• Title/Summary/Keyword: Boltzmann Equation

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The Analysis of Discharge Characteristics for Discharge Excited KrF Laser System (방전여기 KrF 레이저 장치의 방전특성 해석)

  • Jeong, Jae-Keun;Choi, Boo-Yeon;Lee, Choo-Hie
    • Proceedings of the KIEE Conference
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    • 1988.07a
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    • pp.393-396
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    • 1988
  • In discharge excited excimer laser, it is hard to say that the analysis of laser operation was well explained until now. But this can be improved by analysis the nonlinear discharge characteristics in the cavity. The nonlinear characteristics can be analysed by solving the nonlinear resistance which depends on electron mobility and number density. We can calculate the electron mobility and number density each other using Boltzmann equation and Kinetics equation. So we calculated the nonlinear resistance and analysed nonlinear discharge characteristics.

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Analysis of Nano-Scale Heat Conduction in the Quantum Dot Superlattice by Ballistic Diffusive Approximation (Ballistic Diffusive Approximation에 의한 Quantum Dot Superlattice의 나노열전달 해석)

  • Kim, Won-Kap;Chung, Jae-Dong
    • Proceedings of the KSME Conference
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    • 2004.04a
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    • pp.1376-1381
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    • 2004
  • Understanding the thermal conductivity and heat transfer processes in superlattice structures is critical for the development of thermoelectric materials and optoelectronic devices based on quantum structures. $Chen^{(1)}$ developed ballistic diffusive equation(BDE) for alternatives of the Boltzmann equation that can be applied to the complex geometrical situation. In this study, a simulation code based on BDE is developed and applied to the 1-dimensional transient heat conduction across a thin film and transient 2-dimensional heat conduction across the film with heater. The obtained results are compared to the results of the $Chen^{(1)}$ and Yang and $Chen^{(1)}$. Finally, steady 2-dimensional heat conduction in the quantum dot superlattice are solved to obtain the equivalent thermal conductivity of the lattice and also compared with the experimental data from $Borca-Tasciuc^{(2)}$.

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Potential Profiles and Capacitances of an Ideally Polarizable Electrode in a point Charged Electrolyte

  • Sang youl Kim;K. Vedam
    • Bulletin of the Korean Chemical Society
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    • v.10 no.6
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    • pp.585-591
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    • 1989
  • The effects of the charged metal on the overall electrostatic potential profiles and the capacitances of the electrical double layer are brought out. A model with a simplified jellium and a point-charged electrolyte is utilized in the present calculations. Electrons are assumed not to penetrate electrode surface due to a strong screening of electrolyte at the interface. Electron density functions and ion density functions are obtained, which are also based upon the Poisson equation and Boltzmann equation on either side of the interface. A complete potential profile starting from bulk electrode and ending at bulk electrolyte is obtained by connecting the two potential profiles (one inside the metal electrode, the other inside the electrolyte) with proper boundary conditions. In spite of the simplicity of the model, the present model reveals the importance of the effect of the charged metal on the electrostatic potential profile and the electrical double layer capacitances. The results are discussed and compared with the predictions by Gouy Chapman theory.

Emission spectroscopic diagnostics of argon arc Plasma in Plasma focus device for advanced lithography light source (차세대 리소그래피 빛샘 발생을 위한 플라스마 집속장치의 아르곤 아크 플라스마의 방출 스펙트럼 진단)

  • Hong, Y.J.;Moon, M.W.;Lee, S.B.;Oh, P.Y.;Song, K.B.;Hong, B.H.;Seo, Y.H.;Yi, W.J.;Shin, H.M.;Choi, E.H.
    • Journal of the Korean Vacuum Society
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    • v.15 no.6
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    • pp.581-586
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    • 2006
  • We have generated the argon plasma in the diode chamber based on the established coaxial electrode type and investigated the emitted visible light for emission spectroscopy. We applied various voltages $2\sim3.5kV$ to the device by 0.5kV, and obtained the emission spectrum data for the focused plasma in the diode chamber on the argon pressure of 330 mTorr. The Ar I and Ar II emission line are observed. The electron temperature and ion density have been measured by the Boltzmann plot and Saha equation from assumption of local thermodynamic equilibrium (LTE) The Ar I and Ar II ion densities have been calculated to be $\sim10^{15}/cc\;and\;~10^{13}/cc$, respectively, from Saha equation.

