• Computers and Concrete
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• v.10 no.1
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• pp.79-93
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• 2012

This paper estimates theoretically the diffusion-reaction behaviour of sulfate ion in concrete caused by environmental sulfate attack. Based on Fick's second law and chemical reaction kinetics, a nonlinear and nonsteady diffusion-reaction equation of sulfate ion in concrete, in which the variable diffusion coefficient and the chemical reactions depleting sulfate ion concentration in concrete are considered, is proposed. The finite difference method is utilized to solve the diffusion-reaction equation of sulfate ion in concrete, and then it is used to simulate the diffusion-reaction process and the concentration distribution of sulfate ion in concrete. Afterwards, the experiments for measuring the sulfate ion concentration in concrete are carried out by using EDTA method to verify the proposal model, and results show that the proposed model is basically in agreement with the experimental results. Finally, Numerical example has been completed to investigate the diffusion-reaction behavior of sulfate ion in the concrete plate specimen immersed into sulfate solution.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.249-281
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• 2020

A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.

• Korean Journal of Materials Research
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• v.28 no.7
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• pp.428-434
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• 2018

Hydrogen evolution on a steel surface and subsequent hydrogen diffusion into the steel matrix are evaluated using an electrochemical permeation test with no applied cathodic current on the hydrogen charging side. In particular, cyclic operation in the permeation test is also conducted to clarify the corrosion-induced hydrogen evolution behavior. In contrast to the conventional perception that the cathodic reduction reaction on the steel in neutral aqueous environments is an oxygen reduction reaction, this study demonstrates that atomic hydrogen may be generated on the steel surface by the corrosion reaction, even in a neutral environment. Although a much lower permeation current density and significant slower diffusion kinetics of hydrogen are observed compared to the results measured in acidic environments, they contribute to the increase in the embrittlement index. This study suggests that the research on hydrogen embrittlement in ultra-strong steels should be approached from the viewpoint of corrosion reactions on the steel surface and subsequent hydrogen evolution/diffusion behavior.

• Transactions of the Korean hydrogen and new energy society
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• v.18 no.3
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• pp.265-274
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• 2007

A study has been conducted to clarify NO emission behavior through preferential diffusion effects of $H_2$ and H in methane-hydrogen diffusion flames. A comparison is made by employing three species diffusion models. Special concerns are focused on what is the deterministic role of the preferential diffusion effects in flame structure and NO emission. The behavior of maximum flame temperatures with three species diffusion models is not explained by scalar dissipation rate but the nature of chemical kinetics. The preferential diffusion of H into reaction zone suppresses the populations of the chain carrier radicals and then flame temperature while that of $H_2$ produces the increase of flame temperature. These preferential diffusion effects of $H_2$ and H are also discussed about NO emissions through the three species diffusion models.

• 한국연소학회:학술대회논문집
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• 2003.05a
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• pp.129-136
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• 2003

Numerical study with momentum-balanced boundary conditions has been conducted to grasp chemical effects of added $CO_{2}$ and $H_{2}O$ to fuel- and oxidizer-sides on flame structure and NO emission behavior in $CH_{4}$/Air counterflow diffusion flames. The dilution with $H_{2}O$ results in significantly higher flame temperatures and NO emission, but dilution with $CO_{2}$ has much more chemical effects than that with $H_{2}O$. Maximum reaction rate of principal chain branching reaction due to chemical effects decreases with added $CO_{2}$. but increases with added $H_{2}O$. The NO emission behavior is closely related to the production rate of OH, CH and N. The OH radical production rate increases with added $H_{2}O$ but those of CH, N decrease. On the other hand the production rates of OR CH and N decrease with added $CO_{2}$. It is found that NO emission behavior is considerably affected by chemical effects of added $CO_{2}$ and $H_{2}O$.

