• 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.

• 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.

• Macromolecular Research
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• v.10 no.5
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• pp.259-265
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• 2002

The cure kinetics of blends of epoxy (DGEBA, diglycidyl ether of bisphenol A)/anhydride resin with polyamide copolymer, poly(dimmer acid-co-alkyl polyamine), were studied using differential scanning calorimetry (DSC) under isothermal condition. On increasing the amount of polyamide copolymer in the blends, the reaction rate was increased and the final cure conversion was decreased. Lower values of final cure conversions in the epoxy/(polyamide copolymer) blends indicate that polyamide hinders the cure reaction between the epoxy and the curing agent. The value of the reaction order, m, for the initial autocatalytic reaction was not affected by blending polyamide copolymer with epoxy resin, and the value was approximately 1.3, whereas the reaction order, n, for the general n-th order of reaction was increased by increasing the amount of polyamide copolymer in the blends, and the value increased from 1.6 to 4.0. A diffusion-controlled reaction was observed as the cure conversion increased and the rate equation was successfully analyzed by incorporating the diffusion control term for the epoxy/anhydride/(polyamide copolymer) blends. Complete miscibility was observed in the uncured blends of epoxy/(polyamide copolymer) up to 120 $^{\circ}C$, but phase separations occurred in the early stages of the curing process at higher temperatures than 120 "C. During the curing process, the cure reaction involving the functional group in polyamide copolymer was detected on a DSC thermogram.gram.

• 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.

• Journal of Korea Foundry Society
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• v.26 no.1
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• pp.27-33
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• 2006

Phase evolutions involving nucleation stages together with diffusional growth have been examined in order to provide a guideline for determining rate limiting stages during phase evolutions. In multiphase materials systems in coatings, composites or multilayered structures, diffusion treatments often result in the development of metastable/intermediate phases at the reaction interfaces. The development of metastable phases during solid state interdiffusion demonstrates that the nucleation reaction can be one controlling factor. Also, the concentration gradient and the relative magnitudes of the component diffusivities provide a basis for a phase selection and the application of a kinetic bias strategy in the phase selection. For multicomponent alloy systems, the identification of the operative diffusion pathway is central to control phase formation. Experimental access to the nucleation and growth stage is discussed in thin film multi layers and bulk samples.

• Proceedings of the International Microelectronics And Packaging Society Conference
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• 2001.11a
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• pp.134-137
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• 2001

The cure kinetics of a cycloalipatic epoxy / anhydride / Co(II) system for a no-flow underfill encapsulant, has been studied by using a differential scanning calorimetry(DSC) under isothermal and dynamic conditions over the temperature range of $160^{\circ}C ~220^{\circ}C$. The kinetic analysis was carried out by fitting dynamic/isothermal heating experimental data to the kinetic expressions to determine the reaction parameters, such as order of reaction and reaction constants. Diffusion-controlled reaction has been observed as the cure conversion increases and successfully analyzed by incorporating the diffusion control term into the rate equation. The prediction of reaction rates by the model equation corresponded well to experimental data at all temperature.

• Korean Chemical Engineering Research
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• v.52 no.6
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• pp.821-825
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• 2014

Steam gasification of sawdust char was performed in a thermobalance reactor at high temperature. Gasification temperature was changed from $850^{\circ}C$ to $1400^{\circ}C$ and steam partial pressure was 0.3, 0.5 and 0.7 atm. Three models of gas-solid reaction were applied to the reaction kinetics analysis and modified volumetric model was an appropriate model. Reaction control regime and diffusion control regime were distinct depending on the temperature. Apparent activation energy and pre-exponential factors for both of the regimes were evaluated and the effects of steam partial pressure were examined. $H_2$ concentration in the produced gas was two times higher than that of CO due to the gasification accompanying by the water gas shift reaction.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.747-752
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• 1994

Ussing's flux ratio theorem (1978) reflects a reciprocal relationship behavior between the unidirectional fluxes in asymmetric steady diffusion-convection in a membrane slab. This surprising result has led to many subsequent studies in a wide range of applications, in particular involving linear models of time dependent problems in biology and physiology. Ussing's theorem and its extensions are inherently linear in character. It is of considerable interest to ask to what extent these results apply, if at all, in situations involving, for example, nonlinear reaction. A physiologically interesting situation has been considered by Weisiger et at. (1989, 1991, 1992) and by McNabb et al. (1990, 1991) who studied the role of albumin in the transport of ligands across aqueous diffusion barriers in a liver membrane slab. The results are that there exist reciprocal relationships between unidirectional fluxes in the steady state, although albumin is chemically interacting in a nonlinear way of the diffusion processes. However, the results do not hold in general at early times. Since this type of study first started, it has been speculated about when and how the Ussing's flux ratio theorem fails in a general diffusion-convection-reaction system. In this paper we discuss the validity of Ussing-type theorems in time-dependent situations, and consider the limiting time behavior of a general nonlinear diffusion system with interaction.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.04a
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• pp.214-217
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• 2004

The cure kinetics of blends of epoxy(tetraglycidyl-4,4'-diaminodiphenylmethane ; TGDDM)/curing agent(diaminodiphenyl sulfone ; DDS) resin with amine terminated polyetherimide-CTBN-amine terminated polyetherimide triblock copolymer(ABA) were studied using differential scanning calorimetry under isothermal conditions to determine the reaction parameters such as activation energy and reaction constants. By increasing the amount of ABA in the blends, the final cure conversion was decreased. Lower values of the final cure conversions in the epoxy/ABA blends indicated that ABA hinders the cure reaction between the epoxy and curing agents. 1be value of the reaction order, m, for the initial autocatlytic reaction was not affected by blending ABA with epoxy resin, and the value was approximately 1.0. The value of n for the nth order component in the autocatalytic analysis was increased by increasing the amount of ABA in the blends, and the value increased from 2.0-3.4. A diffusion controlled reaction was observed as the cure conversion increased and the rate equation was successfully analyzed by incorporating the diffusion control term for the epoxy/DDS/ABA blends.