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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳宜良(I-Liang Chern) | |
| dc.contributor.author | Cheng-Li Tsou | en |
| dc.contributor.author | 鄒正理 | zh_TW |
| dc.date.accessioned | 2021-06-08T06:01:41Z | - |
| dc.date.copyright | 2011-08-11 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-08-05 | |
| dc.identifier.citation | [1] I-Liang Chern and Yu-Chen Shu, A Coupling Interface Method for Elliptic
Interfac Problems, (2007). [2] David J.Griffiths, Introduction to Electrodynamics 3ed. [3] Fogolari F, Brigo A, Molinari H. (2002). The Poisson–Boltzmann equation for biomolecular electrostatics: a tool for structural biology. J. Mol. Recognit, 15(6):377–392 [4] Michael J. Holst, The Poisson-Boltzmann equation: Analysis and multilevel nu- merical solution, Applied Mathematics and CRPC, California Institute of Tech- nology. (1994). [5] P. Debye-HÄuckel , Physik.Z. 24, 185 (1923). [6] Roman Wienands, Wolfgang Joppich (2005). Practical Fourier analysis for multigrid methods. CRC Press. p 17. ISBN 1584884924. [7] MT Heath (2002). ”§ 11.5.7 Multigrid Methods”. Scientific Computing: An Introductory Survey. McGraw-Hill Higher Education. p. 478 ff. ISBN 007112229X. [8] P Wesseling (1992). An Introduction to Multigrid Methods. Wiley. ISBN 0471930830. [9] D.Kincaid, W.Cheney, Numerical Analysis: Mathematics of Scientific computing ,3rd, 2002 [10] M. Brezina, R. Falgout, S. MacLachlan, T. Manteu®el, S. McCormick, and J.Ruge, Adaptive Algebraic Multigrid, SIAM J. Sci. Comput. 27 (2005), pp. 1261-1286. [11] J. W. Ruge and K. St‥uben, Algebraic multigrid (AMG), in Multigrid Methods, S. F. Mc- Cormick, ed., vol. 3 of Frontiers in Applied Mathematics, SIAM, Philadelphia, PA, 1987, pp. 73–130. [12] Lee B. and Richards F.M. (1971) J. Mol. Biol. 55, 379-400. [13] Richards F.M. (1977) Ann. Rev. Biophys. Bioeng. 6, 151-176. [14] Greer J. and Bush B.L. (1978) Proc. Natl. Acad. Sci. USA., 75, 303-307. [15] Connolly M.L. (1983) J. Appl. Cryst. 16, 548-558. [16] J. G. Kirkwood, J. Chem. Phys. 7, 351(1934). [17] M. F. Sanner, A. J. Olson, and J. C. Spehner, REDUCED SURFACE: an Efficient Way to Compute Molecular Surfaces, Biopolymers 38, 305, (1996). [18] J. G. Kirkwood, J. Chem. Phys. 7, 351 (1934) [19] J.D.Jackson, Classical Electrodynamics 3ed. [20] Jun Wang, Qin Cai, Zhi-Lin Li, Hong-Kai Zhao and Ray Luo, Achieving energy conservation in Poisson-Boltzmann molecular dynamics: Accuracy and precision with finite-difference algorithms, Chem. Phys. Lett., 112,468(2009). [21] I-Liang Chern, Jian-Guo Liu andWei-ChengWang, Accurate Evaluation of Elec- trostatics for Macromolecules in Solution, (2005). [22] Berline, Nicole; Getzler, E.; Vergne, Michèle (2004), Heat Kernels and Dirac Operators, Berlin, New York: Springer-Verlag. [23] Weihua Geng, Sining Yu, and Guowei Wei , Treatment of charge singularities in implicit solvent models , J. Chem. Phys 127,(2007) | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/25075 | - |
| dc.description.abstract | 本篇論文是關於研究泊松-玻爾茲曼方程式(PBE) 的數值解法。在生物物理學當中，PBE 是用來以描述分子在水溶液中的靜電勢能。在玻爾茲曼方程式的數值計算上，我們主要會碰到的兩個困難點：第一點是電荷奇異性，第二點是表面奇異性。前者主要是來自方程當中用來表示分子中電荷的delta 函數(單位脈衝函數)；後者來自複雜的分子表面，介電係數高度的落差。
