Advertisement

Role of Fluctuations in Fluid Mechanics and Dendritic Solidification

  • H. E. Stanley
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 37)

Abstract

Our purpose is to review certain recent advances in understanding the role of fluctuations in fluid mechanics and dendritic solidification; many of these represent joint work of the author and J. Nittmann. If one understands completely the simple Ising models then one understands virtually all systems near their critical points—although the detailed descriptions of many such systems require a suitably-chosen variant of the Ising model (such as the XY or Heisenberg model). By analogy, we shall argue here that if one understands completely the simple diffusion-limited aggregation (DLA) model or the closely related dielectric breakdown model (DBM), then one understands the role of fluctuations in a range of fluid mechanical systems, as well as in dendritic solidification. The detailed descriptions of some such systems require suitably chosen variants, such as DBM with anisotropy and noise reduction.

Keywords

Fractal Dimension Random Walker Ising Model Noise Reduction Laplace Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. AMITRANO, C., CONIGLIO, A., and DI LIBERTO, F., 1986, Phys. Rev. Lett., 57, 1016.ADSCrossRefGoogle Scholar
  2. BALL, R., 1986, Physica, 140A, 62ADSGoogle Scholar
  3. BEN-JACOB, E., GODBEY, R., GOLDENFELD, N. D., KOPLIK, J., LEVINE, H., MUELLER, T., and SANDER, L. M., 1985, Phys. Rev. Lett., 55, 1315.ADSCrossRefGoogle Scholar
  4. BEN-JACOB, E., GOLDENFELD, N., KOTLIAR, B. G., LANGER, J. S., 1984, Phys. Rev. Lett., 53, 2110.ADSCrossRefGoogle Scholar
  5. BENTLEY, W. A., and HUMPHREYS, W. J., 1962, Snow Crystals (Dover, NY).Google Scholar
  6. BOCCARA, N. and DAOUD, M. (eds), 1985, Physics of Finely Divided Matter [Proceedings of the Winter School, Les Houches, 1985] (Springer Verlag, Heidelberg).Google Scholar
  7. BUKA, A., KERTéSZ, J., and VICSEK, T., 1986, Nature, 323, 424.ADSCrossRefGoogle Scholar
  8. CHANDRASEKHAR, S., 1943, Rev. Mod. Phys., 15, 1.MathSciNetADSMATHCrossRefGoogle Scholar
  9. CHEN, J. D. and WILKINSON, D., 1985, Phys. Rev. Lett., 55, 1985.Google Scholar
  10. CONIGLIO, A., 1982, J. Phys. A, 15, 3829.MathSciNetADSCrossRefGoogle Scholar
  11. DACCORD, G., NITTMANN, J., and STANLEY, H. E., 1986, Phys. Rev. Lett., 56, 336.ADSCrossRefGoogle Scholar
  12. DOUGHERTY, A., KAPLAN, P. D., and GOLLUB, J. P., 1987, Phys. Rev. Lett. 58, 1652.ADSCrossRefGoogle Scholar
  13. FAMILY, F. and LANDAU, D. P. (eds), 1984, Kinetics of Aggregation and Gelation (Elsevier, Amsterdam).Google Scholar
  14. GAWLINSKI, E.T., and STANLEY, H. E., 1981, J. Phys. A., 14, L291-L299.MathSciNetADSCrossRefGoogle Scholar
  15. GEIGER, A., and STANLEY, H. E., 1982a, Phys. Rev. Lett., 49, 1749.ADSCrossRefGoogle Scholar
  16. GEIGER, A., and STANLEY, H. E., 1982b, Phys. Rev. Lett., 49, 1895.ADSCrossRefGoogle Scholar
