The Monte Carlo Method and Applications

  • I. Motoc
  • W. Bruns
Part of the Lecture Notes in Chemistry book series (LNC, volume 27)

Abstract

In the present chapter, the main concepts used in this book are discussed (i.e., models, random numbers and computer Monte-Carlo models), and then a short review of Monte Carlo applications in Chemistry and an up-to date review of Monte Carlo application in Polymer Science are given. It is hoped that the large number of references contained in this chapter provides a useful guideline to the relevant literature.

Keywords

Lignin Rubber Fluoride Aldehyde Polysaccharide 

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References

  1. 1.
    C.W. Churchman, in “Symposium on Monte Carlo Methods”, A.C. Hoggart and P.E. Balderton eds., S.W. Publ. Comp., Cincinnati, 1963.Google Scholar
  2. 2.
    S. Wold and M. Sjöström, in “Chemometrics: Theory and Applications”, B.R. Kowalski ed., ACS Symposium Series, No. 52, Washington, 1977.Google Scholar
  3. 3a.
    N.B. Chapman and J. Shorter eds., “Advances in Linear Free Energy Relationships”, Plenum, New York, 1972.Google Scholar
  4. 3b).
    W. Purcell, G. E. Bass and J.M. Clyton, “Strategy of Drug Design. A Guide to Biological Activity”, Wiley, New York, 1973.Google Scholar
  5. 4.
    M.E. Drummond Jr., “Evaluation and Measurement Techniques for Digital Computer Systems”, Prentice-Hall, Englewood Cliffs, N.J., 1973.Google Scholar
  6. 5.
    D.J. Newman, Aust. J. Phys., 31, 489 (1978).Google Scholar
  7. 6.
    P.A.D. de Maine, Comput. Chem., 2, 53 (1978).CrossRefGoogle Scholar
  8. 7.
    R.A. Merikallio and F.C. Holland, in “Simulation Design of a Multiprocessing System”, Proc. FJCC, vol. 33, part 2, 1968, p. 1399–1410.Google Scholar
  9. 8.
    O.J. Campbell and W.J. Heffner, in “Simulation Design of a Multiprocessing System”, Proc. FJCC, vol. 33, part 1, 1968, p. 903–914.Google Scholar
  10. 9.
    M. Greenberger, “A New Methodology for Computer Simulation”, MIT, Cambridge, AD 609288, 1964.Google Scholar
  11. 10.
    T.H. Naylor et al., “Computer Simulation Techniques”, Wiley, New York, 1966.Google Scholar
  12. 11.
    G.W. Evans II, G.F. Wallance and G.L. Sutherland, “Simulation Using Digital Computers”, Prentice-Hall, Englewood Cliffs, N.J., 1967.Google Scholar
  13. 12.
    F.F. Martin, “Computer Modelling and Simulation”, Wiley, New York, 1968.Google Scholar
  14. 13.
    C. Fevrier, “Le Simulation de Systemes”, Dunod, Paris, 1972.Google Scholar
  15. 14.
    J.W. Mayne, J. Can. Operational Res. Soc, 4, 144 (1966).Google Scholar
  16. 15.
    R. von Mises, Math. Z., 5, 52 (1919).CrossRefGoogle Scholar
  17. 16.
    O. Onicescu, “Nombres et Systems Aléatoires”, Editions Eyrolles,. Paris, 1964.Google Scholar
  18. 17.
    M.D. MacLaren and G. Marsaglia, J. Assoc. Comput. Mach., 12, 83 (1965).CrossRefGoogle Scholar
  19. 18.
    B. Jansson, “Random Numbers Generators”, Almqvist and Wiksell, Stockholm, 1966.Google Scholar
  20. 19.
    E.R. Sowey, Internat. Statist. Rev., 40, 355 (1972).Google Scholar
  21. 20.
    O. Dragomir-Filimonescu, Proc. Fifth National Symp. Information Sci., Cluj-Napeca, 1979 (in Roumania).Google Scholar
  22. 21.
    N. Metropolis and S.M. Ulan, J. Am. Statist. Assoc, 44, 335 (1949).CrossRefGoogle Scholar
  23. 22.
    H. Niederreiter, Bull. Am. Math. Soc., 84, 957 (1978).CrossRefGoogle Scholar
  24. 23.
    H. Kahn, “Applications of Monte Carlo”, Rand Memo. RM-1237, 1954.Google Scholar
  25. 24.
    A. Meyer, ed., “Symposium on Monte Carlo Methods”, Wiley, New York, 1956.Google Scholar
  26. 25.
