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

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

doi:10.1016/0378-4371(90)90356-W

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

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

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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?

Original language	English
Pages (from-to)	23-48
Number of pages	26
Journal	Physica A: Statistical Mechanics and its Applications
Volume	168
Issue number	1
DOIs	https://doi.org/10.1016/0378-4371(90)90356-W
State	Published - 1 Sep 1990
Externally published	Yes

Bibliographical note

Funding Information:
First I wish to thank the OrganizingC ommitteefo r inviting me, andf or havingo rganizeda stimulatinpgr ogramW. e are gratefuflo r discussionw ith A. Aharony,P . Alstr~m,R . BlumenfeldT, .C. Halsey,A .B. Harris, D. Stauffer, P. Trunfio and T. Vicsek, and for support from ONR, NSF and NATO. Finally, we thank D. Staufferf or a critical readingo f the manuscript.

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title = "Dynamic mechanisms of disorderly growth: Recent approaches to understanding diffusion limited aggregation",

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?",

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AU - Lee, J.

AU - Roman, E.

AU - Schwarzer, S.

N1 - Funding Information: First I wish to thank the OrganizingC ommitteefo r inviting me, andf or havingo rganizeda stimulatinpgr ogramW. e are gratefuflo r discussionw ith A. Aharony,P . Alstr~m,R . BlumenfeldT, .C. Halsey,A .B. Harris, D. Stauffer, P. Trunfio and T. Vicsek, and for support from ONR, NSF and NATO. Finally, we thank D. Staufferf or a critical readingo f the manuscript.

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N2 - 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?

AB - 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?

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

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