• 제목/요약/키워드: Poisson's equation

검색결과 230건 처리시간 0.028초

Three-Dimensional Simulations of the Jeans-Parker Instability

  • LEE SANG MIN;HONG SEUNG SOO;KIM AND JONGSOO
    • 천문학회지
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    • 제34권4호
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    • pp.285-287
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    • 2001
  • We have studied the nonlinear evolution of a magnetized disk of isothermal gas, which is sustained by its self-gravity. Our objective is to investigate how the Jeans, Parker, and convective instabilities compete with each other in structuring/de-structuring large scale condensations in such disk. The Poisson equation for the self-gravity has been solved with a fourth-order accurate Fourier method along with the Green function, and the MHD part has been handled by an isothermal TVD code. When large wavelength perturbations are applied, the combined action of the Jeans and Parker instabilities suppresses the development of the convection and forms a dense core of prolate shape in the mid-plane. Peripheral structures around it are filamentary. The low density filaments connect the dense core to the diffuse upper region. On the other hand, when small wavelength perturbations are applied, the disk develops into an equilibrium state which is reminiscent of the Mouschovias's 2-D non-linear equilibrium of the classical Parker instability under an externally given gravity.

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Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations

  • Benferhat, Rabia;Daouadji, Tahar Hassaine;Mansour, Mohamed Said;Hadji, Lazreg
    • Earthquakes and Structures
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    • 제10권6호
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    • pp.1429-1449
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    • 2016
  • The effect of porosity on bending and free vibration behavior of simply supported functionally graded plate reposed on the Winkler-Pasternak foundation is investigated analytically in the present paper. The modified rule of mixture covering porosity phases is used to describe and approximate material properties of the FGM plates with porosity phases. The effect due to transverse shear is included by using a new refined shear deformation theory. The number of unknown functions involved in the present theory is only four as against five or more in case of other shear deformation theories. The Poisson ratio is held constant. Based on the sinusoidal shear deformation theory, the position of neutral surface is determined and the equation of motion for FG rectangular plates resting on elastic foundation based on neutral surface is obtained through the minimum total potential energy and Hamilton's principle. The convergence of the method is demonstrated and to validate the results, comparisons are made with the available solutions for both isotropic and functionally graded material (FGM). The effect of porosity volume fraction on Al/Al2O3 and Ti-6Al-4V/Aluminum oxide plates are presented in graphical forms. The roles played by the constituent volume fraction index, the foundation stiffness parameters and the geometry of the plate is also studied.

MPI 기반의 병렬 성층${\cdot}$회전 난류 시뮬레이션 (Parallel Stratified and Rotating Turbulence Simulation based on MPI)

  • 김병욱;양성봉
    • 한국정보처리학회논문지
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    • 제7권1호
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    • pp.57-64
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    • 2000
  • 본 논문에서는 MPI 기반이 성층${\cdot}$회전 난류 시뮬레이션을 위한 LES코드의 기법에 대해 연구하며 그 결과를 실험한다. 본 논문에서는 병렬화 기법을 위해서 순차 LES코드에 내재되어 있는 Tridiagonal solver의 제거를 통한 병렬화의 성능 향상과 포아선 방정식의 병렬화를 위한 영역 분할 방법을 소개한다. 또한 본 논문에서 연구되어진 병렬 LES 코드를 슈퍼컴퓨터에서 다양한 영역 분할에 대한 실험을 수행하며 그 결과에 대해 나타낸다. 실험 환경은 CRAY-T3E에서 수행하였으며, 다양한 영역 분할에 대해 프로세서의 개수를 변화시키며 수행속도와 그에 따른 속도의 향상을 측정하였다. 그 결과 단일 프로세서에서 순차 LES를 수행하는 것보다 병렬 LES코드에서 최고 16배에 해당되는 속도의 향상의 결과를 얻을 수 있었다.

