• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.221-237
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• 2013

In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction-diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.583-599
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• 2018

In this paper, we are concerned with the existence of random dynamics for stochastic non-autonomous reaction-diffusion equations driven by a Wiener-type multiplicative noise defined on the unbounded domains.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.125-141
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• 2003

This paper treats the conditions for the existence and stability properties of stationary solutions of reaction-diffusion equations of Gierer-Meinhardt type, subject to Neumann boundary data. The domains in which diffusion takes place are of three types: a regular hexagon, a rectangle and an isosceles rectangular triangle. Considering one of the relevant features of the domains as a bifurcation parameter it will be shown that at a certain critical value a diffusion driven instability occurs and Turing bifurcation takes place: a pattern emerges.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1035-1054
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• 2010

We consider a mixed type singularly perturbed one dimensional elliptic problem with discontinuous source term. The domain under consideration is partitioned into two subdomains. A convection-diffusion and a reaction-diffusion type equations are posed on the first and second subdomains respectively. Two hybrid difference schemes on Shishkin mesh are constructed and we prove that the schemes are almost second order convergence in the maximum norm independent of the diffusion parameter. Error bounds for the numerical solution and its numerical derivative are established. Numerical results are presented which support the theoretical results.

• 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.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.277-302
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• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• Bulletin of the Korean Chemical Society
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• v.27 no.10
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• pp.1659-1663
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• 2006

A many-body master equation is constructed by incorporating stochastic terms responsible for chemical reactions into the many-body Smoluchowski equation. Two forms of Langevin-type of memory equations describing the time evolution of dynamical variables under the influence of time-independent perturbation with an arbitrary intensity are derived. One form is convenient in obtaining the dynamics approaching the steady-state attained by the perturbation and the other in describing the fluctuation dynamics at the steady-state and consequently in obtaining the linear response of the system at the steady-state to time-dependent perturbation. In both cases, the kinetics of statistical averages of variables is found to be obtained by analyzing the dynamics of time-correlation functions of the variables.

• Journal of the Semiconductor & Display Technology
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• v.19 no.1
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• pp.29-35
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• 2020

The cure characteristics of three kinds of naphthalene type epoxy resins(NET-OH, NET-MA, NET-Epoxy) with a 2-methyl imidazole(2MI) catalyst were investigated for preparing sheet epoxy molding compound(SEMC) for wafer level package(WLP) applications, comparing with diglycidyl ether of bisphenol-A(DGEBA) and 1,6-naphthalenediol diglycidyl ether(NE-16) epoxy resin. The cure kinetics of these systems were analyzed by differential scanning calorimetry with an isothermal approach, and the kinetic parameters of all systems were reported in generalized kinetic equations with diffusion effects. The NET-OH epoxy resin represented an n-th order cure mechanism as like NE-16 and DGEBA epoxy resins, however, the NET-MA and NET-Epoxy resins showed an autocatalytic cure mechanism. The NET-OH and NET-Epoxy resins showed higher cure conversion rates than DGEBA and NE-16 epoxy resins, however, the lowest cure conversion rates can be seen in the NET-MA epoxy resin. Although the NETEpoxy and NET-MA epoxy resins represented higher cure reaction conversions comparing with DGEBA and NE-16 resins, the NET-OH showed the lowest cure reaction conversions. It can be figured out by kinetic parameter analysis that the lowest cure conversion rates of the NET-MA epoxy resin are caused by lower collision frequency factor, and the lowest cure reaction conversions of the NET-OH are due to the earlier network structures formation according to lowest critical cure conversion.

• Journal of the Semiconductor & Display Technology
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• v.13 no.4
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• pp.27-32
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• 2014

The cure properties of self-extinguishing epoxy resin systems with different charge transfer type latent catalysts were investigated, which are composed of YX4000H as a biphenyl epoxy resin, MEH-7800SS as a hardener, and charge transfer type latent catalysts. We designed and used five kinds of charge transfer type latent catalyst and compared to epoxy resin systems with Triphenylphosphine-Benzoquinone(TPP-BQ) as reference system. The cure kinetics of these systems were analyzed by differential scanning calorimetry with an isothermal approach, the kinetic parameters of all systems were reported in generalized kinetic equations with diffusion effects. The epoxy resin systems with Triphenylphosphine-Quinhydrone(TPP-QH), Triphenylphosphine-Benzanthrone(TPP-BT) and Triphenylphosphine-Anthrone(TPP-AT) as a charge transfer type latent catalyst showed a cure conversion rate of equal or higher rate than those with TPP-BQ. These systems with TPP-QH and Triphenylphosphine-Tetracyanoethylene(TPP-TCE) showed a critical cure reaction conversion of equal or higher conversion than those with TPP-BQ. The increases of cure conversion rates could be explained by the decrease of the activation energy of these epoxy resin systems. It can be considered that the increases of critical cure reaction conversion would be dependent on the crystallinity of the biphenyl epoxy resin systems.

• Journal of the Semiconductor & Display Technology
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• v.16 no.2
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• pp.19-26
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• 2017

The cure properties of ethoxysilyl bisphenol A type epoxy resin (Ethoxysilyl-DGEBA) systems with different hardeners were investigated, comparing with DGEBA and Diallyl-DGEBA epoxy resin systems. The cure kinetics of these systems were analyzed by differential scanning calorimetry with an isothermal approach, and the kinetic parameters of all systems were reported in generalized kinetic equations with diffusion effects. The Ethoxysilyl-DGEBA epoxy resin system showed lower cure conversion rates than DGEBA and Diallyl-DGEBA epoxy resin systems. The conversion rates of these epoxy resin systems with DDM hardener are lower than those with HF-1M hardener. It can be considered that the optimum hardener for Ethoxysilyl-DGEBA epoxy resin system is Phenol Novolac type. These lower cure conversion rates in the Ethoxysilyl-DGEBA epoxy resin systems could be explained by the retardation of reaction molecule movements according to the formation of organic-inorganic hybrid network structure by epoxy and ethoxysilyl group in Ethoxysilyl- DGEBA epoxy resin system.