• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.295-309
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• 2010

In this paper, we study delayed high-order Cohen-Grossberg neural networks with reaction-diffusion terms and Neumann boundary conditions. By using inequality techniques and constructing Lyapunov functional method, some sufficient conditions are given to ensure the existence and convergence of the periodic oscillatory solution. Finally, an example is given to verify the theoretical analysis.

• Bulletin of the Korean Chemical Society
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• v.34 no.5
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• pp.1454-1456
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• 2013

The fluctuations in concentrations of reactants dominate the long-time dynamics of the single (A + A ${\rightarrow}$ 0) and two species (A + B ${\rightarrow}$ 0) diffusion-influenced annihilation reactions. Although hierarchical Smoluchowski approaches can provide a systematic and flexible framework to deal with the fluctuation effects, their results are too complicated to be analytically solved. For the efficient numerical calculation of the complicated fluctuation effect terms, we show that the presented point particle approximation is not only practical but also quite accurate for most conditions in diffusion-influenced reaction systems.

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.925-928
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• 2012

The accurate expression for the steady-state velocity of an irreversible enzyme-catalyzed reaction obtained by Shin and co-workers (J. Chem. Phys. 2001, 115, 1455) is generalized to allow for the rebinding of the product. The amplitude of the power-law ($t^{-1/2}$) relaxation of the free- and bound-enzyme concentrations to steady-state values is expressed in terms of the steady-state velocity and the intrinsic (chemical) rate constants. This result is conjectured to be exact, even though our expression for the steady-state velocity in terms of microscopic parameters is only approximate.

• 한국연소학회:학술대회논문집
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• 1998.10a
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• pp.155-164
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• 1998

Numerical analysis was performed with multicomponent transport properties and detailed reaction mechanisms for axisymetric 2-D CH4 jet diffusion, partial premixed, premixed flame. Calculations were carried out twice with C2-Full Mechanism including prompt NO reaction in addition to the above C2-Thermal NO Mechanism. The role of thermal NO mechanism and prompt NO mechanism on each flame's NO production is investigated by using the numerical result. The NOx production of each flame were evaluated Quantitatively in terms of the NOx emission index

• 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.

• Journal of Advanced Navigation Technology
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• v.22 no.6
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• pp.648-653
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• 2018

Analysis of a specific wavelength band of a video signal is an old research field. However, studies on the analysis of signals having the characteristics of a specific wavelength band or the generation of samples have been conducted actively in recent years. In this paper, we analyze the signal of digital halftoned image. The interpretation of halftoning in terms of signals was first made by Ulichney. We have come to the view that the signal characteristics between pixels used for half toning are good for blue noise. Lau has developed a halftoning method that uses green-noise characteristics by using output-dependent feedback as an error diffusion method. Jho has developed a method for producing halftoned images using a reaction diffusion model. In this paper, we analyze reaction diffusion halftoning in terms of signal to show green noise and compare it with existing green noise half tone.

• Journal of the Korean Society of Combustion
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• v.4 no.2
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• pp.97-108
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• 1999

This numerical study was to investigate the effect of $CO_2$ addition on the structures and NOx formation characteristics in $CH_4$ counterflow diffusion flame. The importance of radiation effect was identified and $CO_2$ addition effect was investigated in terms of thermal and chemical reaction effect. Also the causes of NOx reduction were clarified by separation method of each formation mechanisms. The results were as follows : The radiation effect was intensified by $CO_2$ addition. Thermal effect mainly contributed to the changes in flame structure and the amount of NO formation but the chemical reaction effect also cannot be neglected. The reduction of thermal NO was dominant with respect to reduction rate, but that of prompt NO was dominant with respect to total amount.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.441-447
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• 1999

A free boundary problem is derived from a singular limit system of a reaction diffusion equation whose reaction terms are bistable type. In this paper, we shall consider a free boundary problem with two layers satisfying the zero flux boundary condition and shall show that the Hopf bifurcation can not occur as a parameter varies.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.11 no.4
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• pp.160-165
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• 2001

The effects of various metals on Field Aided Lateral Crystallization (FALC) behaviors of amorphous silicon (a-Si) were investigated. Under an influence of electric field, metals such s Cu, Ni and Co were found to fasten the lateral crystallization toward a metal-free region, exhibiting a typical FALC behavior while the lateral crystallization of a-Si was not obvious for Pd. However, Au, Al and Cr did not induce the lateral crystallization of a-Si in metal-free region. Such phenomenological differences in various metals were studied in terms of dominant diffusing species (DDS) in the reaction between metal and Si. It was judged that the applied electric field enhanced the crystallization velocity by accelerating the diffusion of metal atoms since the occurrence of lateral crystallization would be strongly dependent on the diffusion of metal atoms than that of Si atoms. Therefore, it was concluded that he only metal-dominant diffusing species in the reaction between metal and Si results in the crystallization of a-Si in metal-free region.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.