• Journal of applied mathematics & informatics
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• 제15권1_2호
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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.

• 멤브레인
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• 제10권1호
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• pp.19-29
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• 2000

고분자/용매계에서 물질전달현상에 이용되는 용매의 상호확산계수를 예측하기 위하여 기존의 UNFACFV을 적용한 확산식을 유도하였으며, 상호확산계수를 계산하였다. 또한, 새로운 모델식에 의하여 계산한 값을 실험치 및 Vrentas-Duda의 이론치와 비교하였다. 상화확산계수를 구하는데 필요한 자기확산계수는 Vrentas-Duda의 이론을 이용하고, 용매의 화학포텐셜의 농도 미분항은 original UNIFAC-FA와 modified UNIFAC-FV를 사용하였다. Flory-Hugginstlr을 이용한 Vrentas-Duda의 상호확산식은 용매의 화학포텐셜의 농도 미분항을 표현하기 위하여 매개변수 x를 온도와 농도에 무관한 상수로 가정한 단점을 가지고 있으나, 본 연구에서 제시한 방법에서는 이러한 가정이 없으며, 여러 가지 고분자/용매계(polyisobutylene homopolymer 및 polyisobutylene-poly(pmethylstyrene) copolymer와 cyclohexane, n-hexane, n-pentane, chloroform, toluene)에서의 상호확산계수를 잘예측하였다. 특히 PIB/toluene계의 경우, 본 논문에서 사용된 방법이 Vrentas-Duda 이론에 의한 것보다 실험치에 더 가까웠다. 또한, 아무런 가정이나 제약없이, 넓은 온도 및 농도 영역에서 고분자/용매계의 상호확산계수를 예측할 수 있는 좋은 방법임을 알 수 있었다.

• Nuclear Engineering and Technology
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• 제32권6호
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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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• 제52권4호
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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.

• 한국안광학회지
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• 제16권4호
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• pp.403-408
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• 2011

목적: 확산법칙을 이용하여 착색렌즈에서의 농도분포와 확산깊이에 대한 연구를 하였다. 방법: Fick의 제2확산법칙을 바탕으로 유도된 이론적 맞춤곡선을 측정값에 맞춤한다. 결과: 맞춤곡선은 측정값과 매우 잘 일치하였으며, 그 결과로서 착색렌즈의 내부로 확산되어 들어간 단위면적당 착색용액의 질량과 착색시간 사이의 관계, 착색렌즈 내 착색염료에 대한 농도분포, 확산깊이 등을 평가할 수 있었다. 결론: 착색렌즈의 착색기전은 확산법칙으로 잘 설명될 수 있다.

• 한국통신학회논문지
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• 제29권1C호
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• pp.50-58
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• 2004

본 논문은 수정된 이방성 확산 펄터를 이용한 영상 개선 방법을 제안하였다. 이를 위하여 최소 신뢰 스케일을 기반으로 하는 센서 잡음 추정과 스케일 스페이스 방법을 도입하였다. 이때 이방성 필터는 구해진 임계값 함수와 국부 기울기에 의해 수정되었다. 모의 실험을 통해 제안한 방법이 평탄 영역에서의 잡음을 거의 증폭시키지 않으면서도 뛰어난 에지 향상을 보임을 증명할 수 있었다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권3호
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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.

• Computers and Concrete
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• 제34권2호
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• pp.169-178
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• 2024

To circumvent the constraints of time-consuming experimental methods, numerical simulation can be one of the most effective approaches to investigating chloride diffusion behaviors in concrete. However, except for the effect of the external environments, the transport direction of the chloride cannot be neglected when the concrete is exposed to the marine tidal zone, especially in certain areas of concrete members. In this study, based on Fick's second law, considering the effects of timevarying, chloride binding capacity, concrete stress state, ambient temperature, and relative humidity on chloride diffusion coefficient, the modified one-dimensional, two-dimensional, and three-dimensional novel modified chloride diffusion theoretical models were established through defining the current boundary conditions. The simulated results based on the novel modified multi-dimensional model were compared with the experimental results obtained from some previous pieces of literature. The comparing results showed that the modified multi-dimensional model was well-fitted with experimental data, confirming the high accuracy of the novel modified model. The experimental results in literature showed that the chloride diffusion in the corner area of the concrete structure cannot be simulated by a simple one-dimensional diffusion model, where it is necessary to select a suitable multi-dimensional chloride diffusion model for simulation calculation. Therefore, the novel modified multi-dimensional model established in this study has a stronger applicability for practical engineering.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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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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• 제10권3호
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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.