• Proceedings of the KOSOMBE Conference
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• v.1997 no.11
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• pp.161-163
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• 1997

In this paper, a two-dimensional electron beam dose calculational algorithm implented for use in a two-dimensional radiation therapy planning system is described. The 2-D electron beam calculations have been in use clinically for a few decades. Our algorithm uses Age-diffusion model based int the Boltzman Transport Equation. Our implementation provides convenient user interface associated with electron beam therapy planning and displays radiation dose distribution according to different electron energy on patient images.

• Journal of the Korea institute for structural maintenance and inspection
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• v.9 no.4
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• pp.141-148
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• 2005

The nonlinear humidity distribution occurs due to the moisture diffusion when a concrete is exposed to an ambient air. This nonlinear humidity distribution induces shrinkage cracks on surfaces of the concrete. Because shrinkage cracks largely affect the durability and serviceability of concrete structures, the moisture diffusion in concrete must be investigated. The purpose of this paper is to propose a model of the moisture diffusion coefficient that governs moisture diffusion within concrete structures. To propose the model, numerical analysis was performed with several experiments. Because the moisture diffusion coefficient is changed with aging, especially at early ages, the proposed model includes aging effect by terms of the porosity as well as the humidity of concrete.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.11a
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• pp.635-640
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• 2001

In this study, a mathematical model is established for prediction of chloride penetration in unsaturated cracked early-age concrete. The model is combined with models for thermo-hygro dynamic coupling of cement hydration, moisture transport and micro-structure development. Chloride permeability and water permeability at cracked early-age concrete specimens are evaluated using a rapid chloride permeability test and a low-pressure water permeability test, respectively. Then, a homogenization technique is introduced into the model to determine equivalent diffusion coefficient and equivalent Permeation coefficient. Increased chloride transport due to cracks at the specimen could be predicted fairly well by characterizing the cracks using proposed model. Proposed model is verified by comparing diffusion analysis results with test results.

• Ocean and Polar Research
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• v.26 no.1
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• pp.43-50
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• 2004

The diffusion model, which considers diffusion and sorption, is proposed. The FEM program developed on the basis of the diffusion model provides the estimation of chloride concentration according to cyclic humidity and sorption. After the humidity diffusion analysis is carried out, the chloride ion diffusion and sorption analysis are conducted on the basis of the preestimated humidity data in each element. Each element has different analysis variables at different ages and locations. At early ages, the difference between inner and outer relative humidity causes the chloride ion penetration by sorption. As the humidity diffusion reduces the difference with age, the effect of sorption on the chloride ion penetration decreases. By the way, the cyclic humidity increases the effect of sorption on the chloride ion penetration at early ages, and the quantity of chloride ion around steel at later ages. Therefore, the in situ analysis of chloride ion penetration for marine concrete structures must be performed considering the cyclic humidity condition and the long term sorption.

• 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.

• Computers and Concrete
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• v.10 no.5
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• pp.523-539
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• 2012

Silica fume has long been used as a mineral admixture to improve the durability and produce high strength and high performance concrete. And in marine and coastal environments, penetration of chloride ions is one of the main mechanisms causing concrete reinforcement corrosion. In this paper, we proposed a numerical procedure to predict the chloride diffusion in a hydrating silica fume blended concrete. This numerical procedure includes two parts: a hydration model and a chloride diffusion model. The hydration model starts with mix proportions of silica fume blended concrete and considers Portland cement hydration and silica fume reaction respectively. By using the hydration model, the evolution of properties of silica fume blended concrete is predicted as a function of curing age and these properties are adopted as input parameters for the chloride penetration model. Furthermore, based on the modeling of physicochemical processes of diffusion of chloride ion into concrete, the chloride distribution in silica fume blended concrete is evaluated. The prediction results agree well with experiment results of chloride ion concentrations in the hydrating concrete incorporating silica fume.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.149-159
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• 2005

We study an age-dependent s-i-s epidemic model with spatial diffusion. The model equations are described by a nonlinear and nonlocal system of integro-differential equations. Finite difference methods along the characteristics in age-time domain combined with finite elements in the spatial variable are applied to approximate the solution of the model. Stability of the discrete periodic solution is investigated.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.11a
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• pp.641-646
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• 2001

In early-age concrete, volumetric deformations due to thermal expansion and moisture transfer are restrained by various boundary conditions, and then restraint stresses occur in proportion to developed stiffness. With increase of the age, these stresses are gradually relieved by significant relaxation behavior of early-age concrete. Therefore, it is necessary to consider the stress relaxation in order to analyze the behavior of early-age concrete more accurately. In this paper, we propose a unified algorithm which combines a relaxation model with hydration model, heat conduction model, micropore structure formation model, moisture diffusion model and mechanical properties development model and develop a finite element program based on the algorithm. The program is applied to evaluate stress development if a temperature-stress test machine (TSTM) specimen and a massive concrete structure, and then validity of the program is discussed and evaluated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.3
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• pp.189-200
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• 2010

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.

• Computers and Concrete
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• v.11 no.3
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• pp.201-222
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• 2013

A comprehensive simulation model for the transport process of fully coupled moisture and multi-species in non-saturated concrete structures is proposed. The governing equations of moisture and ion diffusion are formulated based on Fick's law and the Nernst-Planck equation, respectively. The governing equations are modified by explicitly including the coupling terms corresponding to the coupled mechanisms. The ionic interaction-induced electrostatic potential is described by electroneutrality condition. The model takes into account the two-way coupled effect of moisture diffusion and ion transport in concrete. The coupling parameters are evaluated based on the available experimental data and incorporated in the governing equations. Differing from previous researches, the material parameters related to moisture diffusion and ion transport in concrete are considered not to be constant numbers and characterized by the material models that account for the concrete mix design parameters and age of concrete. Then, the material models are included in the numerical analysis and the governing equations are solved by using finite element method. The numerical results obtained from the present model agree very well with available test data. Thus, the model can predict satisfactorily the ingress of deicing salts into non-saturated concrete.