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| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 張慶瑞 | zh_TW |
| dc.contributor.advisor | Ching-Ray Chang | en |
| dc.contributor.author | 張宇華 | zh_TW |
| dc.contributor.author | Yu-Hua Zhang | en |
| dc.date.accessioned | 2023-05-18T16:19:55Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-05-10 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-02-15 | - |
| dc.identifier.citation | [1].张志东，伊辛模型的研究进展简介，Chinese Journal of Nature，Vol.30 No.2：98-101；
[2]. Newman, M. E. and G. T. Barkema (1999). Monte Carlo methods in statistical physics, Clarendon Press. [3]. Sandvik, A. W. (2013). "Monte Carlo simulations in classical statistical physics." Departement of Physics, Boston University. [4]. Hastings, W.K. (1970). "Monte Carlo Sampling Methods Using Markov Chains and Their Applications". [5] Pharr, M., et al. (2016). Physically based rendering: From theory to implementation, Morgan Kaufmann. [6] Caflisch, R. E. (1998). "Monte Carlo and quasi-Monte Carlo methods". [7] Box, G. E. P.; Muller, Mervin E. (1958). "A Note on the Generation of Random Normal Deviates" [8] Forsythe, George E. (1972). "Von Neumann's Comparison Method for Random Sampling from the Normal and Other Distributions". Mathematics of Computation. 26 (120): 817–826. [9] Gilks, W. R.; Wild, P. (1992). "Adaptive Rejection Sampling for Gibbs Sampling". Journal of the Royal Statistical Society. Series C (Applied Statistics). 41 (2): 337–348. [10] Gagniuc, Paul A. (2017). Markov Chains: From Theory to Implementation and Experimentation. USA, NJ: John Wiley & Sons. pp. 1–235. [11] Chain, M. (2017). Definition of Markov Chain in US English by Oxford Dictionaries, Oxford Dictionaries. [12] Joseph L. Doob (1990). Stochastipoic processes. Wiley. p. 46 and 47. Archived from the original on 2017-11-20. [13] Kalos, Malvin H.; Whitlock, Paula A. (1986). Monte Carlo Methods Volume I: Basics. New York: Wiley. pp. 78–88. [14] Hastings, W.K. (1970). "Monte Carlo Sampling Methods Using Markov Chains and Their Applications". Biometrika. 57 (1): 97–109 [15] Baxter, Rodney J. (1982), Exactly solved models in statistical mechanics, London: Academic Press Inc. [16] K. Binder (2001) [1994], "Ising model", Encyclopedia of Mathematics, EMS Press [17] Brush, Stephen G. (1967). "History of the Lenz-Ising Model". Reviews of Modern Physics. 39 (4): 883–893. [18] Baumgärtner, A., et al. (2012). The Monte Carlo method in condensed matter physics, Springer Science & Business Media. [19] Aykut Melih Turhana, (2020) A hybrid fix-and-optimize and simulated annealing approaches for nurse rostering problem, Computers & Industrial Engineering [20] Ikeda, K., et al. (2019). "Application of quantum annealing to nurse scheduling problem." Scientific reports 9(1): 1-10. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/87200 | - |
| dc.description.abstract | 本文介紹了蒙地卡羅方法對二維伊辛模型模擬的基本概念，以及用C語言實現此模擬的過程和方法。然後再將護士排班問題套入伊辛模型中，並展示馬爾科夫蒙地卡羅方法對護士排班問題的處理結果。我會先介紹蒙地卡羅方法以及爲什麽要進行重要性抽樣，以及馬科夫過程的基本原理和馬爾科夫蒙地卡羅(MCMC)方法以及Metropolis–Hastings algorithm，然後如何用Single-spin-flip dynamics和Metropolis接受準則製造馬科夫鏈並用此方法解決2D ising model和护士排班问题。最後分析並討論得到的數據。
關鍵詞：蒙地卡羅方法，重要性抽樣，伊辛模型，馬爾科夫鏈，護士排班問題 | zh_TW |
| dc.description.abstract | In this paper I numerically study the two dimensional Ising model using the Monte Carlo method. Then build the Ising model to solve the Nurse Rostering Problem, and show the results of the Markov Monte Carlo method on the nurse scheduling problem. I first introduce the Monte Carlo method with the importance sampling and The basic principle of Markov process and Markov Monte Carlo (MCMC) method and Metropolis–Hastings algorithm, then I describe how to use the single-spin-flip dynamics and Metropolis–Hastings algorithm to simulate the Ising model in 2D square lattice and Nurse Rostering Problem. Finally the simulated results are analyzed and discussed.
