• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.87-95
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• 1997

In general, the positive solution to biological reaction-diffusion equations is not unique. In this paper, we state the sufficient and necessary conditions of the existence of positive solutions, and give and the proof for the uniqueness of positive solutions for a certain elliptic interacting system.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.49-58
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• 2010

In the present article we consider the diffusive Nicholson's blowflies equation with nonlocal delay incorporated into an integral convolution over all the past time and the whole infinite spatial domain $\mathbb{R}$. When the kernel function takes a special function, we construct a pair of lower and upper solutions of the corresponding travelling wave equation and obtain the existence of travelling fronts according to the existence result of travelling wave front solutions for reaction diffusion systems with nonlocal delays developed by Wang, Li and Ruan (J. Differential Equations, 222(2006), 185-232).

• 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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.2
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• pp.605-615
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• 1996

Laminar flows in which mixing and chemical reactions take place between parallel streams of reactive species are studied numerically. The governing equations for laminar flows are from two-dimensional compressible boundary-layer equations. The chemistry is a finite rate single step irreversible reaction with Arrhenius kinetics. Ignition, premixed flame, and diffusion flame regimes are found to exist in the laminar reacting mixing layer at high activation energy. At high Mach numbers, ignition occurs earlier due to the higher temperatures in the unburnt gas. In diffusion regimes, property variations affect the laminar profiles considerably and need to be included when there are large temperature differences. The maximum temperature of a laminar reacting mixing layer is almost linear with the adiabatic flame temperature at low heat release, but only weakly at high heat release.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.495-508
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• 2016

A singularly perturbed reaction-diffusion fourth-order ordinary differential equation(ODE) with discontinuous source term is considered. Due to the discontinuity, interior layers also exist. The considered problem is converted into a system of weakly coupled system of two second-order ODEs, one without parameter and another with parameter ε multiplying highest derivatives and suitable boundary conditions. In this paper a computational method for solving this system is presented. A zero-order asymptotic approximation expansion is applied in the second equation. Then, the resulting equation is solved by the numerical method which is constructed. This involves non-overlapping Schwarz method using Shishkin mesh. The computation shows quick convergence and results presented numerically support the theoretical results.

• 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.

• 한국연소학회:학술대회논문집
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• 2002.06a
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• pp.41-45
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• 2002

The zone-conditioned CMC equations are derived by taking an unconditional average of the generic conservation equations multiplied by delta and Heaviside functions in terms of mixture fraction and reaction progress variable. The resulting equations are essentially in the same form as the single zone CMC equations except for separate flow fields for burned and unburned gas. The zone-conditioned two-fluid equations are applied to a stagnating turbulent premixed flame brush of Cheng and Shepherd[5l. It is shown that the flame stretch factor is of crucial importance to accurately reproduce the measured mean reaction progress variable and conditional velocities. Further work is in progress for the relationship between surface and volume averages and extension to partially premixed combustion on the basis of a triple flame structure, e. g. in a lifted turbulent diffusion flame.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.33-34
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• 2003

• International Journal of Computer Science & Network Security
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• v.22 no.6
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• pp.91-96
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• 2022

The photocatalytic degradation of salicylic acid takes place in several stages involving coupled phenomena, such as the transport of molecules and the chemical reaction. The systems of transport equations and the photocatalytic reaction are numerically solved using COMSOL Mutiphysics (CM) simulation software. CM will make it possible to couple the phenomena of flow, the transport of pollutants (salicylic acid) by convection and diffusion, and the chemical reaction to the catalytic area (bauxite or TiO2 doped by nanoparticles). The simulation of the conversion rate allows to correctly fit the experimental results. The temporal simulation shows that the reaction reaches equilibrium after a transitional stage lasting over one minute. The outcomes of the study highlight the importance of diffusion in the boundary layer and the usefulness of injecting micro-agitation into the microchannel flow. Under such conditions, salicylic acid degrades completely.

• Journal of the Korean Chemical Society
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• v.6 no.1
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• pp.14-18
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• 1962

Solution to the diffusion layer for the first order reaction at a droping mercury electrode (D.M.E.) is presented. Equations are derived for polarographic currents for the reactions at the D.M.E. A factor which is applicable to the D.M.E. is derived, when we use the equations of the polarographic currents for the reactions at a plane electrode(P.E.), and the rate constants of the backward reactions are negligibly small. Polarographic currents from a combination of diffusions and reactions are obtained at the D.M.E. with special approximation. Rate constant for the reaction of ferrous ion with hydrogen-peroxide is determined at the D.M.E.,using the data of Kolthoff and Perry. The agreement of the equation with the data of Kolthoff and Perry for the kinetic current of ferric ion in the presence of hydrogen-peroxide is good. Ratios of diffusion layer at the D.M.E. to the diffusion layer at the P.E. are discussed and show that, when the rate constants of the backward reactions for the first order reactions are larger than 1/0.05 sec-1. and drop-time about 3 sec., these ratioes are about one.