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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 許文翰(Wen-Hann Sheu) | |
| dc.contributor.author | Fan Weng | en |
| dc.contributor.author | 翁凡 | zh_TW |
| dc.date.accessioned | 2021-06-17T09:06:48Z | - |
| dc.date.available | 2020-01-15 | |
| dc.date.copyright | 2020-01-15 | |
| dc.date.issued | 2019 | |
| dc.date.submitted | 2019-12-25 | |
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pressure driven flows in two-dimensional straight channels:Finite Debye layer effects, Anal. Chem., Vol 73, pp. 1979-1986, 2001 [2] Zhang Yao, Wu Jiankang. and Chen Bo, A coordinate transformation method for numerical solutions of the electric double layer and electroosmotic flows in a microchannel Int. J. for Numerical Methods in Fluids , Vol 68, pp. 671-685, 2012 [3] David C. Grahame, The Electrical Double layer and the Theory of Electrocapillary, Chem. Rev., Vol. 44, pp. 441-501, 1947 [4] Neelesh A. Patankar and Howard H. Hu, Numerical Simulation of Electroosmotic Flow, Anal. Chem., Vol. 70, pp. 1870-1881, 1998 [5] Shizhi Qian and Haim H. Bau, Theoretical investigation of electro-osmotic flows and chaotic stirring in rectangular cavities, Applied Mathematical Modeling, Vol. 29, pp. 726-753, 2005 [6] R.-J. Yang, L.-M. Fu, and C.-C. Hwang, Electroosmotic Entry Flow in a Microchannel, Journal of Colloid and Interface Science , Vol 244, pp. 173-179, 2001 [7] W.B. Russel, D.A. Saville, and W.R. Schowalter, Colloidal dispersions, cambridge monographs on mechanics and applied mathematics Cambridge University Press, cambridge, 1989. [8] S. V. Patankar, Numerical Heat Transfer and Fuild Flow, Hemisphere, New York, 1980. [9] Chun Yang, Dongqing Li, , Jacob H. Masliyah, Modeling forced liquid convection in rectangularmicrochannels with electrokinetic effects, Int. J. Heat and Mass Transfer , Vol. 41, pp. 4229-4249, 1998 [10] Jahrul Alam, John C. Bowman, Energy-Conserving Simulation of Incompressible Electro-Osmotic and Pressure-Driven Flow, Theoretical and computational Fluid Dynamics, pp. 1-17, 2002. [11] U. Ghia, K. N. Ghia, High Re Solutions for incompressible Flow Using the Navier- Stokes Equation and a Multigrid Method, J. Comp. Physics, Vol. 48, pp. 387-411, 1982 [12] Ercan Erturk, Numerical solutions of 2-D steady incompressible flow over a backward-facing step, Part I: High Reynolds number solutions, Computers and Fluids, Vol. 37, pp. 633-655, 2008 [13] Tony W. H. Sheu and P. H. Chiu, A divergence-free-condition compensated method for incompressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, Vol. 196, pp. 4479-4494, 2007. [14] Tony W. H. Sheu and R. K. Lin, An incompressible Navier-Stokes model implemented on non-staggered grids, Numer. Heat Transf., B Fundam., Vol. 44(3), pp. 277-294, 2003. [15] 林瑞國, 不可壓縮黏性熱磁流之科學計算方法, 國立台灣大學博士論文, 2005. [16] Christopher K. W. Tam, Jay C. Webb, Dispersion-ralation-preserving finite difference schemes for computational acoustics, Journal of Computational Physics., Vol. 194, pp. 194-214, 1993. [17] Richard D. Handy, A Frank von der Kammer, A Jamie R. Lead A, Martin Hassell ¨ ov, A Richard Owen, A Mark Crane, The ecotoxicology and chemistry of manufactured nanoparticles, Ecotoxicology, Vol. 17, pp. 287-314, 2008. [18] David E Clapham, Symmetry, Selectivity, and the 2003 Nobel Prize, Cell, Vol. 115, pp. 641-646, 2003. [19] 袁聖宗, 在曲線座標下求解非線性EHD方程, 國立台灣大學碩士論文, 2013. [20] 王聖鋒, 發展求解NS與PNP耦合方程之方法, 國立台灣大學碩士論文, 2013. [21] P. H. Chiu, TonyW. H. Sheu, On the development of a dispersion-relation-preserving dual-compact upwind scheme for convection-diffusion equation, Journal of Computational Physics., Vol. 228, pp. 3640-3655, 2009. [22] Peter C. Chu, Chenwu Fan, A three-point combined compact difference scheme, J. Comput. Phys., Vol. 140, pp. 370-399, 1998. [23] Akil J. Harfash, Huda A. Jalob Sixth and Fourth Order Compact Finite Difference Scheme for Two and Three Dimension Poisson Equation with Two Methods to derive These Schemes, Basrah Journal of Science (A), Vol.24(2),1-20, 2006. [24] Hans Johnston, Cheng Wang, Jian-Guo Liu A Local Pressure Boundary ondition Spectral Collocation Scheme for the Three-Dimensional Navier-Stokes Equations, J. Sci. Comput., Vol. 60, pp. 612-626, 2014. [25] 薛向成, 建構在細胞膜離子通道內傳輸行為的PNP-NS數學與數值模型, 國立台灣大學碩士論文, 2015. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/74741 | - |
