• Bulletin of the Korean Chemical Society
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• v.13 no.4
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• pp.398-404
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• 1992

We have investigated the kinetics of diffusion-influenced bimolecular reactions in which one reactant has an internal mode, called the gating mode, that activates or deactivates its reactivity intermittently. The rate law and an expression for the time-dependent rate coefficient have been obtained from the general formalism based on the hierarchy of kinetic equations involving reactant distribution functions. The analytic expression obtained for the steady-state reaction rate constant coincides with the one obtained by Szabo et al., who derived the expression by employing the conventional concentration-gradient approach. For the time-dependent reaction rate coefficient, we obtained for the first time an exact analytic expression in the Laplace domain which was then inverted numerically to give the time-domain results.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.591-612
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• 2021

In this paper, a uniformly convergent numerical scheme is designed for solving singularly perturbed reaction-diffusion problems. The problem is converted to an equivalent weak form and then a Galerkin finite element method is used on a piecewise uniform Shishkin mesh with linear basis functions. The convergence of the developed scheme is proved and it is shown to be almost fourth order uniformly convergent in the maximum norm. To exhibit the applicability of the scheme, model examples are considered and solved for different values of a singular perturbation parameter ε and mesh elements. The proposed scheme approximates the exact solution very well.

• Journal of the Semiconductor & Display Technology
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• v.23 no.2
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• pp.60-64
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• 2024

The threshold voltage shift in thin-film transistors (TFTs) is modeled using stretched-exponential (SE) and stretched-hyperbola (SH) functions. These models are derived by introducing empirical parameters into reaction rate equations that describe defect generation or charge trapping caused by hydrogen diffusion in the dielectric or interface. Separately, the dielectric relaxation phenomena are also described by the same reaction rate equations based on defect diffusion. Dielectric relaxation was initially modeled using the SE model, and various models have been proposed using fractional calculus. In this study, the characteristics of the threshold voltage shift and the dielectric relaxation phenomena are compared and analyzed to explore the applicability of analytical models used in the field of dielectric relaxation, in addition to the conventional SE and SH models.

• 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.

• Polymer(Korea)
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• v.28 no.2
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• pp.121-127
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• 2004

The instantaneous removal of ethylene glycol is very important fur obtaining high molecular weight polymer because of the reversibility of the polycondensation reaction of poly(ethylene naphthalate)(PEN). In this study, we investigated the mass transfer phenomena in the thin film of PEN oligomer where the polycondensation reaction took place at 280$^{\circ}C$ and under 0.1mmHg. In case of less than 0.025cm film thickness the mass transfer resistance through the thin film of the polymer melt was not so high that the overall reaction rate was governed only by the polycondenstion reaction. Both the mass transfer model and the diffusion model predicted the experimenatal data well but the diffusion model showed faster reaction rate in the low molecular weight range than the mass transfer model . It was estimated from the two models that the diffusivity was 4.7${\times}$10$\^$-6/$\textrm{cm}^2$/sec and the mass transfer coefficient was 1.4 ${\times}$10$\^$-4/cm/sec both of which were smaller than In case of poly(ethylene terephthalate).

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.17-26
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• 2002

A stability analysis of a non-linear prey-predator system under the influence of one dimensional diffusion has been investigated to determine the nature of the bifurcation point of the system. The non-linear bifurcation analysis determining the steady state solution beyond the critical point enables us to determine characteristic features of the spatial inhomogeneous pattern arising out of the bifurcation of the state of the system.

• 한국연소학회:학술대회논문집
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• 2000.12a
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• pp.229-235
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• 2000

Soot formation characteristics in counterflow diffusion flames of ethylene/propane/nitrogen mixtures have been studied experimentally to investigate the soot formation mechanism. The effect of HACA reaction on PAH and soot growth has been experimentally investigated by using 2-D planar LII and PAH LIF techniques.

• Journal of the Korean Ceramic Society
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• v.18 no.2
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• pp.79-82
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• 1981

SiC powder was heated in air over the temperature range of 1100-135$0^{\circ}C$. $\beta$-cristobalite was formed to cover the surfaces of SiC particles by the reaction: $SiC(s)+20_2(g)=SiO_2(s)+CO_2(g)$. It is assumed that the diffusion of oxygen ion through the formed surface layer of $\beta$-cristobalite controls the oxidation of the SiC particles. The diffusion coefficient of oxygen ion through the $\beta$-cristobalite layer was obtained as the following equation: $D=3.84{\times}10^{-17}$exp(-14.7/RT)

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1817-1828
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• 2017

We give a simple and direct proof of the characterization of positivity preserving semi-flows for ordinary differential systems. The same method provides an abstract result on a class of evolution systems containing reaction-diffusion systems in a bounded domain of ${\mathbb{R}}^n$ with either Neumann or Dirichlet homogeneous boundary conditions. The conditions are exactly the same with or without diffusion. A similar approach gives the optimal result for invariant rectangles in the case of Neumann conditions.

• 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.