• Proceedings of the KSME Conference
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• 2001.06e
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• pp.760-765
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• 2001

Some multidimentional generalizations of the Fokker-Planck Equation used by Friedrich and Peinke for description of a turbulent cascade was solved by A.A.Donkov, A.D.Donkov, and G.I.Grancharova. The solutions are two types, isotropic and anisotropic diffusion case. We introduce their methods to solve the Equation and solutions. Furthermore we get the more generalized exact solution as combination of two cases and plot to compare those to experimental results for the isotropic case.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.05c
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• pp.164-167
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• 2001

The electron transport coefficients, the electron drift velocity W, the longitudinal diffusion coefficient $ND_L$ and $D_L/{\mu}$, in pure $CO_2$ were calculated over the wide E/N range from 0.01 to 500 Td at 1 Torr by two-term approximation of the Boltzmann equation for determination of electron collision cross sections set and for quantitative characteristic analysis of $CO_2$ molecular gas. And for propriety of two-term approximation of Boltzmann equation analysis, the calculated results compared with the electron transport coefficients measured by Nakamura.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.05a
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• pp.34-39
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• 1996

A consistent general order nodal method for solving the 3-D neutron diffusion equation in (x-y-z) geometry has ben derived by using a weighted integral technique and expanding the spatial variables by the Legendre orthogonal series function. The equation set derived can be converted into any order nodal schemes. It forms a compact system for general order of nodal moments. The method utilizes the analytic solutions of the transverse-integrated quasi -one dimensional equations and a consistent expansion for the spatial variables so that it renders the use of an approximation for the transverse leakages no necessary. Thus, we can expect extremely accurate solutions and the solution would converge exactly when the mesh width is decreased or the approximation order is increased since the equation set is consistent mathematically.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.757-762
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• 2009

In allelic model $X\;=\;(x_1,\;x_2,\;{\cdots},\;x_d)$, $$M_f(t)\;=\;f(p(t))\;-\;{\int}^t_0\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. We can also obtain a new diffusion operator $L^*$ for diffusion coefficient and we prove that unique solution for $L^*$-martingale problem exists. In this note, we define new symmetric preserving transformation. Uniqueness for martingale problem and symmetric property will be proved.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1997.11a
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• pp.87-90
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• 1997

본 논문에서는 영상의 잡음(noise) 제거를 위한 새로운 diffusion모델을 제안한다. MOD모델 (mean curvature diffusion model)은 영상의 잡음 제거 때 유발되는 경계선의 blurring을 지양할 수 있는 장점이 있는 반면에 수렴상태(convergence state)를 갖지 못한 단점을 안고 있다. 본 논문에서는 MCD 모델에 min/max switch를 결합시킴으로써 MCD모델이 갖고 있던 문제점을 개선하였다. 제안하는 diffusion 모델은 scheme의 반복적인 적용에 대해서 실질적으로 그 결과가 더 이상 변동하지 않는 수렴상태(convergence state)를 가진 매우 안정적인 시스템이다.

• East Asian mathematical journal
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• v.40 no.1
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• pp.109-118
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• 2024

This paper proposes a numerical method based on domain decomposition to find approximate solutions for one-dimensional convection-diffusion equations with Neumann boundary conditions. First, the equations are transformed into convection-diffusion equations with Dirichlet conditions. Second, the author introduces the Prediction/Correction Domain Decomposition (PCDD) method and estimates errors for the interface prediction scheme, interior scheme, and correction scheme using known error estimations. Finally, the author compares the PCDD algorithm with the fully explicit scheme (FES) and the fully implicit scheme (FIS) using three examples. In comparison to FES and FIS, the proposed PCDD algorithm demonstrates good results.

• Journal of Korean Port Research
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• v.13 no.2
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• pp.419-426
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• 1999

It is essential for port planning, coastal zone management and environmental impact study to analyze the variation of current and water quality due to the development of water area and discharged water from estuary barrage and basin etc. Mokpo sea area downstreams from a long river and two large basins, the Yongsan river and Yongam-Kumho basins discharging much of water through water gates for the purpose of flood control and prohibition of salt intrusion to the inland fresh water area. In this study, the numerical calculations were carried out for the analysis of diffusion characteristics due to discharging operation, adapting the results of tidal current simulation ADI methord is applied to the governing equation for the movement of sea water and diffusion and 6-point method to the advection terms of diffusion equation. As the results of this study, it is known that the discharging operation causes increasing and/or decreasing of current velocity and enlarging and/or depressing of pollutant diffusion limits depending on the distance from the discharging gates and the mode of discharging operation. To utilize these result, the linked gate operation and the method increasing exchange of sea water must be considered.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 1999.10a
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• pp.253-261
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• 1999

It is essential for port planning, coastal zone management and environmental impact study to analyze the variation of current and water quality due to the development of water area and discharged water from the estuary barrage and basin, etc. Mokpo sea area has downstream from a long river and two large basins, the Yongsan river and Yongam-Kumho basins, discharging much of water through water gates for the purpose of flood and prohibition of salt intrusion to the inland fresh water area. In this study, the numerical calculation were carried out for the analysis of diffusion characteristics due to discharging operation, adopting the results of tidal current simulation. ADI method is applied to the governing equation for the movement of sea water and diffusion and 6-point method to the advection terms of diffusion equation. As the results of this study, it is known that the discharging operation causes increasing and/or decreasing of current velocity and enlarging and/or depressing of pollutant diffusion limits depending on the distance from the discharging gates and the modes of discharging operation. To utilize these result, the linked gate operation and the method increasing exchange of sea water must be considered.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.59-64
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• 2002

This paper investigates a history of Fourier Series for the heat equation and how deeply it is related to modern famous three equations, Navier-Stokes equations in fluid dynamics, drift-diffusion equations in semiconductor, and Black-Scholes equation in finance. We also propose improved models for the heat equation with finite propagation speeds.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.36D no.11
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• pp.45-55
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• 1999

The small signal analyzer for the stationary drift-diffusion equation is developed. The slotboom variables of the potential, electron and hole concentrations for the response of applied small signal are defined and the stationary drift-diffusion equation is linearlized on DC operation point by $S^3A$ method. Frontal solver, which is used to solve the global matrix, progresses the accuracy of the solution in high frequency and minimizes the requirement of the memory. The simulations are executed on the structure of 3 dimensional N'P junction diode and 2 dimensional n-MOSFET to verify the proposed algorithm. The average relative errors of the conductance and the capacitance compared with MEDICI are about 26% and 0.67 for N'P junction diode and 7.75% and 2.24% for n-MOSFET. The simulation by the proposed algorithm can analyze the stationary drift-diffusion equation for applied small signal in high frequency region about 100GHz.