  17. HALSEY, T. C., MEAKIN, P., and PROCACCIA, I., 1986, Phys. Rev. Lett., 56, 854.ADSCrossRefGoogle Scholar
  18. ISING, E., 1925, Ann. Physik, 31, 253–258.ADSGoogle Scholar
  19. KERTéSZ, J., and VICSEK, T., 1986, J. Phys. A, 19, L257.ADSCrossRefGoogle Scholar
  20. KERTéSZ, J., STAUFFER, D., and CONIGLIO, A., 1985, Ann. Israel Phys. Soc. (Adler, Deutscher and Zallen, eds), p. 121–148.Google Scholar
  21. KESSLER, D., KOPLIK, J., and LEVINE, H., 1984, Phys. Rev. A, 30, 3161.ADSCrossRefGoogle Scholar
  22. LACHAPELLE, E. R., 1969, Field Guide to Snow Crystals (U. Washington Press, Seattle).Google Scholar
  23. LANGER, J. S., 1980, Rev. Mod. Phys., 52, 1.ADSCrossRefGoogle Scholar
  24. LENZ, W., 1920, Phys. Z., 21, 613–5.Google Scholar
  25. MåLøY, K. J., FEDER, J., and JøSSANG, T., 1985, Phys. Rev. Lett., 55, 2688.ADSCrossRefGoogle Scholar
  26. MEAKIN, P., STANLEY, H. E., CONIGLIO, A., and WITTEN, T. A., 1985, Phys. Rev. A, 32, 2364.ADSCrossRefGoogle Scholar
  27. MEAKIN, P., CONIGLIO, A., STANLEY, H. E., and WITTEN, T. A., 1986, Phys. Rev. A, 34, 3325–3340.MathSciNetADSCrossRefGoogle Scholar
  28. MEAKIN, P., 1986a, J. Theor. Biol., 118, 101.MathSciNetCrossRefGoogle Scholar
  29. MEAKIN, P., 1986b, Proc. Israel Conference on Fracture. Google Scholar
  30. NAKAYA, U., 1954, Snow Crystals (Harvard Univ Press, Cambridge).Google Scholar
  31. NIEMEYER, L., PIETRONERO, L., and WEISMANN, H. J., 1984, Phys. Rev. Lett., 52, 1033.MathSciNetADSCrossRefGoogle Scholar
  32. NITTMANN, J., DACCORD, G., and STANLEY, H. E., Nature 314, 141 (1985).ADSCrossRefGoogle Scholar
  33. NITTMANN, J., and STANLEY, H. E., 1986, Nature 321, 663–668.ADSCrossRefGoogle Scholar
  34. NITTMANN, J., and STANLEY, H. E., 1987a, J. Phys. A 20, xxxMathSciNetGoogle Scholar
  35. NITTMANN, J., and STANLEY, H. E., 1987b J. Phys. A, 20, xxxMathSciNetGoogle Scholar
  36. NITTMANN, J., STANLEY, H. E., TOUBOUL, E., and DACCORD, G., 1987, Phys. Rev. Lett, 58, 619.ADSCrossRefGoogle Scholar
  37. PIETRONERO, L. and TOSATTI, E. (eds), 1986, Fractals in Physics (North Holland, Amsterdam).Google Scholar
  38. PYNN, R. and SKJELTORP, A. (eds.), 1986, Scaling Phenomena in Disordered Systems (Plenum, N.Y.).Google Scholar
  39. SAITO, Y., GOLDBECK-WOOD, G., and MüLLER-KRUMBHAAR, H., 1987, Phys. Rev. Lett., 58, 1541.ADSCrossRefGoogle Scholar
  40. STANLEY, H. E., 1977, J. Phys. A, 10, L211-L220.ADSCrossRefGoogle Scholar
  41. STANLEY, H. E., 1987 Introduction to Fractal and Multifractal Phenomena (to be published).Google Scholar
  42. STANLEY, H. E., and OSTROWSKY, N. (eds), 1986, On Growth and Form: Fractal and Non-Fractal Patterns in Physics (Martinus Nijhoff, The Hague).MATHGoogle Scholar
  43. TANG, C., 1985, Phys. Rev. A., 31, 1977.ADSCrossRefGoogle Scholar
  44. WITTEN, T. A., and SANDER, L. M., 1981, Phys. Rev. Lett., 47, 1400.ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • H. E. Stanley
    • 1
  1. 1.Center for Polymer Studies and Department of PhysicsBoston UniversityBostonUSA

Personalised recommendations