• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.699-713
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• 2022

This paper proposes a hybrid successive over-relaxation iterative method for the numerical solution of a nonlinear diffusion in a one-dimensional porous medium. The considered mathematical model is discretized using a computational complexity reduction scheme called half-sweep finite differences. The local truncation error and the analysis of the stability of the scheme are discussed. The proposed iterative method, which uses explicit group technique and modified successive over-relaxation, is formulated systematically. This method improves the efficiency of obtaining the solution in terms of total iterations and program elapsed time. The accuracy of the proposed method, which is measured using the magnitude of absolute errors, is promising. Numerical convergence tests of the proposed method are also provided. Some numerical experiments are delivered using initial-boundary value problems to show the superiority of the proposed method against some existing numerical methods.

• Computers and Concrete
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• v.17 no.1
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• pp.53-66
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• 2016

Currently, most of the investigations on chloride diffusion were based on the experiments and simulations concerning single cation type chlorides. Chloride diffusion associated with dual or multi cation types was rarely studied. In this paper, several groups of diffusion experiments are conducted using chloride solutions containing single, dual and multi cation types. A multi-ionic model is also proposed to simulate the chloride diffusion behavior in the experimental tests. The MATLAB software is used to numerically solve the nonlinear PDEs in the multi-ionic model. The experimental and simulated results show that the chloride diffusion behavior associated with different cation types is significantly different. When the single cation type chlorides are adopted, it is found that the bound rates of chloride ions combined with divalent cations are greater than those combined with monovalent cations. When the dual/multi cation type chlorides are adopted, the chloride bound rates increase with the $Ca^{2+}/Mg^{2+}$ percentage in the source solutions. This evidence indicates that the divalent cations would markedly enhance the chloride binding capacity and reduce the chloride diffusivity. Moreover, on the basis of the analysis, it is also found that the complicated cation types in source solutions are beneficial to reducing the chloride diffusivity.

• Computers and Concrete
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• v.8 no.3
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• pp.343-355
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• 2011

This paper presented the model to predict the chloride diffusion coefficient in tension zone of plain concrete under flexural cyclic load. The fictitious crack based analytical model was used together with the stress degradation law in cracked zone to predict crack growth of plain concrete beams under flexural cyclic load. Then, under cyclic load, the chloride diffusion, in the steady state and one dimensional regime, through the tension zone of the plain concrete beam, in which microcracks were formed by a large number of cycles, was simulated with assumptions of continuously straight crack and uniform-size crack. The numerical analysis in terms of the chloride diffusion coefficient, $D_{tot}$, normalized $D_{tot}$, crack width and crack length was issued as a function of the load cycle, N, and load level, SR. The nonlinear model as regarding with the chloride diffusion coefficient in tension zone and the load level was proposed. According to this model, the chloride diffusion increases with increasing load level. The predictions using model fit well with experimental data when we adopted suitable crack density and tortuosity parameter.

• Current Optics and Photonics
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• v.1 no.6
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• pp.587-597
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• 2017

The extraction of the valid measurement region from the interference fringe pattern is a significant step when measuring gear tooth flank form deviation with grazing incidence interferometry, which will affect the measurement accuracy. In order to overcome the drawback of the conventionally used method in which the object image pattern must be captured, an improved segmentation approach is proposed in this paper. The interference fringe patterns feature, which is smoothed by the nonlinear diffusion, would be extracted by the structure tensor first. And then they are incorporated into the vector-valued Chan-Vese model to extract the valid measurement region. This method is verified in a variety of interference fringe patterns, and the segmentation results show its feasibility and accuracy.

• Nuclear Engineering and Technology
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• v.41 no.7
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• pp.885-892
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• 2009

This manuscript will discuss a numerical method where the six equations of two-phase flow, the solid heat conduction equations, and the two equations that describe neutron diffusion and precursor concentration are solved together in a tightly coupled, nonlinear fashion for a simplified model of a nuclear reactor core. This approach has two important advantages. The first advantage is a higher level of accuracy. Because the equations are solved together in a single nonlinear system, the solution is more accurate than the traditional "operator split" approach where the two-phase flow equations are solved first, the heat conduction is solved second and the neutron diffusion is solved third, limiting the temporal accuracy to $1^{st}$ order because the nonlinear coupling between the physics is handled explicitly. The second advantage of the method described in this manuscript is that the time step control in the fully implicit system can be based on the timescale of the solution rather than a stability-based time step restriction like the material Courant limit required of operator-split methods. In this work, a pilot code was used which employs this tightly coupled, fully implicit method to simulate a reactor core. Results are presented from a simulated control rod movement which show $2^{nd}$ order accuracy in time. Also described in this paper is a simulated rod ejection demonstrating how the fastest timescale of the problem can change between the state variables of neutronics, conduction and two-phase flow during the course of a transient.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.15 no.1
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• pp.24-29
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• 2002

