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Characterizing Spatio-Temporal Chaos in Electrodeposition Experiments

  • Chapter
Measures of Complexity and Chaos

Part of the book series: NATO ASI 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.

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Author information

Authors and Affiliations

  1. Chateau Brivazac, Centre de Recherche Paul Pascal, 33600, Pessac Cedex, France

    F. Argoul, A. Arneodo, J. Elezgaray & G. Grasseau

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  1. F. Argoul
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  2. A. Arneodo
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  3. J. Elezgaray
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  4. G. Grasseau
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Editor information

Editors and Affiliations

  1. Department of Physics, Bryn Mawr College, 19010-2899, Bryn Mawr, Pennsylvania, USA

    Neal B. Abraham  & Alfonso M. Albano  & 

  2. Naval Air Development Center, 18974, Warminster, Pennsylvania, USA

    Anthony Passamante

  3. Department of Physiology and Biochemistry, The Medical College of Pennsylvania, 3300 Henry Ave., 19129, Philadelphia, Pennsylvania, USA

    Paul E. Rapp

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© 1989 Plenum Press, New York

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Argoul, F., Arneodo, A., Elezgaray, J., Grasseau, G. (1989). Characterizing Spatio-Temporal Chaos in Electrodeposition Experiments. In: Abraham, N.B., Albano, A.M., Passamante, A., Rapp, P.E. (eds) Measures of Complexity and Chaos. NATO ASI Series, vol 208. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0623-9_60

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  • DOI: https://doi.org/10.1007/978-1-4757-0623-9_60

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