應用分子動力學(MD)搭配平行運算技術，於個人電腦叢集系統進行奈米尺寸之收縮膨脹流場分析，探討不同鏈長之無支鏈烷類分子於流場之基本性值，包括流速分佈、壓力分佈、應力張量以及分子鏈結構性值等。
於固定驅動力下，分別使用不同鏈長的無支鏈分子為基本流體，探討分子鏈鏈長對穩態流動行為之影響；研究結果顯示，奈米系統中流場密度分佈變化相當明顯，尤其在高壓或牆壁分子表面，與連續流場假設的不可壓縮流體有很顯著的差異；除此之外，黏度性質也有明顯的改變，因而使得收縮膨脹流場之速度分佈相當特殊；也因使用無粗糙度的牆壁表面，滑動現象於本系統中相當嚴重。
於相同驅動力下，因鏈長增加導致系統流速變慢，使得流場內系統的壓力與正向應力隨著鏈長下降，但剪切應力則因分子間糾纏、拉伸等作用增加，而有上升的趨勢；分子鏈行為的排向性質也受到流場變化影響，在收縮管處有較大的排向性，且於膨脹管中央因流速過慢，使得多數分子鏈排向幾乎垂直於流場方向，但也因牆壁分子採用強吸附力的金原子分子，使得在牆壁表面有特殊的吸附現象。
平行計算效率會隨著MD計算量多寡而改變，當計算量太小時則無法發揮其效能；而本研究所採用混合原子分散法與力分散法，於少量的平行電腦個數時，有高達九成以上的平行運算效率。

By the use of molecular dynamics and parallel algorithm on PC-cluster, we report a series of properties including velocity distribution, pressure distribution, stress tensor and molecular structure at equilibrium state for nano-scale contraction-expansion flow with different chain length.
There are some interesting effects on chain length of contraction-expansion flow under the same driving force. With the increasing chain length, the density of local system gets more uniform. This is great different form the assumption that the density of fluid is incompressive. For the roughness of wall and the viscosity of fluid, the velocity profile is very special.
Under the same driving force, the flow velocity and shear stress decreases with the chain length while the pressure and normal stress increases with the chain length. The end-to-end distance and orientation factor is large at the contraction flow. Because of the strong attraction of the wall, there is large end-to-end distance and orientation factor in the surface of wall at the expansion flow.
The parallel efficiency changes with the computing data. For small computing data, the parallel method has lower efficiency. We have used the parallel algorithm coupling atomic decomposition and force decomposition parallel method successfully to simulate molecular dynamcis. With the lower number of parallel computer, the efficiency gets much better.

1.林鴻明，"奈米材料未來的發展趨勢"，科技發展政策報導SR9109(2002), pp.648-659。
2.C.-M. Ho, Y.-C. Tai, "Micro-Electro-Mechanical-Systems(MEMS) and Fluid Flows" Annual. Review of Fluid Mechanism, vol.30(1998), pp.579-612.
3.G.E. Karniadakis, A. Beskok, "Micro Flow: Fundamentals and Simulation" Springer, 2001.
4.M. Gad-El-Hak, "The MEMS Handbook", CRC Press, 2001.
5.Sergej Fatikow, Ulrich Rembold. 黃淳權譯 "微機電概論(Microsystem Technology and Microrobotics) "，高立出版社，89年第一版。
6.楊啟榮，"微系統LIGA製程技術"，科儀新知，vol.19(1998) , pp.4-17。
7.楊啟榮，強玲英，黃奇聲 "微系統LIGA製程之精密電鑄技術"，科儀新知　vol.21(2000), pp.15-26。
8.R. Bennett, C. Edwards, J. Lee, K. Silz "Precision Industrial Ink Jet Printing Technology for Full Color PLED Display and TFT-LCD Manufacturing" Litrex Corp, 6670 Owens Drive,U.S.A.(2002)
9.J. M. Haile, "MOLECULAR DYNAMICS SIMULATION ：ElementaryMethods", Wiley, 1997.
