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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/93356Full metadata record
| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 林太家 | zh_TW |
| dc.contributor.advisor | Tai-Chia Lin | en |
| dc.contributor.author | 莊大儒 | zh_TW |
| dc.contributor.author | Da-Ru Zhuang | en |
| dc.date.accessioned | 2024-07-29T16:25:30Z | - |
| dc.date.available | 2024-07-30 | - |
| dc.date.copyright | 2024-07-29 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-07-26 | - |
| dc.identifier.citation | [1] Gene Lamm. The poisson–boltzmann equation. Reviews in computational chemistry 19, pages 147–365, 2003.
[2] Harvey F Lodish. Molecular cell biology. Macmillan, 2008. [3] Petr G. Vikhorev, Natalia N. Vikhoreva, and Alf M ̊ansson. Bending flexibility of actin filaments during motor-induced sliding. Biophysical Journal 95, no. 12, pages 5809–5819, 2008. [4] David J Griffiths. Introduction to electrodynamics. Cambridge University Press, 2023. [5] Long Chen, Michael J. Holst, and Jinchao Xu. The finite element approximation of the nonlinear poisson–boltzmann equation. SIAM journal on numerical analysis 45.6, pages 2298–2320, 2007. [6] Hans-J ̈urgen Butt, Karlheinz Graf, and Michael Kappl. Physics and chemistry of interfaces. John Wiley and Sons, 2023. [7] Lawrence C Evans. Partial differential equations. American Mathematical Society, 2022. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/93356 | - |
| dc.description.abstract | 受到離子溶液中帶電細絲的啟發，我們分析了在二維中泊松-玻爾茲曼方程的輻射對稱解。首先，我們證明了方程解以及其一階和二階導數的單調性。接著，我們確立了方程解的存在性和唯一性。最後，我們導出狄利克雷-諾伊曼映射是單射且滿射的。 | zh_TW |
| dc.description.abstract | Inspired by the study of charged filaments in ionic liquids, we analyzed radially symmetric solutions of the Poisson-Boltzmann equation in 2D. First, we prove the monotonicity of the solution along with its first and second derivatives. Next, we establish the existence and uniqueness of the solution. Lastly, we demonstrate that the Dirichlet- to-Neumann map is 1-1 and onto. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-07-29T16:25:30Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-07-29T16:25:30Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 口試委員審定書 #
Acknowledgements i 摘要 ii Abstract iii Contents iv List of Figures v Chapter 1 Introduction 1 Chapter 2 Literature Review 5 Chapter 3 Main Results 5 3.1 Preliminaries 5 3.2 Existence and Uniqueness 8 3.3 Dirichlet-to-Neumann Map 10 3.4 Physical Interpretation 11 References 12 | - |
| dc.language.iso | en | - |
| dc.subject | 泊松-玻爾茲曼方程 | zh_TW |
| dc.subject | 輻射對稱解 | zh_TW |
| dc.subject | 狄利克雷-諾伊曼映射 | zh_TW |
| dc.subject | 帶電細絲 | zh_TW |
| dc.subject | 離子溶液 | zh_TW |
| dc.subject | radially symmetric solution | en |
| dc.subject | Poisson-Boltzmann equation | en |
| dc.subject | ionic liquids | en |
| dc.subject | charged filaments | en |
| dc.subject | Dirichlet-to-Neumann map | en |
| dc.title | 泊松-玻爾茲曼方程在二維的輻射對稱解 | zh_TW |
| dc.title | Radially Symmetric Solutions of the Poisson-Boltzmann Equation in 2D | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 陳俊全;李俊璋 | zh_TW |
| dc.contributor.oralexamcommittee | Chiun-Chuan Chen;Chiun-Chang Lee | en |
| dc.subject.keyword | 泊松-玻爾茲曼方程,輻射對稱解,狄利克雷-諾伊曼映射,帶電細絲,離子溶液, | zh_TW |
| dc.subject.keyword | Poisson-Boltzmann equation,radially symmetric solution,Dirichlet-to-Neumann map,charged filaments,ionic liquids, | en |
| dc.relation.page | 12 | - |
| dc.identifier.doi | 10.6342/NTU202402023 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2024-07-28 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 應用數學科學研究所 | - |
| Appears in Collections: | 應用數學科學研究所 | |
Files in This Item:
| File | Size | Format | |
|---|---|---|---|
| ntu-112-2.pdf | 1.25 MB | Adobe PDF | View/Open |
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