• Bulletin of the Korean Chemical Society
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• 제12권6호
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• pp.692-698
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• 1991

The reaction path Smoluchowski equation approach developed in a recent work to calculate the rate constant for a diffusive multidimensional barrier crossing process is extended to incorporate the configuration-dependent diffusion matrix. The resulting formalism is then applied to the investigation of stilbene photoisomerization dynamics. Adapting a model two-dimensional potential and a model diffusion matrix proposed by Agmon and Kosloff [J. Phys. Chem.,91 (1987) 1988], we derive an eigenvalue equlation for the relaxation rate constant of the stilbene photoisomerization. This eigenvalue equation is solved numerically by using the finite element method. The advantages and limitations of the present method are discussed.

• Journal of Biosystems Engineering
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• 제33권5호
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• pp.296-302
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• 2008

The effective moisture diffusivity and its dependence on drying temperature during drying of rapeseed were experimentally investigated. The data were recorded from thin layer drying experiments at nine different combinations of drying air temperatures of 40, 50, and $60^{\circ}C$ and the relative humidities of 30, 45, and 60%. The moisture diffusion equation was analyzed using stepwise multiple regression analysis. Effective moisture diffusivities were calculated based on the moisture diffusion equation for a spherical shape using Fick's second law. The effective diffusivities during the drying of rapeseed were $l.72{\times}10^{-11}$, $2.41{\times}10^{-11}$ and $3.31{\times}10^{-11}\;m^2{\cdot}s^{-1}$ at 40, 50 and $60^{\circ}C$, respectively. The activation energy for moisture diffusion during drying was $28.47\;kJ{\cdot}mol^{-1}$. The dependence of moisture diffusivity on temperature was described by an Arrhenius-type equation. Drying occurred in the falling rate period and the internal moisture diffusion phenomenon is the governing physical mechanism of the moisture movement in the particles.

• Fisheries and Aquatic Sciences
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• 제7권2호
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• pp.90-95
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• 2004

An analytical model for predicting the convection-diffusion of solute dumped in a homogeneous open sea of constant water depth has been developed in a time-integral form. The model incorporates spatially uniform, uni-directional, mean and oscillatory currents for horizontal convection, the settling velocity for the vertical convection, and the anisotropic turbulent diffusion. Two transformations were introduced to reduce the convection-diffusion equation to the Fickian type diffusion equation, and then the Galerkin method was then applied via the expansion of eigenfunctions over the water column derived from the Sturm-Liouville problem. A series of calculations has been performed to demonstrate the applicability of the model.

• 한국해양공학회지
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• 제16권5호
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• pp.41-48
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• 2002

Numerical experiments are conducted using a three-dimensional baroclinic equation model and a Lagrangian method for clarifying the effect of th settling velocity on the suspended solids diffusion caused by the dredging and the reclamination works. Diffusion characteristics of the neutral particles and the weighting particles is experimented by the Lagrangian particles trajectory model, The results show that the diffusion characteristics of the suspended solids is effected by the settling velocity classified by the particles size in the density layered semi-closed bay. To estimate exactly the diffusion characteristics of the suspended solids and the contaminant with weight the three-dimensional baroclinic equation model and the three-dimensional Lagrangian particles trajectory model considering the settling velocity of the particle in the density layered semi-closed bay must be used.

• Journal of the Korean Wood Science and Technology
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• 제19권4호
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• pp.27-33
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• 1991

Three kinds of specimens(radiata pine sapwood, radiata pine heartwood and whemlock heartwood) were dried at four temperature levels (30, 40, 50 and $60^{\circ}C$) in an emvironmental chamber. Unsteady-state diffusion coefficients were calculated from obtained drying fates by using infinite slab equation for first half of sorption and interval diffusion equation for second half of sorption. Activation energies for moisture diffusion in wood were calculated from the diffusion coefficients obtained at four temperatures. In most cases diffusion coefficients for radial movement were higher than those for tangential movement. Activation energy differences between sapwood and heartwood weren't significant for radial movement, but were significant for tangential movement. Most activation energies calculated from drying rates were lower than heat of water condensation(about 11,000cal/mole). Specially the avenge activation energy for sapwood tangential movement was only 5,000cal/mole.

• Computers and Concrete
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• 제10권1호
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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 applied mathematics & informatics
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• 제26권5_6호
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• pp.1057-1069
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• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.603-613
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• 2023

In this paper, the concept of geodesic centered tractography is explored for diffusion tensor imaging (DTI). In DTI, where geodesics has been tracked and the inverse of the fourth-order diffusion tensor is inured to determine the diversity. Specifically, we investigated geodesic tractography technique for High Angular Resolution Diffusion Imaging (HARDI). Riemannian geometry can be extended to a direction-dependent metric using Finsler geometry. Euler Lagrange geodesic calculations have been derived by Finsler geometry, which is expressed as HARDI in sixth order tensor.

• Journal of applied mathematics & informatics
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• 제34권5_6호
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• pp.495-508
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• 2016

A singularly perturbed reaction-diffusion fourth-order ordinary differential equation(ODE) with discontinuous source term is considered. Due to the discontinuity, interior layers also exist. The considered problem is converted into a system of weakly coupled system of two second-order ODEs, one without parameter and another with parameter ε multiplying highest derivatives and suitable boundary conditions. In this paper a computational method for solving this system is presented. A zero-order asymptotic approximation expansion is applied in the second equation. Then, the resulting equation is solved by the numerical method which is constructed. This involves non-overlapping Schwarz method using Shishkin mesh. The computation shows quick convergence and results presented numerically support the theoretical results.

• 전기학회논문지P
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• 제64권3호
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• pp.125-129
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• 2015

Energy distribution function for electrons in SF6-Ar mixtures gas used by MCS-BEq algorithm has been analysed over the E/N range 30~300[Td] by a two term Boltzmann equation and a Monte Carlo Simulation using a set of electron cross sections determined by other authors experimentally the electron swarm parameters for 0.2[%] and 0.5[%] $SF_6-Ar$ mixtures were measured by time-of-flight(TOF) method, The results show that the deduced longitudinal diffusion coefficients and transverse diffusion coefficients agree reasonably well with theoretical for a rang of E/N values. The results obtained from Boltzmann equation method and Monte Carlo simulation have been compared with present and previously obtained data and respective set of electron collision cross sections of the molecules.