• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.1-28
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• 2004

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an $H^1$-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index one. A priori error estimates for semidiscrete scheme are derived for both differ-ential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.

• Membrane Journal
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• v.10 no.1
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• pp.19-29
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• 2000

To estimatc mutual diffusion coefficient for the analysis of mass transfer phenomena in polymer/solvent system, two models are proposed and the equations are derived. The estimates of mutual diffusion coefficients are obtained by two models suggested in this work and compared with and experimental data and Vrentas-Duda's. Vrentas-Duda's self diffusion coefficient was used for the mutual diffusion coefficient. Derivative of chemical potential on solvent was derived and used using original UNIFAC-FV and modified UNIFAC-FV. However, Vrentas-Duda's equation for mutual diffusion coefficient contains Flory-Huggins parameter x. For the derivative of chemical potential term, Vrentas-Duda assumed that parameter x was constant and independent of temperatures and concentrations The assumption is one of shortcoming in vrentas-Duda's mutual diffusion coefficient. New methods proposed in this work do not have such assumptions and simplifications. For the solvent of cyclohexane, n-pentane, and n-hexane in PIB(polyisolbutylene) and PMS-BR (poly(p-methylstyrene-co-isobutylene), new methods well correlate the experimental data at various temperatures and concentrations, and predicted the experimental data much better than Vrentas-Duda's for the PIB/toluene system. It is shown that new methods are excellent tools for correlating mutual diffusion coefficient data in polymer/solvent system over wide ranges of temperature and concentration without any assumptions or simplifications.

• Nuclear Engineering and Technology
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• v.32 no.6
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• pp.605-617
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• 2000

Nodal transport methods are studied for the solution of two dimensional discrete-ordinates, simplified even-parity transport equation(SEP) which is known to be an approximation to the true transport equation. The polynomial expansion nodal method(PEN) and the analytic function expansion nodal method(AFEN）which have been developed for the diffusion theory are used for the solution of the discrete-ordinates form of SEP equation. Our study shows that while the PEN method in diffusion theory can directly be converted without complication, the AFEN method requires a theoretical modification due to the nonhomogeneous property of the transport equation. The numerical results show that the proposed two methods work well with the SEP transport equation with higher accuracies compared with the conventional finite difference method.

• Nuclear Engineering and Technology
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• v.52 no.4
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• pp.681-688
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• 2020

The telegrapher's theory was used to develop a new formulation for the neutron noise equation. Telegrapher's equation is supposed to demonstrate a more realistic approximation for neutron transport phenomena, especially in comparison to the diffusion theory. The physics behind such equation implies that the signal propagation speed is finite, instead of the infinite as in the case of ordinary diffusion. This paper presents the theory and results of the development of a new method for calculation of the neutron noise using the telegrapher's equation as its basis. In order to investigate the differences and strengths of the new method against the diffusion based neutron noise, a comparison was done between the behaviors of two methods. The neutron noise based on SN transport considered as a precision measuring point. The Green's function technique was used to calculate the neutron noise based on telegrapher's and diffusion methods as well as the transport. The amplitude and phase of Green's function associated with the properties of the medium and frequency of the noise source were obtained and their behavior was compared to the results of the transport. It was observed, the differences in some cases might be considerable. The effective speed of propagation for the noise perturbations were evaluated accordingly, resulting in considerable deviations in some cases.

• Journal of Korean Ophthalmic Optics Society
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• v.16 no.4
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• pp.403-408
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• 2011

Purpose: To study the concentration distribution and diffusion depth in tinted lenses using the law of diffusion. Methods: The measured values taken from experiments were fitted with the theoretical fitting curve induced on the basis of Fick's second law of diffusion. Results: The fitting curves were in very good agreement with the measured values. As the results, we found the quantitative relationship between mass of dye solution diffused into the tinted lens per unit area and dyeing time, and evaluated concentration distribution of dye in tinted lens, diffusion depth, etc. Conclusions: The dyeing mechanism of tinted lenses can be well described by diffusion theory.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.1C
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• pp.50-58
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• 2004

An image enhancement method using modified anisotropic diffusion filter is proposed in this paper. It employs sensor noise estimation and scale space methods based on the minimum reliable scale. Then the anisotropic diffusion filter is modified by the calculated critical value function and local gradient. Through simulation, it is verified that the proposed algorithm has the capability of little or no noise amplification in homogenous region as well as superior edge enhancement.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.3
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• pp.193-204
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• 2012

This paper is comparing numerical schemes for a differential equation with convection and fourth-order diffusion. Our model equation is $h_t+(h^2-h^3)_x=-(h^3h_{xxx})_x$, which arises in the context of thin film flow driven the competing effects of an induced surface tension gradient and gravity. These films arise in thin coating flows and are of great technical and scientific interest. Here we focus on the several numerical methods to apply the model equation and the comparison and analysis of the numerical results. The convection terms are treated with well known WENO methods and the diffusion term is treated implicitly. The diffusion and convection schemes are combined using a fractional step-splitting method.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.83-92
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• 2021

This paper studies approximate solutions for a class of nonlinear diffusion population models. Our methods are to use the fundamental solution of heat equations to construct integral forms of the models and the well-known Banach compression map theorem to prove the existence of positive solutions of integral equations. Non-steady-state local approximate solutions for suitable harvest functions are obtained by utilizing the approximation theorem of multivariate continuous functions.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.655-663
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• 2003

The fundamental tenn structure model is based on the modelling of the short rate. It is well-known that the short rate depends on the interest rate policy of monetary authorities, especially on the official rate. Babbs and Webber(1994) modelled the tenn structure of interest rates using the official rate. They assume that the official rate follows a jump process. This reflects that the official rate infrequently changes. In this paper, we test this official tenn structure model and compare the jump-diffusion model with the pure diffusion model.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.05a
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• pp.711-714
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• 2003

Factors causing deterioration of concrete structures under marine environment are various, especially penetration and diffusion of chloride ion, carbon dioxide, and water through pore effects on the durability of concrete as well as mechanical properties of concrete. Pore of porous materials like concrete can be classified as micro-, meso-, and macro-pore. And pore of cement matrix is classified as pore which occupied by water, air void, and ITZ between cement paste and aggregates. In this study, to verify the relationship between pore of cement matrix and the property of chloride ion diffusivity, the regression analysis is producted. From the result of regression analysis, the average pore diameter more than total pore volume effects on the diffusivity of chloride ion.