Aggregation Phenomena

Part of the NATO ASI Series book series (NSSB, volume 258)


Growth processes lead to many beautiful and intriguing structures in nature. Here we wish to describe methods to characterize and model such processes. Only recently has one begun to investigate growth phenomena in a systematic fashion. Theoretical investigations are difficult as the processes are far from equilibrium and frequently the structures are disordered. Recent progress came from two sides: 1) Scaling and the notion of fractals provide efficient ways to describe aggregation structures in a quantitative way — analogous to the scaling approach to critical phenomena — and 2) Large scale simulations of basic irreversible processes determine the presumably universal properties which are measured in experiments.


Fractal Dimension Aggregation Process Critical Phenomenon Spinodal Decomposition Gradient Percolation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D’Arcy W. Thompson, ‘On growth and form’, Cambridge 1917/1961Google Scholar
  2. 2.
    ‘Kinetics of aggregation and gelation’, F. Family and D. P. Landau (eds.), North Holland (1984)Google Scholar
  3. 3.
    ‘On growth and form’, H. E. Stanley and N. Ostrowski (eds.), Matinus Nijhoff, Dortrecht (1985)Google Scholar
  4. 4.
    ‘Scaling phenomena in disordered systems’, R. Pynn and A. Skjeltorp (eds.), NATO ASI series B, Vol. 133, Plenum (1985)Google Scholar
  5. 5.
    ‘Physics of finely divided matter’, N. Boccara and M. Daoud (eds.),Springer Proceedings in Physics Vol. 5, Springer (1985)Google Scholar
  6. 6.
    ‘Aggregation’, Film of growth processes, M. Kolb (author), FU Berlin (producer), 1985Google Scholar
  7. 7.
    H. J. Herrmann, Phys. Rept. 136, 153 (1986)CrossRefGoogle Scholar
  8. 8.
    ‘The physics of structure formation’, W. Giittinger (ed.), Springer Series in Synergetics (1987)Google Scholar
  9. 9.
    ‘Random fluctuations and pattern growth: Experiments and models’, H. E. Stanley and N. Ostrowsky (eds.), NATO ASI Vol. 157, Kluwer Academic 1988Google Scholar
  10. 10.
    ‘P. Meakin,’ in ‘Phase transition and critical phenomena’,C. Domb and J. Lebowitz (eds.), Vol. 12, Academic 1989Google Scholar
  11. 11.
    ‘Statistical physics’ (STATPHYS 16), H. E. Stanley (ed.), North Holland 1986Google Scholar
  12. 12.
    B. B. Mandelbrot, ‘Les objets fractals’ (Flammarion 1975);Google Scholar
  13. 13.
    B. B. Mandelbrot, ‘The fractal geometry of nature’ (Freemann 1982)Google Scholar
  14. 14.
    ‘Systeme de creation d’images’, Minis et Micros 219, p. 57Google Scholar
  15. 15.
    I. Stewart, ‘Les fractals’ (Belin, Bande Dessinee)Google Scholar
  16. 16.
    M. Berger, ‘Atelier fractal’, MIB, La Chaux-de Fonds (1986)Google Scholar
  17. 17.
    ‘Fractals in physics’, L. Pietronero and E. Tosatti (eds.), Elsevier (1986)Google Scholar
  18. 18.
    H. U. Peitgen and P. H. Richter, ‘The beauty of fractals’ Springer, 1986CrossRefGoogle Scholar
  19. 19.
    H. U. Peitgen and D. Saupe (eds.) ‘Fractal images’, Springer.Google Scholar
  20. 20.
    J. Feder, ‘Fractals’, Plenum, 1988Google Scholar
  21. 21.
    T. Vicsek, ‘Fractal growth phenomena’, World Scientific.Google Scholar
  22. 22.
    ‘Fractals in physics’, A. Aharony and J. Feder (eds.), North Holland 1989Google Scholar
  23. 23.
    D. Avnir (ed.), ‘Fractal approach to heterogeneous chemistry’, Wiley, 1989Google Scholar
  24. 24.
