Role of Fluctuations in Fluid Mechanics and Dendritic Solidification
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.
KeywordsFractal Dimension Random Walker Ising Model Noise Reduction Laplace Equation
Unable to display preview. Download preview PDF.
- BENTLEY, W. A., and HUMPHREYS, W. J., 1962, Snow Crystals (Dover, NY).Google Scholar
- 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
- CHEN, J. D. and WILKINSON, D., 1985, Phys. Rev. Lett., 55, 1985.Google Scholar
- FAMILY, F. and LANDAU, D. P. (eds), 1984, Kinetics of Aggregation and Gelation (Elsevier, Amsterdam).Google Scholar
- KERTéSZ, J., STAUFFER, D., and CONIGLIO, A., 1985, Ann. Israel Phys. Soc. (Adler, Deutscher and Zallen, eds), p. 121–148.Google Scholar
- LACHAPELLE, E. R., 1969, Field Guide to Snow Crystals (U. Washington Press, Seattle).Google Scholar
- LENZ, W., 1920, Phys. Z., 21, 613–5.Google Scholar
- MEAKIN, P., 1986b, Proc. Israel Conference on Fracture. Google Scholar
- NAKAYA, U., 1954, Snow Crystals (Harvard Univ Press, Cambridge).Google Scholar
- PIETRONERO, L. and TOSATTI, E. (eds), 1986, Fractals in Physics (North Holland, Amsterdam).Google Scholar
- PYNN, R. and SKJELTORP, A. (eds.), 1986, Scaling Phenomena in Disordered Systems (Plenum, N.Y.).Google Scholar
- STANLEY, H. E., 1987 Introduction to Fractal and Multifractal Phenomena (to be published).Google Scholar