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Competition of growth patterns in directed growth

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Nonlinear Physics of Complex Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 476))

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Abstract

A new class of non-equilibrium critical phenomena is defined, which can appear during the growth of one phase at the expense of a second phase. We assume that the growing phase consists of several sub-phases or species or even of several dynamically defined growth patterns, and that the growth takes place by the propagation of an extended front which separates the growing from the shrinking phase. A coarsening process then takes place during growth, leaving a decreasing number of species or sub-phases immediately behind the front as time increases. This directional coarsening process can be described as a critical phenomenon in terms of a scaling theory. We define the relevant parameters, critical exponents and scaling functions, and give explicit values for these quantities for M-species front-growth in two dimensions. The results are compared with Monte-Carlo simulations and implications for experiments are discussed.

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Authors and Affiliations

  1. Institut für Festkörperforschung, Forschungszentrum Jülich, D-52425, Jülich, Germany

    Heiner Müller-Krumbhaar

Authors
  1. Heiner Müller-Krumbhaar
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Editor information

Jürgen Parisi Stefan C. Müller Walter Zimmermann

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© 1996 Springer-Verlag

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Müller-Krumbhaar, H. (1996). Competition of growth patterns in directed growth. In: Parisi, J., Müller, S.C., Zimmermann, W. (eds) Nonlinear Physics of Complex Systems. Lecture Notes in Physics, vol 476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105432

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  • DOI: https://doi.org/10.1007/BFb0105432

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61734-1

  • Online ISBN: 978-3-540-70699-1

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