Numerical Analysis of Optical Damage in Dielectrics Irradiated by Ultra-Short Pulsed Lasers (극초단 펄스 레이저에 의한 절연체의 광학 손상 해석)

  • Lee, Seong-Hyuk;Kang, Kwang-Gu;Lee, Joon-Sik;Choi, Young-Ki;Park, Seung-Ho;Ryou, Hong-Sun
    • Proceedings of the KSME Conference
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    • 2004.11a
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    • pp.1213-1218
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    • 2004
  • The present article reports extensive numerical results on the non-local characteristics of ultra-short pulsed laser-induced breakdowns of fused silica ($SiO_{2}$) by using the multivariate Fokker-Planck equation. The nonlocal type of multivariate Fokker-Planck equation is modeled on the basis of the Boltzmann transport formalism to describe the ultra-short pulsed laser-induced damage phenomena in the energy-position space, together with avalanche ionization, three-body recombination, and multiphoton ionization. Effects of electron avalanche, recombination, and multiphoton ionization on the electronic transport are examined. From the results, it is observed that the recombination becomes prominent and contributes to reduce substantially the rate of increase in electron number density when the electron density exceeds a certain threshold. With very intense laser irradiation, a strong absorption of laser energy takes place and an initially transparent solid is converted to a metallic state, well known as laser-induced breakdown. It is also found that full ionization is provided at intensities above threshold, all further laser energy is deposited within a thin skin depth.

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A Study on Thermal Conductivity Measurement and Optical Characteristics of Thin Films (박막의 열물성 측정 및 광학특성 연구)

  • Gwon, Hyuk-Rok;Lee, Seong-Hyuk
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.56 no.12
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    • pp.2202-2207
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    • 2007
  • The present article investigates experimentally and theoretically thermal and optical characteristics of thin film structures through measurement of thermal conductivity of Pyrex 7740 and reflectance in silicon thin film. The $3{\omega}$ method is used to measure thermal conductivity of very thin film with high accuracy and the optical characteristics in thin films are studied to examine the influence of incidence angle of light on reflectance by using the CTM(Characteristics Transmission Method) and the 633 nm He-Ne laser reflectance measurement system. It is found that the estimated reflectance of silicon show good agreement with experimental data. In particular, the present study solves the EPRT(Equation of Phonon Radiative Transport) which is based on Boltzmann transport equation for predicting thermal conductivity of nanoscale film structures. From the results, the measured thermal conductivity is in good agreement with the previous published data. Moreover, thermal conductivities are estimated for different film thickness. It indicates that as film thickness decreases, thermal conductivity decreases substantially due to internal scattering.

Application of the Laplace transformation for the analysis of viscoelastic composite laminates based on equivalent single-layer theories

  • Sy, Ngoc Nguyen;Lee, Jaehun;Cho, Maenghyo
    • International Journal of Aeronautical and Space Sciences
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    • v.13 no.4
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    • pp.458-467
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    • 2012
  • In this study, the linear viscoelastic response of a rectangular laminated plate is investigated. The viscoelastic properties, expressed by two basic spring-dashpot models, that is Kelvin and Maxwell models, is assumed in the range to investigate the influence of viscoelastic coefficients to mechanical behavior. In the present study, viscoelastic responses are performed for two popular equivalent single-layered theories, such as the first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT). Compliance and relaxation modulus of time-dependent viscoelastic behavior are approximately determined by Prony series. The constitutive equation for linear viscoelastic material as the Boltzmann superposition integral equation is simplified by the convolution theorem of Laplace transformation to avoid direct time integration as well as to improve both accuracy and computational efficiency. The viscoelastic responses of composite laminates in the real time domain are obtained by applying the inverse Laplace transformation. The numerical results of viscoelastic phenomena such as creep, cyclic creep and recovery creep are presented.

