• 한국막학회:학술대회논문집
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• 한국막학회 1995년도 추계 총회 및 학술발표회
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• pp.43-44
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• 1995

The diffusion behavior of liquid into polymer has been described by Fick's law, but the departure from Fickian diffusion is frequently found. In this study, 'noble' expressions for the rates of relaxation and sorption are introduced to eliminate these limitations. The ralaxation-sorption coupled mechanism model are based on the possibility of contacting liquid molecule and the active site which has the numerical concept of free volume. The concept has an analogy of reaction rate expressed by the possibility of collision with molecules and used in adsorption and reactive extraction etc. The new model simulated by Rungc-Kutta method for initial-value problem and Fickian diffusion is caompared with experimental data. The results show that the ralaxation-sorption coupled mechanism is able to account well for Fickian and non-Fickian sorption behavior including sigmoid and two-stage. In addition, this model has a chance of expansion to multi-component sorption with ease.

• 호남수학학술지
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• 제44권3호
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• pp.402-418
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• 2022

Noise is a fundamental factor to increased validity and regularity of spike propagation and neuronal firing in the nervous system. In this paper, we examine the stochastic version of the Izhikevich-FitzHugh neuron dynamical model. This approach is based on techniques presented by Luo and Guo, which provide a general framework for the bifurcation and stability analysis of two dimensional stochastic dynamical system as an Itô averaging diffusion system. By using largest lyapunov exponent, local and global stability of the stochastic system at the equilibrium point are investigated. We focus on the two kinds of stochastic bifurcations: the P-bifurcation and the D-bifurcations. By use of polar coordinate, Taylor expansion and stochastic averaging method, it is shown that there exists choices of diffusion and drift parameters such that these bifurcations occurs. Finally, numerical simulations in various viewpoints, including phase portrait, evolution in time and probability density, are presented to show the effects of the diffusion and drift coefficients that illustrate our theoretical results.

• Nuclear Engineering and Technology
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• 제54권8호
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• pp.3059-3072
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• 2022

A Jacobian-Free Newton Krylov Two-Nodal Coarse Mesh Finite Difference algorithm based on Nodal Expansion Method (NEM_TNCMFD_JFNK) is successfully developed and proposed to solve the three-dimensional (3D) and multi-group reactor physics models. In the NEM_TNCMFD_JFNK method, the efficient JFNK method with the Modified Incomplete LU (MILU) preconditioner is integrated and applied into the discrete systems of the NEM-based two-node CMFD method by constructing the residual functions of only the nodal average fluxes and the eigenvalue. All the nonlinear corrective nodal coupling coefficients are updated on the basis of two-nodal NEM formulation including the discontinuity factor in every few newton steps. All the expansion coefficients and interface currents of the two-node NEM need not be chosen as the solution variables to evaluate the residual functions of the NEM_TNCMFD_JFNK method, therefore, the NEM_TNCMFD_JFNK method can greatly reduce the number of solution variables and the computational cost compared with the JFNK based on the conventional NEM. Finally the NEM_TNCMFD_JFNK code is developed and then analyzed by simulating the representative PWR MOX/UO₂ core benchmark, the popular NEACRP 3D core benchmark and the complicated full-core pin-by-pin homogenous core model. Numerical solutions show that the proposed NEM_TNCMFD_JFNK method with the MILU preconditioner has the good numerical accuracy and can obtain higher computational efficiency than the NEM-based two-node CMFD algorithm with the power method in the outer iteration and the Krylov method using the MILU preconditioner in the inner iteration, which indicates the NEM_TNCMFD_JFNK method can serve as a potential and efficient numerical tool for reactor neutron diffusion analysis module in the JFNK-based multiphysics coupling application.

• 한국에너지공학회:학술대회논문집
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• 한국에너지공학회 2000년도 추계 학술발표회 논문집
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• pp.115-120
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• 2000

The analysis of flux distribution under stead-state in large power reactors with assymetry reactivity insertions requires the use of three-dimensional diffusion calculations. For the purpose, consistently formulated modern nodal methods based on higher order interface techniques have become popular tools for flux distributions in large commercial nuclear reactors. Among the earlier developments, the nodal Green's function method obtains its nodal interface equation from the transverse-integrated integral diffusion equation using a finite-medium Green's function. In this method, the outgoing current from a node surface is formulated as a response of the incoming currents and the spatially integrated neutron source within the same node. The well-known nodal expansion method is also based on an interface partial current formulation. Nodal methods high-level interface variables, i.e., interface net current and flux, may be more computationally efficient than the nodal Green's function method because they have one fewer unknown per interface. The Analytic Nodal Method(ANM), which can be classified as an interface net current technique and, was faster in solving some standard benchmark problems than the other two methods.(omitted)

• 한국연소학회:학술대회논문집
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• 한국연소학회 2004년도 제28회 KOSCO SYMPOSIUM 논문집
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• pp.124-132
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• 2004

Activation energy asymptotics (AEA) for Linan's diffusion-flame regime is revisited in this paper. The main purpose of the paper is to carefully re-examine each AEA analysis step in order to clarify the some concepts that are often misunderstood among the ordinary practitioners of the AEA. Particular attention is focused on the different AEA regimes arising from the double limit of large Zel'dovich and Damkohler numbers. In addition. the expansion procedures are shown in detail and the method that the turning point condition, commonly known as the Linan's extinction condition, is found is explained.