    E.D. Cashwell and C.J. Everett, “Practical Manual on the Monte Carlo Method for Random Walk Problems”, Pergamon, New York, 1959.Google Scholar
  27. 26.
    J.M. Hammersley and D.C. Handscomb, “Monte Carlo Methods”, Wiley, New York, 1964.CrossRefGoogle Scholar
  28. 27.
    Yu.A. Shreider, ed., “The Monte Carlo Method”, Pergamon, New York, 1965.Google Scholar
  29. 28.
    K.F. Iuorno, “Simulation Using the Monte Carlo Method”, Griffiss Air Force Base, N.Y., AD-410290, 1973.Google Scholar
  30. 29.
    N.P. Buslenko et al., “The Monte Carlo Statistical Trials”, Fizmatgis, Moscow, 1962 (in Russian).Google Scholar
  31. 30.
    S.M. Yermakov, “The Monte Carlo Method and Relevant Problems”, Nauka, Moscow, 1971 (in Russian).Google Scholar
  32. 31.
    I.M. Sobol, “Numerical Monte Carlo Methods”, Nauka, Moscow, 1973 (in Russian).Google Scholar
  33. 32.
    K. Binder, ed., “Monte Carlo Methods in Statistical Physics”, Springer, Berlin, 1979.Google Scholar
  34. 33.
    K.F. O’Driscoll, in “Computers in Polymer Sciences”, J.S. Matt-son, H.B. Mark, Jr. and H.C. MacDonald, Jr., eds., Dekker, New York, 1977.Google Scholar
  35. 34.
    G.G. Lowry, ed., “Markov Chains and Monte Carlo Calculations in Polymer Science”, Dekker, New York, 1970.Google Scholar
  36. 35.
    B. Carazza, Nuovo Cimento, 7, 419 (1977).Google Scholar
  37. 36.
    I. Motoc, Math. Chem., 5, 283 (1979).Google Scholar
  38. 37.
    H. Conroy, J. Chem. Phys., 47, 5307 (1967).CrossRefGoogle Scholar
  39. 38.
    L.D. Fosdick, SIAM Rev., 10, 315 (1968).CrossRefGoogle Scholar
  40. 39.
    I. Motoc, Eur. Polym. J. (submitted).Google Scholar
  41. 40.
    A. Gilath, S.H. Ronel, M. Shmueli and D.H. Kohn, J. Appl. Polym. Sci., 14, 1491 (1970).CrossRefGoogle Scholar
  42. 41.
    F.P. Price, J. Polym. Sci., C25, 3 (1968).Google Scholar
  43. 42.
    J.G. Topliss and R.J. Costello, J. Med. Chem., 15, 1066 (1972).CrossRefGoogle Scholar
  44. 43.
    J.G. Topliss and R.P. Edwards, J. Med. Chem., 22, 1238 (1979).CrossRefGoogle Scholar
  45. 44.
    A.T. Balaban, A. Chiriac, I. Motoc and Z. Simon, “Steric Fit in QSAR”, Lecture Notes in Chemistry, vol. 15, Springer, Berlin, 1980.Google Scholar
  46. 45.
    G. Dashevesky and G.N. Srakisov, Mol. Phys., 27, 1271 (1974).CrossRefGoogle Scholar
  47. 46.
    J.C. Owicki and H.A. Scheraga, J. Am. Chem. Soc., 99, 7403 (1977).CrossRefGoogle Scholar
  48. 47.
    O. Matsucka, E. Clementi and M. Yoshimine, J. Chem. Phys., 64, 1351 (1976).CrossRefGoogle Scholar
  49. 48.
    S. Swaminathan and D.L. Beveridge, J. Am. Chem. Soc., 101, 5832 (1979).CrossRefGoogle Scholar
  50. 49.
    S. Okazaki, K. Nakanishi, H. Touhara and Y. Adachi, J. Chem. Phys., 71, 2421 (1979).CrossRefGoogle Scholar
  51. 50.
    C. Pangali, M. Rao and B.J. Berne, J. Chem. Phys., 71, 2975, 2982, (1979).CrossRefGoogle Scholar
  52. 51.
    T.L. Hill and Y. Chen, J. Chem. Phys., 69, 1126 (1978).CrossRefGoogle Scholar
  53. 52.
    T.L. Hill and L. Stein, J. Chem. Phys., 69, 1139 (1978).CrossRefGoogle Scholar
  54. 53.
    T.L. Hill and Y. Chen, Proc. Natl. Acad. Sci. USA, 75, 5260 (1978).CrossRefGoogle Scholar
  55. 54.