關於第一個困難點，我們引進一個點電荷在真空中的位能函數來解決，如在[21] 所提議的。第二點困難，我們提出耦合界面法(CIM) 來對付。對於處理橢圓界面問題，它是一種簡單健全的方法[1]。 數值測試顯示出耦合界面法比其他界面問題的解法來的優異。它在位能和梯度上都可以達到二階收斂。 | zh_TW |
| dc.description.abstract | In this master thesis, we study Poisson-Boltzmann equation (PBE) numerically.In biophysics, the PBE is used to describe the electrostatic potential for molecules in solvent. Two difficulties encountered as we solve PBE numerically: the charge singularities and the surface singularities. The former comes from the point charges of molecule, they are the delta functions in PBEs. The latter comes from the complicated molecular surface, across which the dielectric coefficient has jump.
The 1st difficulty is resolved by introducing a potential induced by those point charges in vacuum, as proposed in [21]. The 2nd difficulty is resolved by using the coupling interface method (CIM) [1], which is a simple and robust method for solving elliptic interface problems. Numerical tests show that the performance of CIM is superior to other interface methods. It is second for both potential and its gradient. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T06:01:41Z (GMT). No. of bitstreams: 1 ntu-100-R97221031-1.pdf: 688658 bytes, checksum: 632082d62659f01ff71be623ac17c8b9 (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | 誌謝 ii
中文摘要 iii 英文摘要 iv 1 Introduction 1 1.1 Derivation of Poisson-Boltzmann equation . . . . . . . . . . . 2 1.2 The Debye-Hückel parameter and interface conditions . . . . . 6 2 Coupling Interface Method 11 2.1 Interface problem . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 The basic idea of couple interface method . . . . . . . . . . . 13 2.2.1 CIM1 in one dimension . . . . . . . . . . . . . . . . . 13 2.2.2 CIM2 in one dimension . . . . . . . . . . . . . . . . . 15 2.3 CIM in d dimensions . . . . . . . . . . . . . . . . . . . . . . . 18 3 Introduction to Multigrid Method 22 3.1 Abstract multigrid method . . . . . . . . . . . . . . . . . . . . 23 3.2 Algebraic multigrid method . . . . . . . . . . . . . . . . . . . 25 4 Construction of the Molecular Surface 30 4.1 Level set method for the van der Waals surface . . . . . . . . 31 4.2 Level set method for the smoothing van der Waals surface . . 32 4.2.1 Solvent excluded surface . . . . . . . . . . . . . . . . . 32 4.2.2 Gaussian ball surface . . . . . . . . . . . . . . . . . . . 39 5 Numerical Experiments 40 5.1 Kirkwood’s dielectric sphere . . . . . . . . . . . . . . . . . . . 42 5.2 Polyatomic systems . . . . . . . . . . . . . . . . . . . . . . . . 52 6 Conclusion 59 References 62 | |
| dc.language.iso | en | |
| dc.title | 利用耦合界面法解決多原子問題 | zh_TW |
| dc.title | Coupling Interface Method for Solving Polyatomic Problems | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 林太家(Tai-Chia Lin),陳鵬文(Peng-wen Chen) | |
| dc.subject.keyword | 泊松-玻爾茲曼方程式,靜電勢能,耦合界面法,多重網格法,水平集方法,柯克伍德球, | zh_TW |
| dc.subject.keyword | Poisson-Boltzmann equation,electrostatic potential,coupling interface method,multigrid method,level set method, | en |
| dc.relation.page | 64 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2011-08-06 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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