation associated with electro-neutrality condition. The coupling parameter taken into account the effect of temperature on ion diffusion obtained from available test data is proposed and explicitly incorporated in the governing equations. The coupled transport equations are solved using the finite element method. The numerical results are validated with available experimental data and the comparison shows a good agreement.

• Analytical Science and Technology
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• v.8 no.4
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• pp.663-668
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• 1995

Ion transport of a polypyrrole/chloride (PPy/Cl) film and a polypyrrole/poly(styenesulfonate) (PPy/PSS) film as a function of applied dc potential was investigated by employing electrogravimetric impedance technique and electrochemical impedance technique. The cation and anion contribution to the whole charge capacitance and the diffusion coefficients of cation and anion in a PPy/PSS film were calculated by fitting the electrogravimetric impedance data with proposed model circuit. The diffusion coefficients of $Na^+$ in a 1 M $NaClO_4$ solution are over 1 order of magnitude larger than those of $ClO{_4}^-$, and $ClO{_4}^-$ contribution to charge compensation decreases as dc potential lowers. The charge compensation of a PPy/Cl film ir a 1 M CsCl solution is carried out largely by $Cl^-$ at 0.2 V vs. Ag/AgCl and by $Cs^+$ as well as $Cl^-$ at -0.4 V.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.4
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• pp.241-251
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• 2018

The present study is carried out to examine the combined effect of heat absorption on flow model. The model consists of unsteady flow of a viscous, incompressible and electrically conducting fluid. The flow is along an impulsively started oscillating vertical plate with variable mass diffusion. The magnetic field is applied perpendicular to the plate. The fluid model under consideration has been solved by Laplace transform technique. The numerical data obtained is discussed with the help of graphs and table. The numerical values obtained for skin-friction have been tabulated. To shorten the lengthy equations in the solution some symbols have been assumed, which are mentioned in appendix. The appendix is included in the article as the last section of the manuscript.