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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/1225完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 林太家 | |
| dc.contributor.author | Hsin-Hsiu Tsai | en |
| dc.contributor.author | 蔡欣修 | zh_TW |
| dc.date.accessioned | 2021-05-12T09:34:31Z | - |
| dc.date.available | 2020-06-26 | |
| dc.date.available | 2021-05-12T09:34:31Z | - |
| dc.date.copyright | 2018-06-26 | |
| dc.date.issued | 2018 | |
| dc.date.submitted | 2018-06-21 | |
| dc.identifier.citation | [1] M.Z. Bazant, K. Thornton, A. Ajdari, Diffuse-charge dynamics in electrochemical systems, Phys. Rev. E 70, 021506 (2004).
[2] J. Bikerman, Structure and capacity of the electrical double layer, Phil. Mag. 33, 384-397 (1942). [3] I. Borukhov, D. Andelman, H. Orland, Steric effects in electrolytes: a modified Poisson–Boltzmann equation, Phys. Rev. Lett. 79, 435 (1997). [4] B. Eisenberg, Y. Hyon, C. Liu, Energy variational analysis of ions in water and channels: field theory for primitive models of complex ionic fluids, J. Chem. Phys. 133, 104104 (2010). [5] Lawrence. C. Evans, Partial Differential Equations, American Mathematical Society (1998). [6] M Fixman, The Poisson–Boltzmann equation and its application to polyelectrolytes, J. Chem. Phys. 70, 4995 (1979). [7] F. Fogolari, A. Brigo, H. Molinari, The Poisson–Boltzmann equation for biomolecular electrostatics: a tool for structural biology, J. Mol. Recognit. 15, 377-392 (2002). [8] David Gilbarg and Neil. s. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer (2001). [9] Chiun-Chang Lee, Hijin Lee, YunKyong Hyon, Tai-Chia Lin and Chun Liu, New Poisson–Boltzmann type equations: one-dimensional solutions, Nonlinearity 24, 431–458 (2011). [10] Qing Han and Fanghua Lin, Elliptic Partial Differential Equations, American Mathematical Society (2000). [11] Bo Li, Pei Liu, Zhenli Xu and Shenggao Zhuo, Ionic size effects: generalized Boltzmann distributions, counterion stratification and modified Debye length, Nonlinearity 26, 2899-2922 (2013). [12] Tai-Chia Lin and Eisenberg. B, Multiple solutions of steady-state Poisson-Nernst-Plank equations with steric effects, Nonlinearity 28, 2053-2080 (2015). [13] W. Liu, Geometric singular perturbation approach to strady-state Poisson-Nernst-Planck systems, SIAM J. Appl. Math., 65(3), 754–766 (2005). [14] P.A. Marcowich, The Stantionary Semiconductor Device Equations, Springer-Verlag (1986). [15] Robin Nittka, Regularity of solitions of linear second order elliptic and parabolic boundary value problems on Lipschitz domains, J. Differential Equations 251, 860-880 (2011). [16] W. Rocchia, E. Alexov, and B. Honig, Extending the Applicability of the Nonlinear Poisson−Boltzmann Equation: Multiple Dielectric Constants and Multivalent Ions, J. Phys. Chem. B, 105 (28), 6507–6514 (2001). [17] Kim A. Sharp and Barry Honig, Calculating Total Electrostatic Energies with the Nonlinear Poisson-Boltzmann Equation, J. Phys. Chem. 94, 7684-7692(1990). [18] J. Zhang, X. Gong, C. Liu, W. Wen and P. Sheng, Electrorheological Fluid Dynamics, Phys. Rev. Lett. 101(19), 194503 (2008). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/handle/123456789/1225 | - |
| dc.description.abstract | 研究離子擴散的行為在很多應用問題上扮演重要的角色，如生物離子通道等等，而泊松-玻爾茲曼方程便是描述此行為的模型且被廣泛應用。隨著奈米科技的發展，許多新的結果被發現。然而，這些結果卻無法用泊松-玻爾茲曼方程解釋，因此有了Bo Li 的模型。本論文研究Poisson-Nernst-Planck 方程with steric effects 的穩定態，New Poisson-Boltzmann 方程with steric effects，並且證明可以從此模型推得Li 的模型。 | zh_TW |
| dc.description.abstract | Studying the transport of ions plays an important role in many problems, such as ion channels. Over the past decades, original Poisson-Boltzmann (PB) equation was widely used to describe the electrolyte solutions. However, due to the development of nanotechnology, some new experiment outcomes were found but could not be described. Therefore, Li’s model was constructed. In this work, we further investigate a new Poisson-Boltzmann (PB) type equation called the PB_ns equation, which is derived from the steady-state of the Poisson-Nernst-Planck system with steric effects and shows that PB_ns equation can reduce to Li’s model. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-12T09:34:31Z (GMT). No. of bitstreams: 1 ntu-107-R05221004-1.pdf: 723994 bytes, checksum: 2abbe903fd0fa2637d3bac8735d0b10f (MD5) Previous issue date: 2018 | en |
| dc.description.tableofcontents | 口試委員審定書 i
致謝 ii 摘要 iii Abstract iv 1 Introduction 1 2 Existence and Uniqueness 6 2.1 Algebraic Equations 7 2.2 Differential Equation 13 3 Limiting Behavior of ϕ and ci 24 3.1 Uniform Boundness of ϕ and ci 25 3.2 Proof of Theorem 3.1 30 4 Generalization of G 37 5 Conclusion Remark 43 | |
| dc.language.iso | zh-TW | |
| dc.subject | 強交互作用 | zh_TW |
| dc.subject | 泊松-玻爾茲曼方程 | zh_TW |
| dc.subject | 泊松-能斯特-普朗克方程 | zh_TW |
| dc.subject | 新泊松-玻爾茲曼方程 | zh_TW |
| dc.subject | 位阻效應 | zh_TW |
| dc.subject | Poisson-Boltzmann equations | en |
| dc.subject | strongly repulsive interactions | en |
| dc.subject | steric effects | en |
| dc.subject | New Poisson-Boltzmann equations | en |
| dc.subject | Poisson-Nerst-Plank equations | en |
| dc.title | 考慮粒子大小與強交互作用之新泊松-玻爾茲曼方程 | zh_TW |
| dc.title | New Poisson-Boltzmann Models with Steric Effects and
the Strongly Repulsive Interactions | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳俊全,李俊璋 | |
| dc.subject.keyword | 泊松-玻爾茲曼方程,泊松-能斯特-普朗克方程,新泊松-玻爾茲曼方程,位阻效應,強交互作用, | zh_TW |
| dc.subject.keyword | Poisson-Boltzmann equations,Poisson-Nerst-Plank equations,New Poisson-Boltzmann equations,steric effects,strongly repulsive interactions, | en |
| dc.relation.page | 45 | |
| dc.identifier.doi | 10.6342/NTU201801038 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2018-06-22 | |
| 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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