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Aggregation of Particles with Deterministic Trajectories

  • Y-h. Taguchi
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 43)

Abstract

The diffusion-limited aggregation (DLA)[1] is currently of major interest in the field of physics of pattern formation, because it is a simple model of several physical phenomena: metal leaves, viscous fingerings, and dielectric breakdown, etc. In all of the phenomena, growth probabilities depend on the gradient of a solution of the Laplace equation. DLA and these physical phenomena are known to show fractal patterns. Hence much effort has been made to obtain the fractal dimension d f of DLA. Remarkably, in some dimension analysis treatments [2,3], though the Laplace equation is not taken into account at all, the result (d f = 5/3) agrees with that of numerical simulations (d f = 1.7) [1]. The fact they make use of is that only trajectories of particles have fractal dimension d w of two. Here we notice a possibility that other trajectories with d w of two can also generate fractal patterns with the same d f as that of DLA. To clear up this point, we consider trajectories which are not diffusive but have d w of 2.

Keywords

Fractal Dimension Physical Phenomenon Pattern Formation Fractal Pattern Laplace Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    P. Meakin, Phase Transitions and Critical Phenomena, ed. by C. Domb, J. L. Lebowitz, vol. 12 ( Academic, New York 1988) p. 335Google Scholar
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    M. Matsushita, K. Honda, H.Toyoki, Y. Hayakawa, H. Kondo: J. Phys. Soc. Jpn. 55, 2618 (1986)ADSCrossRefGoogle Scholar
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    Y-h. Taguchi J. Phys. A 21, 4235 (1988)ADSCrossRefGoogle Scholar
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    Y-h. Taguchi J. Phys. A (1988) submittedGoogle Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • Y-h. Taguchi
    • 1
  1. 1.Department of PhysicsTokyo Institute of TechnologyMeguro-ku, TokyoJapan

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