Laplacian Growth (e.g. viscous fingering)
and Diffusion-Limited-Aggregation(DLA) are two basic models that demonstrate
the spontaneous emergence of fractal patterns in nature. The two models are
closely related to each other, being respectively deterministic and stochastic
versions of the same equations of motion. As such, they were believed to share
a similar asymptotic dynamics. I will use the Hastings-Levitov formalism,
based on iterations of conformal maps, in order to define a discrete version
of Laplacian Growth processes. This construction serves to clarify the basic
differences between Viscous Fingering and DLA. It will be shown that
inspite of the strong resemblance between the two models, the resulting fractal
patterns are very different, and in particular, contrary to the common intuition,
do not have the same fractal dimension. The results indicate that Viscous
Fingering gives rise to very dense patterns which may be even compact.
Benny Davidovitch
Post-Doctoral Researcher
Tel: 908-730-3662
Fax: 908-730-3232
b.davidovitch@exxonmobil.com
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Room LD362
Corporate Strategic Research
ExxonMobil Research and Engineering
Route 22, Annandale, NJ 08801
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