• Bulletin of the Korean Chemical Society
• /
• v.20 no.1
• /
• pp.35-41
• /
• 1999

Stability characteristics of hyperbolic reaction-diffusion equations with a reversible Brusselator model are investigated as an extension of the previous work. Intensive stability analysis is performed for three important parameters, Nrd, β and Dx, where Nrd is the reaction-diffusion number which is a measure of hyperbolicity, β is a measure of reversibility of autocatalytic reaction and Dx is a diffusion coefficient of intermediate X. Especially, the dependence on Nrd of stability exhibits some interesting features, such as hyperbolicity in the small Nrd region and parabolicity in the large Nrd region. The hyperbolic reaction-diffusion equations are solved numerically by a spectral method which is modified and adjusted to hyperbolic partial differential equations. The numerical method gives good accuracy and efficiency even in a stiff region in the case of small Nrd, and it can be extended to a two-dimensional system. Four types of solution, spatially homogeneous, spatially oscillatory, spatio-temporally oscillatory and chaotic can be obtained. Entropy productions for reaction are also calculated to get some crucial information related to the bifurcation of the system. At the bifurcation point, entropy production changes discontinuously and it shows that different structures of the system have different modes in the dissipative process required to maintain the structure of the system. But it appears that magnitude of entropy production in each structure give no important information related for states of system itself.

• Corrosion Science and Technology
• /
• v.8 no.2
• /
• pp.81-88
• /
• 2009

Chloride induced corrosion of steel reinforcement inside concrete is a major concern for concrete structures exposed to a marine environment. It is well known that transport of chloride ions in concrete occurs mainly through ionic/molecular diffusion, as a gradient of chloride concentration in the concrete pore solution is set. In the process of chloride transport, a portion of chlorides are bound in cement matrix then to be removed in the pore solution, and thus only the rest of chlorides which are not bound (i.e. free chlorides) leads the ingress of chlorides. However, since the measurement of free/bound chloride content is much susceptible to environmental conditions, chloride profiles expressed in total chlorides are evaluated to use in many studies In this study, the capacity of chloride binding in cement matrix was monitored for 150 days and then quantified using the Langmuir isotherm to determine the portions of free chlorides and bound chlorides at given total chlorides and the redistribution of free chlorides. Then, the diffusion of chloride ion in concrete was modeled by considering the binding capacity for the prediction of chloride profiles with the redistribution. The predicted chloride profiles were compared to those obtained from conventional model. It was found that the prediction of chloride profiles obtained by the model has shown slower diffusion than those by the conventional ones. This reflects that the prediction by total chloride may overestimate the ingress of chlorides by neglecting the redistribution of free chlorides caused by the binding capacity of cement matrix. From the evaluation, it is also shown that the service life prediction using the free chloride redistribution model needs different expression for the chloride threshold level which is expressed by the total chlorides in the conventional diffusion model.

• Journal of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1227-1237
• /
• 2021

This paper is concerned with a reaction-diffusion logistic model. In [17], Lou observed that a heterogeneous environment with diffusion makes the total biomass greater than the total carrying capacity. Regarding the ratio of biomass to carrying capacity, Ni [10] raised a conjecture that the ratio has a upper bound depending only on the spatial dimension. For the one-dimensional case, Bai, He, and Li [1] proved that the optimal upper bound is 3. Recently, Inoue and Kuto [13] showed that the supremum of the ratio is infinity when the domain is a multi-dimensional ball. In this paper, we generalized the result of [13] to an arbitrary smooth bounded domain in ℝⁿ, n ≥ 2. We use the sub-solution and super-solution method. The idea of the proof is essentially the same as the proof of [13] but we have improved the construction of sub-solutions. This is the complete answer to the conjecture of Ni.

• Journal of the Korean Society of Safety
• /
• v.37 no.2
• /
• pp.1-9
• /
• 2022

Most factories deal with toxic or flammable chemicals in their industrial processes. These hazardous substances pose a risk of leakage due to accidents, such as fire and explosion. In the event of chemical release, massive casualties and property damage can result; hence, quantitative risk prediction and assessment are necessary. Several methods are available for evaluating chemical dispersion in the atmosphere, and most analyses are considered neutral in dispersion models and under far-field wind condition. The foregoing assumption renders a model valid only after a considerable time has elapsed from the moment chemicals are released or dispersed from a source. Hence, an initial dispersion model is required to assess risk quantitatively and predict the extent of damage because the most dangerous locations are those near a leak source. In this study, the dispersion model for initial consequence analysis was developed with three-dimensional unsteady advective diffusion equation. In this expression, instantaneous leakage is assumed as a puff, and wind velocity is considered as a coordinate transform in the solution. To minimize the buoyant force, ethane is used as leaked fuel, and two different diffusion coefficients are introduced. The calculated concentration field with a molecular diffusion coefficient shows a moving circular iso-line in the horizontal plane. The maximum concentration decreases as time progresses and distance increases. In the case of using a coefficient for turbulent diffusion, the dispersion along the wind velocity direction is enhanced, and an elliptic iso-contour line is found. The result yielded by a widely used commercial program, ALOHA, was compared with the end point of the lower explosion limit. In the future, we plan to build a more accurate and general initial risk assessment model by considering the turbulence diffusion and buoyancy effect on dispersion.

