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Dynamic mechanisms of disorderly growth: Recent approaches to understanding diffusion limited aggregation

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  • Stanley, H.E.
  • Bunde, A.
  • Havlin, S.
  • Lee, J.
  • Roman, E.
  • Schwarzer, S.

Abstract

We briefly review some recent attempts to achieve some genuine understanding of diffusion-limited aggregation (DLA), the paradigm model for dynamical mechanisms of disorderly growth processes. We shall see that the seminal ideas of Professor Cyril Domb have influenced to a great degree many of the recent theoretical approaches. In particular, the Domb-Hunter constant-gap scaling hypothesis becomes replaced by a continuum of gap exponents. Moreover, while the growth probabilities for the tips of the DLA structure do scale in the conventional fashion, there is evidence that the growth probabilities of the fjords do not scale. Does this competition between one part of DLA that does scale, and another that does not, underlie many of the unusual properties of this model?

Suggested Citation

  • Stanley, H.E. & Bunde, A. & Havlin, S. & Lee, J. & Roman, E. & Schwarzer, S., 1990. "Dynamic mechanisms of disorderly growth: Recent approaches to understanding diffusion limited aggregation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(1), pages 23-48.
    • Handle: RePEc:eee:phsmap:v:168:y:1990:i:1:p:23-48
    DOI: 10.1016/0378-4371(90)90356-W
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    Cited by:

    1. Salcedo-Sanz, S. & Cuadra, L., 2019. "Quasi scale-free geographically embedded networks over DLA-generated aggregates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1286-1305.
    2. Arneodo, A. & Bacry, E. & Muzy, J.F., 1995. "The thermodynamics of fractals revisited with wavelets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 213(1), pages 232-275.
    3. Zheng, Xiaojing & Lu, Jinfei & Chen, Yanbin & Cong, Xinrong & Sun, Cuiping, 2021. "Random belief system dynamics in complex networks under time-varying logic constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    4. Aharony, Amnon, 1990. "Multifractals in physics: Successes, dangers and challenges," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(1), pages 479-489.
    5. Salcedo-Sanz, S. & Cuadra, L., 2019. "Hybrid L-systems–Diffusion Limited Aggregation schemes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 592-605.

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