    J. F. Gouyet, ‘Physique et structures fractales’ Cours d’option’, 1989Google Scholar
  25. 25.
    B. Sapoval, ‘Les fractales’, Additech Paris, 1990Google Scholar
  26. 26.
    A. le Mehaute, ‘Les geometries fractales’, Hermes 1990Google Scholar
  27. 27.
    ‘Fractals in the physical sciences’, H. Takayasu, Manchester Univ. Press 1990Google Scholar
  28. 28.
    H. Thiele and H. S. von Levern, J. Coll. Sci. 20, 679 (1965)CrossRefGoogle Scholar
  29. 29.
    F. G. Karioris and B. R. Fish, J. Coll. Sci. 17, 155 (1962)CrossRefGoogle Scholar
  30. 30.
    S. R. Forrest and T. A. Witten, J. Phys. A12,L109 (1979)Google Scholar
  31. 31.
    D. A. Weitz and M. Oliveria, Phys. Rev. Lett. 52, 1433 (1984)CrossRefGoogle Scholar
  32. 32.
    D. A. Weitz, M. Y. Lin and C. J. Sandroff, Surf. Sci. 158, 147Google Scholar
  33. 33.
    D. W. Schaefer, J. E. Martin, P. Wiltzius and D. S. Cannell, Phys. Rev. Lett. 52, 2371 (1984)CrossRefGoogle Scholar
  34. 34.
    K. D. Keefer, Mat. Res. Soc. Proc. 73,295 (1986)CrossRefGoogle Scholar
  35. 35.
    A. Hurd and D. W. Schaefer, Phys. Rev. Lett. 54, 1043 (1985)CrossRefGoogle Scholar
  36. 36.
    M. Broide, Thesis, MIT, CambridgeGoogle Scholar
  37. 37.
    J. Cahill, P. G. Cummins, E. J. Staples and L. Thoson, unpublishedGoogle Scholar
  38. 38.
    F. W. Wiegel and A. S. Perelson, J. Stat. Phys. 29, 813 (1982)CrossRefGoogle Scholar
  39. 39.
    P. Richetti, J. Prost and P. Barois, J. Physique Lett. 45, 1137Google Scholar
  40. 40.
    C. Camoins and R. Blanc, J. Physique Lett. 46, 67 (1985)CrossRefGoogle Scholar
  41. 41.
    R. H. Giese, K. Weiss, R. H. Zerull and T. Ono, Astron. Astrophys. 65, 265 (1978)Google Scholar
  42. 42.
    M. Matsushita, M. Sano, Y. Hayakawa, H. Honjo and Y. Sawada, Phys. Rev. Lett. 53, 286 (1984)CrossRefGoogle Scholar
  43. 43.
    J. Nittmann, G. Daccord and H. E. Stanley, Nature 314, 141Google Scholar
  44. 44.
    Y. Sawada, Physica 140A, 134 (1986)Google Scholar
  45. 45.
    J. S. Langer, Rev. Mod. Phys. 52,1 (1980)CrossRefGoogle Scholar
  46. 46.
    R. Lenormand, C. Zarkone and A. Sarr, J. Fluid. Mech. 135, 337 (1983)CrossRefGoogle Scholar
  47. 47.
    H. D. Bale and P. W. Schmidt, Phys. Rev. Lett. 53, 596 (1984)CrossRefGoogle Scholar
  48. 48.
    Physikalische Blatter, Cover photograph, 1986Google Scholar
  49. 49.
    L. Niemeyer, L. Pietronero and H. J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984)CrossRefGoogle Scholar
  50. 50.
    G. Deutscher, A. Kapitulnik and M. Rappaport, in ‘Percolation structures and processes’, G. Deutscher, R. Zallen and J. Adler (eds.), Ann. Isr. Phys. Soc. (1983)Google Scholar
  51. 51.
    H. Stiller, private communicationGoogle Scholar
  52. 52.