• 한국연소학회지
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• 제9권2호
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• pp.1-9
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• 2004

Activation energy asymptotics (AEA) for Linan#s diffusion-flame regime is revisited in this paper. The main purpose of the paper is to carefully re-examine each AEA analysis step in order to clarify the some concepts that are often misunderstood among the ordinary practitioners of the AEA. Particular attention is focused on the different AEA regimes arising from the double limit of large Zel#dovich and Damkohler numbers. In addition, the expansion procedures are shown in detail and the method that the turning point condition, commonly known as the Linan#s extinction condition, is found is explained.

• Nuclear Engineering and Technology
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• 제16권2호
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• pp.70-79
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• 1984

대형 고속증식로용 핵계산 체제(KAERI-26군 단면적 library/1DX/2DB)를 이용하여 SUPER-PHE-NIX I 평형 노심의 초기상태에서의 diagrid 및 Pad팽창에 대한 반응도 계수를 계산, 검토하였다. 노심은 R-Z등가 model로 묘사하고, 2차원 다군 확산 이론 전산코드인 2DB를 사용하여 임계도를 계산하였다. 기초계산으로서 반경방향 및 축방향 균일 괭창에 대한 반응도 계산과 노심구성물질의 원자수 밀도 변화와 노심체적 변화에 대한 반응도 변화량계산을 수행하였다. 균일 팽창으로 고려한 diagrid팽창에 대한 반응도 계수는 -0.553pcm/mil로 계산되었다. 한편 반응도의 온도계수는 -1.0766pcm/$^{\circ}C$로 환산되어 프랑스 발표치 -1.09pcm/$^{\circ}C$와 1.2%오차내로 일치하였다. Diagrid 팽창효과 졔산방법을 활용하여 노심의 불균일 팽창을 유발하는 pad팽창에 대한 반응도 계수 계산을 수행한 바 매우 유용함을 알았다. Pad팽창에 대한 반응도 계수는 평균팽창 model의 경우 -0.2743pcm/mi1, pancake집적 model의 경우 -0.2786pcm/mi1로 각각 계산되었다. 또한 자유팽창 노심에서의 온도변화에 따른 pad 팽창에 대한 반응도 계수는 각 model에 대하여 -0.5766pcm/$^{\circ}C$, -0.5858pcm/$^{\circ}C$로 계산되어 프랑스 발표치 -0.574pcm/$^{\circ}C$와 2% 오차내로 일치하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권3호
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• pp.253-266
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• 2019

In this article, a systematic solution based on the sequence of expansion method is planned to solve the time-fractional diffusion equation, time-fractional telegraphic equation and time-fractional wave equation in three dimensions using a current and valid approximate method, namely the ADM, VIM, and the NIM subject to the estimate initial condition. By using these three methods it is likely to find the exact solutions or a nearby approximate solution of fractional partial differential equations. The exactness, efficiency, and convergence of the method are demonstrated through the three numerical examples.

• Journal of the Korean Wood Science and Technology
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• 제22권2호
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• pp.61-70
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• 1994

This study was executed to find the applicability of press drying of tree disk by investigating the shrinkage and drying defect and to form appropriate model by comparing the actual moisture content(MC) and internal temperature in respect of drying time with calculated values based computer simulation to which was applied finite difference method. In press drying disk, heating period, constant drying rate period maintained plateau temperature at 100$^{\circ}C$ and falling drying rate period were significantly distinguished. Actual MC and internal temperature were analogous to those calculated at comparing points. Heat transfer model formed by Fourier's law using specific heat of moist wood and conduction coefficient considering fractional volume of each element of wood cell wall, bound water, free water and air showed applicability as basic data to developing heat expansion, shrinkage and drying stress during press drying. Also mass transfer model formed by Fick's diffusion law using water vapor diffusion coefficient showed applicability. Longitudinal shrinkage was developed by pressure of hot press and tangential shrinkage was restrained by hygrothermal recovery. The heart check, surface check and ring failure were occurred differently in species, but V-shaped crack didn't develop.

• 한국진공학회:학술대회논문집
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• 한국진공학회 2014년도 제46회 동계 정기학술대회 초록집
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• pp.160.2-160.2
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• 2014

Recently silicon has attracted intense interest as a promising anode material of lithium-ion batteries due to its extremely high capacity of 4200 mA/g (for Li4.2Si) that is much higher than 372 mAh/g (for LiC6) of graphite. However, it seriously suffers from large volume change (even up to 300%) of the electrode upon lithiation, leading to its pulverization or mechanical failure during lithiation/delithiation processes and the rapid capacity fading. To overcome this problem, Si nanowires have been considered. Use of such Si nanowires provides their facile relaxation during lithiation/delithiation without mechanical breaking. To design better Si electrodes, a study to unveil atomic-scale mechanisms involving the volume expansion and the phase transformation upon lithiation is critical. In order to investigate the lithiation mechanism in Si nanowires, we have developed a reactive force field (ReaxFF) for Si-Li systems based on density functional theory calculations. The ReaxFF method provides a highly transferable simulation method for atomistic scale simulation on chemical reactions at the nanosecond and nanometer scale. Molecular dynamics (MD) simulations with the ReaxFF reproduces well experimental anisotropic volume expansion of Si nanowires during lithiation and diffusion behaviors of lithium atoms, indicating that it would be definitely helpful to investigate lithiation mechanism of Si electrodes and then design new Si electrodes.