    M.E. Craig and D.M. Crothers, Biopolymers, 6, 385 (1968).CrossRefGoogle Scholar
  56. 55.
    I.R. Epstein, Biopolymers, 18, 2037 (1979).CrossRefGoogle Scholar
  57. 56.
    I. Motoc, Math. Chem., 4, 113, (1978).Google Scholar
  58. 57.
    I. Motoc, R. Vancea and I. Muscutariu, Math. Chem., 5, 263 (1979)Google Scholar
  59. 58.
    I. Motoc, I. Gotaescu and R. Vancea, Nouv. J. Chim., (in press).Google Scholar
  60. 59.
    I. Motoc, S. Holban, R. Vancea and Z. Simon, Studia Biophys. (Berlin), 66, 75 (1977).Google Scholar
  61. 60.
    I. Motoc and R. Valceanu, Rev. Chim. (Bucharest), (in press).Google Scholar
  62. 61.
    J.A. Barker and R.O. Watts, Chem. Phys. Letts., 3, 144 (1969).CrossRefGoogle Scholar
  63. 62.
    J.A. Barker and R.O. Watts, Molec. Phys., 26, 792 (1973).CrossRefGoogle Scholar
  64. 63.
    G.N. Sarkisov and R. Dashevskii, Z. Strukturnoi Khim., 13, 199 (1972).Google Scholar
  65. 64.
    H. Popkie, H. Kistenmacher and E. Clementi, J. Chem. Phys., 59, 1325 (1973).CrossRefGoogle Scholar
  66. 65.
    J.K. Lee, J.A. Barker and F.F. Abraham, J. Chem. Phys., 58, 3166 (1971).CrossRefGoogle Scholar
  67. 66.
    R.O. Watts, E. Clementi and R.O. Watts, J. Chem. Phys., 61, 2550 (1974).CrossRefGoogle Scholar
  68. 67.
    J. Fromm, E. Clementi and R.O. Watts, J. Chem. Phys., 62, 1388 (1975).CrossRefGoogle Scholar
  69. 68a).
    J.C. Owicki and H.A. Scheraga, J. Am. Chem. Soc., 99, 7403 (1977).CrossRefGoogle Scholar
  70. 68b).
    S. Swaminathan and D.L. Beveridge, J. Am. Chem. Soc., 99, 8392 (1977).CrossRefGoogle Scholar
  71. 69.
    M. Mezei, S. Swaminathan and D.L. Beveridge, J. Am. Chem. Soc., 100, 3255 (1978).CrossRefGoogle Scholar
  72. 70.
    F.H. Stillinger and A. Rahman, J. Chem. Phys., 68, 666 (1978).CrossRefGoogle Scholar
  73. 71.
    I.R. McDonald and M.L. Klein, J. Chem. Phys., 68, 4875 (1978).CrossRefGoogle Scholar
  74. 72.
    M.L. Klein, I.R. McDonald and S.F. O’Shea, J. Chem. Phys., 69, 63 (1978).CrossRefGoogle Scholar
  75. 73.
    W.L. Jörgensen, “Monte Carlo Simulation of Liquid Hydrogen Fluoride”, preprint (1978).Google Scholar
  76. 74.
    G. Jacucci, I.R. MacDonald and R. Taylor, J. Phys., F8, 1121 (1978).Google Scholar
  77. 75.
    R.D. Mountain, J. Phys., F8, 1637 (1978).CrossRefGoogle Scholar
  78. 76.
    T. Lee, J. Bishop, W. van der Lugt and W.F. Van Gunsteren, Physica, B93, 59 (1978).Google Scholar
  79. 77.
    E. Michler, H. Hahn, and P. Schofield, J. Phys., F6, 319 (1976).CrossRefGoogle Scholar
  80. 78.
    G. Jacucci, M.L. Klein and R. Taylor, Solid State Com., 19, 657 (1976).CrossRefGoogle Scholar
  81. 79.
    S. Miller and H.R. Clarke, J. Chem. Soc. Faraday Trans. 2, 72, 1372 (1976).CrossRefGoogle Scholar
  82. 80.
    M. Dixon and M.J.L. Sangster, J. Phys., C10, 3015 (1977).Google Scholar
  83. 81.
    D.J. Adams, J. Chem. Soc. Faraday Trans. 2, 72, 1372 (1976).CrossRefGoogle Scholar
  84. 82.
    A.T. Hagler and J. Moult, Nature, 272, 222 (1978).CrossRefGoogle Scholar
  85. 83.
    B. Robson and M.N. Jones, Nature, 272, 206 (1978).CrossRefGoogle Scholar
  86. 84.