    S. Lovejoy and B. B. Mandelbrot, Tellus 37A, 209 (1985)CrossRefGoogle Scholar
  53. 53.
    G. B. West, Los Alamos Science 11, 2 (1984)Google Scholar
  54. 54.
    T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia and B. I. Shraiman, Phys. Rev. A33, 1411 (1986)Google Scholar
  55. 55.
    M. Eden, in ‘Proc of 4. Berkeley Symp. on Math. Statistics and Probabilities’, F. Neyman (ed.), UC Press (1961)Google Scholar
  56. 56.
    M. Kardar, G. Parisi and V. C. Zhang, Phys. Rev. Lett. 56, (1986)Google Scholar
  57. 57.
    T. A. Witten and L. M. Sander, Phys. Rev. Lett. 37, 1400 (1981)CrossRefGoogle Scholar
  58. 58.
    P. Meakin, Phys. Rev. Lett. 51, 1119 (1983)CrossRefGoogle Scholar
  59. 59.
    M. Kolb, R. Botet and R. Jullien, Phys. Rev. Lett. 51, 1123 (1983)CrossRefGoogle Scholar
  60. 60.
    M. Kolb and H. J. Herrmann, J. Phys. A18, L435 (1985)Google Scholar
  61. 61.
    H. J. Herrmann and M. Kolb, J. Phys. A19, L1027 (1986)Google Scholar
  62. 62.
    M. Kolb and R. Jullien, J. Physique Lett. 45, 2977 (1984)CrossRefGoogle Scholar
  63. 63.
    W. D. Brown and R. C. Ball, J. Phys. A18, L517 (1985)Google Scholar
  64. 64.
    J. A. Helsen and J. Texeira, Coll. Poly. Sci. 264, 619 (1986)CrossRefGoogle Scholar
  65. 65.
    P. Mills, J. de Physique Lett. 46, L301 (1985)CrossRefGoogle Scholar
  66. 66.
    J. S. Langer, Ann. Phys. (N. Y.) 41,108 (1967); ibid. 54, 258 (1969); ibid. 65, 53 (1971)CrossRefGoogle Scholar
  67. 67.
    J. D. Gunton, M. San Miguel, and P. S. Sahni, in ‘Phase transitions and critical phenomena’, Vol. 8, C. Domb and J. L. Lebowitz, eds. (Academic 1983)Google Scholar
  68. 68.
    H. Furukawa, Adv. Phys. 34, 703 (1985)CrossRefGoogle Scholar
  69. 69.
    I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961)CrossRefGoogle Scholar
  70. 70.
    C. Wagner, Z. Electrochem. 65, 581 (1961)Google Scholar
  71. 71.
    D. A. Huse, Phys. Rev. B34, 7845 (1986)Google Scholar
  72. 72.
    P. Guenoun, ‘Journees de physique statistique’, Janvier 1989, Paris (France)Google Scholar
  73. 73.
    M. Kolb, T. Gobron, J-F. Gouyet and B. Sapoval, Europhys. Lett. 11, 601 (1990)CrossRefGoogle Scholar
  74. 74.
    S. Mazur and S. Reich, J. Phys. Chem. 90, 1365 (1986)CrossRefGoogle Scholar
  75. 75.
    R. P. Wool, B. -L. Yuan and O. J. Mcgarel, Poly. Eng. Sci. 29, 1340 (1989)CrossRefGoogle Scholar
  76. 76.
    B. Sapoval, M. Rosso and J. -F. Gouyet, J. Physique Lett. 46, 149 (1985)CrossRefGoogle Scholar
  77. 77.
    M. Kolb, J. -F. Gouyet and B. Sapoval, Europhys. Lett. 3, 33 (1987)CrossRefGoogle Scholar
  78. 78.
    T. Grossmann and A. Aharony, J. Phys. A19, L745 (1986); ibid. A20, L1193 (1987)Google Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • M. Kolb
    • 1
  1. 1.Laboratoire de Chimie ThéoriqueEcole Normale SupérieureLyon Cedex 07France

Personalised recommendations