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Laplacian growth on a random lattice

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  • Moukarzel, C.

Abstract

Several properties of DLA and DBM clusters grown with infinite noise reduction on a recently proposed vectorizable random lattice are described. The purpose of this work is twofold; to see how the cluster shapes are affected when these random lattices are continuously changed into regular lattices, and on the other side to study the properties of these lattices themselves. For DBM growth the shapes of the clusters are continuously changed into the ordered shapes that one finds on a regular lattice. DLA rules, on the other hand, present a sharp transition at zero disorder. Even on infinitesimally disordered lattices will DLA models give rise to random-looking clusters, and only for zero disorder lattices one recovers the usual needle-type structures. The origin of this behavior is discussed. For full disorder in the lattices, we analyze the statistical properties of the mass distribution of four possible growth models, finding that a mild anisotropy is still present in these lattices. DLA with counters on sites (SDLA) is the model which most strongly reflects this anisotropy.

Suggested Citation

  • Moukarzel, C., 1992. "Laplacian growth on a random lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 190(1), pages 13-23.
    • Handle: RePEc:eee:phsmap:v:190:y:1992:i:1:p:13-23
    DOI: 10.1016/0378-4371(92)90074-Z
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    1. Coniglio, A. & De Arcangelis, L. & Herrmann, H.J., 1989. "Fractals and multifractals: Applications in physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(1), pages 21-30.
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