Keywords：Monte Carlo method, Importance sampling, Ising model, Markov chain, Nurse Scheduling Problem | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-05-18T16:19:54Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-05-18T16:19:55Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 誌謝.................................................................................................i
口試委員審定書............................................................................ii 摘要................................................................................................iii Abstract..........................................................................................iii 圖目錄...........................................................................................v 表目錄............................................................................................v 第一章 引言..................................................................................1 第二章 數值方法..........................................................................2 2.1 Monte Carlo method..........................................................2 2.2 蒙地卡羅積分………......................................................3 2.3 Box-Muller transform.......................................................4 2.4 接受拒絕採樣(Acceptance-Rejection Sampling)...........4 2.5 Importance sampling in statistical physical system…......6 2.6 馬爾科夫过程…………………………………….……7 2.7馬爾科夫鏈蒙地卡羅算法(MCMC)……………..…….10 2.7.1細緻平衡條件(Detailed Balance)…………....…..10 2.7.2 M-H算法(Metropolis–Hastings algorithm)...........11 第三章 伊辛模型(Ising model)...................................................12 3.1 伊辛模型的能量與晶格……………………..………..12 3.2 Metropolis–Hastings algorithm in ising model..……….14 3.3 模擬過程........................................................................15 3.4程式主體.........................................................................15 3.5結果與分析.....................................................................16 第四章 護士排班問題(Nurse Scheduling Problem)...................19 4.1約束條件和系統能量.......................................................20 4.2模擬與結果.......................................................................20 第五章 結論.................................................................................24 參考文獻.......................................................................................25 | - |
| dc.language.iso | zh_TW | - |
| dc.subject | 蒙地卡羅方法 | zh_TW |
| dc.subject | 伊辛模型 | zh_TW |
| dc.subject | 重要性抽樣 | zh_TW |
| dc.subject | 馬爾科夫鏈 | zh_TW |
| dc.subject | 護士排班問題 | zh_TW |
| dc.subject | Importance sampling | en |
| dc.subject | Ising model | en |
| dc.subject | Markov chain | en |
| dc.subject | Monte Carlo method | en |
| dc.subject | Nurse Scheduling Problem | en |
| dc.title | 伊辛模型的退火計算應用 | zh_TW |
| dc.title | Application of Simulated Annealing in Ising Model | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-1 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 陳繩義;傅昭铭 | zh_TW |
| dc.contributor.oralexamcommittee | Seng Ghee Tan;Chao-Ming Fu | en |
| dc.subject.keyword | 蒙地卡羅方法,重要性抽樣,伊辛模型,馬爾科夫鏈,護士排班問題, | zh_TW |
| dc.subject.keyword | Monte Carlo method,Importance sampling,Ising model,Markov chain,Nurse Scheduling Problem, | en |
| dc.relation.page | 26 | - |
| dc.identifier.doi | 10.6342/NTU202300478 | - |
| dc.rights.note | 未授權 | - |
| dc.date.accepted | 2023-02-16 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 物理學系 | - |
| Appears in Collections: | 物理學系 | |
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| File | Size | Format | |
|---|---|---|---|
| ntu-111-1.pdf Restricted Access | 2.12 MB | Adobe PDF |
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