• Journal of Welding and Joining
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• v.32 no.5
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• pp.13-20
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• 2014

A brief overview is given of the corrosion and hydrogen diffusion behaviors of high strength pipe steel in sour environment. Firstly, hydrogen adsorption and diffusion mechanism of the pipe steel is introduced. Secondly, the effect of iron sulfide film precipitated as a result of the corrosion reaction on the steel surface on hydrogen reduction reaction and subsequent hydrogen permeation through the steel is discussed. Moreover, the hydrogen diffusion behavior of the pipe steel under tensile stress in both elastic and plastic ranges is reviewed based on a number of experimental permeation data and theoretical models describing the hydrogen diffusion and trapping phenomena in the steel. It is hoped that this paper will result in significant academic contributions in the field of corrosion and hydrogen related problems of the pipe steel used in sour environment.

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.1015-1019
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• 2012

The direct calculation method is generalized to the excited-state diffusion-influenced reversible reaction of a neutral and a charged particle under an external field with two different lifetimes and quenching in three dimensions. The present method provides an alternative way to calculate the binding probability density functions and the survival probabilities from the corresponding irreversible results. The solutions are obtained as the series solutions by the diagonal approximation due to the anisotropy of the unidirectional external field. The numerical results are found to be in good agreement with those of the previous study [S. Y. Reigh et al. J. Chem. Phys. 132, 164112 (2010)] within a weak field limit. The solutions of two approaches show qualitatively the same overall behavior including the power laws at long times.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.747-752
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• 1994

Ussing's flux ratio theorem (1978) reflects a reciprocal relationship behavior between the unidirectional fluxes in asymmetric steady diffusion-convection in a membrane slab. This surprising result has led to many subsequent studies in a wide range of applications, in particular involving linear models of time dependent problems in biology and physiology. Ussing's theorem and its extensions are inherently linear in character. It is of considerable interest to ask to what extent these results apply, if at all, in situations involving, for example, nonlinear reaction. A physiologically interesting situation has been considered by Weisiger et at. (1989, 1991, 1992) and by McNabb et al. (1990, 1991) who studied the role of albumin in the transport of ligands across aqueous diffusion barriers in a liver membrane slab. The results are that there exist reciprocal relationships between unidirectional fluxes in the steady state, although albumin is chemically interacting in a nonlinear way of the diffusion processes. However, the results do not hold in general at early times. Since this type of study first started, it has been speculated about when and how the Ussing's flux ratio theorem fails in a general diffusion-convection-reaction system. In this paper we discuss the validity of Ussing-type theorems in time-dependent situations, and consider the limiting time behavior of a general nonlinear diffusion system with interaction.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.161-193
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• 2024

In this paper, we consider the asymptotic behavior of solutions for the partly dissipative reaction diffusion systems of the FitzHugh-Nagumo type with hereditary memory and a very large class of nonlinearities, which have no restriction on the upper growth of the nonlinearity. We first prove the existence and uniqueness of weak solutions to the initial boundary value problem for the above-mentioned model. Next, we investigate the existence of a uniform attractor of this problem, where the time-dependent forcing term h ∈ L²_b(ℝ; H^-1(ℝ^N)) is the only translation bounded instead of translation compact. Finally, we prove the regularity of the uniform attractor A, i.e., A is a bounded subset of H²(ℝ^N) × H¹(ℝ^N) × L²_µ(ℝ⁺, H²(ℝ^N)). The results in this paper will extend and improve some previously obtained results, which have not been studied before in the case of non-autonomous, exponential growth nonlinearity and contain memory kernels.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.11
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• pp.1527-1537
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• 1997

Extinction characteristics and acoustic response of hydrogen-air diffusion flames at various pressures are numerically studied by employing counterflow diffusion flame as a model flamelet in turbulent flames in combustion chambers. The numerical results show that extinction strain rate increases linearly with pressure and then decreases, and increases again at high pressures. Thus, flames are classified into three pressure regimes. Such nonmonotonic behavior is caused by the change in chemical kinetic behavior as pressure rises. The investigation of acoustic-pressure response in each regime, for better understanding of combustion instability, shows different characteristics depending on pressure. At low pressures, pressure-rise causes the increase in flame temperature and chain branching/recombination reaction rates, resulting in increased heat release. Therefore, amplification in pressure oscillation is predicted. Similar phenomena are predicted at high pressures. At moderate pressures, weak amplification is predicted since flame temperature and chain branching reaction rate decreases as pressure rises. This acoustic response can be predicted properly only with detailed chemistry or proper reduced chemistry.