10.J.M. Haile "Molecular Dynamics Simulation: Elementary Methods", Wiley Professional Paperback Edition Published ,1997.
11.M.P. Allen, J.P. Tildesley "Computer simulation of Liquids" Oxford Science Publications ,1987.
12.Richard J. Sadus. "Molecular Simulatin of Fluids: Theory, Algorithms and Object-Orientation" New York, Elsevier, 1999.
13.D.C. Rapaport, "The Art of Molecular Dynamics Simulation", Cambridge University Press, 1995.
14.R. E. Tuzun, D. W. Noid, B. G. sumpter, R. C. Merkle, "Dynamics of fluid flow inside carbon nanotubes" Nanotechnology, vol.7(1996), pp.241-246.
15.M. Matsumoto, S. Saito, L. Ohmine, “Molecular dynamics simulation of the ice nucleation and growth process leading to water freezing”, Nature, vol.416(2002), pp409-413.
16.鄭守成，"漫談平行電腦與平行計算"，國家高速電腦中心，高速計算世界，第七卷第四期，1996 12。
17.蔡佳璋，張西亞，黃國展，李先知，周朝宜，鄭守成，陳敏，沈澄宇，“科學計算應用之新寵：個人電腦叢集”，國家高速電腦中心，高速計算世界，第七卷第四期，1999 12。
18."The Beowulf Project", Scyld Computing Corporation, Available from: http://www.beowulf.org/ .
19.R. Buyya, "High Performance Cluster Computing", Prentice Hall PTR Published, vol. 1(1999), pp.625-645.
20.徐宏昌，"平行計算在押出成型模擬分析和模具設計上之應用"，碩士論文，國立清華大學，2000。
21.G. C. Fox, "Parallel Problem Architectures and Their Implications for Portable Parallel Software Systems", Tech. Report CRPC-TR91120, Center for Research on Parallel Computation, Rice Univ., Houston, Texas, 1991.
22.曾耀寰，"企鵝雄兵-以Linux進行電腦叢集計算"，學貫科技文化，2001。
23.M. Snir, S. Otto, S. Huss-Lederman, D. Walker, J. Dongarr, "MPI：The Complete Reference", MIT Press ,1996.
24.鄭守成，"MPI平行計算程式設計"，國家高速電腦中心，2002。
25.B.J. Alder, T.E. Wainwright "Phase Transition for A Hard Sphere System", Journal of Chemical Physics vol.27 (1957), pp.1208-1209.
26.A. Rahman, "Correlations in the Motion of Atoms in Liquid Argon", Physical Reivew, vol.136(1964) pp.A405-A411.
27.B. J. Berne, R. Gordon, V. F. Sears, "On the Mechanics of Vibrational Relaxation", Journal of Chemical Physics vol.49(1968), p.475.
28.A. Rahman and F. H. Stillinger, "Molecular Dynamics Study of Liquid Water", J. Chem. Phys. vol.55(1971), pp.3336-3359.
29.J. A. McCammon, B. R. Gelin and M. Karplus, "Dynamics of Folded Proteins", Nature, vol.267 (1977), pp.585-590.
30.U. Heinbuch, J. Fischer, "Liquid Flow in pores: Slip, no-slip,or multilayer sticking", Physical Review A, vol.40(1989), pp.1144-1146.
31.J. Koplik, J.R. Banavar, J.F. Willemsen "Molecular Dynamics of Poiseuile Flow and Moving Contact Lines", Physical Review Letters, vol.60(1988), pp.1282-1285.
32.J Koplik, J.R. Banavar, J.F. Willemsen, "Molecular Dynamics of Fluid Flow at Solid Surface", Phys. Fluids A , vol.1(1989), pp.781-794.
33.P.A. Thompson, M.O. Robbins, "Simulation of Contact-Line Motion: Slip and the Dynamic Contact Angle", Physical Review Letters, vol. 63(1989), pp. 766-769.