In this paper, the microstructure and the dielectric properties of Sr$\_$1-x/CaxTiO$_3$(0$\leq$x$\leq$0.2)-based grain boundary layer ceramics were investigated. The sintering temperature and time were 1420∼152 0$\^{C}$ and 4 hours in N$_2$ gas, respectively. The average grain size and the lattice constant were decreased with increasing content of Ca, but the average grain size was increased with increase of sintering temperature. The second phase foamed by the thermal diffusion of CuO from the surface leads to verb high apparent dielectric constant, $\xi$$\_$r/>50000 and low dielectric loss, tan$\delta$<0.05. X-ray diffraction patterns of Sr$\_$1-x/CaxTiO$_3$ exhibited cubic structure, and the peaks shifted upward and the peak intensity were decreased with x. This is due to the lattice contraction as Sr is replaced by Ca with a smaller ionic radius. The specimens treated thermal diffusion for 2hrs in 1150$\^{C}$ exhibited nonlinear current-voltage characteristic, and its nonlinear coefficient(a) was overt 7.

• The Journal of Bigdata
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• v.7 no.1
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• pp.193-212
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• 2022

The Bass Diffusion Model is one of the most successful models in marketing research, and management science in general. Since its publication in 1969, it has guided marketing research on diffusion. This paper illustrates the usage of the Bass diffusion model, using mobile cellular subscription diffusion as a context. We fit the bass diffusion model to three large developed markets, South Korea, Japan, and China, and the emerging markets of Vietnam, Thailand, Kazakhstan, and Mongolia. We estimate the parameters of the bass diffusion model using the nonlinear least square method. The diffusion of mobile cellular subscriptions does follow an S-curve in every case. After acquiring m, p, and q parameters we use k-Means Cluster Analysis for grouping countries into three groups. By clustering countries, we suggest that diffusion rates and patterns are similar, where countries with emerging markets can follow in the footsteps of countries with developed markets. The purpose was to predict the timing and the magnitude of the market maturity and to determine whether the data follow the typical diffusion curve of innovations from the Bass model.

• Journal of the Korean Society of Combustion
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• v.22 no.2
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• pp.19-26
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• 2017

An experimental study investigates the flame response characteristics of jet-diffusion flame and premixed flame. The experiment was conducted while varying the amplitude. Flame lengths were quantified for OH chemiluminescence measurement and compared with the result of the flame transfer function. Flame length and flame velocity perturbation were normalized and compared with the result of the flame transfer function. The comparison results appear that velocity perturbation and flame length oscillation of premixed flame show linear behaviors on the other hand jet-diffusion flame, amplitudes are more thant 0.20, shows nonlinear behaviors of flame velocity perturbation and flame length oscillation.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.9
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• pp.1185-1191
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• 1999

Radiation-induced oscillatory instability in diffusion flames is numerically investigated with nonlinear dynamics considered. As the simplest flame model, a diffusion flame established in the stagnant mixing layer is employed with optically thin gas-phase radiation and unity Lewis numbers for all species. Attention is focused on the radiation-induced extinction regime, which occurs at large $Damk\ddot{o}hler$ number. Once the steady flame structure is obtained for a prescribed value of the initial $Damk\ddot{o}hler$ number, transient solution of the flame is calculated after a finite amount of the $Damk\ddot{o}hler$-number perturbation is imposed on the steady flame. Transient evolution of the flame exhibits three types of flame-evolution behaviors, namely decaying oscillatory solution, diverging solution to extinction and stable limit-cycle solution. A dynamic extinction boundary is identified for laminar flamelet library.

• Journal of the Korean GEO-environmental Society
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• v.7 no.1
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• pp.41-53
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• 2006

In this study, estimation of nonlinear adsorption isotherms(Langmuir & Freundlich adsorption isotherm) and advection-dispersion model parameters was conducted using genetic algorithm(GA) for Zn and Cd adsorption. Estimated parameters of nonlinear adsorption isotherms, which were obtained from the optimization process using genetic algorithm(GA), are nearly same with the parameters obtained from a linearization process of the nonlinear isotherms. Estimated effective diffusion coefficients, which were obtained from a finite element analysis of the advection-dispersion model and an optimization procedure using the genetic algorithm, for the metals were approximately in the order of $10^{-7}cm^2/s$ which could be obtained based on the linear distribution coefficient. The effective diffusion coefficients based on the nonlinear retardation factors were in the range of $10^{-6}{\sim}10^{-5}cm^2/s$. As a result, the correlation coefficient obtained between the measured and calculated concentration was over 0.9 which means that the genetic algorithm should be successfully applied to estimate the unknown parameters of the nonlinear adsorption isotherms and advection-dispersion model.