• Macromolecular Research
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• v.11 no.5
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• pp.311-316
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• 2003

The kinetics of photoinitiated polymerization of dimethacrylate macromonomers have been studied to determine the diffusion-controlled reaction parameters using attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR). A predicted kinetic rate expression with a diffusion control factor was employed to estimate an effective rate constant and to define the reaction-controlled and diffusion-controlled regimes in the photopolymerization. An effective rate constant, k$_{e}$, can be obtained from the predicted kinetic rate expression. At the earlier stages of polymerization, the average values of kinetic rate constants do not vary during the reaction time. As the reaction conversion, $\alpha$, reaches the critical conversion, $\alpha$$_{c}$, in the predicted kinetic expression, the reaction becomes to be controlled by diffusion due to the restricted mobility of dimethacrylate macromonomers. A drop in value of effective rate constant causes a drastic decrease of reaction rate at the later stages of polymerization. By determining the effective rate constants, the reaction-controlled and diffusion-controlled regimes were properly defined even in the photopolymerization reaction system.m.m.

• Computers and Concrete
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• v.10 no.1
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• pp.79-93
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• 2012

This paper estimates theoretically the diffusion-reaction behaviour of sulfate ion in concrete caused by environmental sulfate attack. Based on Fick's second law and chemical reaction kinetics, a nonlinear and nonsteady diffusion-reaction equation of sulfate ion in concrete, in which the variable diffusion coefficient and the chemical reactions depleting sulfate ion concentration in concrete are considered, is proposed. The finite difference method is utilized to solve the diffusion-reaction equation of sulfate ion in concrete, and then it is used to simulate the diffusion-reaction process and the concentration distribution of sulfate ion in concrete. Afterwards, the experiments for measuring the sulfate ion concentration in concrete are carried out by using EDTA method to verify the proposal model, and results show that the proposed model is basically in agreement with the experimental results. Finally, Numerical example has been completed to investigate the diffusion-reaction behavior of sulfate ion in the concrete plate specimen immersed into sulfate solution.

• The Pure and Applied Mathematics
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• v.8 no.1
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• pp.47-51
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• 2001

We establish the global existence of nonnegative solutions to some reaction-diffusion equation for exponential nonlinearity for small initial data.

• The Korean Journal of Ceramics
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• v.4 no.3
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• pp.235-239
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• 1998

Ultrafine $SnO_2$ powder was prepared by the diffusion mixing gas-phase reaction of $SnCl_4$(g) and water vapor. The effects of reaction variables, such as the chloride partial pressure, the reaction temperature, and the residence time is the reactor, on the powder size were examined systematically. Calculated concentration and distribution of chemical species, using the Burke-Schumann diffusion mixing model, were compared with the experimetal results. The effects of the reaction variables on the powder size were also discussed qualitatively.

• Nuclear Engineering and Technology
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• v.49 no.5
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• pp.1019-1030
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• 2017

Diffusion is a crucial mechanism that regulates the migration of radioactive nuclides. In this study, an innovative numerical method was developed to simultaneously calculate the diffusion coefficient of both parent and, afterward, series daughter nuclides in a sequentially reactive through-diffusion model. Two constructed scenarios, a serial reaction (RN_1 ${\rightarrow}$ RN_2 ${\rightarrow}$ RN_3) and a parallel reaction (RN_1 ${\rightarrow}$ RN_2A + RN_2B), were proposed and calculated for verification. First, the accuracy of the proposed three-member reaction equations was validated using several default numerical experiments. Second, by applying the validated numerical experimental concentration variation data, the as-determined diffusion coefficient of the product nuclide was observed to be identical to the default data. The results demonstrate the validity of the proposed method. The significance of the proposed numerical method will be particularly powerful in determining the diffusion coefficients of systems with extremely thin specimens, long periods of diffusion time, and parent nuclides with fast decay constants.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.457-470
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• 2008

This paper is concerned with the robust boundary control of the chemotaxis reaction diffusion system. That is, we show that the existence of the saddle point for the robust control problem when the control and the disturbance are given by the boundary condition.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.469-478
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• 2008

This paper is concerned with the boundary control of the chemotaxis reaction diffusion system. That is, we show the existence of the solution for the chemotaxis system with the boundary control and the existence of the optimal boundary control.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.1-20
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• 2006

This paper presents the interior penalty discontinuous Galerkin finite element methods (DGFEM) for solving the rotating disk electrode problems in electrochemistry. We present results for the simple E reaction mechanism (convection-diffusion equations), the EC' reaction mechanism (reaction-convection-diffusion equation) and the ECE and $EC_2E$ reaction mechanisms (linear and nonlinear systems of reaction-convection-diffusion equations, respectively). All problems will be in one dimension.

• Bulletin of the Korean Chemical Society
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• v.21 no.12
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• pp.1213-1216
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• 2000

Localized structures with fronts connecting a Turing patterns and Hopf oscillations are found in discrete reaction-diffusion system. The Chorite-Iodide-Malonic Acid (CIMA) reaction model is used for a reaction scheme. Localized structures in discrete reaction-diffusion system have more diverse and interesting features than ones in continuous system. Various localized structures can be obtained when a single perturbation is applied with variation of coupling strength of two intermediates. Roles of perturbations are not so simple that perturbations are sources of both Turing patterns and Hopf oscillating domains, and spatial distribution of them is determined by strength of a perturbation applied initially.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.249-281
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• 2020

A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.