• Title/Summary/Keyword: Transport Equation

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Fundamentals of Stress-Induced Diffusion: Theoretical Approach to Hydrogen Transport through Self-Stressed Electrode

  • Lee, Sung-Jai;Pyun, Su-Il
    • Journal of the Korean Electrochemical Society
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    • v.8 no.1
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    • pp.47-54
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    • 2005
  • This article covers the fundamentals of stress-induced diffusion, focusing on the theoretical model for hydrogen transport through self-stressed electrode. First, the relationship between hydrogen diffusion and macroscopic deformation of the electrode specimen was briefly introduced, and then it was classified into the diffusion-elastic and elasto-diffusive phenomena. Next, the transport equation for the flux of hydrogen caused simultaneously by both the concentration gradient and the stress gradient was theoretically derived. Finally, stress-induced diffusion was discussed on the basis of the numerical solutions to the derived transport equation under the permeable and impermeable boundary conditions.

Analysis of Transport Characteristics for FinFET Using Three Dimension Poisson's Equation

  • Jung, Hak-Kee;Han, Ji-Hyeong
    • Journal of information and communication convergence engineering
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    • v.7 no.3
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    • pp.361-365
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    • 2009
  • This paper has been presented the transport characteristics of FinFET using the analytical potential model based on the Poisson's equation in subthreshold and threshold region. The threshold voltage is the most important factor of device design since threshold voltage decides ON/OFF of transistor. We have investigated the variations of threshold voltage and drain induced barrier lowing according to the variation of geometry such as the length, width and thickness of channel. The analytical potential model derived from the three dimensional Poisson's equation has been used since the channel electrostatics under threshold and subthreshold region is governed by the Poisson's equation. The appropriate boundary conditions for source/drain and gates has been also used to solve analytically the three dimensional Poisson's equation. Since the model is validated by comparing with the three dimensional numerical simulation, the subthreshold current is derived from this potential model. The threshold voltage is obtained from calculating the front gate bias when the drain current is $10^{-6}A$.

The study of electron transport coefficients in pure Xe by 2-term approximation of the Boltzmann equation (2항근사 볼츠만 방정식을 이용한 Xe분자가스의 전자수송계수의 해석)

  • Ma, Su-Young;Jeon, Byung-Hoon;Kim, Song-Gang
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.174-177
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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 Xe 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 Xe molecular gas.

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The study of electron transport coefficients in pure Ne by 2-term approximation of the Boltzmann equation (2항근사 볼츠만 방정식을 이용한 Ne분자가스의 전자수송계수의 해석)

  • Jeon, Byung-Hoon;Gang, Myung-Hee;Kim, Song-Gang
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.182-185
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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 Ne were calculated over the wide E/N range from 0.01 to 300 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 Ne molecular gas.

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Single-shot Transport-of-intensity Equation Using a Wollaston Prism for Biological Samples

  • Joseph Vermont Bunyi Bandoy;Cuong Manh Nguyen;An Nazmus Sakib;Suhyeon Kim;Hyuk-Sang Kwon
    • Current Optics and Photonics
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    • v.8 no.5
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    • pp.502-507
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    • 2024
  • The Wollaston prism (WP) has shown promise in enabling single-shot transport-of-intensity equation (ssTIE) measurements, facilitating efficient phase retrieval in microscopy. The 1-degree prism which produces the minor beam-separation angle is used to prevent distortions. An optical-glass plate is employed in the duplicated beam path to introduce defocusing. This configuration is also advantageous when aligning the beams laterally caused by the refraction of the optical-glass plate, thus allowing another method for single-shot measurements. We applied the proposed method to image the red blood cells (RBCs), demonstrating that the proposed method could be useful in various biological and medical applications.

Mathematical Model for Analysis on the Behaviours of Submerged Mound Constructed by the Dredged Materials (수중둔덕의 거동특성 해석을 위한 수학적 모형)

  • Choi, Han-kyu;Lee, Oh-Sung
    • Journal of Industrial Technology
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    • v.19
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    • pp.391-402
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    • 1999
  • The numerical model predicting the behaviours of submerged mound constructed by dredged material is developed in this paper. The model is based on the Bailard's sediment transport formula, Stokes' second-order wave theory and the sediment balance equation. Nonlinear partial differential equation which is the same form as convection-dispersion equation which represents change of bed section can be obtained by substituting sediment transport equation for equation of sediment conservation. By this process, the analytical solution by which the characteristic of the behaviours of submerged mound can be estimated is derived by probably combining the convention coefficient and the dispersion coefficient governing the behaviours of submerged mound and the probability density function representing the wave characteristics. The validity of the analytical solution is verified by comparing the analytical solution which is assumed to estimate the movement rate submerged mound by bed-load with the field data of the past and its characteristic is analyzed quantitatively by obtaining the mean of the dispersion coefficient representing the extent of the decrease rate of the submerged mound height.

