• Journal of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.377-385
• /
• 2002

In this paper, we concentrate on the uniquencess of the positive solution for the general elliptic system $\Delta$u+u($g_1$(u)-$g_2$(v))=0 $\Delta$u+u($h_1$(u)-$h_2$(v))=0 in$R_{+}$ $\times$ $\Omega$, $u\mid\partial\Omega = u\mid\partial\Omega = 0$. This system is the general model for the steady state of a competitive interacting system. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.

• 제어로봇시스템학회:학술대회논문집
• /
• 1992.10b
• /
• pp.100-105
• /
• 1992

A mathematical model is developed for a CSTR in which free radical solution polymerization of methyl methacrylate(MMA) takes place. It turns out that five ordinary differential equations are to be treated simultaneously in order to predict the reactor performance. Although the reaction proceeds under the conditions of relatively low temperature and pressure, the system shows very complex bifurcation features due to the diffusion limitation (gel effect) and the temperature dependence of the kinetic parameters and physical properties. The effects of various system parameters on the reactor performance as well as on the polymer properties are investigated by using the bifurcation analysis. The application of the singularity theory enables us to divide the parameter space into several different regions, in each of which the system takes a unique steady state structure. Under certain circumstances, complex dynamic features such as HB points and limit cycles are observed and these should be taken into consideration in the reactor design.

• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.49-65
• /
• 2006

A robust numerical method for a singularly perturbed second-order ordinary differential equation having two parameters with a discontinuous source term is presented in this article. Theoretical bounds are derived for the derivatives of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are provided to illustrate the convergence of the numerical approximations.

• 한국전산유체공학회:학술대회논문집
• /
• 1997.10a
• /
• pp.106-112
• /
• 1997

The effects of radiative heat transfer are investigated in a turbulent combustion flow field with highly non-adiabatic flames. Turbulent combustion is modeled by the $k-{\varepsilon}-g$ model and a one step irreversible reaction scheme for the combustion chemistry. The radiative trasport equation is solved by the finite volume method considering the radiative transfer from $CO_2,\;H_{2}O$ and soot only. Gray gas is assumed to calculate the radiative properties of $CO_2\;and\;H_2O$. A two-equation soot formation model is applied to predict soot volume faction distribution. All equations are solved in a coupled manner and the numerical results are compared with available experimental data.

• Journal of the Korean Society of Combustion
• /
• v.3 no.2
• /
• pp.51-63
• /
• 1998

Air-assisted atomizer flames are investigated numerically to study spray structures in nonburning and burning conditions based on experimental data. A PDA is used to measure droplet size, velocity, and number density for both nonburning and burning spray. Computations utilize time-averaged gas-phase equations and $k-{\varepsilon}$ turbulence model for simplicity. The major features of the liquid-phase model are that a SSF approach is used to represent the effect of gas-phase turbulence on droplet trajectories and vaporization, an infinite-diffusion model is employed to represent the transient liquid-phase process. Computation and experiment results show that the droplet acceleration and evaporation proceed quickly in near the atomizer, characterizing high number densities and a strong convective effect. The primary combustion zone, however, is dorminated by the gas phase reaction and exhibits a sheath combustion.

• Nuclear Engineering and Technology
• /
• v.32 no.6
• /
• pp.549-558
• /
• 2000

A transient model for hydrogen generation in molten metal-water interactions was developed with separate models for two stages of coarse mixing and stratification. The model selves the mechanistic equations (heat and mass transfer correlation, heat conduction equation and the concentration diffusion equation) of each stage with non-zero boundary conditions. Using this model, numerical simulations were performed for single droplet experiments in the Argonne National Laboratory tests and for FITS tests that simulated dynamic fragmentation and stratification. The calculation results of hydrogen generation showed better agreement to the experiment data than those of previous works. It was found from the analyses that the steam concentration to be reached at the reaction front might be the main constraint to the extent of the metal droplet oxidized. Also, the hydrogen generation rate in the coarse mixing stage was the higher than that in the stratification stage. The particle size was the most important factor in the coarse mixing stage to predict the amount of hydrogen generation.

• Proceedings of the Korean Nuclear Society Conference
• /
• 1996.05a
• /
• pp.21-27
• /
• 1996

KAERI has recently developed the nuclear design code MASTER for the application to reactor physics analyses for pressurized water reactors. Its neutronics model solves the space-time dependent neutron diffusion equations with the advanced nodal methods. The major calculation categories of MASTER consist of microscopic depletion, steady-state and transient solution, xenon dynamics, adjoint solution and pin power and burnup reconstruction. The MASTER validation analyses, which are in progress aiming to submit the Uncertainty Topical Report to KINS in the first half of 1996, include global reactivity calculations and detailed pin-by-pin power distributions as well as in-core detector reaction rate calculations. The objective of this paper is to give an overall description of the CASMO/MASTER code system whose verification results are in details presented in the separate papers.

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

• East Asian mathematical journal
• /
• v.39 no.3
• /
• pp.271-278
• /
• 2023

We consider a 1-dimensional reaction diffusion equation with the following boundary conditions arising in a theory of the thermal explosion {-u"(t) = λf(u(t)), t ∈ (0, l), -u'(0) + C(0)u(0) = 0, u'(l) + C(l)u(l) = 0, where C : [0, ∞) → (0, ∞) is a continuous and nondecreasing function, λ > 0 is a parameter and f : [0, ∞) → (0, ∞) is a continuous function. We establish the extension of Quadrature method introduced in [8]. Using this extension, we provide numerical results for models with a typical function of f and C in a thermal explosion theory, which verify the existence, uniqueness and multiplicity results proved in [6].

• 한국신재생에너지학회:학술대회논문집
• /
• 2008.05a
• /
• pp.33-36
• /
• 2008

The transient behavior of a passive air breathing direct methanol fuel cell (DMFC) operated on vapor-feeding mode is studied in this paper. It generally takes 30 minutes after starting for the cell response to come to its steady-state and the response is sometimes unstable. A mathematical dynamic one-dimensional model for simulating transient response of the DMFC is presented. In this model a DMFC is decomposed into its subsystems using lumped model and divided into five layers, namely the anodic diffusion layer, the anodic catalyst layer, the proton exchange membrane (PEM), the cathodic catalyst layer and the cathodic diffusion layer. All layers are considered to have finite thickness, and within every one of them a set of differential-algebraic governing equations are given to represent multi-components mass balance, such as methanol, water, oxygen and carbon dioxide, charge balance, the electrochemical reaction and mass transport phenomena. A one-dimensional, isothermal and mass transport model is developed that captures the coupling between water generation and transport, oxygen consumption and natural convection. The single cell is supplied by pure methanol vapor from a methanol reservoir at the anode, and the oxygen is supplied via natural air-breathing at the cathode. The water is not supplied from external source because the cell uses the water created at the cathode using water back diffusion through nafion membrane. As a result of simulation strong effects of water transport were found out. The model analysis provides several conclusions. The performance drop after peak point is caused by insufficiency of water at the anode. The excess water at the cathode makes performance recovery impossible. The undesired crossover of the reactant methanol through the PEM causes overpotential at the cathode and limits the feeding methanol concentration.