• Journal of Environmental Science International
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• v.26 no.5
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• pp.609-619
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• 2017

The removal characteristics of 2,4-dinitrophenol (2,4-DNP) from an aqueous solution by commercial Wood-based Activated Carbon (WAC) have been studied. The effects of various experimental parameters were investigated using a batch adsorption technique. The adsorption capacity of 2,4-DNP by WAC increased with a decrease in the dosage and particle size of WAC, temperature and the initial pH of the solution, and increased with an increase in the initial concentration of the solution. The adsorption equilibrium data were best described by the Redlich-Peterson isotherm model. The maximum adsorption capacities of 2,4-DNP by WAC were 573.07 mg/g at 293 K, 500.00 mg/g at 313 K, and 476.19 mg/g at 333 K, decreasing with increasing temperature. The kinetic data were well fitted to the pseudo-second-order model, and the results of the intra-particle diffusion model suggested that the adsorption process was mainly controlled by particle diffusion. The thermodynamic analysis indicated that the adsorption of 2,4-DNP by WAC was an endothermic and spontaneous process.

• Computers and Concrete
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• v.3 no.6
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• pp.401-422
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• 2006

A multi-species model based on the Nernst-Planck equation has been developed by using a finite volume method. The model makes it possible to simulate transport due to an electrical field or by diffusion and to predict chloride penetration through water saturated concrete. The model is used in this paper to assess and analyse chloride diffusion coefficients and chloride binding isotherms. The experimental assessment of the effective chloride diffusion coefficient consists in measuring the chloride penetration depth by using a colorimetric method. The effective diffusion coefficient determined numerically allows to correctly reproduce the chloride penetration depth measured experimentally. Then, a new approach for the determination of chloride binding, based on non-steady state diffusion tests, is proposed. The binding isotherm is identified by a numerical inverse method from a single experimental total chloride concentration profile obtained at a given exposure time and from Freundlich's formula. In order to determine the initial pore solution composition (required as initial conditions for the model), the method of Taylor that describes the release of alkalis from cement and alkali sorption by the hydration products is used here. Finally, with these input data, prediction of total and water-soluble chloride concentration profiles has been performed. The method is validated by comparing the results of numerical simulations to experimental results obtained on various types of concretes and under different exposure conditions.

• Environmental Engineering Research
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• v.23 no.4
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• pp.442-448
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• 2018

This paper presents the numerical simulation of advection-diffusion mechanism of BOD concentration which was used as an indicator of waste only in one flow-direction of waste stabilization ponds (1-dimension (1-D)). This model was represented in partial differential equation order 2. The purpose of this paper was to determine the simulation of the model 1-D of wastewater transport phenomena based advection-diffusion mechanism and did validate the model. Numerical methods which was used for the solution of this model is finite difference method with Forward Time Central Space scheme. The simulation results which was obtained would be compared with field observation data as a validation model. Collection of field data was carried out in the Wastewater Treatment Plant Sewon, Bantul, D.I. Yogyakarta. The results of numerical simulations were indicate that the advection-diffusion mechanism takes place continuously over time. Then validation of the model was state that there was a difference between the calculation results with the field data, with a correlation value of 0.998.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.455-466
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• 1999

In this note we present a numerical scheme for finding an approxximate solution of an equation which can be viewed as a model for spatial diffusion of age-depednent biological populations. Discretization of the model yields a linear system with a block tridi-agonal matrix. Our main concern will be discussion of stability for this scheme by examining the eigenvalues of the block tridiagonal matrix. Numerical results are presented.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.383-398
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• 2006

We consider a geometric Levy process for an underlying asset. We prove first that the option price is the unique solution of certain integro-differential equation without assuming differentiability and boundedness of derivatives of the payoff function. Second result is to provide convergence rate for option prices when the small jumps are removed from the Levy process.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.337-345
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• 2004

