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Characterizing Spatio-Temporal Chaos in Electrodeposition Experiments

  • F. Argoul
  • A. Arneodo
  • J. Elezgaray
  • G. Grasseau
Part of the NATO ASI Series book series (NSSB, volume 208)

Abstract

Pattern formation in systems far from equilibrium is a subject of considerable current interest1–5. Recently, much effort has been directed toward the study of fractal growth phenomena in physical, chemical and biological systems. Unfortunately, the understanding of phenomena like viscous fingering in Hele-Shaw cells6 and electrochemical deposition7 is hampered by the mathematical complexity of the problem. Highly ramified structures generally are produced in the zero surface tension limit. In this limit both processes are equivalent to the Stefan problem8: a diffusion problem for the pressure or the electrochemical potential, with boundary values specified on the moving interface, whose local velocity is in turn determined by the normal gradient of the Laplace field. This highly nonlinear problem is not readily amenable even to modern numerical simulations. When solving the Stefan problem by direct means, the interface develops unphysical cusps in a finite time6. One is thus led to introduce some short-distance cutoff which in some sense mimics surface-tension9,10. Thus far no computer simulations of the equations of motion achieve the necessary size to make definite conclusions about the deterministic character of the fractal patterns observed in the experiments1–5.

Keywords

Phase Portrait Stefan Problem Deterministic Chaos Zinc Tree Poincare Section 
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.

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Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • F. Argoul
    • 1
  • A. Arneodo
    • 1
  • J. Elezgaray
    • 1
  • G. Grasseau
    • 1
  1. 1.Chateau BrivazacCentre de Recherche Paul PascalPessac CedexFrance

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