34.P.A. Thompson, M.O. Robbins, "Shear Flow Near Solids: Epitaxial order and Flow boundary condition", Physical Review A, vol.41 (1990), pp.6830-6837.
35.J. Koplik, J. FL Banavar, "Corner Flow in the Sliding Plate Problem", Phys. Fluids, vol.7(1995), pp.3118-3125.
36.P.A. Thompson and S.M. Troian, "A general boundary condition for liquid flow at solid surfaces", Nature, vol.389(1997), pp.360-362.
37.A. Satoh, "Stability of Computational Algorithms Used in Molecular Dynamics Simulations", Journal of Fluids Engineering, Vol.117 (1995), pp.531-534.
38.A. Satoh, "Stability of Various Molecular Dynamics Algorithms", Journal of Fluids Engineering, Vol.119 (1997), pp.476-480.
39.M. Cieplak, J. Koplik, J. R. Bavanar, " Molecular dynamics of flows in the Knudsen regime", Physica A, vol.287(2000), pp.153-160.
40.X.J. Fan, N. Phan-Thien, N.T. Yong ,X. Diao, "Molecular Dynamics Simulation of A Liquid in A Complex Nano Channel Flow", Physical of Fluid, vol.14 (2002), pp.1146-1153.
41.G. Nagayama, P. Cheng, "Effects of interface wettability on microscale flow by molecular dynamics simulation", International Journal of Heat and Mass Transfer, vol.47(2004), pp.501-513.
42.J. Koplik, J.R. Banavar "Reentrant corner flows of Newtonian and non-Newtonian fluids" Journal of Rheology, vol.41(1997), pp.787-805.
43.A. Jabbarzadeh, J.D. Atkinson, R.I. Tanner, "Nanorheology of Molecularly Thin Films of n-hexadecane in Couette Shear Flow By Molecular Dynamcis Simulation", Journal of Non-Newtonian Fluid Mech. vol.77(1998), pp.53-78.
44.A. Jabbarzadeh, J.D. Atkinson, R.I. Tanner, “Wall slip in the molecular dynamics simulation of thin films of hexadecane", Journal of Chemical Physics, vol.110 (1999), pp.2612-2620.
45.J.D. Moore, S.T. Cui, H.D. Cochran, P.T. Cummings, "A molecular dynamics study of a short chain polyethylene melt I. Steady state shear", Journal of Non-Newtonian Fluid Mechanism, vol.93(2000), pp.83-99.
46.J.D. Moore, S.T. Cui, H.D. Cochran, P.T. Cummings, "A molecular dynamics study of a short chain polyethylene melt II. Transient response upon onset shear", Journal of Non-Newtonian Fluid Mechanism, vol.93(2000), pp.101-116.
47.A. Jabbarzadeh, J.D. Atkinson, R.I. Tanner, “Effect of the wall roughness on slip and rheological properties of hexadecane in molecular dynamics simulation of Couette shear flow between two sinusoidal walls”, Physical Review E, Vol. 61(2000), pp.690-699.
48.S.T. O’Connell, P.A. Thompson, "Molecular Dynamics-Continuum Hybrid Computations：A Tool for Studying Complex Fluid Flows", Physical Review E, vol.52 (1995), pp.5792-5795.
49.J. Li, D. Liao, S. Yip, "Coupling continuum to molecular-dynamics simulation: Reflecting particle method and the field estimator", Physical Review E, vol.57(1999), pp.7359-7367.
50.S. Plimpton, "Fast Parallel Algorithms for Short-Range Molecular Dynamics", Journal of Computational Physics, vol.117(1995), pp.1-19.
51.H.Schreiber, O, Steinhauser, P. Schuster, "Parallel molecular dynamics of biomolecules", Parallel computing, vol.18(5)(1992) pp.557-573.
52.Y. Hwang, R. Das, F.H. Saltz, M. Hadošcek, B.R. Brooks, "Parallelizing molecular dynamics programs for distributed-memory machines", IEEE comput. Sci. and Engrg. vol.2 (1995) pp.18-29.
