• Journal of Electrochemical Science and Technology
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• v.8 no.4
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• pp.344-355
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• 2017

In this study, a numerical approach is adopted to investigate the effectiveness factors for distributed electrochemical reactions in thin active reaction layers of solid oxide fuel cells (SOFCs), taking into account the Butler-Volmer reaction kinetics. The mathematical equations for the electrochemical reaction and charge conduction process were formulated by assuming that the active reaction layer has a small thickness, homogeneous microstructure, and high effective electronic conductivity. The effectiveness factor is defined as the ratio of the actual reaction rate (or equivalently, current generation rate) in the active reaction layer to the nominal reaction rate. From extensive numerical calculations, the effectiveness factors were obtained for various charge transfer coefficients of 0.3-0.8. These effectiveness data were then fitted to simple correlation equations, and the resulting correlation coefficients are presented along with estimated magnitude of error.

• International Journal of Reliability and Applications
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• v.9 no.2
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• pp.141-152
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• 2008

This paper presents equations, which can be used to evaluate the failure frequency and the failure rate of a two identical component parallel redundant system in which each component can operate in its wear out period, and the failure rate of each component is exponential power distribution. The optimum maintenance interval for a two identical component parallel redundant system can be obtained using these equations. The proposed approach is presented and illustrated using several numerical examples. The optimum maintenance interval for each component in a two identical parallel redundant system will depend on factors such as: failure rate, repair and maintenance times of each component in the parallel redundant systems.

• BMB Reports
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• v.30 no.1
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• pp.7-12
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• 1997

The kinetics of the interesterification of triolein and stearic acid catalyzed by immobilized Rhizopus delemar lipase were studied in a batch operation. In order to clarify the mechanisms of this reaction, three models are discussed under various conditions in terms of the ratio of triolein and stearic acid. The rate constants involved in the proposed model were determined by combining the numerical Gauss-elemination method, and the trial-and-error method so as to fit the calculated results with the experimental data. The accuracy of the obtained rate constants was confirmed after they were substituted for simultaneous differential equations and the equations simulated using an adaptive step-size Runge-Kutta method. Finally, the model which agrees with the calculated results and the experimental data was selected.

• Journal of the Korean Vacuum Society
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• v.8 no.4B
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• pp.548-555
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• 1999

The NBI (Neutral BGeam Injection) System for the Korea Superconducting Tokamak Advanced Research (KSTAR) is composed of ion sources, neutralizers, bending magnets, ion dumps, and calorimeter. The vacuum chamber, in which all of the beam line components are enclosed, is composed of differential pumping system for the effective transfer of the neutral beams. The needed pumping speeds of each of the divided vacuum chamber and the optimized gas flow rate ot the neutralizer were calculated with the help of the particle balance equations. The minimum gas flow rate to the ion sources for producing needed beam current (120kV, 65A, 78MW), the pressure distributions in the vacuum chamber for minimizing re-ionization loss, and the beam loss rate on the beam line components were used as the input in the calculation. Also the scenario for short pulse operation was determined by analysing the time dependent equations. It showed that beam extraction during less than 0.5 sec could be made only with TMP.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.1
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• pp.31-39
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• 2007

A pedagogic model for blood flow is introduced to help medicine majors understand a simplified version of Navier-Stokes equations which is known to be a good tool for interpreting the phenomena in blood flow. The pressure gradient consists of a time-independent part known as Hagen-Poiseuille's gradient and a time-dependent part known as Sexl's, and the model formula for the volume rate of blood flow is reduced to a very simple form. For demonstration, the blood rate in human aorta system is analyzed in connection with the time-dependence of pressure gradient. It is shown for Sexl's part that the flow rate lags the pressure gradient by ${\pi}/2$, which is thought to be due to the relaxation process involved.

• Biomaterials and Biomechanics in Bioengineering
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• v.5 no.1
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• pp.51-64
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• 2020

In this study, the mathematical model that describes blood cell development in the bone marrow (i.e., hematopoiesis) has been studied via the Homotopy Perturbation Method (HPM). The results from the present work compared very well with the numerical solutions from published literature. This work has shown that the HPM is viable for solving delay differential equations born from hematopoiesis problem. The influence of the proliferating cells loss rate, time delay rate and the phase re-entry rate on the population densities of both the proliferating and resting cells were also determined through the underlined procedure.

• Journal of the Optical Society of Korea
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• v.13 no.3
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• pp.386-391
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• 2009

PSPICE circuit parameters of the blue laser diodes grown on wurtzite AlGaInN multiple quantum well structures were extracted directly from the three level rate equations. The relevant optical gain parameters were separately calculated from the self-consistent multiband Hamiltonian. The resulting equivalent circuit model for a blue laser diode was schematically presented, and its modulation characteristics, including the pulse response and the frequency response, have been demonstrated by using a conventional PSPICE.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.155-166
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• 2006

Many software reliability growth models (SRGMs) based on nonhomogeneous Poisson process (NHPP) have been developed and applied in practice. NHPP SRGMs are characterized by their mean value functions. Mean value functions are usually derived from differential equations representing the fault detection/removal process during testing. In this paper such differential equations are regarded as frameworks for generating mean value functions. Currently available frameworks are theoretically discussed with respect to capability of representing the fault detection/removal process. Then two general frameworks are proposed.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.1
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• pp.91-100
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• 1986

The nonlinear rate equations are solved analytically by using the singular perturbation method to study effects of the spontaneous emission factor and the photon lifetime on the primary resonance and the first subharmonic generation(i.e., the onset of the periocd-doubling route to chaos). By large signal modulation of Hitachi CSP laser HLP 1400, the resonance frequency shift than 100 ps with 1 GHz repetition rate are generated. The experimental observations are in reasonable agreement with the theoretical results obtained using measured parameters of the rate equations.

• The Journal of Engineering Research
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• v.3 no.1
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• pp.223-233
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• 1998

The kinetic and mechanism of the hydrothermal reaction between lime and quartz used solid state reaction equations have been investigated. Hydrothermal reaction on the starting materials was carried out in an autoclave that quartz mixed with calcium hydroxide in CaO/$SiO_2$ ratio of 0.8-1.0 for 0.5-8 hour at saturated steam pressure of $180-200^{\circ}C$. The rate of reaction was given from the ratio of uncombined lime and quartz content to the total lime and quartz content. The rate of reaction was obtained the results by the Jander's equation $[1-(1-\alpha)^{1/3}]^N=Kt$. The reaction of lime is controlled mainly by the dissolution such as N=1, and the reaction of quartz is controlled mostly by the diffusion such as $N\risingdotseq2$. The rate of hydrothermal reaction in the calcium silicate hydrates system is suggested to be determined generally by the mass transfer through the product laver formed around the reactant particles. The rate equation for whole hydrothermal reaction is shown that it is converted into the rate determining step by the diffusion from the boundary reaction such as approximately $N=1-2$.