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Related Experiment Videos

Random walks, diffusion limited aggregation in a wedge, and average conformal maps.

Leonard M Sander1, Ellák Somfai

  • 1Michigan Center for Theoretical Physics, Department of Physics, University of Michigan, Ann Arbor, MI 48109-1120, USA. lsander@umich.edu

Chaos (Woodbury, N.Y.)
|July 23, 2005
PubMed
Summary
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Diffusion-limited aggregation (DLA) in a wedge geometry was studied. The ensemble average of DLA cluster density does not perfectly match noise-free Saffman-Taylor fingers, questioning simple transcription of noise-free growth results.

Area of Science:

  • Complex Systems
  • Statistical Physics
  • Fractal Growth

Background:

  • Diffusion-limited aggregation (DLA) models fractal growth phenomena.
  • The Saffman-Taylor finger describes noise-free viscous fingering.
  • Previous work suggested DLA averages approximate noise-free solutions.

Purpose of the Study:

  • To investigate DLA in a wedge geometry.
  • To compare ensemble averages of DLA with noise-free Saffman-Taylor fingers.
  • To evaluate the hypothesis of simple transcription of noise-free results to noisy growth.

Main Methods:

  • Simulating diffusion-limited aggregation in a wedge.
  • Calculating ensemble averages of DLA cluster density.
  • Analyzing ensemble averages of conformal maps associated with DLA clusters.

Related Experiment Videos

Main Results:

  • The ensemble average of DLA cluster density in a wedge is not identical to the Saffman-Taylor finger.
  • A related average of conformal maps yields a shape near the Saffman-Taylor finger.
  • Previous studies showed DLA in a channel does not yield the Saffman-Taylor finger.

Conclusions:

  • The ensemble average of DLA in a wedge geometry does not precisely replicate the noise-free Saffman-Taylor finger.
  • The findings cast doubt on the direct transcription of noise-free growth dynamics to noisy DLA.
  • This suggests more complex mechanisms govern the averaging of noisy diffusion-limited growth.