• Membrane Journal
• /
• v.26 no.3
• /
• pp.187-196
• /
• 2016

Pressure-assisted forward osmosis (PAFO) process has recently been under spotlight for its potential to improve forward osmosis (FO) process performance by applying low hydraulic pressure on the feed side. Structure parameter, one of the governing factors in estimating water flux and solute flux across FO membranes in the solution-diffusion model (S-D model), determines solute resistivity in FO and PAFO processes. This study aims to estimate the trend of structure parameter change with respect to varying additional hydraulic pressure condition in PAFO.

• Journal of Environmental Science International
• /
• v.6 no.3
• /
• pp.239-247
• /
• 1997

The numerical experiments using a particle tracking model have been performed for predicting the change of water Quality and shoreline. In present study, comparison of the numerical model results with the analytic solution shows that the point of the mainmum concentration and the distribution pattern is very similar. The reflection effect from the boundary was newly Introduced for making clear the effect of the closed boundary which set limits to application of a particle tracking model. The present model seems to reappear physical phenomenon well. This model shows well qualitative appearance of pollutant diffusion in Kwangan beach. Therefore, this model is regarded as a useful means for predicting diffusion movement of suspended sand, and change of water quality.

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

• Journal of Environmental Science International
• /
• v.27 no.3
• /
• pp.167-177
• /
• 2018

The removal characteristics of As and Se ions from aqueous solution by hexadecyl trimethyl ammonium bromide (HTMAB) modified anthracite (HTMAB-AT) were investigated under various conditions of contact time, pH and temperature. When the pH is 6, the zeta potential value of anthracite (AT) is -24 mV and on the other hand, the zeta potential value of the HTMAB-AT is +44 mV. It can be seen that the overall increase of about 60 mV. Increasing the (+) potential value indicates that the surface of the adsorbent had a stronger positive charge, so adsorption for the anion metal was increased. The isotherm data was well described by Langmuir and Temkin isotherm model. The maximum adsorption capacity was found to be 7.81 and 6.89 mg/g for As and Se ions from the Langmuir isotherm model at 298 K, respectively. The kinetic data was tested using pseudo first and pseudo second order models. The results indicated that adsorption fitted well with the pseudo second order kinetic model. The mechanism of the adsorption process showed that adsorption was dependent on intra particle diffusion model according to two step diffusion. The thermodynamic parameters(${\Delta}G^{\circ}$, ${\Delta}H^{\circ}$, and ${\Delta}S^{\circ}$) were also determined using the equilibrium constant value obtained at different temperatures. The thermodynamic parameters indicated that the adsorption process was physisorption, and also an endothermic and spontaneous process.

• Journal of the Korean Society of Visualization
• /
• v.20 no.3
• /
• pp.74-85
• /
• 2022

We propose a Cubic-Interpolated Pseudo-Particle Lattice Boltzmann method (CIP-LBM) for the convection-diffusion equation (CDE) based on the Bhatnagar-Gross-Krook (BGK) scheme equation. The CIP-LBM relies on an accurate numerical lattice equilibrium particle distribution function on the advection term and the use of a splitting technique to solve the Lattice Boltzmann equation. Different schemes of lattice spaces such as D1Q3, D2Q5, and D2Q9 have been used for simulating a variety of problems described by the CDE. All simulations were carried out using the BGK model, although another LB scheme based on a collision term like two-relation time or multi-relaxation time can be easily applied. To show quantitative agreement, the results of the proposed model are compared with an analytical solution.

• Journal of Environmental Science International
• /
• v.27 no.5
• /
• pp.299-308
• /
• 2018

The adsorption characteristics of Cu ions were studied using the zeolite Na-A synthesized from Jeju volcanic rocks. The effects of various operating parameters such as initial concentration of Cu ions, contact time, solution pH, and solution temperature were investigated in batch experiments. The adsorption of Cu ions by Na-A zeolite was fitted well by pseudo-second-order kinetics and the Langmuir isotherm model. The maximum adsorption capacity determined using the Langmuir isotherm model was 152.95 mg/g. In addition, the adsorption of Cu ions by zeolite Na-A was primarily controlled by particle diffusion model in comparison with the film diffusion model. As the temperature increased from 303 K to 323 K, ${\Delta}G^o$ decreased from -2.22 kJ/mol to -3.41 kJ/mol, indicating that the adsorption of Cu ions by Na-A zeolite is spontaneous process.