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3차원 10절점-상당요소에 의한 굽힘문제의 정적.동적해석 (Static and Dynamic Analyses of Bending Problems Using 3-Dimensional 10-Node Equivalent Element)

  • 권영두;윤태혁
    • 전산구조공학
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    • 제10권4호
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    • pp.117-130
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    • 1997
  • 본 논문에서는 등방성판의 인장이나 전단변형은 물론 굽힘문제에도 적용할 수 있는 3차원 고체요소들 중에서 최소의 자유도를 갖는 수정 10절점 상당요소를 제안하였다. 제안된 수정 10절점 상당요소는 Q11요소나 20절점요소로부터 자유도가 줄어듬에 기인한 과대한 굽힘강성을 나타낸다. 이러한 상대적 강성과잉 현상을 수정하기 위한 효과적인 방법으로 가우스 적분점 수정 방법을 제안하였다. 수정량은 포아송 비의 함수이다. 수정 10절점 상당요소의 효과를 여러 가지 예에 적용하여 검증하였다. 제안된 수정 10절점 상당요소에 의한 등방성판의 정적해석과 자유진동 해석의 결과들은 20절점요소를 사용한 결과들과 잘 일치하였다.

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SOI형 대칭 DG MOSFET의 문턱전압 도출에 대한 간편한 해석적 모델 (A simple analytical model for deriving the threshold voltage of a SOI type symmetric DG-MOSFET)

  • 이정호;서정하
    • 대한전자공학회논문지SD
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    • 제44권7호통권361호
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    • pp.16-23
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    • 2007
  • 본 논문에서는 완전 공핍된 SOI형 대칭 이중게이트 MOSFET의 문턱 전압에 대한 간단한 해석적 모델을 제시하고자 실리콘 몸체 내의 전위 분포를 근사적으로 채널에 수직한 방향의 좌표에 대해 4차 다항식으로 가정하였다. 이로써 2차원 포아송 방정식을 풀어 표면 전위의 표현식을 도출하고, 이 결과로부터 드레인 전압 변화에 의한 문턱 전압의 roll-off를 비교적 정확하게 기술할 수 있는 문턱 전압의 표현식을 closed-form의 간단한 표현식으로 도출하였다. 도출된 표현식으로 모의 실험을 수행한 결과 $0.01\;[{\mu}m]$의 실리콘 채널 길이 범위까지 채널 길이에 지수적으로 감소하는 것을 보이는 비교적 정확한 결과를 얻을 수 있음을 확인하였다.

침-평판 전극 사이에서 중간 압력 질소 방전의 시뮬레이션 (Numerical Simulation of Nitrogen Discharge at Medium Pressure between Point-Plane Electrodes)

  • 고욱희;박인호
    • 한국진공학회지
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    • 제17권6호
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    • pp.487-494
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    • 2008
  • 준 2차원 수치적 모델을 사용하여 침-평판(point-plane)형의 전극 사이에 있는 중간 압력 질소의 방전에 대한 시뮬레이션을 수행하였다. 이 모델에서는 전자와 이온에 대한 연속방정식을 풀어 시. 공간적으로 변하는 전하분포를 계산하고, 공간 전하 분포의 변화에 따라 결정되는 전기장은 푸아송 방정식을 풀어 얻는다. 연속 방정식은 FCT (Flux-corrected transport) 알고리즘과 FEM (Finite Element Method) 방법을 적용하여 수치적으로 다루어 졌다. 50Torr 압력에서의 질소 방전에 대한 시뮬레이션 결과는 중간 압력 질소 방전의 물리적 특성에 관한 상세한 이해를 제공한다. 또 계산 결과와 실험 결과[1]와의 비교는 정성적으로 잘 일치하는 것을 보여 준다.

Microflow of dilute colloidal suspension in narrow channel of microfluidic-chip under Newtonian fluid slip condition

  • Chun Myung-Suk;Lee Tae Seok;Lee Kangtaek
    • Korea-Australia Rheology Journal
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    • 제17권4호
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    • pp.207-215
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    • 2005
  • We present a finite difference solution for electrokinetic flow in rectangular microchannels encompassing Navier's fluid slip phenomena. The externally applied body force originated from between the nonlinear Poisson-Boltzmann field around the channel wall and the flow-induced electric field is employed in the equation of motion. The basic principle of net current conservation is applied in the ion transport. The effects of the slip length and the long-range repulsion upon the velocity profile are examined in conjunction with the friction factor. It is evident that the fluid slip counteracts the effect by the electric double layer and induces a larger flow rate. Particle streak imaging by fluorescent microscope and the data processing method developed ourselves are applied to straight channel designed to allow for flow visualization of dilute latex colloids underlying the condition of simple fluid. The reliability of the velocity profile determined by the flow imaging is justified by comparing with the finite difference solution. We recognized the behavior of fluid slip in velocity profiles at the hydrophobic surface of polydimethylsiloxane wall, from which the slip length was evaluated for different conditions.

