• 공업화학
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• 제3권2호
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• pp.349-359
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• 1992

염료속에 함유된 무기염(NaCl, $Na_2SO_4$)의 선택적 제거를 위해 역확산과 역삼투를 결합한 방법과 nanofiltration(NF)을 각각 이용하였다. 역확산에 의한 염의 제거율은 염의 종류에 따라 1회(one pass)에 1~30%를 나타냈으며 염과 염료의 분리비는 10~500의 매우 큰 값을 갖는 반면 염료의 손실율은 0.3% 이하였다. 염료용액을 순환시킬수록 음이온인 $Cl^-$ 이온의 제거율이 증가하고 양이온인 $Na^+$ 이온의 제거율이 감소하는 도난투석현상이 관찰되었다. 또한 공급용액의 유속이 염의 제거에 미치는 영향을 살펴보았다. 역확산에 의해 염이 제거된 염료를 평판형 역삼투막을 사용하여 농축하였으며 $Cl^-$ 이온의 배제율을 solution-diffusion 모델식에 적용하였다 2회의 Diafiltration(DF)을 수행한 NF에서도 역확산에서와 마찬가지로 도난투석에 의해 $Cl^-$ 이온의 배제율 감소와 음배제율을 관찰하였다. 특히 두번째 DF에서 도난투석의 효과는 더욱 크게 나타났다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권1호
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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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• 제33권3호
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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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• 제16권1_2호
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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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• 제32권3호
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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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• 제22권1호
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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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• 제15권5호
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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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• 제13권2호
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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.

• 분석과학
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• 제8권4호
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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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• 제22권4호
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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.