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Model Development for Analysis of Nitrate Leaching and Its Field Application in a Rural Area (농촌지역의 질산성질소 거동 해석을 위한 모델 개발 및 현장 적용)

  • Suk, Hee-Jun;Chon, Chul-Min
    • Economic and Environmental Geology
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    • v.42 no.6
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    • pp.561-574
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    • 2009
  • Unsaturated/saturated groundwater flow and solute transport model, VSFRT2D(Variable Saturated Flow and Reactive Transport model) was developed considering effects of pumping, irrigation, and denitrification. VSFRT2D employed Richards equation as governing equation for groundwater flow and previously existing unsaturated models modified by including computational procedure of evapotranspiration at surface using Thornthwaite method when precipitation doesn't occur. Bioremediation processes based on monod kinetics are described using four nonlinear contaminant transport equations and three nonlinear microbes transport equations. The developed model was applied to field data in Hongsung area contaminated with nitrate. In order to identify the effect of precipitation, pumping, evapotranspiration, irrigation, fertilizer application, and various bioremediations on groundwater flow and contaminant transport, individual processes were separated and simulated. Then all results obtained from the individual processes are compared with each other. The simulation results show that bioremediation had a negligible effect on nitrate concentration change. However, pumping for irrigation, precipitation, and nitrogen fertilizer application showed profound influences on nitrate concentration change.

CONVERGENCE OF APPROXIMATE SOLUTIONS TO SCALAR CONSERVATION LAWS BY DEGENERATE DIFFUSION

  • Hwang, Seok
    • Communications of the Korean Mathematical Society
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    • v.22 no.1
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    • pp.145-155
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    • 2007
  • In this paper, we show the convergence of approximate solutions to the convective porous media equation using methodology developed in [8]. First, we obtain the approximate transport equation for the given convective porous media equation. Then using the averaging lemma, we obtain the convergence.

Effect of Nonuniform Vertical Grid on the Accuracy of Two-Dimensional Transport Model

  • Lee, Chung-Hui;Cheong, Hyeong-Bin;Kim, Hyun-Ju;Kang, Hyun-Gyu
    • Journal of the Korean earth science society
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    • v.39 no.4
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    • pp.317-326
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    • 2018
  • Effect of the nonuniform grid on the two-dimensional transport equation was investigated in terms of theoretical analysis and finite difference method (FDM). The nonuniform grid having a typical structure of the numerical weather forecast model was incorporated in the vertical direction, while the uniform grid was used in the zonal direction. The staggered and non-staggered grid were placed in the vertical and zonal direction, respectively. Time stepping was performed with the third-order Runge Kutta scheme. An error analysis of the spatial discretization on the nonuniform grid was carried out, which indicated that the combined effect of the nonuniform grid and advection velocity produced either numerical diffusion or numerical adverse-diffusion. An analytic function is used for the quantitative evaluation of the errors associated with the discretized transport equation. Numerical experiments with the non-uniformity of vertical grid were found to support the analysis.

Analysis of Electron Transport Coefficients in Binary Mixtures of TEOS Gas with Kr, Xe, He and Ne Gases for Using in Plasma Assisted Thin-film Deposition

  • Tuan, Do Anh
    • Journal of Electrical Engineering and Technology
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    • v.11 no.2
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    • pp.455-462
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    • 2016
  • The electron transport coefficients in not only pure atoms and molecules but also in the binary gas mixtures are necessary, especially on understanding quantitatively plasma phenomena and ionized gases. Electron transport coefficients (electron drift velocity, density-normalized longitudinal diffusion coefficient, and density-normalized effective ionization coefficient) in binary mixtures of TEOS gas with buffer gases such as Kr, Xe, He, and Ne gases, therefore, was analyzed and calculated by a two-term approximation of the Boltzmann equation in the E/N range (ratio of the electric field E to the neutral number density N) of 0.1 - 1000 Td (1 Td = 10−17 V.cm2). These binary gas mixtures can be considered to use as the silicon sources in many industrial applications depending on mixture ratio and particular application of gas, especially on plasma assisted thin-film deposition.