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研究生: 鄭烈烈
Cheng, Lieh-Lieh
論文名稱: 分子運動模擬環境於Matlab中之建立
Simulations of Molecular Motion in Matlab
指導教授: 楊憲東
Yang, Ciann-Dong
學位類別: 碩士
Master
系所名稱: 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年: 2006
畢業學年度: 94
語文別: 中文
論文頁數: 49
中文關鍵詞: 表面張力徑向分布函數分子控制分子動力學
外文關鍵詞: surface tension, radial distribution function, molecular control, molecular dynamics, Matlab
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  • 近年來,在分子運動控制的領域,已經有了相當多的研究及成果,然而卻因為模型皆過於簡化,使得應用的層面大大地受到限制。基於Matlab在控制領域應用上的便利性,本論文的目的為在Matlab中建立一真實的分子運動模擬環境,期望將來能夠與分子控制作一結合。文中以分子動力學為基礎,來為分子運動系統建立模型。先是以計算氬(argon)之徑向分布函數(Radial Distribution Function, RDF),來初步驗證程式的正確性。緊接著探討液態氬之表面張力性質,計算出氬液滴在不同系統參數下之表面張力值,並與文獻作一比較,以對建立的模擬環境作更進一步的驗證。

    There has been a great deal of effort made on the control of molecular systems in recent years. However, their applications are greatly restricted because the models are all too simple. Owing to the convenience of applications of Matlab to control, the thesis is to establish a realistic simulation environment for the motion of molecules in Matlab which we can connect with molecular control in the future. In this thesis, we model molecular systems using molecular dynamics. To verify the designed program, we calculate the radial distribution function of argon first. Next, we discuss liquid argon droplets and calculate the values of surface tension under different system parameters. Finally, the results of calculation are compared with those in the literature to verify the model further.

    授權書 簽署人須知 中文摘要 i 英文摘要 ii 誌謝 iii 目錄 iv 表目錄 vi 圖目錄 vii 第一章 緒論 1 1.1研究動機與目的 1 1.2文獻回顧 3 1.3論文架構 5 第二章 分子動力學理論 6 2.1 勢能函數與分子間作用力 7 2.2 運動方程式 9 2.3 截斷勢能 10 2.4 截斷半徑法 12 2.4.1 Verlet表列法 13 2.4.2 Cell link表列法 14 2.4.3 Verlet表列法結合Cell link表列法 15 2.5 邊界條件 18 第三章 實例模擬 19 3.1 徑向分布函數 19 3.2 液態氬物理模型 20 3.3 勢能函數的選取 21 3.4 物理參數與無因次化 21 3.5 設定初始條件 22 3.6 邊界條件設定 24 3.7 模擬流程圖 29 第四章 初步模擬結果分析與討論 32 4.1 氬之徑向分布函數 32 4.2 液態氬之表面張力 35 第五章 結論暨未來展望 45 5.1 結論 45 5.2 未來展望 46 參考文獻 47 自述 49

    [1] G.M. Huang and T.J. Tarn, “On the Controllability of Quantum-Mechanical Systems,” Journal of Mathematics and Physics, 24(11), pp.2608-2618, 1983
    [2] C.K. Ong, G.M. Huang, T.J. Tarn and J.W. Clark, “Invertibility of Quantum-Mechanical Control Systems,” Mathematical Systems Theory, 17, pp.335-350, 1984
    [3] R.S. Judson and H. Rabitz, “Teaching Laser to Control Molecules,” Phys. Rev. Lett., vol.68, pp.1500-1503, 1992
    [4] W.S. Warren, H. Rabitz and M. Dahleh, “Coherent Control of Quantum Dynamics: The Dream Is Alive,” Science, 259(12), pp.1581-1585, 1993
    [5] H. Zhang and H. Rabitz, “Robust Optimal Control of Quantum Molecular Systems in the Presence of Disturbances and Uncertainties,” Phys. Rev. A, vol.49, 4, 1994
    [6] J.H. Irving and J.G. Kirkwood, “The Statistical Mechanics of Transport Process. IV. The Equation of Hydrodynamics,” J. Chem. Phys., 18, pp.817-820, 1950
    [7] B.J. Alder and T.E. Wainwright, J. Chem. Phys. 27, 1208, 1957
    [8] J.B. Gibson, A.N. Goland, M. Milgram and G.H. Vineyard, Phys. Rev. 120, 1229, 1960
    [9] A. Rahman, “Correlations in the Motion of Atoms in Liquid Argon,” Phys. Rev. 136A, 405, 1964
    [10] L.A. Girifalco and V.G. Weizer “Application of the Morse Function to Cubic Metals,” Phys. Rev., Vol.114, No.3, pp.687-690, 1959
    [11] L. Verlet, “Computer ‘Experiments’ on Classical Fluids II, Equilibrium Correlation Function,” Phys. Rev., Vol.165, pp.201-214, 1968
    [12] M.P. Allen and T.J. Tildesley, “Computer Simulation of Liquids,” Oxford: Clarendon, 1970
    [13] D.C. Rapaport, “Large-Scale Molecular Dynamics Simulation Using Vector and Parallel Computers,” Comput. Phys. Rep. Vol.9, pp.1-53, 1988
    [14] J.M. Haile, “Molecular Dynamics Simulation,” John Wiley & Sons, Inc., 1992
    [15] Jacon N. Israelachvili, “Intermolecular and Surface Forces,” 2nd Edition, Academic Press, 1992
    [16] F. London, “Properties and Applications of Molecular Forces,” Zeit. Physik. Chem. B, 11, 222, 1930
    [17] D.C. Rapaport, “The Art of Molecular Dynamics Simulation,” 2nd Edition, Cambridge University Press, 2004
    [18] D. Frenkel and B. Smith, “Understanding Molecular Simulation,” Academic Press, San Diego, 1996
    [19] 朱訓鵬, “分子動力學與平行運算於奈米薄膜沉積模擬之應用,” 國立成功大學機械工程學系博士論文, 2001
    [20] S. Goldman, “An Explicit Equation for the Radial Distribution Function of a Dense Lennard-Jones Fluid,” J. Phys. Chem., 83, 3033, 1979

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