Journal of Statistical Physics

, Volume 145, Issue 4, pp 919–931 | Cite as

On a Competitive Model of Laplacian Growth

  • Igor LoutsenkoEmail author
  • Oksana Yermolayeva
  • Michel Zinsmeister


We introduce a competitive model of Laplacian growth in both stochastic and deterministic versions. This defines two different aggregation laws with probabilities λ and 1−λ. The parameter λ varying from 0 to 1 is used to weight a ratio between the inner and outer harmonic measures that leads to a competition between the Eden-like process and the DLA solved with site-sticking conditions. We perform numerical and qualitative analysis of the competitive growth.


Free-boundary problems Laplacian growth Diffusion limited aggregation Eden process Fractal growth 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Igor Loutsenko
    • 1
    Email author
  • Oksana Yermolayeva
    • 2
  • Michel Zinsmeister
    • 3
  1. 1.Institute de Mathématiques de JussieuUniversité Paris Diderot Paris 7ParisFrance
  2. 2.Institut Henri PoincaréParis Cedex 05France
  3. 3.MAPMO (Mathematiques, Applications et Physique mathematique a Orleans)Université d’OrléansOrleans cedexFrance

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