    N. Metropolis et al., J. Chem. Phys., 21, 1087 (1953).CrossRefGoogle Scholar
  87. 85.
    H.L. Frisch, M. Bishop and J. Roth, J. Chem. Phys., 67, 1082 (1977).CrossRefGoogle Scholar
  88. 86.
    M. Bishop, J. Roth and H.L. Frisch, J. Phys. Chem., 81, 2500 (1977).CrossRefGoogle Scholar
  89. 87.
    H.L. Frisch, B. Bishop and J. Roth, in “Statistical Mechanics and Statistical Methods in Theory and Application”, V. Landman ed., Plenum, New York, 1977.Google Scholar
  90. 88.
    G.G. Lowry, in “Markov Chains and Monte Carlo Calculations in Polymer Science”, Dekker, New York, p. 309–316.Google Scholar
  91. 89.
    G.G. Lowry, Polym. Letts., 1, 489 (1963).CrossRefGoogle Scholar
  92. 90.
    D.A. McQuarrie, C.J. Jachimowski and M.E. Russel, J. Chem. Phys. 40, 2917 (1964).Google Scholar
  93. 91.
    E. Klesper, W. Gronski and V. Barth, Makromol. Chem., 150, 223 (1971).CrossRefGoogle Scholar
  94. 92.
    E. Klesper, A. Johnson and W. Gronski, Makromol. Chem. 160, 167 (1972).CrossRefGoogle Scholar
  95. 93.
    E. Klesper and A.O. Johnson, in “Computers in Polymer Sciences”, eds. J.S. Mattson, H.B. Mark Jr. and H.C. MacDonald Jr., Dekker, New York, 1977, ch.1.Google Scholar
  96. 94.
    H.J. Harwood, K.G. Kempf and L.M. Landoll, 16, 91, 109, (1978).Google Scholar
  97. 95.
    A.D. Litmanovich, N.A. Plate, O.V. Noah and V.I. Golyakov, Eur. Polym. J., Suppl., 1969, 517.Google Scholar
  98. 96.
    N.A. Plate and O.V. Noah, in “Advances in Polymer Science”, vol. 31, ed. H.J. Cantow, Springer, Berlin, 1979.Google Scholar
  99. 97.
    I. Motoc, Math. Chem., 8 (1980) — in press.Google Scholar
  100. 98.
    I. Motoc, S. Holban and D. Ciubotariu, J. Polym. Sci. Chem., 15, 1465 (1977).CrossRefGoogle Scholar
  101. 99.
    I. Motoc, S. Holban and R. Vancea, J. Polym. Sci. Chem., 16, 1601 (1978).CrossRefGoogle Scholar
  102. 100.
    I. Motoc, R. Vancea and S. Holban, J. Polym. Sci. Chem., 16, 1587 (1978).CrossRefGoogle Scholar
  103. 101.
    I. Motoc and I. Muscutariu, J. Polym. Sci., Polym. Lett. Ed., in press.Google Scholar
  104. 102.
    I. Motoc, J. Macromol. Sci. Chem. (1980) — in press.Google Scholar
  105. 103.
    J.R. Ebdon, Polymer, 15, 782 (1974).CrossRefGoogle Scholar
  106. 104.
    P.W. Bechnken, J. Polym. Sci., A 2, 645 (1964).Google Scholar
  107. 105.
    P.W. Tidwell and G.A. Mortime, J. Polym. Sci., A3, 369 (1965).Google Scholar
  108. 106.
    D. Braun, W. Brendlein and G. Mott, Eur. Polym. J., 9, 1007 (1973).CrossRefGoogle Scholar
  109. 107.
    R.J. Eldridge and F.E. Treloar, J. Polym. Sei. Chem., 14, 2831 (1976).CrossRefGoogle Scholar
  110. 108.
    I. Motoc, I. Muscutariu and S. Holban, “Preprints MakroMainz”, vol. 1, eds. I. Lüdenwald and R. Weis, 1979 (26th Internat. Symp. Macromolecules).Google Scholar
  111. 109.
    O. Smidsrod, B. Larsen and T. Painter, Acta Chem. Scand., 24, 3201 (1970).CrossRefGoogle Scholar
  112. 110.
    J.J. Gonzales, “Cooperative Reactions on Polymers and Sequential Analysis”, Institut for Teoretisk Fysikk, Trondheim, 1977.Google Scholar
  113. 111.
    W.G. Glasser and H.R. Glasser, Macromolecules, 7, 17 (1974).CrossRefGoogle Scholar
  114. 112.
