Diffusion-limited aggregation and regular patterns

Fluctuations versus anisotropy

J. Kertesz, T. Vicsek

Research output: Contribution to journalArticle

134 Citations (Scopus)

Abstract

The authors show that the patterns in diffusion-limited aggregation (DLA) on a lattice emerge from the interplay of lattice anisotropy and fluctuations. These fluctuations can be damped by Monte Carlo averaging. Increasing its amount, the effective anisotropy becomes larger and a crossover from tip splitting typical for continuum DLA to stable tips is observed, in analogy with a number of recent experiments. The simulations suggest the following scenario for the transitions which take place as a function of the increasing effective anisotropy: disordered patterns to dendritic structures to needle crystals. It is shown that DLA clusters go through the same sequence of transitions as a function of their size. Therefore, diffusion-limited aggregates on a lattice are asymptotically not fractals.

Original languageEnglish
Article number008
JournalJournal of Physics A: Mathematical and General
Volume19
Issue number5
DOIs
Publication statusPublished - 1986

Fingerprint

Diffusion-limited Aggregation
Anisotropy
Agglomeration
Fluctuations
anisotropy
Damped
Averaging
Crossover
Analogy
Fractal
Continuum
Crystal
needles
Fractals
Needles
fractals
Scenarios
crossovers
continuums
Crystals

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Diffusion-limited aggregation and regular patterns : Fluctuations versus anisotropy. / Kertesz, J.; Vicsek, T.

In: Journal of Physics A: Mathematical and General, Vol. 19, No. 5, 008, 1986.

Research output: Contribution to journalArticle

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