• Title/Summary/Keyword: The Boltzmann equation

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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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A Simulation of the Mean energy of electrons in $SF_6$-Ar Mixtures Gas (시뮬레이션을 이용한 $SF_6$-Ar혼합기체의 전자 평균에너지)

  • Kim, Sang-Nam
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2005.07a
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    • pp.578-580
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    • 2005
  • Energy distribution function for electrons in SF6-Ar mixtures gas used by MCS-BEq algorithm has been analysed over the E/N range 30~300[Td] by a two term Boltzmann equation and by a Monte Carlo Simulation using a set of electron cross sections determined by other authors, experimentally the electron swarm parameters for 0.2[%] and 0.5[%] $SF_6$-Ar mixtures were measured by TOF method, The results show that the deduced electron drift velocities, the electron ionization or attachment coefficients, longitudinal and transverse diffusion coefficients and mean energy agree reasonably well with theoretical for a rang of E/N values. The results obtained from Boltzmann equation method and Monte Carlo simulation have been compared with present and previously obtained data and respective set of electron collision cross sections of the molecules.

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Diffusion Coefficients for Electrons in SF6-Ar Gas Mixtures by MCS-BEq (MCSBEq에 의한 SF6-Ar혼합기체의 확산계수)

  • Kim, Sang-Nam
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.64 no.3
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    • pp.125-129
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    • 2015
  • Energy distribution function for electrons in SF6-Ar mixtures gas used by MCS-BEq algorithm has been analysed over the E/N range 30~300[Td] by a two term Boltzmann equation and a Monte Carlo Simulation using a set of electron cross sections determined by other authors experimentally the electron swarm parameters for 0.2[%] and 0.5[%] $SF_6-Ar$ mixtures were measured by time-of-flight(TOF) method, The results show that the deduced longitudinal diffusion coefficients and transverse diffusion coefficients agree reasonably well with theoretical for a rang of E/N values. The results obtained from Boltzmann equation method and Monte Carlo simulation have been compared with present and previously obtained data and respective set of electron collision cross sections of the molecules.

NUMERICAL ANALYSIS OF GAS FLOWS IN ULTRA-THIN FILM GAS BEARINGS USING A MODEL BOLTZMANN EQUATION (모델볼츠만 방정식을 이용한 초박막 개스베어링 기체유장 수치해석)

  • Chung, C.H.
    • Journal of computational fluids engineering
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    • v.14 no.1
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    • pp.86-95
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    • 2009
  • A kinetic theory analysis is used to study the ultra-thin gas flow field in gas bearings. The Boltzmann equation simplified by a collision model is solved by means of a finite difference approximation with the discrete ordinate method. Calculations are made for flows inside micro-channels of backward-facing step, forward-facing step, and slider bearings. The results are compared well with those from the DSMC method. The present method does not suffer from statistical noise which is common in particle based methods and requires less computational effort.

Analysis of Microchannel Flows Using a Model Boltzmann Equation (모델 볼츠만방정식을 이용한 마이크로채널 유동 해석)

  • Chung C. H.
    • 한국전산유체공학회:학술대회논문집
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    • 2004.03a
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    • pp.99-105
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    • 2004
  • A kinetic theory analysis is made of low-speed gas flows in microchannels. The Boltzmann equation simplified by a collision model is solved by means of a finite difference approximation with the discrete ordinate method. The method does not suffer from statistical noise which is common in particle based methods and requires much less amount of computational effort. Calculations are made for flows in simple microchannels and a microfluidic system consisting of two microchannels in series. The method is assessed by comparing the results with those from several different methods and available experimental data.

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ResNet based solver for Poisson-Boltzmann equation (ResNet을 기반으로 한 Poisson-Boltmann 방정식의 풀이법)

  • Jo, Gwanghyun
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2022.05a
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    • pp.216-217
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    • 2022
  • Poisson-Boltzmann equation (PBD), which describes the effects of charges inside cells, plays important roles in various disciplinaries including biology. In this presentation, we introduce a ResNet based method to predict solution of PBE. First, we generate solutions of PBE based on FEM. Next, we train networks whose input shape includes location of charge and shape of cell and while output shape includes the electronic potential.

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Electrokinetic flow and electroviscous effect in a charged slit-like microfluidic channel with nonlinear Poisson-Boltzmann field

  • Chun, Myung-Suk;Kwak, Hyun-Wook
    • Korea-Australia Rheology Journal
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    • v.15 no.2
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    • pp.83-90
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    • 2003
  • In cases of the microfluidic channel, the electrokinetic influence on the transport behavior can be found. The externally applied body force originated from the electrostatic interaction between the nonlinear Poisson-Boltzmann field and the flow-induced electrical field is applied in the equation of motion. The electrostatic potential profile is computed a priori by applying the finite difference scheme, and an analytical solution to the Navier-Stokes equation of motion for slit-like microchannel is obtained via the Green's function. An explicit analytical expression for the induced electrokinetic potential is derived as functions of relevant physicochemical parameters. The effects of the electric double layer, the zeta potential of the solid surface, and the charge condition of the channel wall on the velocity profile as well as the electroviscous behavior are examined. With increases in either electric double layer or zeta potential, the average fluid velocity in the channel of same charge is entirely reduced, whereas the electroviscous effect becomes stronger. We observed an opposite behavior in the channel of opposite charge, where the attractive electrostatic interactions are presented.

Electrokinetically Flow-Induced Streaming Potential Across the Charged Membrane Micropores: for the Case of Nonlinear Poisson-Boltzmann Electric Field (하전된 멤브레인 미세기공에서의 계면동전기적 유동에 의한 흐름전위: 비선형 Poisson-Boltzmann 전기장을 갖는 경우)

  • Myung-Suk Chun
    • Membrane Journal
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    • v.13 no.1
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    • pp.37-46
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    • 2003
  • The electrokinetic effect can be found in cases of the fluid flowing across the charged membrane micropores. The externally applied body force originated from the electrostatic interaction between the nonlinear Poisson-Boltzmann field and the flow-induced electrical field is taken into the equation of motion. The electrostatic potential profile is computed a priori by applying the finite difference scheme, and an analytical solution to the Navier-Stokes equation of motion for slit-like pore is obtained via the Green's function. An explicit analytical expression for the flow-induced streaming potential is derived as functions of relevant physicochemical parameters. The influences of the electric double layer, the surface potential of the wall, and the charge condition of the pore wall upon the velocity profile as well as the streaming potential are examined. With increasing of either the electric double layer thickness or the surface potential, the average fluid velocity is entirely reduced, while the streaming potential increases.

Numerical Simulation on Phase Separation by Using the Lattice-Boltzmann Method (Lattice-Boltzmann Method를 이용한 기체-액체 상분리 시뮬레이션)

  • Jung, Rho-Taek
    • Journal of the Korean Society for Marine Environment & Energy
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    • v.12 no.3
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    • pp.197-201
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    • 2009
  • As one of the promising model on the multiphase fluid mixtures, the Lattice-Boltzmann Method(LBM) is being developed to simulate flows containing two immisible components which are different mass values. The equilibrium function in the LBM can have a nonideal gas model for the equation of state and use the interfacial energy for the phase separation effect. An example on the phase separation has been carried out through the time evolution. The LBM based on the statistic mechanics is appropriate to solve very complicated flow problems and this model gives comparative merits rather than the continuum mechanics model.

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