A Two-Dimensional Particle-in-cell Simulation for the Acceleration Channel of a Hall Thruster

  • Lim, Wang-Sun;Lee, Hae-June;Lee, Jong-Sub;Lim, Yu-Bong;Seo, Mi-Hui;Choe, Won-Ho;Seon, Jong-Ho;Park, Jae-Heung
    • 한국추진공학회:학술대회논문집
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    • 한국추진공학회 2008년 영문 학술대회
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    • pp.557-560
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    • 2008
  • A two-dimensional particle-in-cell(PIC) simulation with a Monte-Carlo Collision(MCC) has been developed to investigate the discharge characteristics of the acceleration channel of a HET. The dynamics of electrons and ions are treated with PIC method at the time scale of electrons in order to investigate the particle transport. The densities of charged particles are coupled with Poisson's equation. Xenon neutrals are injected from the anode and experience elastic, excitation, and ionization collisions with electrons, and are scattered by ions. These collisions are simulated by using an MCC model. The effects of control parameters such as magnetic field profile, electron current density, and the applied voltage have been investigated. The secondary electron emission on the dielectric surface is also considered.

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대칭형 무접합 이중게이트 MOSFET에서 스케일 길이를 이용한 문턱전압 이하 스윙 모델 (Subthreshold Swing Model Using Scale Length for Symmetric Junctionless Double Gate MOSFET)

  • 정학기
    • 한국전기전자재료학회논문지
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    • 제34권2호
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    • pp.142-147
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    • 2021
  • We present a subthreshold swing model for a symmetric junctionless double gate MOSFET. The scale length λ1 required to obtain the potential distribution using the Poisson's equation is a criterion for analyzing the short channel effect by an analytical model. In general, if the channel length Lg satisfies Lg > 1.5λ1, it is known that the analytical model can be sufficiently used to analyze short channel effects. The scale length varies depending on the channel and oxide thickness as well as the dielectric constant of the channel and the oxide film. In this paper, we obtain the scale length for a constant permittivity (silicon and silicon dioxide), and derive the relationship between the scale length and the channel length satisfying the error range within 5%, compared with a numerical method. As a result, when the thickness of the oxide film is reduced to 1 nm, even in the case of Lg < λ1, the analytical subthreshold swing model proposed in this paper is observed to satisfy the error range of 5%. However, if the oxide thickness is increased to 3 nm and the channel thickness decreased to 6 nm, the analytical model can be used only for the channel length of Lg > 1.8λ1.

자기공명유속계 (MRV) 에서 3차원 다중경로 선적분법을 활용한 비침습적 압력예측 방법 개발 (Development of Non-Invasive Pressure Estimation Using 3D Multi-Path Line Integration Method from Magnetic Resonance Velocimetry (MRV))

  • 장일훈;무함마드 하피즈 아리푸딘;송시몬
    • 한국가시화정보학회지
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    • 제21권2호
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    • pp.14-23
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    • 2023
  • The pressure difference across stenotic blood vessels is a commonly used clinical metric for diagnosing many cardiovascular diseases. At present, most clinical pressure measurements rely solely on invasive catheterization. In this study, we propose a novel method for non-invasive pressure estimation using the incompressible Navier-Stokes equations and a 3D multi-path integration approach. We verify spatio-temporal convergence on an in-silico dataset of a cylindrical straight pipe phantom with steady and pulsatile flow fields. We then evaluate the proposed method on an in vitro dataset of reconstructed control, pre-operative, and post-operative carotid artery cases acquired from 4D flow MRI. The performance of our method is compared to existing approaches based on the pressure Poisson equation and work-energy relative pressure. The results demonstrate the proposed method's high accuracy, robustness to spatio-temporal subsampling, and reduced sensitivity to noise, highlighting its great potential for non-invasive pressure estimation.