In allelic model X = ($\chi_1\chi$_2ㆍㆍㆍ, \chi_d$), M_f(t) = f(p(t)) - ${{\int^t}_0}\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we can show existence and uniqueness of solution for stochastic differential equation and martingale problem associated with mean vector. Also, we examine that if the operator related to this martingale problem is connected with Markov processes under certain circumstance, then this operator must satisfy the maximum principle.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.5
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• pp.695-702
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• 2002

Nonlinear dynamics of striped diffusion flames, by the diffusional-thermal instability with Lewis numbers sufficiently less than unity, is numerically investigated by examining various two-dimensional flame-structure solutions. The Lewis numbers for fuel and oxidizer are assumed to be identical and an overall single-step Arrhenius-type chemical reaction rate is employed in the model. Particular attention is focused on identifying the flame-stripe solution branches corresponding to each distinct stripe pattern and hysteresis encountered during the transition. At a Damkohler number slightly greater than the extinction Damkohler number, eight-stripe solution first emerges from one dimensional solution. The eight-stripe solution survives Damkohler numbers much smaller than the extinction Damkohler number until the transition to four-stripe solution occurs at the first forward transition Damkohler number. At the second forward transition Damkohler number, somewhat smaller than the first transition Damkohler number, the transition to two-stripe solution occurs. However, anu further transition from two-stripe solution to one-stripe solution is not always possible even if one-stripe solution can be independently accessed for particular initial conditions. The Damkohler number ranges for two-stripe and one-stripe solutions are found to be virtually identical because each stripe is an independent structure if distance between stripes is sufficiently large. By increasing the Damkohler number, the backward transition can be observed. In comparison with the forward transition Damkohler numbers, the corresponding backward transition Damkohler numbers are always much greater, thereby indicating significant hysteresis between the stripe patterns of strained diffusion flames.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.3 no.2
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• pp.85-93
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• 2005

Isotopes of alkali and alkaline earth metals (AM and AEM) are the main contributors to the heat load and the radiotoxicity of spent fuel (SF) . These components are separated from the SF and dissolved in a molten LiCl in an electrolytic reduction process. A mass transfer model is developed to describe the diffusion behavior of Cs, Sr, and Ba in the SF into the molten salt. The model is an analytical solution of Fick's second law of diffusion for a cylinder which is the shape of a cathode in the electrolytic reduction process. And the model is also applied to depict the concentration profile of the oxygen ion which is produced by the electrolysis of Li$_{2}$O. The regressed diffusion coefficients of the model correlating the experimentally measured data are evaluated to be greater in the order of Ba, Cs, and Sr for the metal ions and the diffusion of the oxygen ion is slower than the metal ions which implies that different mechanisms govern the diffusion of the metal ions and the oxygen ions in a molten LiCl.

• Journal of the Korean Society of Safety
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• v.19 no.3 s.67
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• pp.89-94
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• 2004

Most reinforcements in concrete are constructed by steel. Corrosion of reinforcement is the main cause of damage and early failure of reinforced concrete structures. The corrosion is mainly professed by the chloride ingress. In general, chloride in concrete can be discriminated by two components, total chloride and fire chloride. This paper provides a testing method on the coefficient of chloride diffusion in concrete and the relationship between total chloride and free chloride in concrete for the composition of predicting model on diffusion rate of chloride. In order to complete this predicting model, this study will use chloride penetration characteristic, diffusion coefficient and experiment of color change on silver nitrate solution. This predicting model is going to help that grasp special quality on salt content inclusion of concrete structure that is exposed in chloride environment. Accurate predicting model can be effectively used not only in selecting of repair time but also in preventing from various deteriorations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.1
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• pp.21-29
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• 2009

This paper treats the conditions for the existence and stability properties of stationary solutions of a predator-prey interaction with self and cross-diffusion. We show that at a certain critical value a diffusion driven instability occurs, i.e. the stationary solution stays stable with respect to the kinetic system (the system without diffusion) but becomes unstable with respect to the system with diffusion and that Turing instability takes place. We note that the cross-diffusion increase or decrease a Turing space (the space which the emergence of spatial patterns is holding) compared to the Turing space with self-diffusion, i.e. the cross-diffusion response is an important factor that should not be ignored when pattern emerges.