Europhys. Lett.
Volume 76, Number 2, October 2006
Page(s) 257 - 263
Section Condensed matter: structural, mechanical and thermal properties
Published online 06 September 2006
Europhys. Lett., 76 (2), pp. 257-263 (2006)
DOI: 10.1209/epl/i2006-10246-x

The universality class of diffusion-limited aggregation and viscous fingering

J. Mathiesen1, I. Procaccia2, H. L. Swinney3 and M. Thrasher3

1  Department of Physics, Norwegian University of Science and Technology 7491 Trondheim, Norway
2  The Department of Chemical Physics, The Weizmann Institute of Science Rehovot 76100, Israel
3  Center for Nonlinear Dynamics and Department of Physics University of Texas at Austin - Austin, TX 78712, USA

received 1 May 2006; accepted in final form 17 August 2006
published online 6 September 2006

We investigate whether fractal viscous fingering and diffusion-limited aggregates are in the same scaling universality class. We bring together the largest available viscous fingering patterns and a novel technique for obtaining the conformal map from the unit circle to an arbitrary singly connected domain in two dimensions. These two Laplacian fractals appear different to the eye; in addition, viscous fingering is grown in parallel and the aggregates by a serial algorithm. Nevertheless, the data strongly indicate that these two fractal growth patterns are in the same universality class.

61.43.Hv - Fractals; macroscopic aggregates (including diffusion-limited aggregates).
05.45.Df - Fractals.
05.70.Fh - Phase transitions: general studies.

© EDP Sciences 2006