DeNOx modeling in $N_{2}/O_{2}$ gas by pulsed corona discharge ($N_{2}/O_{2}$ 혼합가스에서 펄스코로나 방전을 이용한 NOx 제거 모델링에 관한 연구)

  • Park, Kwang-Seo;Lee, Hyoung-Sang;Chun, Bae-Hyeock;Shin, Hyun-Ho;Yoon, Woong-Sup;Chun, Kwang-Min
    • 한국연소학회:학술대회논문집
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    • 1999.10a
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    • pp.117-128
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    • 1999
  • The removal of nitrogen oxides(NOx) from $N_{2}/O_{2}$ gas using a pulsed corona discharge was investigated as a function of the reduced electric field(E/N) and the energy density(J/L). A kinetic model was developed to characterize the chemical reactions taking place in a pulsed corona discharge reactor. The model calculates the fractional concentrations of radical species at each pulse-on period and utilizes the radicals to remove NOx for the subsequent pulse-off period. Electron collision reaction data are calculated using ELENDIF program to solve Boltzmann equation for electron energy distribution function, and the subsequent chemical reactions are calculated using CHEMKIN-II program to solve stiff ODE(ordinary differential equation) problems for species concentrations. The corona discharge energy per pulse and the time-space averaged E/N were obtained by fitting the model to experimental data. The model calculation shows good agreement with the experimental data, and predicts the formation of other species such as $NO_{2}$, $O_{3}$ and $N_{2}O$.

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Sensitivity Analysis of Effective Viscosity Coefficients for Computing Characteristics of Ultrathin Gas Film Bearings (초미세 틈새의 기체 베어링 해석용 유효 점도의 표현식과 관련 계수들의 민감도 해석)

  • Kim, Ui Han;Rhim, Yoon Chul
    • Tribology and Lubricants
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    • v.30 no.1
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    • pp.15-20
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    • 2014
  • A more accurate expression for effective viscosity is obtained using a linear regression of the data from Fukui-Kaneko's model, which are obtained through numerical calculations based on the linearized Boltzmann equation. Veijola and Turowski's expression is adopted as a base function for effective viscosity. The four coefficients in that equation are optimized, and sensitivity analysis is conducted for these coefficients. The results show that the coefficient for the first-order Knudsen number is the most accurate, whereas the coefficient in the exponential of the Knudsen number is the least accurate compared with Fukui-Kaneko's results. The expression for effective viscosity is accurate within 0.02% rms of Fukui-Kaneko's results for the inverse Knudsen numbers from 0.01 to 100 and surface accommodation coefficients ranging from 0.7 to 1.

Numerical Investigation on Nonequilibrium Energy Transfer in Thin Metal Film Structures during the Irradiation of Femtosecond Pulse Laser (펨토초 레이저가 조사되는 동안의 금속 박막내의 비평형 에너지 전달 현상에 대한 수치해석 연구)

  • Sim, Hyung-Sub;Lee, Seong-Hyuk
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.56 no.2
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    • pp.367-373
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    • 2007
  • The present study investigates numerically nonequilibrium energy transfer between electrons and phonons in metal thin films irradiated by ultrashort pulse lasers and it also provides the temporal and spatial variations of electron and phonon temperatures using the well-established two-temperature model(TTM) on the basis of the Boltzmann transport equation(BTE). This article predicts the crater shapes in gold film structures, and compares the results by using two-dimensional energy transport equation. From the results, it is found that nonequilibrium energy transfer between electrons and phonons takes place, and the equilibrium time increases with the increase of laser fluence. On the other hand, above threshold fluence the ablation time doesn't change nearly with increasing fluences. Compared with one-dimensional TTM, it also reveals that the temporal distributions of electron and phonon temperatures at the top surface estimated by using two-dimensional TTM have a similar tendency. The results show that two-dimensional TTM can simulate the crater shape of metals during the irradiation of femtosecond pulse lasers and the absorbed energy is propagated to z-direction faster than to r-direction.