    M. Falk and R.E. Thomas, Can. J. Chem., 52 (1974) — cited in ref. 33.Google Scholar
  115. 113.
    M.I. Siling, V.N. Krivsunov et al., Visokomol. Soed., 16, 2550 (1974).Google Scholar
  116. 114.
    P.J. Flory, “Principles of Polymer Chemistry”, Cornell Univ. Press, Ithaca, New York, 1953, ch. 9.Google Scholar
  117. 115.
    S.G. Whiteway, I.B. Smith and C.R. Masson, Can. J. Chem., 48, 33 (1970).CrossRefGoogle Scholar
  118. 116.
    C.R. Masson, I.B. Smith and S.G. Whiteway, Can.J. Chem. 40, 201, 1456 (1970).CrossRefGoogle Scholar
  119. C.R. Masson, I.B. Smith and S.G. Whiteway, Can.J. Chem. 51, 1422 (1973).CrossRefGoogle Scholar
  120. 117.
    H. Staudinger, Makromol. Chem., 1, 7 (1947).CrossRefGoogle Scholar
  121. 118.
    A.A. Whitehouse, E. Pritchett and G. Barnett, “Phenolic Resins”, London, 1967.Google Scholar
  122. 119.
    R. Inoue, T. Minami and T. Ando, 61, 1340 (1958).Google Scholar
  123. 120.
    L.M. Yedanapalli and A.K. Kuriakose, J. Scient. Ind. Res., B18, 467 (1959).Google Scholar
  124. 121.
    H. Horinti, Gosei Kagaku, 66, 1379 (1963).Google Scholar
  125. 122.
    T. Yoshikawa and I. Kumanotani, Makromol. Chem., 131, 273 (1970).CrossRefGoogle Scholar
  126. 123.
    I. Motoc, S. Holban and D. Ciubotariu, Preprint, Timisoara Univ., 1975.Google Scholar
  127. 124.
    R. Vancea, I. Motoc, D. Ciubotariu and S. Holban, Preprint, Timisoara Univ., 1975.Google Scholar
  128. 125.
    P.C. Wu, J.A. Howell and P. Ehrlich, Ind. Eng. Chem. Prod. Res. Develp., 11, 35 (1972).CrossRefGoogle Scholar
  129. 126.
    A.M. Kotliar and S. Podgor, J. Polym. Sci., 55, 423 (1961).CrossRefGoogle Scholar
  130. 127.
    A.M. Kotliar, J. Polym. Sci., A1, 3175 (1963).Google Scholar
  131. 128.
    P.J. Meddings and O.E. Potter, Adv. Chem. Series, 109, 96 (1972).Google Scholar
  132. 129.
    J. Malac, J. Polym. Sci., C33, 233 (1971)Google Scholar
  133. 130.
    J. Malac, J. Polym. Sci., A-1, 9, 3563 (1971).CrossRefGoogle Scholar
  134. 131.
    J. Malac, J. Macromol. Sei. — Chem., A7, 923 (1971)Google Scholar
  135. 132.
    O. Smidsrod and S.G. Whittington, Macromolecules, 2, 42 (1969).CrossRefGoogle Scholar
  136. 133.
    E. Tsuchida, K. Mishima, K. Kitamura and I. Shinohara, J. Polym. Sci. Chem., 10, 3615 (1972).CrossRefGoogle Scholar
  137. 134.
    E. Tsuchida, T. Yao, K. Kitamura and I. Shinohara, J. Polym. Sci., Chem., 10, 3605 (1972).CrossRefGoogle Scholar
  138. 135.
    E. Tsuchida, K. Mishima, K. Kitamura and I. Shinohara, J. Polym. Sci. Chem., 10, 3627 (1972)CrossRefGoogle Scholar
  139. 136.
    E. Tsuchida, K. Kitamura and I. Shinohara, J. Polym. Sci. Chem., 10, 3639 (1972).CrossRefGoogle Scholar
  140. 137.
    R.H. MacDowell and E. Percival, “Chemistry and Enzymology of Marine Algol Polysaccharides”, Academic Press, New York 1967.Google Scholar
  141. 138.
    T. Fueno and J. Furukawa, J. Polym. Sci. A, 2, 3681 (1964).CrossRefGoogle Scholar
  142. 139.
    Knuth, The art of computer programming, vol. 2, Addison-Wesley, New York, 1971.Google Scholar
  143. 140.
    F. Gantmacher, Matrizenrechnung, VEB Deutscher Verlag der Wissenschaften, Berlin.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • I. Motoc
  • W. Bruns

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