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)


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.


Fractal Dimension Random Walker Ising Model Noise Reduction Laplace Equation 
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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

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