53.V.E. Taylor, R.L. Stevens, K.E. Arnold, "Parallel Molecualr Dynamics：Implications for Massively Parallel Machines", Journal of Parallel and Distributed Computing, vol.45(1997), pp.166-175.
54.R. Murty, D. Okunbor, "Efficient parallel algorithms for molecular dynamics simulation", Parallel Computing, vol.25(1999), pp.217-230.
55.J. W. Shu, B. Wang, M. Chen, J. Z. Wang, W. M. Zheng, " Optimization techniques for parallel force-decomposition algorithm in molecular dynamic simulations", Computer Physics Communications, vol.154(2003), pp.121-130.
56.S.G. Srinivasan, I. Ashok, Hannes Jonsson, Gretchen Kalonji, John Zahorjan, "Dynamic-domain-decomposition parallel molecular dynamics", Computer Physics Communications. vol.102 (1997), pp.44-58.
57.R. Hayashi, S. horiguchi, "Efficiency of dynamic Load Balancing Based on Permanent Cells for Parallel Molecular Dynamics Simulation", 14th International Parallel and Distributed Processing Symposium(2000), p.85.
58.D. Brown, H. Minoux, Bernard Maigret, "A domain decomposition parallel processing algorithm for molecular dynamics simulations of system s of arbitrary connectivity", Computer Physics Communications, vol.103(1997), pp.170-186.
59.D. Brown, J.H.R. Clarke, M. Okuda, T. Yamazaki, "A domain decomposition parallel processing algorithm for molecular dynamics simulations of polymers", Computer Physics Communications, vol.83(1994), pp.1-13.
60.G. Eisenhauer, K. Schwan, "Design and Analysis of a Parallel Molecular Dynamics Application", Journal of Parallel and Distributed Computing, vol.35(1996), pp.76-90.
61.M. Moseler, U. Landman, "Formation, Stability, and Breakup of Nanojets", Science, vol.289(2000), pp.1165-1169.
62.A. Jabbarzadeh, J.D. Atkinson, R.I. Tanner, "A parallel algorithm for molecular dynamics simulation of branched molecules, " Computer Physics Communications 150(2003), pp.65-84.
63.G. S. Heffelfinger, "Parallel atomistic simulations", Computer Physics Communications, vol.128(2000), pp.219-237.
64.J.N. Israelachvili, "Intermolecular and Surface Force, 2nd ed. " Academic, New York (1992).
65.W.G.. Hoover, "Canonical dynamics: Equilibrium phase-space distributions", Physical Review A, vol.31(1985), pp.1695-1697.
66.S. Nosé, "A unified formulation of the constant temperature molecular dynamics methods", Journal of Chemical Physics, vol.81(1984), pp.511-519.
67.D.D. Humphreys, R.A. Friesner, B.J. Berne, "A Multiple-Time-Step Molecular Dynamics Algorithm for Macromolecules", Journal of Physics Chemical, vol.98(1994), pp.6885-6892.
68.A. Rahman, "Correlations in the Motion of Atoms in Liquid Argon, " Physical Review, vol.136(1964), p.405.
69.C. W. Gear, "Numerical Initial Value Problems in Ordinary Differential Equations", Prentice-Hall, Englewood Cliffs, NJ, 1971, Chapter 9.
70.D. Wolff, W.G. Rudd, "Tabulated potentials in molecular dynamics simulations", Comput. Phys. Commun., vol 120(1999), pp.20-32.
71.M. Kröger, W. Loose, S. Hess, "Rheology and structural changes of polymer melts via nonequilibrium molecular dynamics", Journal of Rheology, vol.37(1993), pp.1057-1079.
72.Y. Yamaguchi, S. Maruyama, "A molecular dynamics simulation of fullerene formation process", Chemical Physies Letters, vol.286(1998), pp.336-342.
73.王鎮杰，"以分子動力學模擬高分子在奈米尺度下之流變性質與擠出行為"，碩士論文，國立清華大學，2003。