| dc.description.abstract | 本論文改善及平行化一有限差分的高階數值方法來求解非正交座標複雜外型的PNP-NS方程組，此方程組包含了描述外加電場電位勢的Laplace方程、描述壁面電位勢的Poisson方程、描述離子濃度分布的Nernst-Planck方程以及由庫倫力驅動的不可壓縮Navier-Stokes方程組。論文內容主要描述因電位差開啟的各種不同邊界外型離子通道，其內部流體經由通道留出至外部的物理行為，以及模擬完整細胞膜上多離子通道的傳輸行為。 | zh_TW |
| dc.description.abstract | Abstract
In this study, a high-order numerical method of finite difference is improved and parallelized to solve the PNP-NS equations of complex external shape with non-orthogonal coordinates. The equations under investigation includes the Laplace equation for potential of the applied electric field and the Poisson equation describing the potential of the wall potential. The Nernst-Planck equation describing the ion concentration distribution and the incompressible Navier-Stokes equations for the Coulomb force. The content of the paper mainly describes the various boundary-shaped ion channels opened by the potential difference, the physical behavior of the internal fluid leaving the channel through the channel, and the transmission behavior of the multi-ion channel on the intact cell membrane. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T09:06:48Z (GMT). No. of bitstreams: 1 ntu-108-R04525099-1.pdf: 2963864 bytes, checksum: 8a01a694fc3d7b45eed2fe8cc4e4f501 (MD5) Previous issue date: 2019 | en |
| dc.description.tableofcontents | Table of Contents i
List of Figures v 中文摘要 vii Abstract viii Explanation of Symbols ix Chapter 1. Introduction 1 1.1 Preface 1 1.2 Research motivation 2 1.3 Literature Review 4 1.4 Thesis outline 8 Chapter 2.Theoretical Background 9 2.1 Introduction to Cells and Cell Structure 9 2.2 Introduction of Cell membrane 11 2.3 Introduction of Transphospholipid bilayer transport 15 2.4 Introduction of Ion channels 16 2.5 Introduction of Action potential 17 Chapter 3.The Establishment of Mathematical Models 20 3.1 Basic assumptions 20 3.2 The governing equation 21 3.2.1 Laplace equation describing the potential of the applied electric field 21 3.2.2 Poisson equation describing wall electric potential 22 3.2.3 Nernst-Planck equation describing positive and negative ion distribution 23 3.2.4 Navier-Stokes equation for incompressible viscous flow 24 3.3 Coordinate Transformation Equation 25 Chapter 4.Numerical Model 29 4.1 Discrete Time 30 4.2 Discrete Space 31 4.3 Discreteness of the pressure equation 36 4.4 Numerical verification 38 4.5 Calculation procedures 40 4.6 Parallelization 42 Chapter 5.Numerical Simulation of Ion Channels 45 5.1 Description of the problem 45 5.1.1 Parameter setting 46 5.2 Flow field analysis of rectangular non-periodic boundary 46 5.2.1 Initial and boundary conditions of the calculation model 46 5.3 Flow field analysis of rectangular periodic boundary 50 5.3.1 Initial and boundary conditions of the calculation model 50 5.4 Flow field analysis of sector-shaped periodic boundary conditions 52 5.4.1 Initial and boundary conditions of the calculation model 53 5.5 Discussion 55 Chapter 6.Conclusion 64 6.1 Research results and discussion 64 6.2 Future work and outlook 66 References 67 | |
| dc.language.iso | en | |
| dc.subject | 仿離子通道 | zh_TW |
| dc.subject | Poisson-Nernst-Planck方程組 | zh_TW |
| dc.subject | Navier-Stokes方程組 | zh_TW |
| dc.subject | 週期性邊界條件 | zh_TW |
| dc.subject | 平行化 | zh_TW |
| dc.subject | PNP | en |
| dc.subject | Periodic boundary condition | en |
| dc.subject | Imitation ion channels | en |
| dc.subject | Parallelization | en |
| dc.subject | NS | en |
| dc.title | 使用經平行化後的PNP-NS數學與數值模型模擬細胞膜上多離子通道之傳輸行為 | zh_TW |
| dc.title | Simulation of Transport Phenomena in Multiple Ions Channels on Cell Membrane with Parallelized PNP-NS Mathematical and Numerical Models | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 108-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 蔡順峰(Shun-Feng Tsai),高仕超(Shih-Chao Kao),馬克沁(Maxim Soluvchuk) | |
| dc.subject.keyword | 平行化,Poisson-Nernst-Planck方程組,Navier-Stokes方程組,週期性邊界條件,仿離子通道, | zh_TW |
| dc.subject.keyword | Parallelization,PNP,NS,Periodic boundary condition,Imitation ion channels, | en |
| dc.relation.page | 70 | |
| dc.identifier.doi | 10.6342/NTU201904404 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2019-12-25 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 工程科學及海洋工程學研究所 | zh_TW |
| 顯示於系所單位： | 工程科學及海洋工程學系 | |
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